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The Lattice Parameter of Gamma Iron and Iron – Chromium Alloys

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The Lattice Parameter of Gamma Iron and Iron – Chromium Alloys THE LATTICE PARAMETER OF GAMMA IRON AND IRON-CHROMIUM ALLOYS By Zhiyao Feng Submitted in partial fulfillment of the requirements For the degree of Master of Science Thesis Advisor: Dr. David. Matthiesen Department of Materials Science and Engineering CASE WESTERN RESERVE UNIVERSITY May, 2015 CASE WESTERN RESERVE UNIVERSITY SCHOOL OF GRADUATE STUDIES We hereby approve the thesis/dissertation of Zhiyao Feng candidate for the degree of Master of Science in Materials Science and Engineering. Committee Chair Dr. David Matthiesen Committee Member Dr. Matthew Willard Committee Member Dr. Frank Ernst Date of Defense Mar. 26. 2015 *We also certify that written approval has been obtained for any proprietary material contained therein. II Table of Contents ACKNOWLEDGEMENTS ................................................................................................................ 11 ABSTRACT ......................................................................................................................................... 13 CHAPTER ONE. INTRODUCTION ...................................................................................... 14 CHAPTER TWO. LITERATURE REVIEW ......................................................................... 15 2.1 Lattice Parameter and Lattice Parameter Expansion of Pure Iron ........................................ 15 2.2 Lattice Parameter of α-Fe (ferrite) with Binary Additions of Transition Metals .................. 19 2.3 Lattice Parameter of γ-Fe (Austenite) in Literature .............................................................. 26 CHAPTER THREE. THESIS OBJECTIVES ........................................................................ 29 CHAPTER FOUR. EXPERIMENTAL PROCEDURE ......................................................... 32 4.1 Experimental Equipment Introduction ................................................................................. 32 4.2 Determination of Temperature Offset ................................................................................... 33 4.3 High Temperature X-ray Experiment Procedure .................................................................. 34 CHAPTER FIVE. RESULTS AND DISCUSSION ................................................................ 36 III 5.1 Starting Material ................................................................................................................... 37 5.2 Adjustment of Sample Height .............................................................................................. 40 5.3 Determination of Errors ........................................................................................................ 42 5.4 Lattice Parameter Determination of AHC 100.29 Powder at Room Temperature ................ 48 5.5 Temperature Offset Determination ....................................................................................... 52 5.6 Variation of Lattice Parameter with Temperature ................................................................. 55 5.6.1 Measurements of AHC 100.29 Iron Powder at High Temperatures ................................. 56 5.6.2 Measurement of AMES Fe – Cr Powder at High Temperatures ....................................... 60 5.6.3 Measurement of CrA Fe – Cr Powder at High Temperatures ........................................... 62 CHAPTER SIX. CONCLUSIONS .......................................................................................... 70 CHAPTER SEVEN. SUGGESTIONS FOR FUTURE WORK ............................................ 73 APPENDIX 1: AHC 100.29 POWDER LATTICE PARAMETER DATA ..................................... 74 APPENDIX 2: AMES FE – 1CR POWDER LATTICE PARAMETER DATA ............................ 76 APPENDIX 3: ASTALOY CRA FE–CR POWDER LATTICE PARAMETER DATA ............... 78 IV REFERENCES .................................................................................................................................... 80 V List of Tables Table 1. Resulting equations for the linear least squares regression analysis on Hume-Rothery’s lattice expansion data of α and γ-phases of Fe as a function of temperature. .................................................. 19 Table 2. Lattice parameters and thermal expansion coefficients for Fe austenite in literature [7, 17-20]. ............................................................................................................................................................... 27 Table 3. Data of X-ray diffraction peaks of α-phase pure iron with 0.04 second / degree scan rate and 0.02°PU step size scanned from 30°PU to 150°P. .......................................................................................... 44 Table 4. Data of X-ray diffraction peaks of α-phase pure iron with 0.1 second / degree scan rate and 0.05°PU step size, scanned from 40°PU to 90°P. ........................................................................................... 45 Table 5 Lattice parameter of α-phase iron calculated from the data in Table 3 and Table 4. ................ 47 Table 6. Comparison of the result for linear least squares regression analysis performed on data of AHC 100.29 and Sutton and Hume-Rothery. ........................................................................................ 59 Table 7. Result for linear least squares regression analysis performed on the data of Ames Fe – Cr sample. .................................................................................................................................................. 61 Table 8. Results of linear least squares regression analysis performed on the Astaloy CrA sample data. ............................................................................................................................................................... 64 VI Table 9. Summary of lattice parameters of the γ-phase and the α-phase at 20℃PU of AHC 100.29, Ames Fe – Cr, and Astaloy CrA samples......................................................................................................... 64 Table 10. Results of linear least squares regression analysis performed on the data of AHC pure iron sample, Ames Fe – Cr sample, and Astaloy CrA Fe – Cr sample. ........................................................ 71 VII List of Figures Figure 2-1. (a) Face-centered cubic arrangement of iron atoms and (b) body-centered cubic arrangement of iron atom. ..................................................................................................................... 16 Figure 2-2. (a) (100) plane in face-centered cubic lattice and (b) (110) plane in body-centered cubic lattice ..................................................................................................................................................... 17 Figure 2-3. Variation of lattice parameter of pure iron with temperature [7]. ....................................... 19 Figure 2-4. Comparison between Sutton and Hume-Rothery’s experimental data [1] and Vegard’s law about the change in lattice parameter of α iron with binary additions of chromium. ............................ 22 Figure 2-5 Change in lattice parameter of α iron with binary additions of chromium [2]. ................... 23 Figure 2-6. Change in lattice parameter of α iron with binary additions of chromium plotted with measured data points [2]. ...................................................................................................................... 24 Figure 2-7. Change in lattice parameter of α iron with binary additions of chromium from Sutton and Hume-Rothery’s [1] and Abrahamson and Lopata’s data [2]. ............................................................... 26 Figure 2-8. Literature data of lattice parameter of austenite as a function of temperature [7, 17-20]. .. 28 Figure 3-1. Equilibrium binary phase diagram of Fe-N system [21]. ................................................... 30 VIII Figure 4-1. (a) The exterior appearance and (b) interior chamber of high temperature X-ray system. 32 Figure 4-2. (a)The front and (b) back view of the thermocouple on the sample holder. ....................... 33 Figure 5-1. SEM image of Astaloy AHC 100.29 iron powder. ............................................................. 38 Figure 5-2. SEM image of Ames Fe-1Cr powder. ................................................................................. 39 Figure 5-3. SEM image of Astaloy CrA powder. .................................................................................. 40 Figure 5-4. Effect of sample displacement on the diffraction peak position and peak shape. ............... 42 Figure 5-5 Extrapolation of measured lattice parameters of AHC 100.29 powder against Nelson-Riley function, calculated from the data in Table 3. ....................................................................................... 46 Figure 5-6 Extrapolation of measured lattice parameters of AHC 100.29 powder against Nelson-Riley function, calculated from the data in Table 4. ....................................................................................... 47 Figure 5-7. Diffraction Pattern of AHC 100.29 pure iron powder at 20℃PU by Scintag X-1 Cu source. ............................................................................................................................................................... 49 Figure 5-8. The variation of with . .......................................................................................... 50 Figure 5-9. Extrapolation of measured lattice parameters
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