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Kuryachiy, Viacheslav G.
Irradiated single crystal 3C-SiC as a maximum temperature sensor
h [electronic resource] /
by Viacheslav G. Kuryachiy.
[Tampa, Fla] :
b University of South Florida,
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Thesis (M.S.M.E.)--University of South Florida, 2008.
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ABSTRACT: A neutron flux on the order of 210 neutrons/cm at 0.18 MeV induces formation of point defects (vacancies and interstitials) in single crystal 3C-SiC causing a volume lattice expansion (swelling) of over 3% that can be measured by X-Ray diffraction. The crystal lattice can be completely restored with an annealing temperature equal to or higher than the irradiation temperature. This phenomenon serves as a basis for temperature measurements and allows the determination of the maximum temperature, if the exposure time is known. The single crystal 3C-SiC sensor is applicable to small, rotating and hard to access parts due to its size of 300-500 microns, wide temperature range of 100-1450 C, "no-lead" installation, inert chemical properties and high accuracy of temperature measurements. These features make it possible to use the sensor in gas turbine blades, automotive engines, valves, pistons, space shuttle ceramic tiles, thermal protection system design, etc. This work describes the mechanism of neutron irradiation of single crystal 3C-SiC, the formation of point defects and their concentration, the different temperature measurement techniques, and the application of Maximum Temperature Crystal Sensors (MTCS) for maximum temperature measurements in both stationary and non-stationary regimes.
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Advisor: Alex Volinsky, Ph.D.
x Mechanical Engineering
t USF Electronic Theses and Dissertations.
Irradiated Single Crystal 3C-SiC as a Maximum Temperature Sensor by Viacheslav G. Kuryachiy A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Mechanical Engineering Department of Mechanical Engineering College of Engineering University of South Florida Major Professor: Alex Volinsky, Ph.D. Craig Lusk, Ph.D. Jose Porteiro, Ph.D. Date of Approval: November 6, 2008 Keywords: neutron irradiation, xray diffraction, lattice parame ter, point defects, thermal annealing Copyright 2008 Viacheslav G. Kuryachiy
Acknowledgements First of all, I would like to thank my advisor Dr. Alex Volinsky for assistance through the entire process of my research and thesis preparation. I am grateful to him as well as to the Universi ty of South Florida for giving me such a great opport unity to study, work and earn my MasterÂ’s Degree. I woul d also like to thank the faculty of the Mechanical Engineering Department for all the knowledge I have gained, namely to Dr. Porteiro, Dr. Dubey, Dr. Lusk a nd Dr. Rahman. In addition, my gratitude is to the staff of the ME department, specifically to Sue Brit ten for being patient and kind throughout my entire stay at USF.
i Table of Contents List of Tables iv List of Figures v List of Nomenclature viii ABSTRACT xi Chapter 1. Introduction 1 1.2 Statement of work 2 1.3 Hard to access parts temperature measurement tools 3 Chapter 2. The Maximum Te mperature Crystal Sensor 7 2.1 Material selection for MTCS 7 2.2 Technical characteristics of MTCS 8 2.3 Manufacturing of MTCS 10 2.4 MTCS design and installation techniques 13 Chapter 3. Neutron Irradiation of Silicon Carbide 17 3.1 Features of neutron irradiation of materials 17 3.2 Principle of neutron irradiation 17 3.3 Atoms displacement ener gy of irradiated 3C-SiC 19 3.4 Volume change of 3C-SiC due to neutron irradiation 20 3.5 Point defects in 3C-SiC 24 3.6 Defects concentration in 3C-SiC 26 3.7 Annealing temperature of irradiated 3C-SiC 28
ii Chapter 4. Diffraction Analysis 30 4.1 Diffractometer method 30 4.2 Application of BraggÂ’s law 31 4.3 Lorenz factor 35 Chapter 5. Preparation and Analysis of MTCS 38 5.1 Calibration of MTCS 38 5.2 Data reduction and analysis 40 Chapter 6. Interpretation of Experimental Results 43 6.1 Operation of the laboratory diffractometer 43 6.2 Experimental diffraction analysis of 3C-SiC 44 Chapter 7. Summary and Future Work 50 7.1 Summary 50 7.2 Future work 52 References 55 Appendices 58 Appendix A. DSO-1M X-ray di ffractometer description 59 Appendix B. Radicon Devi ce Programming Workbench 60 B.1 Speed bar 60 B.2 Installable Device Drivers 61 B.3 Radicon hardware server window 61 B.3.1 Controller window 62 B.3.2 High voltage unit window 63 B.3.3 Motor window 63 B.3.4 Power transmission of the step motor 65 B.3.5 Speed of rotation of the step motor 66 B.3.6 Operation points of the step motor 67 B.4 Angle encoder window 68 B.4.1 Position-sensitive detector window 70
iii B.4.2 Settings of the position-sensitive detector 71 B.5 Relays window 73 Appendix C. DSO-1M operation manual 75 C.1 Mechanical initialization 75 C.2 Instrument alignment 77 C.3 Detector calibration 80 C.4 Crystal lattice parameter measurement 82 Appendix D. Temperature Measurement Analysis 85 D.1 Real temperature estimation 85 D.2 Statistical measurement error 88 D.3 Measurement error estimation 91 D.4 Comparison of MTCS with other measurement techniques 93
iv List of Tables Table 1. MTCS characteristics 9 Table 2. Macroscopic and X-ray densit ies of 3C-SiC i rradiated at 100 C  26 Table 3. Final experimental results 49 Table 4. Brief characteristics of te mperature measurements methods in hard to access places 51 Table B1. MotorÂ’s gear ratios 65 Table B2. Recommended frequency values for motors 67 Table B3. EncoderÂ’s gear ratios 69 Table C1. Pre-alignment conditions 77 Table D1. Temperature measurements a nd errors for MTCS at stationary regimes  86 Table D2. Calculated values of linear regr ession and mean squared deviation of empirical data for MTCS  87 Table D3. Parameters of and of the function ( TM) for MTCS  90
v List of Figures Figure 1. a) MTCS size comparison; b) SEM micrograph of MTCS  9 Figure 2. Atomic model of 3C-SiC crystal 10 Figure 3. Dependence of crystal lattice expansion of SiC on the neutron flux for different temperatures  11 Figure 4. Block-scheme of MTCS application  12 Figure 5. Single 3C-SiC crysta l installation methods  14 Figure 6. Schematics of multi-crystal MTCS positioning in a rocket nozzle  14 Figure 7. Rocket engine combustion ch amber turbo pump cross-section  15 Figure 8. Temperature gradient map of the Â“BuranÂ” spacecraft  15 Figure 9. Stored energy per unit mass as a function of a crysta l lattice expansion for irradiated 3C-SiC  21 Figure 10. Dependence of volume ch ange, passed through a disturbance stage k -times, on time  22 Figure 11. Isochronous annealing of 3C-SiC irradiated at 100 C  29 Figure 12. Crystal rotation axes 31 Figure 13. Diffraction of X-rays by a crystal 32 Figure 14. Schematic position of the 420 reflection plane in 3C-SiC 33 Figure 15. Crystal rotation scheme 34 Figure 16. Diffraction by a crystal rota ted through the BraggÂ’s angle  35
vi Figure 17. X-ray scattering in a fixed direction during crystal rotation 36 Figure 18. Calibration plot for 3C-SiC crys tal lattice expansion as a function of annealing time and temperature  39 Figure 19. Curves of isochronal annealing  40 Figure 20. Temperature determination pl ot for MTCS at the non-stationary regime  41 Figure 21. Photo of the lab diffractometer DSO-1M 43 Figure 22. Search of the beginning of a peak; 0.1 step 45 Figure 23. Maximum peak search; 0.05 step 46 Figure 24. Azimuth scan at s=50.75 ; 1 step 47 Figure 25. Azimuth scan at S =50.75 ; 0.5 step 48 Figure 26. Omega ( S) scan at the maximum intensity; 0.005 step 48 Figure 27. Isochronous annealing of diam ond and 3C-SiC irradiated at the temperature of 196 C and stored at 0 C  53 Figure A1. DSO-1M diffractometer 59 Figure B1. RDPW Speed bar 60 Figure B2. Radicon hardware server window 61 Figure B3. Controller window 62 Figure B4. High voltage unit window 63 Figure B5. Motor window 64 Figure B6. Mechanic tab; motor window section capture 65 Figure B7. Frequencies tab; mo tor window section capture 66 Figure B8. MotorÂ’s operation points; motor window section capture 67
vii Figure B9. MotorÂ’s operation points scheme 67 Figure B10. Angle encoder window 69 Figure B11. Position-sensitive detector window 70 Figure B12. Settings window of position-sensitive detector 72 Figure B13. Calibration tab; positio n-sensitive detector window 73 Figure B14. Relays window 74 Figure C1. Initial data input window 76 Figure C2. Main form tab and the Relays sub tab 78 Figure C3. Photo of the measuring un it of the diffractometer DSO-1M 78 Figure C4. Calibration curve; positi on-sensitive detector window 81 Figure C5. Measurement input data 83 Figure D1. Estimation pattern of (SD) as a function of a measured temperature  89 Figure D2. Standard deviation ( ) as a function of time 94
viii List of Nomenclature a crystal lattice parameter z zone volume microscopic section of average neutrons scattering neutron flux density t irradiation time k number of passes thr ough a disturbance zone E energy V volume V volume change Vk volume of material passed th rough a disturbance stage (zone) k -times Vk,max maximum volume of material pa ssed through a disturbance zone V* total volume of material passe d through a disturbance zone k -times N point defect concentration average number of displacements per one neutron collision Tirr irradiation temperature Tirr activation degree of neutron irradiation NC number of elementary unit cells NC number of additional unit cells C concentration of point defects Cv concentration of vacancies Ci concentration of interstitials CF Frenkel pairs concentration ( / )m variation of macroscopic density ( / )x variation of X-ray density
ix ai interstitials contribution to a crystal expansion av vacancies contribution to a crystal expansion aF Frenkel pairs contribut ion to a crystal expansion r interatomic distance n bond order BraggÂ’s diffraction angle rotation angle a bout vertical axis azimuth rotation angle s sampleÂ’s rotation angle about its vertical axis d detectorÂ’s rotation angl e about its vertical axis wavelength d lattice plane spacing h,k,l MillerÂ’s indices Fe-K iron X-ray source n BraggÂ’s law integer FWHM Full Width Half Maximum Na total planeÂ’s length 1Â’2Â’ X-ray path length difference T annealing temperature Tmax maximum annealing temperature Imax maximum intensity (counts) I max rev maximum intensity per sampleÂ’s revolution IBG background noise level TM measured temperature Treal real temperature L() estimated measured temperature limit L(+) upper estimated measured temperature limit L(Â–) lower estimated measured temperature limit fexp experimental function of measured temperature temperature measurement error
x q measurementÂ’s order TM,q measured temperature at q measurement Treal,q real temperature at q measurement c,q systematic temperature measurement error a, b linear regression values R1, R2 mean squared deviations of temperature measurements standard deviation (SD) i subsample number Ni subsample volume i, i estimated regression parameters for the i -series eff M T effective (measured) temperature Tub unbiased real temperature estimation P real temperature values portion 0() x normalized LaplaceÂ’s function iT transient condition temperature 1 iT the nearest temperature 1NTT measured temperature range
xi Irradiated Single Crystal 3C-SiC as a Maximum Temperature Sensor Viacheslav G. Kuryachiy ABSTRACT A neutron flux on the order of 2 1020 neutrons/cm2 at 0.18 MeV induces formation of point defects (vacancies and inte rstitials) in single crys tal 3C-SiC causing a volume lattice expansion (swe lling) of over 3% that ca n be measured by X-Ray diffraction. The crystal lattice can be complete ly restored with an annealing temperature equal to or higher than the irradiation temperature. This phenomenon serves as a basis for temperature measurements and allows the dete rmination of the maxi mum temperature, if the exposure time is known. The single crystal 3C-SiC sensor is appl icable to small, rotating and hard to access parts due to its size of 300-500 microns wide temperature range of 100-1450 C, Â“no-leadÂ” installation, inert chemical pr operties and high accuracy of temperature measurements. These features make it possibl e to use the sensor in gas turbine blades, automotive engines, valves, pistons, space shuttle ceramic tiles, thermal protection system design, etc. This work describes the mechanism of ne utron irradiation of single crystal 3CSiC, the formation of point defects and thei r concentration, the different temperature measurement techniques, and the applicati on of Maximum Temperature Crystal Sensors (MTCS) for maximum temperature measuremen ts in both stationary and non-stationary regimes.
1 Chapter 1 Introduction Building more efficient engines and be tter thermal protection design are two important challenges facing the automobile and the space industries. The engine efficiency increases with the operating temper atures rise, which is limited by materials properties. New high-temperature material s are being developed and include hightemperature alloys, composites, and ceramic ma terials. Since materi al strength decreases with temperature, it is essential to develop adequate cooling systems that are efficiently monitored by thermal sensors. As the maximum operating temperature is normally just under a hundred degrees below the maximum temperature allowed for a particular material, it is extremely important to gain knowledge of the temperatures reached by operating devices. Today, with the appearance of more comp lex devices, the design requirements for temperature sensors become more demanding. It is challenging to measure temperatures of machine elements because of many factors. Among them are high operating temperatures, large temperature gradients a nd the complexity, geometry and decreasing size of engine elements. In addition, the ther mal sensor should not interfere or disturb the integrity of engine elements or their thermal properties. All experimental temperature measurements are based on some sort of property or matter state change. It is a pre ssure of a fluid, volume of a fl uid, electric resistance of a material, electric force induced by two dissim ilar materials in contact and others. There are over thirty different phenomena and material properties used for measuring temperature , with even a larger number of temperature measurement tools available today. There is a vast variety of applicat ions that have the need for new methods, enhanced measurement range, better accur acy, further reduced sensor size, etc.
2 Technical progress is determined mostly by the development of energy supplies, both stationary and mobile. One of the majo r characteristics for these supplies is a coefficient of efficiency defined by th e operation temperatures. Usually, these temperatures can be accurately determined experimentally. For this reason, accurate temperature measurement techniques become especially important during the engine design, testing and fine tuning. 1.2 Statement of work The current work is aimed for the devel opment of a procedure for adjustment and precision alignment of the DSO-1M X-ray diffr actometer for the accurate 3C-SiC crystal lattice parameter measurements. Discussion of the measurement results is presented. The developed methodology is described and used for measuring the neutron irradiated 3C-SiC lattice parameter, which enables one to determine the maximum temperature of the single crystal 3C-SiC sensor. The work reviews both the theoretical and pr actical aspects of u tilizing the single crystal 3C-SiC as the Maximum Temperatur e Crystal Sensor (MTCS). The theoretical part discusses the neutron irradiation and X -ray diffraction analysis of 3C-SiC turning it to the MTCS sensor. The practical part pr esents the X-ray diffraction results of the MTCS sensor proving its capability of us ing as a maximum temperature sensor. The DSO-1M X-ray diffractometer adjustment a nd alignment procedures are given in the appendices. Chapter 2 through Chapter 5 contain review of the current knowledge in the field of single crystal 3C-SiC neutron irradiation and it s use for high temperature measurements. The neutron irradiation infl uence on the 3C-SiC crystal lattice is discussed, describing the mechanism of cr ystal volume expansion due to vacanciesinterstitials formation. Chapter 6 presents the X-ray diffraction anal ysis of the neutron irradiated single crystal 3C-SiC. Here, the procedure for meas uring the BraggÂ’s angle by the DSO-M1
3 X-ray diffractometer is described. The BraggÂ’ s angle obtained from the X-ray diffraction analysis is used to calculate the crystal lattice parameter of the MTCS sensor. Summary of the conducted work and future outlook of the MTCS technique and ways for its improving are outlined in Chaper 7. 1.3 Hard to access parts temperature measurement tools Temperature measurement methods in hard to access parts ar e divided in two categories based on their readout mechanism: c ontact and non-contact. The use of either one depends on the actual application. Each category has its corresponding advantages and disadvantages. The contact readout mechanism category incl udes devices that have an electrical connection between a temperature sensor fixed on a part and a stati onary readout device. While these units are complex and expensiv e, they are able to conduct continuous measurements during stationary and transient regimes. There is also an opportunity for using automation with the contact units, for ex ample, to disconnect a unit at dangerously high temperatures. Contact rea dout devices are thermocouples, resistance sensors, thinfilm resistance sensors, si ngle and twin-lead thin-film resistance sensors . Thermocouples and resistance sensors have minimal measurement errors and have a wide application range. However, thei r use with relatively small parts has great disadvantages. When thermocouples are installe d on such parts, real temperature readings can be significantly distorted due to disturbances in heat exchange conditions with the environment. Thermo-electric heterogeneity of thermocouples over their length at high temperature gradients also increases the measurement error. High temperature gradients limit the application of resistance sensors due to averaging the temperature over time [2, 3]. Micro thermocouples are produced by draw ing the wire thermocouples, covered with the organic-silicon insulation and placed inside a stainless capillary tube. The final diameter of the thermocouple is about 0.33 mm. The sensor is very flexible, and can be
4 easy installed in the device. One of the installa tion techniques is placing the sensor inside specially prepared ch annels. Micro thermocouples are limited in application for smallsize parts that are subject to loads due to their weakening by channel making . Surface thin-film resistance sens ors are deposited in the form of thin films on a substrate made of a non-conductive layer. A di sadvantage of the sens ors is that the film structure is sensitive to environment influe nce. Furthermore, there is a temperature averaging over the filmÂ’s area making the temperature measurements not accurate . Single and twin-lead high temperature thin -film resistance sensors are produced by deposition of insulation layers made of enam els, heat-resistant cement or metal oxides. A hot junction of the thin film resistance sens or is deposited directly on the measured surface. It provides a reliable contact between a film resistance sensor and a measured part. Thickness of the high temp erature thin-film resistance sensors ranges from 0.01 to 0.1 mm. Due to these small changes; they do not distort the temper ature of measured parts. A disadvantage of the sensors is their sealed area, which becomes a source of additional voltage transmitted from the sensor; this occurs due to a difference in thermoelectric properties between the film and a wire made of the same material. This additional voltage depends on the temperature in the junctio n point. Therefore, it requires additional circuits or measuring temperature at this poi nt. Some of the high temperature thin film resistance sensors are also not stable enough and are subject to the environment influence . Non-contact readout devices include fusi ble metal thermometers, thermal paints, thermal plugs, Maximum Temperature Cr ystal Sensors (MTCS). The non-contact measurement methods allow the maximum te mperature to be determined after the experiment is done; when the sensors are to be extracted from the measuring part and then analyzed later. These methods are not applicable for auto mation or temperature control and are not conv enient for transient behavior studi es. At the same time, they are indispensable for certain conditions where leading-out wires is very complex or not applicable. Fusible metal sensors consist of a steel close-ended tube with metal or alloy insertions of different melting temperatures, spaced inside the tube. The insertions are
5 placed in order of increasing melting temperature. After a part is tested, the sensor is extracted, and then it is opened or X-rayed in order to determin e the condition of the insertions. The maximum temperature of th e tested part is defined by the melting temperature of two neighboring insertions Â– one fused and one unfused. It is obvious that the maximum temperature can be determined as close as an interval between the melting temperatures of the two neighboring insertio ns. This is the main disadvantage of the sensor. Furthermore, the size of the sensor is relatively large; thus, it is not applicable for temperature measurements of relatively sma ll parts. In addition, there are some cases where none of the insertions are fused or, co nversely, all of them are fused. If this happens, the observer can only conclude that the measured temperature was higher or lower a certain temperature dictated by the melting temperature if the spacers. The thermal paint temperature measuri ng technique is ba sed on changing the paint color depending on the temperature . The main advantage of thermal paints is that they do not cripple a tested part. Among the disadvantages of the thermal paints are the aliasing of readings, the r eadingÂ’s sensitivity to the heat ing rate and exposure time at maximum temperature, unreliable results in hostile environments. Furthermore, thermal paints may fall due to vibrations of the tested parts. The thermal plug temperature measuring technique is based on the ability of certain austenitic steels to age depending on the temperature and exposure time [1, 7]. The aging consists on the appearance of additional phases and corresponding changes in material hardness. The temperat ure range is usually from 150 C up to 800 C. The temperature is defined by the size of the imprint on the sensorÂ’s surface left by the diamond pyramid tip during the hardness test. Th e temperature measurem ent error of this method is 20 C; and the plug size is 2.5x2.5x2.5 mm3. A disadvantage of the method is the inability to produce a large number of thermal plugs with similar properties. Surface temperature measurements can also be conducted using a method where the radioactive 85Kr tracer is introduced into the pa rt by ion bombardment or by heating the part in 85Kr vapor under high pressure. After that, the part saturated with the 85Kr tracer is tested under opera ting conditions, undergoing the annealing at gradually increasing temperatures. During this process, the annealing temperature and the amount
6 of escaping 85Kr gas are controlled. When the te mperature becomes higher than the temperature at which the part was test ed, the leaving amo unt of radioactive 85Kr gas increases rapidly. This temperature is cons idered as the testing temperature. The advantage of this method is that there is no chemical or phys ical crippling of the tested part. The disadvantage is the highly complex process of saturation the part with the 85Kr gas . Another surface temperature measurement t echnique, used in hard to access parts is the pyrometer method. The main disadvantag e of the method is that the pyrometers can only test surface temperature. In addition, th e absolute temperature measurement error can be quite large. One of the advanced temperature measuring techniques is the Maximum Temperature Crystal Sensor (MTCS). Both diamond and 3C-SiC can be used in MTCS, which work in a similar manner. MTCS are primarily used for measuring the maximum temperature in stationary conditions. The non-stationary conditions, when the temperature changes with time, can be also measured using MTCS if the temperature variation with time is known. The maximum temperature that can be measured with diamond is about 900 C while 3C-SiC MTCS are capable of measuring temperatures up to 1400 C.
7 Chapter 2 The Maximum Temperature Crystal Sensor 2.1 Material selection for MTCS The Maximum Temperature Crystal Se nsor (MTCS) was developed by the Kurchatov Institute of Atomic Energy in Moscow, Russia. The MTCS measuring technique is based on the phenomenon of high temperatures to restore a crystal lattice changed by neutron irradiation. The materials used for MTCS must satisfy the following requirements: 1. significant crystal lattice expansi on due to neutron irradiation; 2. small determination error of the crystal lattice expansion; 3. wide temperature range for crystal lattice restoring; 4. insignificant materialÂ’s radioactiv ity caused by neutron irradiation; 5. ability to produce a larg e amount of sensors with similar properties. There are many materials which experience a crystal lattice change due to neutron irradiation, namely: 3C-SiC, diamond, graphi te, beryllium oxide, alumina oxide, boron nitride, boron carbide and some others. The most suitable materials for using in MTCS are 3C-SiC and diamond. Both materials have similar properties, and work in a similar manner. However, they have different temperature ranges; 3C-SiC is capable of measuring the temperatures in the range of 100 Â– 1400 C, while the range for diamond is 100 Â– 900 C. Moreover, synthetically produced di amonds and natural SiC and all their modifications cannot be used for MTCS due to their impurities wh ich get activated by neutron irradiation causing radi oactivity . All these features make 3C-SiC more attractive to the current work and future research. At a temper ature of about 100 C, a
8 neutron flux on the order of 2*1020 neutron/cm2 (E>0.18MeV) causes a lattice volume expansion in 3C-SiC of up to 2.5-3%. Th e volume expansion erro r is about 0.01 Â– 0.02%. A crystal lattice star ts shrinking after expansion at the temperatures of 100Â–1400 C (annealing). This temperature range determ ines the operational ra nge of the 3C-SiC sensor. The impurities, which contribute to radioactivity of the 3C-SiC after neutron irradiation are 125Sb, 113Sn and 60Co. These elements belong to the Â“BÂ” group of radioactivity, and according to the safety rule s, their overall allowa ble radioactivity for the workplace is 10 Ci or 3.7*105 radioactive decays per second . The amount of the impurities is so small, that it is allowe d to work with 60,000 MTCS without special precautions. The stability of the 3C-SiC crysta l lattice along with the uniformity of its properties changes during neutron irradiati on and annealing makes it possible to produce a large amount of sensors with similar properties. The single crystal 3C-SiC temperature sensor has been proven to be one of the best measuring devices for applications in cluding large temperat ure gradients, high complexity and geometry of tested elem ents. Understanding how the sensor works requires the examination of several topics, whic h are directly related to a sensor usage, namely irradiation, annea ling and X-ray diffraction. 2.2 Technical characteristics of MTCS Single crystal silicon carbide has been ex tensively studied and used in various applications due to its unique physical, ch emical and mechanical properties. In electronics, 3C-SiC is a possi ble replacement for silicon for high temperature, high power and high frequency applications. It performs well in a radioactive environment, as it hardly gets activated due to neutr on bombardment. A good knowledge of 3C-SiC behavior during and after irradiation is a prere quisite for all the applications listed above. In fact, during neutron irradiat ion, lattice atoms are displace d, resulting in the formation of structural defects such as interstitials and vacancies.
9 3C-SiC is now a favored sensor material due to its high melting temperature of 2830 C, inert properties, and extreme hardness. MTCS characteristics are listed in Table 1. A size comparison photo of MTCS and its scanning electro microscope micrograph are shown in Figure 1. Table 1. MTCS characteristics Measured temperature range 100 Â– 1400 C Maximum use temperature 1450 C Maximum heating/cooling rate < 200 C/sec Exposure time range 1 C Â– 1450 C Measuring accuracy (s tandard deviation) 15 C Sensor size 0.3 Â– 0.5 mm Density 3.21 g/cm3 Chemical stability in acids and bases Stable Lead wire / connectors No required Figure 1. a) MTCS size comparison; b) SEM micrograph of MTCS  a) b)
10 2.3 Manufacturing of MTCS Both powder and grains of 3C-SiC up to 0.4 mm in diameter can be used for MTCS. The structure of the 3C-SiC may be considered as two face-centered cubic lattices stacked one into anothe r. One of these face-centered c ubic lattices is composed of carbon atoms, another of silicon atoms. F our silicon atoms surround each carbon atom. Silicon atoms, in turn, are surrounde d by four carbon atoms (Figure 2). Figure 2. Atomic model of 3C-SiC crystal The lattice parameter a, for a strain-free 3C-SiC is equal to 4.3608 . Bonds between carbon and silicon atoms in 3C-SiC ar e covalent, each atom shares one of its electron with the neighboring atoms. Before a sensor becomes MTCS, it needs to be irradiated by ne utrons in a nuclear reactor. The value of a neutron-flux, necessary for irradiation, is defined by the condition for large enough swelling of a cr ystal lattice, and on the other hand, it is defined by the condition of a limitation in the mean-square displacement of atoms. The growth originated by this displacement causes a lattice parameter alteration. As seen in Figure 3, for a small neutron-flux F at 0.18 MeV, in the beginning of irradiation the crystal lattice parameter of 3C-SiC increases linearly. After defects concentration reaches a certain point, the linear increase of the lattice parameter continues with a lower slope .
110 0.5x10 F, neutron/c m 20102021 2 3V/V, % 150C 200C 300C 400C 500C 1.5x10202x1020 Figure 3. Dependence of crystal lattice expansion of SiC on the neutron flux for different temperatures  The mean-square displacement of atoms in a crystal lattice during irradiation depends on the neutron-flux value, and increases slightly in the be ginning. Then, at the flux of 20310 neutrons/cm2 a drastic rise is observed. The optimal neutron-flux value, obtained from experiments, is about (2 Â– 3)*1020 neutrons/cm2 at 0.18 MeV. At these conditions, a crystal lattice sw elling of 3C-SiC is larg e enough. The required time for irradiation can be calculated quite precisely due to the known neutron-flux density in the nuclear reactor. For neutron irradiation, 3C -SiC is placed inside cassettes. The length and diameter of the cassettes shoul d satisfy a condition of consta nt neutron-flux in terms of the cassette height and perimeter. It is necessary to provide such conditions during irradiation, where a difference in the lattic e swelling throughout the whole volume of the cassette does not exceed 0.02%. In order to provide such a difference in the lattice swelling, the flux difference throughout the casse tteÂ’s volume should not exceed 3*1018 neutrons/cm2 or 2% from the overall irradiation dose. Because of this, irradiation always takes place in the middle of the nucle ar reactor where the neutron-flux is more uniform .
12 Another important factor of MTCS manuf acturing is the temperature of neutron irradiation. It is known that any material plac ed in a reactor become s a source of heat due to -ray absorption. Therefore, th is heat needs to be rem oved by cooling with water flowing through the cas setteÂ’s center . After a cassette with 3C-SiC is irradiat ed, it needs to be stored in a special repository. Storage is necessary to allow fo r the decay of short lif e isotopes accumulated in 3C-SiC inside a cassette during irradiat ion. The storing time is about 1 month. Then, the cassettes are opened inside a special box and the irradiated powder or crystals, extracted from the cassettes, undergo the followi ng stages: washing in acids and distilled water, drying and calibration. The amount of 3C-SiC irradiated in one cassette is usually about 5-10 g. This amount is enough to produce 50-100 thousand of MTCSs. The application of MTCS can be described in the following stages, shown in Figure 4. First, the crystal has to be grown. Then it un dergoes neutron irradiation followed by calibration. After the sensor is r eady for temperature measurements, it can be installed in the tested part us ing different techniques. When th e test is over, the sensor has to be extracted and examined separately. Al l these stages will be covered in the next several chapters. Figure 4. Block-scheme of MTCS application 
13 2.4 MTCS design and installation techniques There are several designs of MTCS with different dimensions and different materials being used for temperature measurem ents. The design of MTCS is dictated by the dimensions of the tested part, the temper ature to be measured, and other experimental requirements. A capsule-type MTCS is a steel capsule w ith the ends welded and 3C-SiC crystals inside. Prior to welding one of the ends, a steel tab needs to be plugged between the sensor and this end to avoid annealing the sensor during welding. The capsule is usually made of a stainless steel; however, other mate rials may be used. The capsule is usually 5 mm long with 1 mm in diameter and may contai n a mix of irradiated and unirradiated 3CSiC powder. The unirradiated powder is used to decrease the measurement error. The manufactured MTCSs are placed in pl astic boxes labeled w ith the number of the irradiated powderÂ’s set th ey belong to. Each set has it s own calibration diagram for temperature determination. For temperature measurements of small-si ze parts, 3C-SiC powde r can be directly placed inside a hole in the part. In this case, the volume of the temperature sensor can be decreased by a factor of 10 in comparison with the capsule-type MTCS. This method consists of drilling a small 1-2 mm deep a nd 0.5 mm diameter hole in the tested part. Then the hole is cleaned, degreased and filled with powder of irradiated 3C-SiC. It needs to be mentioned that unirradiat ed powder is to be added to the exposed 3C -SiC after the testing prior to the X-ray diffraction measuremen t. Then the hole is closed with a plug or pressure-contact-welded foil. Thus, it prot ects the powder from being blown away. Finally, the part is mounted into the machin e and tested under the de sired conditions . Sometimes it is preferable to drill a hole at an angle. This method is recommended for temperature measurements of turbine blades and turbine disks . In this case, the centrifugal forces press the powder to the bottom of the hole protecting it from being blown away. The length and diamet er of the hole may be varied, but should have a volume equal to about 0.5 mm3 necessary for placing about 1 mg of the 3C-SiC.
14 Another way of using MTCS on a tested part is by installing 3C-SiC into machine parts using thermo-cement; and if necessary, th e crystal is covered with nichrome foil (Figure 5). After the sensor is imbedded in a machine part, it is exposed to the test environment. Tested part Cement powder Thermo-cement Nichrome tape Figure 5. Single 3C-SiC crystal installation methods  Besides single crystal MTCS there are al so a multi-crystal MTCS. This type of sensor is designed for temperature gradient m easurements. The sensor is manufactured as a 5 mm long steel capillary, with several 3C-SiC crystals inside spaced with steel spacers. One of the ends of such a capil lary is marked in order to determine where the top or the bottom are and installed in the tested part. Such multi-crystal MTCSs are widely used for temperature measurements in turbines, in rocket nozzles and spacecraftÂ’s shell. The positioning scheme for multicrystal MTCS on the example of the ro cket nozzle is shown in Figure 6. steel capilary 5 mm3C-SiC crystals steel spacers Figure 6. Schematics of multi-crystal MTCS positioning in a rocket nozzle 
15 The positioning scheme of MTCS on the example of the rocket engine combustion chamber turbo pump is shown in Figure 7. The numbers show the corresponding measured temperatures in C. 753 730 683 683 681 790 709 605 608 610 642 661 614 526 440 750 722 685 680 763 716 627 602 608 640 657 606 627 436 Figure 7. Rocket engine combustion chamber turbo pump cross-section  Based on these temperature measurements obtained with the multi-crystal MTCS, the temperature gradient map can be obtaine d. Figure 8 shows the temperature gradient map of the Â“BuranÂ” spacecraftÂ’s shell. Figure 8. Temperature gradient map of the Â“BuranÂ” spacecraft 
16 The temperature gradient map shows the temperatures that the spacecraft experiences while entering the atmosphere. There are two aircraftÂ’s surfaces shown on the gradient temperature map, the upper and th e lower. The map shows that the highest temperature zones are on the leading edges of the wings and the nose of the aircraft entering the top layer of atmosphere at about a 40 angle from horizontal with its wings level. Such temperature gradient map is nece ssary for designing the ai rcraftÂ’s temperature protection system.
17 Chapter 3 Neutron Irradiation of Silicon Carbide 3.1 Features of neutron irradiation of materials Neutron irradiation of materials has a gr eat importance and practical significance in industry. Irradiation makes it possible to alter the properties of most materials in various ways by means of changing their micros tructure. In the case of solid materials, these changes correspond to crystal lattice transformations. Material irradiation with high-energy par ticles leads to impe rfection Â– vacancies and interstitials, so called point defects or Frenkel pairs . Defect appearance, hence structural alteration in most cases degrades the materialÂ’s propertie s. On the other hand, this disadvantage may be used in a practical way. For example, here is a possibility of using a stored energy: defect appearance in a crystalline lattice of a solid body leads to excess energy. During annealing this energy is released. Therefore, graphite irradiated by high energy neutrons possesses stored energy, that when quickly released can warm up graphite by hundreds of degrees. It is a non-desirable property if a material is supposed to work in a nuclear reactor. On the other ha nd, the excess energy can be used in chemical reactions which require an additional heat source. 3.2 Principle of neutron irradiation The principle of SiC sensor operation is based on the dependence of annihilated radiation defects on the exposur e temperature and time. Therefor e, it is important to look
18 at the irradiation mechanism, the type of defects created by neut ron irradiation, their transformation and annealing. In regards to the value of energy and i rradiation type, materials experience the following effects: ionization, atom displacement in a crystalline lattice leading to Frenkel pairs formation (vacancy Â– interstitial), atomÂ’s substitution, displacement peaks (zones with high defects concentration), and nucl ear transformation. These and some other effects lead to changes in materialÂ’s physical and mechanical propert ies such as electrical conductivity, hardness, density, etc. Heating of the irradiated material leads to the disappearance of some of the defects (Frenkel pairs); it also leads to the transformation of the defects. Among them are double-vacancies, complexes, extra planes a nd others. During this heating process, the properties of the material are partially re stored. This process is called annealing. Irradiation by electrons, protons, ions, Â– rays, etc. causes ionization and atom displacements. Atom displacements due to Â– irradiation are less possible, and present a secondary process in which electrons are knocked out by neutrons . Neutrons do not have a char ge, and consequently react directly with the atomic nuclei of the irradiated materi al. During collision, neutrons transport their energy to the nuclei and turn them into high-energy ions, causing ionization and new atom displacements. During neutron irradiation the number of secondary, tertiar y, quaternary, etc. knocked out atoms greatly exceeds the number of primary atoms. To estimate all these displacements, it is necessary to analyze the cascade proces s started by the primary atom. It is assumed that there is some displacem ent energy threshold, required to move atoms from their lattice cells. It may be defined as the minimal kinetic energy that has to be transferred to a lattice atom in order to create a stable Frenkel pair. This quantity is rather difficult to measure, since defects have to be identified during expe riments, associated with well-defined irradiation en ergy . So, if an atom in a crystalline lattice receives energy higher than the energy th reshold, it gets displaced fr om its lattice site. If the gained energy is less than the energy thre shold, no displacement takes place. In addition to the displacement energy threshold there is also, the so-called ionization energy
19 threshold. If a primary atom is knocked out and has less energy than the ionization energy threshold, its energy is spent on elastic events (collisions). Therefore, there is a cascade of displacements and a region with high concentration of point defects at the end of the travel path of the neutron. This regi on is called a zone, or peak of displacement. The size of such a zone is 20-100 . During energy release, a substance in a zone is completely melted and some of the atoms leave this zone. Right after that the energy is released to a surrounded area. At the same time most of the created point defects recombine; however, the zone continues to be a high point defect de nsity zone. Later on, a concentration of defects in the zone decr eases due to thermal annealing. The annealing rate is controlled by temperature. As neutron irradiation continues, the di splaced atoms will continue to displace. This happens at the moment when the displa cement zones overlap. Such a process leads to a dependence of defect con centration of the irra diation dose which is characterized by a saturation of defects. However, a transformation of the point defects into more complex forms as well as existing in irradiated material and other effects make the results more complicated. A defect concentration cannot be simply quant ified; therefore, a correlation between changes of material properties and defect sÂ’ concentration has to be taken into consideration. 3.3 Atom displacement energy of irradiated 3C-SiC Neutron irradiation alters electrical conductivity, hardness, density, and other physical and mechanical properties. One of th e most important effects on 3C-SiC caused by neutron irradiation is the change of the cr ystal volume. When a vacancy is formed and the surrounded atoms are not relaxed, the knoc ked out atoms move from their original lattice sites and hence increas e the crystal volume (density decrease). Conversely, with the formation of interstitials, the density of the material increases.
20 The amount of energy required to displa ce silicon and carbon atoms from their lattice sites to interstitial positions in SiC have been determined using molecular dynamic simulations and first principl es calculations . The valu es of displacement energies averaged over all directions in SiC have b een determined to be 20 eV for carbon and 35 eV for silicon, and it is recommended that thes e values be used unive rsally for calculating displacements per atom in irradiated SiC . There are four minimum recoil damage energies required to create displacements in SiC, depending on the projectile/target combinations: 41 eV (C/Si), 35 eV (Si/Si), 24 eV (Si/C) and 20 eV (C/C). The minimum recoil damage energies for the C/Si and Si/C projectile/target combinations can be easily derived from the self-ion combinations. For example, a carbon atom must have kinetic energy of at least 41 eV to provide the 35 eV to a silicon atom that is necessary to displace it . Perlado et al.  have also perform ed molecular dynamics simulations of neutron damage in 3C-SiC. They described a case of damage accumulation by Â“ductileÂ” silicon sublattice and Â“fragil eÂ” carbon sublattice to express an outstanding capability of recombination of silicon recoils, as many more defects were produced on the carbon sublattice than on the silicon sublattice. These simulations treated the defects configurations after the cascade damage occurred. 3.4 Volume change of 3C-SiC due to neutron irradiation As previously mentioned, point defects in a crystalline lattice cause a lattice parameter alteration and internal energy increas e. Alterations of the lattice parameter and internal energy are proportional to the dens ity of point defects. Figure 9 shows a dependence of the stored ener gy per unit mass on the lattice expansion for irradiated 3CSiC . It indicates that the lattice expansio n (up to 3-4%) is proportional to the accumulated energy.
21 Es, J/kg V/V, % 123 0 5x10510x10515x105 4 Figure 9. Stored energy per unit mass as a function of a crystal lattice expansion for irradiated 3C-SiC  One of the most important factors influenc ing the degree of neutron irradiation is the temperature of irradiation. As the temper ature rises, the activa tion of thermal defects increases. Because their concentration is de creasing, mechanical and physical properties change caused by irradiation becomes smaller. This effect is described in Figure 3, where it is shown that for the same energy flux, th e higher the irradiation temperature, the smaller point defect density is . Crystal lattice expansion of 3C-SiC is determined by both thermal and neutron irradiation annealing. As the irradiation e xposure time increases, more material passes through the disturbance stage Â– peaks or di splacement zones. During irradiation, some material regions pass through the disturbance stage twice, or more. These regions of a crystal as well as once disturbed regions have almost the same defect density. The volume of material that passes through a disturbance stage (zone) k-times can be written as : kk kztexpzt V k (1)
22 where z is the zone volume; Â– is a microscopic section of average neutrons scattering; Â– is the neutron flux density; t Â– irradiation time [5, 16]. The maximum amount of volume that pass es through a disturbance zone 1, 2, 3,Â… k -times can be expressed as: 1 k kmaxVkexpk (2) The graphs, showi ng a dependence of Vk on radiation time for different number of passes k are plotted in Figure 10 . V* is a total volume of material passed through a disturbance zone k -times and is equal to Vk at all k -values. The curve V* is shown as a dash line (Figure 10). Vmax k=1Vmax k=2Vmax k=3123 0 0.2 0.4 0.6 0.8 VkV Time, t, a.u. 45 Figure 10. Dependence of volume change, passed through a disturbance stage k -times, on time  The analytical expression of the curve is the following : 1 1 k k kVVexpzt (3)
23 If there was no thermal annealing, expr ession (3) would describe an expansion process of 3C-SiC due to neutron irradiatio n (experimental curves shown in Figure 3). However, the defect density in irradiated ma terial is proportional to a number of zones and depends on their Â“ageÂ”. The Â“olderÂ” the zone, the smaller the defect density is in this zone. This effect happens due to th e thermal annealing of defects. A concentration of the point defects can be also decreased by the influence of Â“bombardingÂ” particles and secondary shif ted atoms, whose en ergy is less than displacement energy but high enough for atoms to be activated  Defect activation due to neutron irradiation occurs mostly by -irradiation. Such additional annealing of defects is equivalent to thermal annealin g at a higher temperat ure. The differential equation, describing the point de fects appearance in materials due to neutron irradiation, and also depending on the neutron flux density, irradiation temperature and Â– irradiation density, is written as : [1 Â– (, )] Â– irrirrdN TTzN dt (4) where N Â– is a point defect con centration at present time; Â– is an average number of displacements per one neutron collision; 1 Â– (Tirr, Tirr) Â– is the probability of the displaced atom staying at its displaced position at the irradiation temperature Tirr and its corresponding degree of activat ion of neutron irradiation, Tirr. Tirr is determined by the ratio of the primary collision number to th e overall collision number where atoms receive the energy smaller than the displacement energy threshold. The probability 1 Â– (Tirr, Tirr) is determined experimentally by the slope of the curves in the beginning of irra diation (Figure 3). The first pa rt of equation (4) describes defect accumulation; the second part descri bes the decrease of accumulation of defects due to irradiation annealing. The ge neral solution of equation (4) is: [1(, )]irrirrNtTTexpzt z (5)
24 In the beginning of 3C-SiC crystal expans ion, the point defects concentration at neutron irradiation corresponds to equation (5). As the irra diation time becomes longer, deviation takes place Â– a monot onic increase is observed. This is described by the fact that at high concentration of point defects, the probability for complex defects to appear becomes higher, which, in turn, has a differe nt effect on the latti ce expansion [18, 19]. As the lattice expands beyond 14%, it is impossible to m easure the lattice parameter of the irradiated 3C-SiC, but the macro-density keeps decreasing to 45% of the lattice expansion. At this point, 3C-SiC becomes amorphous. The possibility of the presence of both poi nt defects and more complex defects in the crystalline lattice makes the relationshi p between defects con centration and changed properties more complicated. However, if the la ttice volume increase does not exceed 3-4%, contributions from the complex defect s may be neglected, especially because the complex defects have a weak influence on the average crystal lattice parameter. 3.5 Point defects in 3C-SiC The concentration of the point defects, interstitials and vacancies can be calculated by knowing the volume V of the specimen (3C-SiC crystal) and the crystal lattice parameter, a [20, 21] The number of elementary unit cells in the ideal crystal with the cubic structure is: NC=V/a3. (6) The formation of vacancies and interstiti als in the crystal causes a change in volume. A number of additiona l cells created by the defects and their further relaxation can be calculated using the following expression: //CCCNNVVNaa (7)
25 Substituting equation (6) into (7) gives: 3413CV NVa aa (8) Dividing both parts of equatio n (8) by the cell number give s a relationship between the defects concentration and the crystal lattice parameter alteration : 3 C CN Va NVa (9) where ( V/V) represents a fractional variation of macroscopic density ( / )m with the opposite sign; ( 3 a/a ) is a fractional variation of X-ray density or the theoretical density taken with the opposite sign. The following equatio n is valid if there is only one type of defects in the crystal: Â–XMC (10) where C is a concentration of point defects; ( / )m and ( / )x are the variation of macroscopic and X-ray de nsities, respectively. The variation of macroscopic and X-ray densities can be either negative or positive. If a part in the right side of equation (10) is positive, it means that a number of cells N/N increases. In this case, C is a concentration of vacancies Cv. A negative number gives a concentra tion of interstitials, C = Ci (a number of cells decreases). The equilibrium of macroscopic and X-ra y densities means that a number of cells is constant; hence, the concentration of v acancies is equal to the concentration of interstitials ( Cv = Ci) . Thus, to determinate the type and concentr ation of point defects, the macroscopic and X-ray densities have to be measured. The most accurate data obtained on single crystals, is shown in Table 2 [22, 16].
26 Table 2. Macroscopic and X-ray dens ities of 3C-SiC irradiated at 100 C  Density, % F, 1020 neutrons/cm2Type Density, % F, 1020 neutrons/cm2 Type Macroscopic X-ray macroscopic X-ray 1.1 1.34 0.25 Â– 3.3 3.50 3.4 Â– 1.72 1.78 3.6 3.49 3.4 2.5 2.25 5 Â– 4.2 3.39 5.8 2.6 2.90 5.5 Â– 3.7 3.41 5.8 3.1 3.27 2.5 7.4 7.0 9.9 3.7 3.16 2.5 7.1 7.3 9.9 Â– 3.15 3.01 7.2 6.3 13.2 Â– 3.37 3.38 7.7 7.3 13.2 During annealing, the crystalline struct ure gradually shrinks to its original volume. However, annealing of highly irradiat ed 3C-SiC can lead to further expansion of volume. At this point, annealing works as if 3C-SiC was irradiat ed further [18, 23]. While annealing at normal (atmospheric) pressure of highly irradiated 3C-SiC decreases the crystalline structure volume, hi gh pressure present du ring annealing leads to greater volume reduction. It is describe d by a presence of long-range order in the position and stacking sequence of atoms in the lattice of almost amorphous 3C-SiC. 3.6 Defect concentration in 3C-SiC As already discussed, crys tal lattice expansion occurs due to the formation of Frenkel pairs. In this chapter, the reasons fo r an increase of volume of crystal lattice will be discussed. An estimation of the cont ribution to a crystal expansion from both interstitials ai, and vacancies av is presented. A relations hip between Frenkel pairs concentration and crystal lattice expansion is established by :
27 ( ) ivFV aaCaC V (11) Estimated non-dimensional values of ai and av have been alre ady presented in KonobeevskyÂ’s et al. work , where he explains the lattice expansion of carbon materials. When the vacancy is created, the neighboring atoms Â“drawÂ” into the centers of trianguls, formed by the nearest atoms. Base d on this idea, the es timated value of the Frenkel pairs contribution to the lattice expansion is aF = 0.6 . As it will be shown later, this approximation is very close to the real contribution. Estimation of ai and av values is based on the relationship between the interatomic distance r (in our case for 3C-SiC) and the bond order n which shows the number of bonds between a pair of atoms. A function r=f(n) must give a real in teratomic distance if the bond order is known. The number of point defects created at moderate neutron irradiation doses does not usually exceed several percent, and the original bonds are remained in a crystal. However, the bonds located near by the defects are changed. To characterize these new bonds, the bond order must be assumed: an in terstitial and a vacan cy are electrically neutral; the interstitial atomÂ’s electrons a nd the electrons that are separated from the neighboring atoms to a vacancy are used to cr eate new bonds within the first coordination surroundings. In order to explain a swelling effect of 3C-SiC, it is requir ed to examine the vacancy-interstitial contribution to the crystal lattice expansion. When the interstitial atom is located in the center of a free octahedral site in the 3C-SiC lattice, a bond order creat ed by this interstitial atom and its nearest surrounding atoms is n = 0.5 because its four free electrons are used to create four bonds. At n = 0.5 a distance between the central (inter stitial) and corner atoms in the octahedral site will be r = 1.99 . When a volume of the octahedral si te in the 3C-SiC lattice corresponds to the atomic volume, then it increases from 5.67 3 to 12.23 3 and leads to the value of ai = 1.16 .
28 A vacancy position is determined by the position of a regular atom. When a vacancy is created, each of the four su rrounding atoms loses one electron. These electrons are used to creat e bonds with the nearest thr ee neighbors. The new bond order in these groups of atoms is n = 1.17 instead of n = 1.0. Consequently, the interatomic distance decreases (volume of the contact decreases from 5.67 3 to 4.98 3). A vacancy is surrounded by eight smaller oc tahedral sites, four of wh ich are shrinking and the other four remain unchanged. So, av = 0.49 . V.M. Koshkin et al.  speculate that the atoms next to a vacancy are more likely to be shifted towards the vacancy due to rapidly growing repulsive forces if the atoms move towards the neighboring atoms. That is why the overall crystal volume decreases mostly due to the volume of vacan cies, and due to surface tension effects, the absolute volume of vacancies should always be less than the volume of the interstitials. A simple correlation gives a contribution of vacancies in the 3C-SiC compression, av = 0.61. The total contribution of the Fre nkel pairs to latt ice expansion is 0.67Fivaaa Interstitials expand the crysta l lattice while vacancies cause shrinking. Since neutron irradiation on 3C-SiC causes the formation of Frenkel pairs, lattice expansion occurs. The coefficient aF = 0.67 makes it possible to determine the concentration of the Frenkel pairs based on the experimental lat tice expansion value: /1.47FFVV Ca VV (12) 3.7 Annealing temperature of irradiated 3C-SiC During neutron irradiation of materials, defects are i nduced mostly due to highspeed neutrons, and by high-speed electrons created by -rays. Electrons turn defects into a different state, changing their activation energy. Therefore, depending on the intensity
29 of -irradiation accompanying neutron-irradiation, the defects annealing rate changes. This rate is determined by the activation energy spectrum. An increase of the irradiation dose leads to a defect density rise, which in turn causes a decrease of the annealing rate. One reas on for this is that a defect density rise causes a higher probability appearance of mo re stable complex defects with high activation energy. Experiments prove that the crystal latti ce parameter of 3C-SiC starts changing when the temperature of isochronous anneal ing reaches the temperature under which the crystal was irradiated . Fi gure 11 shows that 3C-SiC starts shrinking at a temperature equal or higher than the i rradiation temperature of 100 C. In case of irradiation with a higher temperature, a break point of the isoc hronous annealing curve would also coincide with the irradiation temperature. 0.00 1.00 2.00 3.00 4.00 5.00 0100200300400500Tirr oC V/V0 Figure 11. Isochronous annealing of 3C-SiC irradiated at 100 C 
30 Chapter 4 Diffraction Analysis 4.1 Diffractometer method Determination of the unknown spacing of crystal planes requires a diffraction analysis. The diffraction analysis can be perfor med with a diffractometer which uses X-rays of known wavelength. Single crystal specimens such as 3C-SiC can be examined in a diffractometer by mounting the crystal on a goniometer whic h will allow independe nt rotation of the specimen and a detector about the diffractometer axis an d another axis passing through the specimen. In the diffractometer, a single crystal wi ll produce a reflection only when its orientation is such that a certain set of reflecti ng planes is inclined to the incident beam at a 2 angle. Assuming, that a reflection is produced, the inclination of the reflecting planes with respect to any c hosen line or plane on the cr ystal surface is known from the crystal position. Two kinds of operations are required: 1. Rotation of the crystal about various axes until a position is found for which reflection occurs; 2. Location of the normal to the reflecting pl ane on a stereographic projection from the known angle of rotation. The diffractometer method has many varia tions, depending on the particular type of goniometer used to hold a nd rotate the specimen. The diffractometer used in the current work is equipped with a sample hol der, which provides the possible rotation axes
31 shown in Figure 12: one coincides with the diffractometer axis ( ), while the other (BB') is normal to the specimen surface ( ). I Â– is an incident beam; D Â– a diffracted beam; C Â– a specimen; S Â– slits. X-ray source B IC SDetectorB'D Figure 12. Crystal rotation axes The diffractometer method is faster than many other methods such as the Laue, the Guinier-Tennevin [25, 26], the Lang and the Borrmann methods . Furthermore, using narrow slits in order to reduce the divergence of the incident beam can yield results of greater accuracy. However, using extremely narrow slits will make it more difficult to locate the reflecting positions of the crystal, or to direct th e incident beam upon the target as in the current work. 4.2 Application of BraggÂ’s law Experimentally, BraggÂ’s law can be a pplied in two ways. By using X-rays of known wavelength and measuring it is possible to determine the spacing d of various planes in a crystal. Alternat ively, the radiation wavelength can be determined for a crystal with planes of known spacing dhkl and measured (Figure 13). In the current
32 work, the first approach has been utilized in order to determine the lattice parameter of the 3C-SiC crystal, and hence, the volume e xpansion of the crystal. The target (anode) element used as the X-ray source is Fe-K with a wave length of 1.936 and was selected in order to give the best accuracy in comparison with ot her widely used X-ray sources such as Cu-K ( =1.541 ) or Cr-K ( =2.291 ) . 2sinhklnd (13) where n Â– is an integer. For all cases of interest, it is allowed to take n = 1 and write the expression (13) as follows : 2sinhkld (14) Incident beam Diffracted beam dhkl '' Figure 13. Diffraction of X-rays by a crystal The measuring procedure consists of the following steps: 1. MTCS is mounted on the X-ray diffr actometer in the path of the X-ray beam; 2. The crystal is illuminated with X-r ay and the diffraction angle is recorded; 3. The d -spacing is calculated using BraggÂ’s law. The X-ray diffractometer used in the curre nt work is described in the appendix A and is designed to measure 3C-SiC si ngle crystals 420 refl ections (Figure 14).
33 The value of d the distance between adjacent planes in the set ( hkl ), can be found from the following equation for the cubic structure : 222 221()hklhkl da (15) Combining BraggÂ’s law and equation (15) yields: 2 2222 2sin() 4 hkl a (16) For a particular incident wavelength and a particular cubic crystal with a unit cell size a this equation predicts all th e possible Bragg angles at wh ich diffraction can occur from the ( hkl ) planes. For 420 planes, the equation (16) becomes : 2 2 420 25 sin a (17) 4205 sin a (18) A schematic position of the 420 reflection pl ane in 3C-SiC singl e crystal is shown in Figure 14. c b a(420) Figure 14. Schematic position of the 420 reflection plane in 3C-SiC
34 In order for the diffracted X-ray beam fr om the 420 plane to be registered by the detector, the crystal must be rotated to the position where diffracti on occurs. The position of the 3C-SiC crystal where th e diffraction occurs is sche matically shown in Figure 15. The position of the crystal is described by the XYZ coordinate system. Both, the detectorÂ’s and the crystalÂ’s rotations are controlled by the goniometer. The detector is located at the 2 d angle, while the 3C-SiC crystal rotates at and angles till the diffraction is found. This rotation of the 3C -SiC crystal is sufficient to obtain the diffraction from the 420 reflection plane of the crystal by the detector positioned at the 2 d angle. The incident X-ray beam (1 ) hits the 3C-SiC crystal and diffracts (2 ) from the 420 reflection plane at the 2 angle. At this condition, the crystalÂ’s 420 reflection plane would be located at the angle with the YZ axis (Figure 15). b a c Z Y X (420) Incident X-ray direction Diffracted X-ray direction Detector 1' 1 1' 1 2G 2 Figure 15. Crystal rotation scheme
35 4.3 Lorenz factor In order to understand how the peak or the maximum intensity is created, it is necessary to consider certain trigonometrical factors which in fluence the intensity of the reflected beam. Suppose there is a narrow X-ray beam on a crys tal, and let the crystal be rotated at a uniform angular ve locity about an axis through C and normal to the drawing, so that a particular set of reflecting planes, assumed for convenience to be parallel to the crystal surface, pa sses through the angle B, at which BraggÂ’s law is exactly satisfied (Figure 16a). The intensity of reflection is greatest at the exact BraggÂ’s angle but still appreciable at angles deviating slightly from it, so that the curve of intensity vs. 2 is of the form shown in Figure 16b. If all the diffr acted beams are registered by the detector, one can calculate the total energy of the diffr acted beam by integrating the curve. This energy is called the integrated inte nsity of the reflection (Figure 16b). Imax1 2 FWHMIntensityDiffraction angle 2 2 I maxC a) b) Figure 16. Diffraction by a crystal rotated through the BraggÂ’s angle  The integrated intensity of a reflect ion depends on the particular value of B. It is possible to find this dependence by consideri ng separately two aspects of the diffraction curve: the maximum intensity and th e Full Width Half Maximum (FWHM).
36 2 B2BB1 2 1 N 122' 1' a a a) b) Figure 17. X-ray scattering in a fixe d direction during crystal rotation When the reflecting planes make an angle B with the incident beam, BraggÂ’s law is satisfied and the intensity of the diffracted beam is the maximum. But some energy is still diffracted when the angle of incidence differs slightly from B. The value of Imax therefore depends on the angular range of crystal rotation ove r which the energy diffracted in the B direction is appreciable. In Figure 17a, the dashed lines show the position of the crystal after rotation through a small angle from the Bragg position. The incident and the diffracted beams make unequal angles w ith the reflecting planes: the former making an angle 1 = B + and the latter 2 = B Â– This case is shown in Figure 17b, where it is allowed to consider on ly a single set of planes, since the rays scattered by all the planes ar e in phase with the corresponding rays scattered by the first plane. Let a be equal to the atom spacing in the plane and Na the total length of the plane. The difference 1Â’2Â’ in path length for rays 1' and 2' scattered by adjacent atoms is given by equationÂ” (19) : 1'2'21coscos[cos()cos()]BBADCBaaa (19) By expanding the cosine terms and setting sin( ) equal to for small ( < 1 ) Then, 1Â’2Â’ can be expressed as: 1'2'2sinBa (20)
37 The path difference between the rays scattere d by atoms at either end of the plane is simply ND times this quantity. When the rays scattered by the two end atoms are one wavelength out of phase, the diffracted inte nsity will be zero. The condition for zero intensity is therefore : 2sinDBNa (21) or : 2sin D BNa (22) This equation gives the maximum angular range of crystal rotation over which appreciable energy will be diffracted in the 2 B direction. Since Imax depends on this 2 range, it would be proportional to 1/sin( B). Other things being equal, Imax is therefore large at low scattering angles and small in the region of back reflected X-rays. The breadth of the diffractio n curve varies in the opposit e way, being larger at large values of 2 B, where the FWHM was found to be proportional to the product Imax, which is in turn proportional to (1/sin B)(1/cos B) or to 1/sin2 B. Thus, as a crystal is rotated through the BraggÂ’ s angle, the integrated intensity of a reflection turns out to be greater for larger and small values of 2 B than for intermediate values .
38 Chapter 5 Preparation and Analysis of MTCS 5.1 Calibration of MTCS The calibration process cons ists of annealing irradi ated crystals at known temperatures and different times. The basic re quirements for calibration are the precise setting and maintaining of the annealing temperature, the exposure time measurement during annealing, and the crystal lattice volume change measurements. The crystal volume change is obtained from the crysta l lattice parameter measuring using the diffractometer method described in the previous chapter. A plot used for determination of the te mperature, measured by MTCS is a series of isotherms plotted every 10 C. The abscissa serves as an exposure time expressed by a logarithmic scale in minutes, and the ordinate serves as the lattice expansion expressed in percent. To plot such a graph it is necessary to test about one hundred sensors from irradiated 3C-SiC set. First, they are exposed to annealing at constant time (isochronous nnealing) in the range of 100 Â– 1300 C. The exposure time is 1, 10, 102, 103 and sometimes 104 minutes. After the annealing, 3C-S iC undergoes X-ray analysis and the results are used for plotting a graph (Figure 18). The principles used for plotting the graph are the following: the annealing is to be done in increasing steps of 50 C. After each annealing an X-r ay analysis is taken and the crystal lattice parameter is measured. The re sults are then plotted where the abscissa shows the annealing temperature and the ordi nate shows the percen tage of the crystal
39 volume change. The points of each isochrono us annealing are to be outlined with a smooth curve shown in Figure 18. 10 Time, minV/Vo, %1010 1 1.50 1 0 5 0 C2.30 2.50 2.70 2.90 2.10 1.90 1.70 9 0 0 C 7 0 0 C510234 Figure 18. Calibration plot for 3C-SiC crystal lattice expansion as a function of annealing time and temperature  It is obvious that for MTCS sensors th e temperature measurement error depends on the accuracy of plotting the graph. The absolute error when measuring the annealing temperature should not exceed 2 C. A temperature pertur bation at any point of exposure time cannot exceed 1 C; accuracy of the exposure time duration must be less than 5%. The measurement error of the 2 diffraction angle of MTCS must be less than 2'. The graphs of isochronous and isothermal annealing have to be drawn in scale without distortion of the temperature, the e xposure time and the crystal lattice parameter alteration expressed in th e crystal volume change.
40 5.2 Data reduction and analysis As mentioned in earlier chapters, the princi ple of operation of the 3C-SiC sensor is based on the annealing of point defects created by neutron irra diation. The Frenkel pairs cause crystal lattice expa nsion. The distance between th e Frenkel pairs is variable. Depending on this parameter, they have differe nt annealing activation energy. Due to this phenomenon, defects in the irradiated 3C -SiC are annealed gradually with the temperature increase. At this, the crystal lattice shrinks. There is a functional relationship be tween three parameters: lattice volume expansion, temperature and exposure time. If the exposure time is known, and the lattice volume expansion after annealing is known, the temperature can be determined. Vice versa, if the temperature and the expa nsion are known, the exposure time can be determined (Figure 19). T, oC V/V0, % 1 min 100 min 1000 min Figure 19. Curves of isochronal annealing  Figure 20 shows the crys tal volume expansion V/V as a function of the exposure time at the maximal temperature T expressed in logarithmic scale.
41 10 t, min2 V/V o, % 1010103413.40 3.57 3.73 3.90 520 C 420 C 340 C 280 C 470 C A B C 105 Figure 20. Temperature determination plot for MTCS at the non-stationary regime  The temperature, at which the sensor wa s exposed, is defined by the isotherm at the intersection of the exposure time t, and the crystal lattice expansion V/V0. Let us assume that the sensor is exposed to the maximum temperature for 30 minutes. A lattice expansion of 3.4% corresponds to the maximum temperature of 470 C. This way of finding the maximum temperature is applicable for a stationary heating regime. However, it is important that the sensor can also work at more complicated non-stationary regimes, where the temperature is changing during the test. In this case, MTCS is exposed to the maximu m temperature during a certain period of the overall testing time. Therefore, it is necessary to take into consideration the effect of the annealing at lower temperatures, and introdu ce the appropriate corrections to determine the maximum temperature. The same value of the crystal lattice expansion of 3C-SiC can be obtained by annealing at different temperatur es and different exposure times.
42 Consider an example where a tested part was heated to Tmax for 100 minutes, then to 95% of Tmax for 150 minutes, and then to 90% of Tmax for 300 minutes, resulting in the total lattice expansion of 3. 49% which corresponds to 420 C. First, the approximate upper bound of the maximum temperature achi eved in 100 minutes for the lattice expansion of 3.49% needs to be determined. According to the plot, shown in Figure 20, a crystal lattice expansion of 3.49% corresponds to 420 C. This temperature is assumed as the maximum temperature Tmax=420 C. Then all the relative temperatures are to be converted to the absolute temper atures: 100 minute exposure at 420 C, followed by 150 minute exposure at T=0.95 Tmax=399 C, followed by 300 minute exposure at T =0.90* Tmax = 378 C. It should also be noted that th e lattice expansion decrease caused by the exposure of 378 C for 300 minutes is equivale nt to 60 minute exposure at Tmax=420 C (point A in Figure 20). Similarly, annealing at the temperature of 399 C for 150 minutes is equivalent to a 90 minute anneal at 420 C (point B). Therefore, this particular non-stationary hea ting regime is equivalent to the maximal temperature anneal for 100 + 60 + 90 = 250 minutes. This would be an equivalent time of 250 minutes anneal at the maximum temperature Tmax as the non-stationary annealing gives the same result in terms of the crystal lattice expansion chan ge. Now, the maximum temperature of 370 C is determined from the lattice paramete r change, expressed in the crystal lattice expansion of 3.49 % and the equivalent time of 250 minutes (point C). The equivalent time is always less then the actual testing tim e, but greater than the time of exposure at the maximum temperature.
43 Chapter 6 Interpretation of Experimental Results 6.1 Operation of the laboratory diffractometer An X-ray diffractometer DSO-1M used fo r measuring the diffraction angle and hence a lattice parameter value of 3C-SiC si ngle crystals, is shown in Figure 21. The diffractometer and the operational software Â“Radicon Device Programming WorkbenchÂ” (RDPW) were developed by Radicon Inc. in Saint-Petersburg, Russia. The diffractometer was designed to measure the lattice parameter of 3C-SiC single crystals by the diffraction from its 420 reflection plane. The proced ure of finding the re flection plane was schematically shown in Chapter 4. Figure 21. Photo of the lab diffractometer DSO-1M
44 The diffractometer DSO-1M consists of the following units: 1 Â– adjustable column; 2 Â– X-ray source unit; 3 Â– collimator tube; 4 Â– sample holder; 5 Â– detector; 6 Â– goniometer; 7 Â– X-ray generator (not shown); 8 Â– control block (not shown). A detailed description of the diffractometerÂ’ operation an d the software is given in Appendix A and Appendix B, respectively. The samples are inserted inside the specia lly designed cuvettes made of plastic or plexiglass with a hole drilled in the center. The holes are designe d for different size crystals and have a range of 0.3-0.6 mm. A detailed procedur e of the sampleÂ’s installation is given in the Appendix C.4. The sample holder is capable of rotati on about its vertical axis at angle s and is also capable of providing rota tion of the sample at angle The detector is rotated at the angle 2 d equal to 162.5 while a sample holder is rotated at the angle s=50 The Bragg angle ( ) of the original not irradi ated 3C-SiC is about 83.1 and therefore 2 =166.2 The detectorÂ’s position at 2 d =162.5 and its registration range of 6.0 is sufficient to register the diffraction of the BraggÂ’s angle at =83.1 6.2 Experimental diffrac tion analysis of 3C-SiC The measuring procedure consists of finding the diffracted beam maximum intensity at the fixed position of the detector 2 d and the variable sample angle s. Using BraggÂ’s law, the crystal lattice parameter of 3C-SiC is calculated from the angle that corresponds to the found maximum intensity The measurement is based on the 420 reflection from 3C-SiC crystal lattice and is carried out in a fully automated manner. The measurement starts with a launc hing the software Â“Radicon Device Programming WorkbenchÂ” (RDPW) and r unning the macro command Â“MeasureÂ”. The program will ask to name a sample and sp ecify the measuring mode. The measuring mode consists of either finding a diffraction angle of the X-ray beam from the sample or finding the intensity values for a range that can be manually specified. The initial angle scanning positions for the sample ( s) is equal to 50 with a 0.1 scanning step, while the
45 detectorÂ’s center is fixed at the angle 2 d =162.5 The entire measurement procedure may be divided into several steps described below. 1. Positioning of the sample and the detector at the 50 and 162.5 angles, respectively. 2. Adjusting the high-voltage power s upply of the X-ray tube to 25 kV, 2 mA. 3. A preliminary search of the intensity peak. The sample is rotating at the azimuth angle with the rate of 1/6 rev/sec; s rotation of the sample with a step of 0.1 (Figure 21). Every step is followed by searching the maximum intensity per every revolution of the sample. The scanning stops when the maximum intensity Imax becomes higher than a background noise level IBG by the value of the square root of its value (23): rev maxBGBG I II (23) The inequality (23) is an empirical constrain which was obtained in order to register the actual maximum (peak) and disregard the false peaks. The detector is fixed at the 162.5 position ( d); the specimen is at the 50 position ( s), the step is 0.1 The results are shown in Figure 22. 0 2 4 6 8 10 12 49.85050.250.450.650.8 Intensity Bg LevelIntensity, a.u.S degrees Figure 22. Search of the beginning of a peak; 0.1 step
46 The maximum found intensity is 11 photons/sec that corresponds to s =50.70 (Figure 22). 4. Confirmation of the peak. Analog ous to step 3 except for the azimuth rotation of the sample with the rate of 1/30 rev/sec and the s rotation with a step of 0.05 If the background noise level rise is not found after thr ee steps, the procedure returns to step 3. Otherwise, it proceeds to the next step. 5. Search for the peak end at rotation the sample at 1/30 rev/sec. Stepping of the s rotation of the sample is 0.05 The maximum intensity value is registered for every step. Search for the s, corresponding to the maximum intensity per revolution of the sample. The scanning process stops when the empi rical constrain (24) is reached : maxmax2rev max I II (24) where rev max I is the maximum intensity per revolution of the sample; max I is a maximum intensity over three 0.05 steps. A rough determination of the sample position for the angle happens when the peak is observed. The accuracy of the angle is 15 The results of the maximum peak se arch are shown in Figure 23. 10 20 30 40 50 60 70 80 50.65150.70150.75050.80050.84950.900 Intensity Imax-2*sqrt(Imax)Intensity, a.u.S, degrees 327.60328.86328.90326.66329.80328.94o, degrees Figure 23. Maximum peak search; 0.05 step
47 The rough and s positions for the sample at the maximum intensity are 328.90 and 50.750 respectively (Figure 23). 6. Positioning of the sample at the s and the corresponding to the maximum value of intensity found in the previous steps: s = 50.750, = 328.90. 7. Azimuth ( ) scanning in 1 increments. Determination of the angle position of the sample at the maximum intensity and fixed s (Figure 24). 1 10 100 1000 320325330335340 IntensityIntensity, a.u., degrees Figure 24. Azimuth scan at s=50.75 ; 1 step The values of the maximum intensity and the corresponding sample position are 155 and 325.90 respectively. 8. Accurate determination of the sample position at the fixed S with the step of 0.5 (Figure 25). Searching th e position within the 1 range of the value found in the previous step.
48 0 50 100 150 200 324.5325325.5326326.5327Intensity, a.u. degrees Y = M0 + M1*x + M2*x2 -1.1424e+07 M0 70067 M1 -107.43 M2 0.94368 R Figure 25. Azimuth scan at S =50.75 ; 0.5 step The polynomial fit curv e shows the value of corresponding to the maximum intensity. Calculation of the position is carried out usi ng the center of mass method: ii imr R m (25) The calculated value of is equal to 326.10 and is corresponding to the maximum intensity of 170 photons/sec. 9. Accurate positioning of the sample at the s angle. Measuring the X-ray intensity for 90 seconds and determination of the peak position as 2 (Figure 26). 70 80 90 100 110 120 130 50.6650.6850.750.7250.7450.7650.78Intensity, a.u.s, degrees Y = M0 + M1*x + M2*x2 -4.641e+07 M0 1.8297e+06 M1 -18034 M2 0.84832 R2 Figure 26. Omega ( S) scan at the maximum intensity; 0.005 step
49 The polynomial fit curve shows the value of s, which corresponds to the maximum intensity. Using the center of mass method (20), the s position of the sample corresponding to the maximum intensity is at 50.7322 The actual maximum intensity registered during the scan is 124 photons/sec. The results obtained from the measurem ent process are shown in Table 3. Table 3. Final expe rimental results Specimen position ( ) 50.732 Detector position 162.501 Maximum intensity 124 photons/sec Peak relative position -4.115 Peak absolute position (2 ) 158.386 Theta ( ) 79.193 Lattice constant (a) 4.407281
50 Chapter 7 Summary and Future Work 7.1 Summary Today, with the increasing interest of designing more efficient engines and turbines, improving their performance, the ac curate measurements of high temperatures become more demanding. Neutron irradiation and the X-ray diffraction analysis of the single crystals 3C-SiC turns them to the Maximum Temperature Cr ystal Sensors (MTCS) enabling to measure the maximum temperatur es. The sensorsÂ’ small size, weight and capability of measuring the high temperatures in hard to access places make them attractive for many applications Moreover, a wide measuri ng temperature range of the MTCS sensors (100 Â– 1400 C) along with their unique physical and chemical properties makes them applicable in almost any environment. In order to determine the crystal latti ce parameter of 3C-SiC, the adjustment and precision alignment procedures of the DSO1M X-ray diffractometer were developed. The methodology of the neutron irradiated 3C-SiC lattice parameter was described by the X-ray diffraction analysis enabling one to determine the maximum temperature of the MTCS sensor.
51 Table 4. Brief characteristics of temperature m easurements methods in hard to access places Type measurement category, characteristics Applicable device Operation Advantages Disadvantages Contact readout methods provide continuous measurements at stationary and transient regimes; possible automation; output readout mechanism is necessary. Resistance sensors Electrical resistivity as a function of temperature High accuracy of measurements, wide measurement range Averaging-out of temperature over the length of a sensor Thin-film resistance sensors No temperature distortion Averaging-out of temperature of a sensor, low stability. Film thickness prop. dependence Thermocouples Voltage at the welding joint as a function of temperature High accuracy of measurements, wide measurement range Size of a sensor, temperature distortion of tested parts Micro thermocouples Relatively small size, wide measurement range, high accuracy Not applicable for micro parts Single and twin-lead high temperature thin-film resistance sensors Applicable for micro parts temperature measurements Temperature measurement distortion due to a voltage at the welding joint Non-contact readout methods provide measurements where the contact readout methods are not applicable; maximum temperature measurements only; readings are possible to obtain after the test is completed only Fusible metal thermocouples Melting of metal plugs Simplicity of readings decoding Size, discontinuity of readings Thermal paints Thermal paint color or its conditions change with temperature PartÂ’s integrity Discontinuity of readings, subjectivity of color change estimation Thermoplugs Steel hardness as a function of temperature and exposure time Relatively small size High complicity of production of a big set of plugs with equal properties, exposure time data is necessary Radioactive tracers Dependence of the tracerÂ’s discharge speed from the tested part on temperature No changes in physical or chemical properties of tested parts High complicity of saturation of the tested part with radioactive tracer, complicity if readings decoding MTCS Dependence of crystal lattice parameter of the irradiated crystal on temperature and exposure time. High accuracy of measurements, wide measurement range, small size Exposure time data is necessary
52 7.2 Future work Small sensorÂ’s size, its wide range of measured temperatures and high accuracy makes MTCS widely used in many applications. However, the MTCS method requires some improvements. First of all, it is the temperature measuring range which is limited by the temperature of 1400 C for 3C-SiC based MTCSs. Increasing the temperature range of 3C-SiC sensor towards the higher temperatures is limited by the fact that the majority of defects are annealed prior the temperature reaching 1400 C. The following increase of temperature causes annealing of a small portion of defects only. This phenom enon negatively affects the accuracy of temperature measurements. One of the other materials suggested fo r high temperature measurements is an unannealed graphite . Its lattice parameter is considerably larger than for the annealed graphite and depends on the annealing temp erature. The higher the temperature, the smaller lattice parameter is. While a crystal lat tice change of 3C-SiC is almost negligible in the high temperature range, a lattice paramete r change of graphite is at its maximum. Realization of this method is facing some obs tacles due to a low chemical stability of graphite and a low accuracy of temperatur e measurements. The error can reach 50 C due to inaccurate determination of the latti ce parameter of unannealed graphite measured with the diffractom eter method . Increase of a higher level of the measur ed temperature range also assumes finding new materials where defects are annealed at higher temperatures than for 3C-SiC or diamond. At this point, it would be interesting to investigate behavior s of beryllium oxide with its melting temperature of 2530 C and a high thermal conductivity. Another material that would be interesting to examin e is a cubic modificati on of boron nitride. It is known that the boron nitrid e can exist as various polymorphic forms, one of which is analogous to diamond and one anal ogous to graphite. These feat ures make it an attractive material as a possible alternative to 3C-SiC and diamond. MTCS, investigated in the current work, ha ve been irradiated in a nuclear reactor at 100 C. This temperature determines a lower level of the temperature range measured
53 with MTCS. At some nuclear reactors, it is possible to irradiate materials at lower temperatures. Thus, the defects will start to recombine at the lower irradiation temperatures, thereby increasing the temper ature range towards the low temperatures. However, it has been experimentally proved th at a lower temperature limit cannot be less than 50 C , . Experiments showed that a 3C-SiC crystal lat tice does not change much at the irradiation te mperatures starting from th e room temperature up to 100 C. It can be seen from a plot in Figure 27 obt ained from data collected in . A 50 C lower limit of the temperatures measured with MTCS has a significant importance as some of the devices operate at the temperature range from a room temperature to 100 C. At the same time, such a temperature range brings a restriction for storing the sensors as they have to be kept at low temperatures to a void undesirable anneali ng of defects prior to testing. V/V,% 0.8 1.0 1.2 1.4 050100150200250 T,C Figure 27. Isochronous annea ling of diamond and 3C-SiC irradiated at the temperature of 196 C and stored at 0 C  Broadening of a range of exposure time during tests may be achieved by increasing the exposure time while calibrati on of MTCS. However, prolongation of the exposure time experiences some difficulties du e to a complexity of maintaining a fixed temperature for a long period of time. Many experiments require a short exposure time of less than 100 seconds. Such a short exposure time is usually followed by a rapid heating that may cause sensor overheating. Defects created by neutron irradiat ion that cause crystal lattice expansion of
54 3C-SiC have an excess energy of 2 MJ/kg. Heat created by a nnealed defects during rapid temperature increase, can not be efficien tly removed from the sensor. It causes overheating of 3C-SiC to the te mperatures higher then the actual measured temperature. As a result, readings obtained from the overheated MTCS are significantly overestimated. In order reduce the energy release at high hea ting rates, MTCS has to be preliminarily annealed at the temperature of 100 Â– 200 C less then expected temperature during the test. A heating rate during annealing should not exceed 200 C/sec, while the exposure time cannot be much larger than the expect ed time for the followi ng test. At this, a significant portion of the stored en ergy can be released from 3C-SiC. Besides a lattice parameter change, other materials properties may be considered for temperature indication, such as electro or thermo conductivity change.
55 References 1. D.F. Simbirsky, Â“Temperature diagnostics of enginesÂ”, Technics, 208 (1976) 2. J.I. Bramman, A.S. Fraser, W.H. Martin International Conf erence on Fastreactor Irradiation Testing, 14 (1969) 3. Templug User Information Guide, Testing-Engineers, Inc., Rev.2.0, 1997 4. A.N. Gordov, A.S. Arzhanov, V.Y. Bilyk et al., Â“Temperature measurement techniques in industryÂ”, 432 (1952) 5. V. A. Nickolaenko, V. I. Karpukhin, Â“Temperature Measurements by means of irradiated materialsÂ”, Energoatomizdat, 35, 117 (1986) 6. Thermal Paint Technical Information, Rolls-Royce Inc., ( www.rolls-roice.com ) 7. A. Guiner and G. Tennevin, Acta Cryst., 2,133 (1949) 8. A.A. Volinsky, L. Ginzbursky. Â“Irradiated Cubic Single Crystal SiC as a High Temperature SensorÂ”, Mat. Res. Soc. Symp. Proc. Vol. 792, R5.3 (2003) 9. V.A. Nikolaenko, V.A. Morozov, Russian Re search Center Â“Kur chatov InstituteÂ”, Moscow, Russia V.P. Timoshe nko Molniya-T, Moscow, Russia 10. A.A. Volinsky, V. Timoshenko, V. Nikolaenko, V. Morozov. Â“Irradiated Single Crystals for High Temperature Meas urements in Space ApplicationsÂ”, Mat. Res. Soc. Solid State Phenomena, Vols. 108-109, 671-676 (2005) 11. R. Devanathan, W.J. Weber, J. Nucl. Mater, 258, 278 (2000) 12. R. Devanathan, W.J. Weber, F. Gao, J. Appl. Phys, 90 (2001) 13. H. Heinisch, L.R. Greenwood, W.J. Webe r, R.E. Willi-ford, J. Nucl. Mater. 307Â–311 (2002)
56 14. J. M. Perlado, L. Malerba, and T. Diaz de la Rubia, Mater. Res. Soc. Symp. Proc. 540, 171 (1999) 15. V. A. Nickolaenko, V. I. Karpukhin, S. I. Alekseev, I. D. Konozenko, Â“Physics of Radiation of non-metallic crystalsÂ”, Naykova dymka, 322-329 (1971) 16. V. I. Karpukhin, O. K. Chugunov, Â“ReactorÂ’s -irradiation and its influence on annealing of defecsÂ”, 38 (1949) 17. V. A. Nickolaenko, V. G. Gordeev, M. I. Baneeva, Â“Super hard materialsÂ”, 15-19 (1983) 18. E. R. Vance, J. Phys, Solid State Phys, 257-262 (1971) 19. A. Damask, G. Jeans, Â“Point defects in materialsÂ”, 17-26 (1966) 20. S. T. Konobeevsky, Â“Irradiation effect on materialsÂ”, 201 (1967) 21. V. A. Nickolaenko, International conference summary, Â“Radiation physics of semiconductors and relative materialsÂ”, (1987) 22. J.R. Saltvold, Â“A survey of temperature measurementÂ”, Atomic Energy of Canada Limited, AECL, 51 (1976) 23. V.M. Koshkin, Y.A. Frayma n, L.P. Galchinezky, Â“Physics of SolidsÂ”, 212-214 (1977) 24. A. Guiner and G. Tennevin. Â“Progress in Metal PhysicsÂ”, 2, 177 (New-York: Interscience, 1950) 25. B.D. Cullity. Â“Elements of X-ray diff raction, second editionÂ”, by. Department of Metallurgical Engineering a nd Materials Science, University of Notre Dame, (1978) 26. Craig R. Barrett, William D. Nix, Alan S. Tetelman. Â“The principles of Engineering MaterialsÂ”. Department of Materials Science and Engineering, Stanford University; Materials Department, Universi ty of California. 56 (1978) 27. H. Huang, N. Ghoniem, J. of Nuclear Mater. 250, 192-199 (1997)
57 28. W.J. Weber, F. Gao, R. Devanathan, W. Jiang, Y. Zhang, Â“Experimental and Computational Studies of Ion-Solid Interactions in Silicon CarbideÂ”, Mater. Res. Symp. Proc., Vol. 792 R5.1 (2004) 29. A.A. Volinsky, L.G. Ginzbursky, V.A. Morozov, Â“Crystal Temperature Sensor Technology Status and Future ResearchÂ”, 2003 ASME Mechanics and Materials Conference book abstracts. June 2003, Scottsdale AZ, 10 (2003) 30. V.N. Kuznetcov, V.A. Nikolaenko, Â“Maximum Temperature Measurement Metrology by means of MTCSÂ”, Institute of Atomic Energy by I.V.Kurchatov (1979) 31. G. Borrmann. Â“Physik Z.Â”, 42, 157 (1941) 32. N.V. Smirnov, I.V. Dunin-Barkovsky, Pr obability and Statis tical Methods in Technical Applications Â“ScienceÂ”, (1969) 33. B.S. Dubov, N.M. Kopytin, Â“Measuri ng techniquesÂ”, Vol.12, 70 (1969)
59 Appendix A. DSO-1M X-ray di ffractometer description Figure A1. DSO-1M diffractometer The diffractometer DSO-1M is produced by Radicon Ltd. (Saint-Petersburg, Russia) and includes the following major comp onents: 1 Â– adjustable column; 2 Â– X-ray source unit; 3 Â– collimator tube; 4 Â– sample holder; 5 Â– detector; 6 Â– goniometer; 7 Â– X-ray generator; 8 Â– control block. The diffractometer is designed for determin ation the orientation of single crystals 3C-SiC and calculation the crystal lattice parameters. The 2 angle range is 0-168. The angle measurement accuracy is 0.01. The X-ray source is Fe-K with the wave length of 1.936 . The diffractometer is equipped w ith the position-sensitive detector which is capable of registering the X-rays with the wave length within the 1.0 2.5 range. The goniometer provides the rotation (Figure 21) of the sample in the range of 0 360 with the error of 0.005; the rotatation of the sample is in the range of 0 360 with the error of 0.02.
60 Appendix B. Radicon De vice Programming Workbench Radicon Device Programming Workbench (RDP W) is an application software for IBM-clone personal computers aimed to program and automate the operation of various hardware components of X-ray diffractomete rÂ’s position-sensitive detectors, motors, relays and angular encoders. RDPW main shell is hardware indepe ndent. All specific hardware-dependent functions are provided by instal lable device drivers. Apart fr om RDPW the device drivers provide the manual control of device operations For each part of the system a separate interactive control window is provided. RD PW integrates various device drivers in a unique system and enables the user to auto mate all the operations. In addition, RDPW provides programmable data ac quisition as well as monitori ng of system operation both in text and graphic representation. RDPW offers flexible user interface, including standard file and edit operations, compilati on and execution of user programs written in Radicon Device Programmi ng Language (RDPL). The control block is assembled in euro -standard 19Â” 3U rack s and connected to the computer via an RS-232 port. The c ontrol block has a control card with a microprocessor and power supplies on board. It allows operating two stepping motors, two couplings, two angular encoders, a shutter, position-sensitive detector, high voltage generator and limit stops. B.1 Speed bar The RDPW speed bar provides shortcuts for the commands , , and menu (Figure B1). The speed bar ha s help hints which display a small pop-up window containing the name or brief descripti on of the button when the cursor is over the button for longer than one second. Figure B1. RDPW Speed bar
61 Appendix B (Continued) B.2 Installable Device Drivers Installable Device Driver (IDD) represents a linkable module that provides full hardware control. IDD is a dynamic link libr ary, which exports th e set of predefined functions. These functions provide all necessa ry information about hardware that this IDD supports, such as names and types of objects, their parameters and functions. B.3 Radicon hardware server window The Radicon hardware server window c ontains collection of command buttons, labeled with device system names (Figure B2). Figure B2. Radicon hardware server window Radicon hardware server provides several types control windows aimed to operate the devices of appropriate t ype. The control windows are: 1. Controller; 2. HV Unit; 3. Motor window; 4. Angular encoder window;
62 Appendix B (Continued) 5. Detector window; 6. Relays window. B.3.1 Controller window The Controller window is opened by se lecting the button in the Radicon Server window (Figure B3). The C ontroller window allows to choose the RS-232 port for connection with a computer. A green color in the window indicates that a device is connected to a computer successively and is ready for work. Any mistake in connection is show n with a red color indicator. Figure B3. Controller window
63 Appendix B (Continued) B.3.2 High voltage unit window The High voltage unit window allows contro lling and setting th e high voltage and anode current of the X-ray tube (Figure B4). The high voltage range is 15 kV 45 kV, the tube current range is from 0. 2 mA 5 mA. The limit power of X-ray tube is 75 watts. The product of high voltage by current s hould not exceed this limit power. Figure B4. High voltage unit window B.3.3 Motor window The current status of the motor, its pos ition and status of the motorÂ’s limit stops are shown on the top of the Motor window (Figure B5). Th e operation block includes the commands controlling the motor. The first row of the buttons and rotate the motor at the angle specified in the field in between. The angle is taken
64 Appendix B (Continued) relatively to the current position. The next row of two buttons and serves for continuous rotati on of the motor to one of the selected directions. Figure B5. Motor window When one of these buttons is pressed, the motor starts to rotate at the selected direction continuously or until its driven el ement reaches one of the limit stops. The lower row of buttons is responsible for stoppi ng and turning off the motor. In order to stop the motor in the normal regime, the butt on has to be pressed. If it is necessary to stop the motor instantly, press the button . The button relieves a stress at the mo tor due to the emergency stop. One motor (Motor 1) can move both, the position-sensitive detector and the sample holder depending on the coupling positio n. The coupling position is selected from the Relays window (Figure C2).
65 Appendix B (Continued) B.3.4 Power transmission of the step motor Three tabs in the bottom of the Motor window show the parameters of power transmission, acceleration parameters of th e motor and the operational currents of the motor (Figure B6). Figure B6. Mechanic tab; motor window section capture There two options that can be adjusted in the Mechanic tab are the number of steps per turn and the gear ratio. Both mo tors installed in the diffractometer DSO-1M have the rate of 200 steps per revolution. The first gear ratio number is a number of cogs of the driven gear wheel; the second is a num ber of cogs of the driving gear wheel, which is rotating with the motorÂ’s spindle. The gear ratios used in DSO-1M are shown in Table B1. Table B1. MotorÂ’s gear ratios Gear Gear ratio Position-sensitive detector 1500:1 Sample holder 3000:1 Azimuth rotation 90:1 In order to change and save the settings the button has to be pressed. To restore the settings after the accidenta l change, press the button .
66 Appendix B (Continued) B.3.5 Speed of rotation of the step motor The second tab in the bottom of the Mot or window shows the frequency settings of the motor (Figure B7). Figure B7. Frequencies tab; motor window section capture The motor cannot start with the high fre quency rotation, so it accelerates with time. The maximum frequency of rotation is also limited by the motors mechanical features. Furthermore, the motors have the resonant speeds at which they can work during acceleration only. The field shows a starting freque ncy of rotation of the motor (Hz). The field shows a maximum frequenc y of rotation of the motor (Hz); the frequency rises to the maximum chosen freque ncy and the motor starts rotating at this frequency continuously. The field shows a value of acceleration (Hz/sec). Practically, the frequency value represen ts a number of steps made by the motor per second. The Half step regime reduces the number of steps of the motor per impulse by half, while at the regime of a full step one impulse corresponds to one step. In that way the motor which makes 200 steps per one revo lution at the freque ncy of 600 Hz will rotate at the speed of 3 rev/sec in the full st ep regime or 1.5 rev/ sec in the half step regime. The values of frequency recommende d for the motors are shown in Table B2.
67 Appendix B (Continued) Table B2. Recommended frequency values for motors Motor 1 (SM1) 400 Â– 4000 Hz Motor 2 (SM2) 450 Â– 3500 Hz, resonance frequency range: 700 Â– 2500 Hz B.3.6 Operation points of the step motor The last tab in the bottom of the Motor window shows the settings for the motorÂ’s operation points (Figure B8). Figure B8. MotorÂ’s operation points; motor window section capture A change of the current with time at different operational points are shown schematically in Figure B9. Figure B9. MotorÂ’s operation points scheme
68 Appendix B (Continued) The scheme shows how the value of current changes in different motorÂ’s operation modes. At the working mode the moto r is supplied with the Fix Current that is enough only to keep the motor in current posi tion. When the command Start is launched, the current value jumps to th e Start acceleration current value producing the stepping impulses in the motor. The motor starts accel erating with time and the current value rises linearly to the value of Finish accelerat ing current. When the maximum rotation frequency is reached, the motor switches to th e mode of continuous ro tation. At the same time the current jumps down to the value of Constant rotating current. Before reaching the stop point, the motor slows down in order to stop completely at the specified position. A deceleration process is in a reverse order of the acceleration process. First, the current value jumps up to the Finishing accelerating cu rrent value and then linearly decreases to the Start acceleration current value. When the motor is stopped, the current value drops down to the value of the Fix current. The co mmand Loose relieves a stress at the motor due to a stop. B.4 Angle encoder window The optical angle encoders are used to control the positions of both the positionsensitive detector and the sample holder. Th e sample holder is c ontrolled by the Angle Encoder 1, while the position-sensitive detector is controlled by the Angle Encoder 2. The operation window for the Angle Encoders is shown in Figure B10. The position of the angle encoders is shown in the top right corner of the Angle encoder window. The Settings block shows the mechanical settings for the encoder. Â“Discrets per turnÂ” means a number of counts per one revolution of the position-sensitive detector. Both angle encoders have 4000 counts per revolution. The reverse option indicate s that the direction for positive counting of the angle is opposite to the positive direction of the encoder rotation.
69 Appendix B (Continued) Figure B10. Angle encoder window The gear ratios used in DS O-1M for the sample holder and the detector are shown in Table B3. Table B3. EncoderÂ’s gear ratios Name Gear ratio Reverse Sample holder AE1 360:1 No Detector AE2 360:1 Yes In order to input new setting for the sens or press the button in the Settings block. Then it is necessary to run the sensor for one turn. The block Start values initialize the sensor by its current position. Enter a value of the angle in the field Start and press the button in the St art values block.
70 Appendix B (Continued) B.4.1 Position-sensitive detector window The position-sensitive dete ctor window shows the parameters of the positionsensitive detector. The window has two tabs : Spectrum and Calibration (Figure B11). Figure B11. Position-sensitive detector window The most part of the window shows a dist ribution of the intensity registered by the position-sensitive detector. The current se ttings of the position-sensitive detector are shown in the right top corner of the window. The settings can be changed by clicking the button . The Intensity block shows a current intensit y of X-ray radiation. The intensity is presented by a red color horizontal stripe. Bo th the maximum and the current intensity are shown in a numerical form in the fiel ds below the stripe. The button resets a value of the maximum intensity.
71 Appendix B (Continued) The position-sensitive detect or is controlled by the buttons located in the right bottom corner of the detectorÂ’s window. Ther e are two data fields above the controlling buttons. The data filed on the left count s the time since starting the intensity measurement. The data field on the right is the input field where the time of measurement has to be entered in seconds. If the time of me asurement entered in this field is zero, the position-sensitive detector will be working unt il the operator stops it with the button . In order to start the measurement of intensity, click the button. The position-sensitive detector will be measuring the intensity of the X-ray radiation for the time entered in the right bottom input field. The measurement can be stopped with the button and resumed w ith the button . The measured intensity is presented in the form of a spectrum. The upper field of the position-sensitive detector window shows a map of the sp ectrum, while the large part of the window shows the curren t section of the spectrum. Th e value of intensity in a channel can be seen by clicking on the channe l of the spectrum. A scale of the spectrum can be changed by holding the button on the keyboard and left/right clicking on the selected part of the spectrum. The channel mode, its value and the total number of counts are shown in the fields below the spectrum image. B.4.2 Settings of the position-sensitive detector The work regime of the position-sensitive dete ctor can be selected in the Â“Analyse modeÂ” box in the detector settings window (F igure B12). There are two modes available: the amplitude mode and the position mode. In the amplitude mode, the power distribution is registered by the registered photons, while the position mode registers the places of the detector where the interacti on with the photons occurred.
72 Appendix B (Continued) Figure B12. Settings window of position-sensitive detector The first and the last channel values define the range of the de tectorÂ’s operational channels. There are 4096 channels in the position-sensitive detector. However, the outermost channels are not us ually used as they register the apparatus background noise only. Thresholds value defines the energy range registered by th e position-sensitive detector. The voltage bar defines the current value for the position-sensitive detector in kV. The voltage has to be set up at the va lue when the intensity maximum value (peak) corresponds to the channelÂ’s value of approximately 500. The next tab represents th e calibration function of the position-sensitive detector (Figure B13). The calibration tab is used for plotting a calibration curv e of the channel as a function of the detectorÂ’s po sition angle. The calibration pr ocedure is described in the Appendix C.3.
73 Appendix B (Continued) Figure B13. Calibration tab; position-sensitive detector window B.5 Relays window All the relay elements are shown in Figure B14: the shutter, the position-sensitive detector and the sample holder (specimen). Each element has a reserved designation RS0Â…RS3 used by macro commands. By clicking the buttons on the right, the el ements switch their re gime to the On/Off mode. The elements names may be changed by clicking the button . The elements with the reserved name RS0 is not used for the diffractometer DSO-1M.
74 Appendix B (Continued) Figure B14. Relays window
75 Appendix C. DSO-1M operation manual C.1 Mechanical initialization When all the units are assembled, all cab les are connected and the software that operates a diffractometer is installed, the devi ce can be turned on. There are three power switches which are located on the goniometer control block and X-ray generator, respectively. The last two switches are allowed to be kept in the Â“ onÂ” position. The one on the goniometer is a main switch witch tu rns on the diffractometer and shuts it down. The next step is initialization. The initialization macro command correlates the readings from both mechanical and optical gauges. It also do es a precise positioning of the position-sensitive detector so that it is perpendicular to the X-ray beam. The initialization process is executed using the software Â“Radicon Device Programming WorkbenchÂ” (RDPW) with the macro command Â“InitializeÂ”. Prior the initialization it is necessary to remove both a cuvette from a sa mple holder and a plug fr om another side of the sample holder. It will allow the X-ray beam to go through the sample holder and be registered by the position-sensitive detector. The plug is made of niobium and designed to minimize a value of a backscatte red intensity of the primary beam. The positionsensitive detector is equipped with a damper in the form of a nickel stripe that is recommended to be used during initializati on and following calibration with the installed 0.25 mm vertical (SL2) and 0.25 mm horizontal (SL3) slits (Figure C3). With the vertical and horizontal slits of 0.1 m and at the 15kV x 0.2mA regime of X-ray tube power supply, both initialization and calibration can be performed without a damper. The last option is more preferable. A manganese filter F (Figure C3) should be always inserted in order to avoid a damage of the detector. In the beginning of initialization, an operator will be asked to enter the position readings for both the position-sensitive dete ctor and the sample holder into a window shown in Figure D1. The readings can be found on the mechanical gauges on the face panel of the goniometer (Figure C3).
76 Appendix C (Continued) Figure C1. Initial data input window At the end of initialization, if the X-ra y optics scheme of the diffractometer is perfectly aligned, the sample holder and the position-sensitive detector will be located at the normal positions of s=90 and d=0 respectively. Otherwise, they have to be moved at their normal positions manually using a m acro command Â“MoveÂ”. It means that the XRay optical scheme of the diffract ometer is not adjusted right. The security lock is located on the back side of the goniometer and should be at the Â“offÂ” position during initialization and following adjustment procedures. Operations executed by the initialization macro command are: 1. Initialization of optical angle gauges. 2. Moving both the position-sensitive detector and the sample holder to their normal positions perpendicular to the incident X-ray beam. 3. Adjusting the work regime for a high-volta ge power supply of the X-ray tube to 15 kV, 0.2 mA voltage and cu rrent values, respectively. 4. Opening a shutter for 90 seconds to ramp the intensity of X-ray beam to its maximum and closing the shutter. 5. Locating the position-sensitive detector at the position where its 2048th channel coincides with the center of the peak obtained in the fourth step. The initialization has to be launched ev ery time when the diffractometer or the controlling RDPW soft ware was shut down.
77 Appendix C (Continued) C.2 Instrument alignment The adjustment procedure consists of ali gning of the X-ray optical scheme of the diffractometer. The procedure is necessary afte r transportation of the device or due to a misalignment of the X-ray optical scheme. The objective of the alignment is to obtain a narr ow X-ray beam passing through the intersection of the axis of the goniometer with the crystal rotation azimuth axis. The next step is to locate a surface of the crys tal at the normal measuring position using the X-ray beam. The pre-alignment c onditions are shown in Table C1. Table C1. Pre-alignment conditions DetectorÂ’s position d=0 Sample holderÂ’s position s=90 Manganous filter, F inserted Slit, SL1 1 mm, horizontal Slit, SL2 removed Slit, SL3 0.1 mm, horizontal Niobium plug removed Nickel damper installed Sample plate removed Security lock off In the beginning of the adjustment, start the position-sensitive detector and open the shutter. These commands can be executed with the software RDPW at the main form tab shown in Figure C2. The butto n starts counting the impulses, while the button opens a shutter.
78 Appendix C (Continued) Figure C2. Main form tab and the Relays sub tab Figure C3. Photo of the measuring unit of the diffractometer DSO-1M
79 Appendix C (Continued) At first, the X-ray source position has to be adjusted in the vertical and horizontal directions and rotated at the correct angle about the column supporting the source. In order to adjust a height of the X-ra y source position it is necessary to release the screw SCR1 (Figure C3). After that, the column with the X-ray source, which has two degrees of freedom, needs to be moved up or down using the nut N and manually rotated about its vertical axis. The maximum intensity can be ob tained by rotating the nut N clockwise and counter-clockwise as well as moving the column about its vertical axis. For a more precise vertical adjustment of th e X-ray source position, it is necessary to use the adjustment tool AT that has to be instal led at the sample holde r. The tool has a 0.2 mm diameter hole in the center, where the X-ray beam has to be pointed at. By doing the described above manipulations, one can achieve the maximum intensity at the detector. The adjustment tool needs to be installed so that its chamfers are horizontal. The hole has a small displacement (<0.1 mm) outwards th e center of the tool. When the maximum intensity at the detector is achieved, the screw SCR1 can be tightened. The next step is the adjustment of the X-ray source along the direction perpendicular to the X-ray beam. The adjust ment tool AT has to be removed and two vertical slits are to be installed; the verti cal 0.1 mm and 0.25 mm slits at the positions SL2 and SL3, respectively. The 1 mm vertical slit remains in the position SL1. The locking screws L1 have to be released. Using the screw SCR2 the column can be moved across the X-ray beam direction achieving the maximum intensity at the detector. At the new position of the X-ray source, the screw SCR1 must be released in order to achieve a higher intensity by rotating the column about its vertical axis. After that, it is required to check the existence of the incident X-ray be am in the center of the adjacent tool AT. If the position-sensitive detector is not registering the intensity of the beam, it is necessary to release the locking screws L2 and move the collimator block C until the X-ray beam hits the center of the adjacent tool. The movi ng of the collimator is possible using the screw SCR3. By replacing the slit SL3 with the 0.1 mm horizontal slit, the vertical adjustment of the X-ray source has to be verifi ed. In order to make sure in the accuracy of
80 Appendix C (Continued) the X-ray source positioning relative to the sa mple holder, it is necessary to move the source gently at all degrees of freedom: across the beam direction, up and down and around the axis of the column. The adjustment is considered to be legitimate if the difference in intensities with the adjacent tool and without one is not higher than 30 Â– 40 %. After every stage of the adjustment, the locking screws have to be tightened while checking the intensity at the same time. The final stage of the adjustment is the dividing of the X -ray beam with the adjacent tool AT. It can be done by rotation of the sample holder with the installed adjacent tool at its zero positi on. At such position, the tool will cut half of the intensity obtained in the previous stage. If the beam di d not lose its intensity or lost all of its intensity, then the position of the adjacent tool has to be corrected using the screws SCR4 and SCR5. C.3 Detector calibration Prior to the measurement, when the diffr actometer is correctly adjusted, it is required to calibrate the position-sensitive detector. It is suggested to warm up the deffractometer for 30 minutes before runni ng the calibration. The procedure of calibration consists in the drawing a scale for the angles of th e detectorÂ’s position relatively to the incident X-ra y beam in accordance with the channels of the detector. The center of the detector serves as a base point of the scale. The calibration process is executed by the macro command Â“CalibrByRayÂ” from the main form tab or from the drop down me nu list in RDPW. An operator will be asked to enter the position readings for both the detector and the sample holder into a window shown in Figure C1. The readings are show n on the mechanical gauges on the face panel of the goniometer. The calibration of the detect or needs to be done every month or after
81 Appendix C (Continued) replacement of the X-ray tube. The detector has to be calibrated with the nickel damper and the removed niobium plug from the sample holder. The hinged doors must be closed. The calibration process by the macro command Â“CalibrByRayÂ” may be described in the following steps: 1. Positioning of the sample and the detector at their initial positions of d=0 s=90 respectively (Figure 21). 2. Adjusting the work regime for a highvoltage power supply of the X-ray tube to the 15 kV, 0.2 mA voltage and current values, respectively. 3. Measuring the intensity in the center of the position-sensitive detector. 4. Designation of the detectorÂ’s edge co rresponding to a zero channel (the positionsensitive detector moves to the position of approximately +5 +7 from its initial d position). 5. Scanning the position-se nsitive detector from one e dge to another with the 2 step. Determination of the correspondence between th e angle of the detectorÂ’s position relative to the incident X-ray beam and the channe l corresponding to the center of a peak. The results may be plotted in the form of a calibration curve shown in Figure C4. Figure C4. Calibration curve; position-sensitive detector window
82 Appendix C (Continued) When the calibration is finished, the hi nged doors can be opened. The nickel damper has to be removed from the position-sensitive detector, while the niobium plug is to be installed at the back side of the sample holder. Th e diffractometer is ready for measurements. C.4 Crystal lattice parameter measurement The measuring process is based on the 420 reflection from 3C-SiC crystal lattice and is carried out in a fully automated re gime. It is executed by the macro command Â“MeasureÂ” and consists of the finding a maximu m intensity of the diffracted beam at the fixed position of the detector at angle 2d and specified scanning s range of the sample. Using the BraggÂ’s law, a crystal lattice parameter of 3C-SiC is calculated from the sample angle that corresponds to the found maximum intensity. The measuring procedure may be de scribed in the following sequence: 1. Activation of the safety switch at the Â“LockÂ” position on the back side of the goniometer. During the measurement, the hing ed doors of the diffractometer must be closed. If any of the doors are opened, the sa fety switch blocks th e macro command from running. 2. Warming up the diffractometer for 20 minutes. 3. Insertion of the samples. The cuvettes are made of the plastic or plexiglass with the hole drilled in the center. The range of the holes is 0.3-0.6 mm, and designed for different size crystals. If the size of the crystals is relatively different, it is necessary to use the cuvette of the appropriate size. This is important for an accurate centering of the crystal; if the crystal is not centered well in the cuvette, the incident X-ray beam may hit only a part of the crystal. Th is causes a lowering of the in tensity of the diffracted beam, which, in turn, decreases the measurements accuracy. It is recommended to use the technical vaseline for inserting the samples in the cuvettes. However, soft plasticine may
83 Appendix C (Continued) also be used using the same in stallation technique. If the technical vaseline is used, it is required to deposit a small qua ntity of the vaseline on the inside of the cuvette untill it appears beyond the flat surface of the cuvette. Th en the crystal can be placed in the center of the cuvette using a sharp needle. It is recommended to use a microscope or a magnifying lens. After that, the crystal has to be pressed with the polished glass surface or other flat surface plate in or der to push the crystal into the hole. It is important that the crystal is inserted flush with the surface of the cuvette; othe rwise the error of measurements will be too high. It is also very important to avoid any damages of the cuvette while inserting a crystal as any defo rmation of the surface of the cuvette will cause additional measurement errors. If the crysta l has a quite distinct flat surface, then it is recommended to use this surface in flush w ith the cuvetteÂ’s surface in order to decrease a time of finding the wanted diffraction. It also gives the more accurate result. 4. Installation of the cuvette with the crystal in the sample holder. The cuvette with the crystal inside has to be inserted into the bushing in the center of the sample holder and fixed by pushing and rotating the cuvette at 90 5. Closing the hinged doors. 6. Running the macro command Â“MeasureÂ”. After launching the command, an operator will be asked to name a sample a nd specify a measuring mode in the window shown in Figure C5. Figure C5. Measurement input data
84 Appendix C (Continued) SampleÂ’s name would be a name of the log file with the measurement results. The measurement mode can be either to find a di ffraction angle of the X-ray beam from the sample or to find the intensity values for a range that can be ma nually specified. The initial scanning positions for the sample and the position-sensitive de tector have to be taken as default, equal to 50 and 162.5 respectively, with the scanning step of 0.1 The position of the center of the detector is fixed and equal to 162.5 which corresponds to the angle of 2d. During the measurement process, the measurement results can be viewed in the Â“Log windowÂ” opened from the me nu Â“ViewÂ” of the controlling software RDPW. 7. If the macro command did not finish the measurement and did not give a result, then it is recommended to stop the command and run it again with the smaller initial sampleÂ’s scanning angle (s=10 ). 8. If the peak still can not be found, it is nece ssary to reinsert th e crystal and repeat the steps described above. It usually takes not more then 30 minutes to find the peak of the intensity diffracted from the crystal. 9. When the measurement is done, the results of the measurement are saved in a file with the name given in step 6.
85 Appendix D. Temperature Measurement Analysis D.1 Real temperature estimation A significant portion of systematic erro r can be excluded us ing the calibration function (26) : realexpM() TfT (26) where Treal Â– is a real temperature; fexp is an experimental function; TM is a value of the temperature measured with MTCS. The function (26) can be obtained based on the temperature measurements data using both the MTCS and another more accura te temperature measuring device. If the readings of the last device has an error much smaller than that of the MTCS method, the systematic error may be neglected. In this case, the adequacy estimation for calibration function (18) can only be achieved using random uncertainties . The empirical interpretation of the function (26) is based on the MTCS temperature measurement results provided by the research university of Mendeleyev D.I. and Scientific Industrial Union Â“Termopri borÂ” in Moscow, Russia. The temperature measurement error is 0.2 C and 0.9 C for the temperatures of 100 C and 1000 C, respectively. The temperatures of 100 C and 1000 C are taken as real as the error for these temperatures is very small. The value of the error for every measurement q, is determined as a difference between the temperature meas ured by the MTCS method TM,q and the real temperature of measurement Treal,q. ,, kMqrealqTT. (27) All temperatures measured by the MTCS method and their real values along with the systematic error values, c,q for every measurement q are given in Table D1.
86 Appendix D (Continued) Table D1. Temperature measurements and erro rs for MTCS at stationary regimes  q M,qT real,qT q c,q 1 590 595.8 5.8 4.97 2 590 598.2 8.2 4.97 3 590 597.9 7.9 4.97 4 598 600.0 2.0 4.97 5 788 798.5 10.5 4.88 6 793 797.3 4.3 4.88 7 796 799.0 3.0 4.88 8 803 799.4 3.6 4.87 9 973 981.0 8.0 4.79 10 982 979.0 3.0 4.79 11 996 1000.8 4.8 4.78 12 1087 1100.7 13.7 4.74 13 1096 1100.7 4.7 4.73 14 1103 1100.7 2.3 4.73 15 1178 1192.5 14.5 4.69 16 1190 1198.3 8.3 4.69 17 1193 1193.3 0.3 4.69 18 1197 1196.6 0.4 4.68 The empirical function (26) can be obtaine d using regression analysis . The analysis is executed by searching the consis tently increasing de gree polynomials using the least-squares method. The values of the coefficients of regressions are obtained by comparison of dispersions of the successive approximations using th e statistical F-test . As a result of the anal ysis, a linear function of TM is obtained:
87 Appendix D (Continued) ()empMMTfTabT (28) The values of the conducted analys is are shown in Table D2 . Table D2. Calculated values of linear regres sion and mean squared deviation of empirical data for MTCS  MTCS type Linear regression values, degree Degree of freedom Mean squared deviation of empirical data, oC2 a b R1 R2 3C-SiC 5.3 0.9995 16 50.5 27.3 A mean square deviation, R, is obtained from the expressions : 2 1,, 11 ()q realqMq qRTT q, (29) 2 2,, 11 ()q realqMq qRTabT q. (30) A relative decrease of the R2 value in comparison with the initial R1 indicates a preference for using the calibra tion function, which excludes the systematic error. The value of the excluded systematic error is a linear function of a level of measured temperature: ,()(1)ckMMTTba (31)
88 Appendix D (Continued) The excluded systematic error for 3C -SiC MTCS is approximately -5 C in the temperature range of 600 Â– 1200 C. The corresponded values of the excluded systematic error c,k are shown in Table D1 . So, the measurements of the maximum temp erature using MTCS can be evaluated with the following equation : 5.30.9995 M TT for oo600C1200CMT (32) D.2 Statistical measurement error The residual variance and the standard deviation (SD), can be obtained for both the entire and localized subsamples. Us ing the localized subsamples of volume Ni it is possible to establish a relationship between SD and a measured temperature. The minimum and maximum values of the subs ample have been chosen to be equal N1=2 and Nmax=15, respectively. Such organization of th e subsample excludes th e previous data and gradually involves the new ones to the point of excluding all the pr evious data. A volume of the subsample remains constant at every evaluation. Using a mean value of TM in compliance with every subsample makes it possible to find values of the correlatin g equation (28) for every series i. Thus, the most accurate values of the subsample can be obtained : ()iMiiMTT T (33)
89 Appendix D (Continued) where i is an estimated value of SD; i and i are the estimated regression parameters for the i-series. The estimation technique is shown in Figure D1, where q Â– is a number of experimental data, q = 1, 2, Â…, Q; i Â– is a number of subsamples I of different volume, I = 1, 2, Â…, I. The calculated number Ji of (SD) values would be j = 1, 2, Â…, Ji (Ji =K Â– i) which correlates with a measured temp erature. Using the data from Table D1 and Table D2, the plot shown in Figure D1 can be obtained: a Treal, CT (k)T (k+1) T T =a+bTTM (i,j)effM M M M Figure D1. Estimation pattern of (SD) as a function of a measured temperature  The measured or effective temperature is a mean temperature of measurements of a subsample. A value of the effective te mperature changes with every subsample. ,1 1Qji eff M Mq QjTT i (34)
90 Appendix D (Continued) A two-dimensional array of SD values against the regression T/TM can be written as: 22 ,,1 ()Qji ijqMq QjTT i (35) The parameters of and shown in Table D3, can be found from the linear regression. Table D3. Parameters of and of the function (TM) for MTCS  i N i Estimation regression parameters ,iC 310,iC 1 2 -0.64 6.6 2 3 -1.02 7.3 3 4 -0.97 7.3 4 5 -0.61 7.0 5 6 -1.06 7.5 6 7 -0.67 7.2 7 8 -0.01 6.6 8 9 -0.18 6.9 9 10 -0.28 7.2 A volume of the subsample, Ni is limited to a value of 19 due to a drastic increase of error for MTCS temperature measurements. The equation of SD as a function of time would be the following : ()0.60.0071 M MTT (36)
91 Appendix D (Continued) From the equation (36), it is obvious that a value of SD increases with a measured temperature rise for MTCS. D.3 Measurement error estimation As was discussed, a calibration function of the annealing temperature estimation measured with MTCS is a simple linear eq uation. The estimated parameters of the correlation function (tolerance limits) have to be applied to the entire measurement data including further measurements in order to estimate a truthfulness of the calibration function by means of a tolerance range for a measuring device. In this case, it is necessary to use a method of tolerance limits . A value distribution of TM (37) is expressed as a genera l equation for the limits of a tolerance range and can be written as (38) : ,,1,2,...,,18MqqabTTqQQ ; (37) () ,,() M PNiLTq, (38) where q ,P,Q is a coefficient of tolerance; Ni Â– is a volume of a subsample; subscript Â– is a confidence probability. Therefore : ()() ubub realPTLTTL (39) where P Â– is a portion Treal values within the tolerance range; T Â– is an unbiased real temperature estimation. A value of q is obtained from the following equation :
92 Appendix D (Continued) 2 ,,510 (1) 12 2PQxx qq q q (40) where q can be determined form the function (41) : 02() qP (41) and x can be determined from the function (42) : 0()0.5 x (42) 0() x is a normalized LaplaceÂ’s function (43)  3/20 01 () 2x u x edu. (43) Therefore, for P = 0.95, =0.9, Q = 18, a coefficient of tolerance q ,P,Q = 2.544. Then, from the equation (38), the limits of a tolerance range are: ()(0.60.0071)2.544,CMLT (44) Therefore, for a measured temperature range 6001200,MCTC a tolerance range is: ()9.420.0CLC. (45)
93 Appendix D (Continued) D.4 Comparison of MTCS with other measurement techniques In order to estimate how the MTCS me thod compares with other methods of temperature measurements in hard to acce ss places, it is necessary to compare the (SD) values of the measurements as a function of time. Techniques such as fusible plugs, ther mal paints, thermoplugs and method of radioactive 85Kr tracer are considered as the cl osest competitors to the MTCS among widely used non-contact readout methods [32, 22]. As for th e method of fusible plugs and thermal paints method, the temperature m easurements are obtained gradually. Using these methods it is possible to determine a te mperature range for a uniform distribution of real temperature (46); 1irealiTTT (46) where iTis a temperature of transient condition of an indicator (melting of plugs or a change of the color of thermal paints) for the lower temperature range; 1iT is the nearest temperature for the upper temperature range for the gauges, which remained in their initial condition. The methods are characterized by three parameters: the number of stages in measurement, N; the range of measured temperature,1NTT ; and the uniformity of values for each stage. The value (SD) for each stage of measured temperatures for fusible plugs and thermal paints are determined using the condition of the uniform distribution of maximum temperatures. Acco rding to the method given by V. Kuznecov and V. Nikolaenko , the value is determined by a half of a range, divided by 3. For example, one of the two neighboring paints of the German thermal paint Â“ThermocolorÂ” changes its color at 520 C while the second Â– at 560 C. A temperature range for this case is 40 C. If the Â“520Â” paint change d its color during measurement,
94 Appendix D (Continued) and the Â“560Â” did not, then the would be: 560520 12 23C (47) The values of (SD) as a function of time, determined in the same manner for Â“ThermocolorÂ” (Germany) and Â“TempilacÂ” th ermal paints (USA) are shown in Figure D2; where 1 Â– diamond; 2 Â– 3C-SiC (MTCS); 3 Â– therma l paints Â“TempilacÂ” (USA); 4 Â– fusible plugs; 5 thermal paints Â“Termocolo rÂ” (Germany); 6 Â– thermoplugs; 7 Â– 85Krtracers . C20 10 2006001000 T,C 7 5 6 4 3 2 1 1400 Figure D2. Standard deviation ( ) as a function of time
95 Appendix D (Continued) Below are the equations of (SD) for different measurements as a function of temperature : 1. Â“TermocolorÂ” thermal paints (Germany), N=30; 401300C T ; ()3.190.019554 TT 2. Â“TempilacÂ” thermal paints (USA), N=83; 1001350C T ; 62()1.020.017137.9610 TTT 3. Fusible plugs (USA), N=34; 50750C T ; ()2.910.00707 TT Values of SD as a function of temperature T for fusible plugs, as well as the for MTCS and radioactive 85Kr tracer are also shown in Fi gure D2. It is obvious that the method of MTCS gives the hi ghest precision among the othe r methods used in hard accessible parts. The most accurate data fo r MTCS are achieved for the temperature range of 400 Â– 1200 C. The closest to the MTCS method by the value of SD is the thermal paint Â“ThermocolorÂ” method. However, the method of thermal paints has a considerable disadvantage that the paints ma y fall off the measured part during intensive gas flow or during vibrations, incr easing the error of measurements.