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Specific Heat and Thermodynamic Properties of Metallic Systems: Instrumentation and Analysis Brigham Young University BYU ScholarsArchive Theses and Dissertations 2005-10-12 Specific Heat and Thermodynamic Properties of Metallic Systems: Instrumentation and Analysis Brian E. Lang Brigham Young University - Provo Follow this and additional works at: https://scholarsarchive.byu.edu/etd Part of the Biochemistry Commons, and the Chemistry Commons BYU ScholarsArchive Citation Lang, Brian E., "Specific Heat and Thermodynamic Properties of Metallic Systems: Instrumentation and Analysis" (2005). Theses and Dissertations. 785. https://scholarsarchive.byu.edu/etd/785 This Dissertation is brought to you for free and open access by BYU ScholarsArchive. It has been accepted for inclusion in Theses and Dissertations by an authorized administrator of BYU ScholarsArchive. For more information, please contact [email protected], [email protected]. SPECIFIC HEAT AND THERMODYNAMIC PROPERTIES OF METALLIC SYSTEMS: INSTRUMENTATION AND ANALYSIS by Brian Edward Lang A dissertation submitted to the faculty of Brigham Young University in partial fulfillment of the requirements for the degree of Doctor of Philosophy Department of Chemistry and Biochemistry Brigham Young University December 2005 Copyright c 2005 Brian Edward Lang All Rights Reserved BRIGHAM YOUNG UNIVERSITY GRADUATE COMMITTEE APPROVAL of a dissertation submitted by Brian Edward Lang This dissertation has been read by each member of the following graduate committee and by a majority vote has been found satisfactory. Date Brian F. Woodfield, Chair Date Juliana Boerio-Goates Date David V. Dearden Date Roger Harrison Date Gerald D. Watt BRIGHAM YOUNG UNIVERSITY As chair of the candidate’s graduate committee, I have read the disseration of Brian E. Lang in its final form and have found that (1) its format, citations, and bib- liographical style are consistant and acceptable and fulfill university and department style requirements; (2) its illustrative materials including figures, tables, and charts are in place; and (3) the final manuscript is satifactory to the graduate committee and is ready for submission to the university library. Date Brian F. Woodfield Chair, Graduate Committee Accepted for the Department David V. Dearden Graduate Coordinator Accepted for the College G. Rex Bryce Associate Dean, College of Physical and Mathematical Sciences ABSTRACT SPECIFIC HEAT AND THERMODYNAMIC PROPERTIES OF METALLIC SYSTEMS: INSTRUMENTATION AND ANALYSIS Brian Edward Lang Department of Chemistry and Biochemistry Doctor of Philosophy A small-scale adiabatic calorimeter has been constructed as part of a larger project to study nano-particles and to facilitate specific heat measurements on samples where it is difficult to obtain enough material to run on the current large-scale adiabatic apparatus. This calorimeter is designed to measure sample sizes of less than 0.8 cm3 over a temperature range from 13 K to 350 K. Specific heat results on copper, sapphire, and benzoic acid show the accuracy of the measurements to be better than ±0.4% for temperatures higher than 50 K. The reproducibility of these measurements is generally better than ±0.25 %. Experimental specific heat data was collected on this new apparatus for synthetic akagan´eite, β-FeOOH, for samples with varying degrees of hydration. Our results 298.15 ◦ −1 −1 −1 −1 yield values for ∆0 Sm of 79.94 ±0.20 J·K ·mol and 85.33 ±0.021 J·K ·mol for samples of β-FeOOH·0.551H2O and β-FeOOH·0.652H2O, respectively. From this data, we were able to determine the standard molar entropy for bare β-FeOOH, as 298.15 ◦ −1 −1 ∆0 Sm = 53.8 ±3.3 J·K ·mol , based on subtractions of the estimated contri- bution of water from the hydrated species. Additionally, the specific heats of α-uranium, titanium diboride, and lithium flouride have been measured on a low-temperature, semi-adiabatic calorimeter down to 0.5 K. For the α-uranium, the specific heat of a polycrystalline sample was com- pared to that of a single crystal, and it was found that there was a significant difference in the specific heats, which has been attributed to microstrain in the polycrystal. The 298.15 ◦ third law entropy for the polycrystal at 298.15 K, ∆0 Sm, calculated from these heat capacities is 50.21 ±0.1 J·K−1·mol−1, which is good in agreement with previously 298.15 ◦ published values of polycrystal samples. For the single crystal ∆0 Sm, calculated using the thermodynamic microstrain model, is 49.02 ± 0.2 J·K−1·mol−1. The low-temperature specific heats of titanium diboride and lithium fluoride have been measured from 0.5 K to 30 K as part of a larger project in the construction of a neutron spectrometer. For this application, the measured specific heats were used to extrapolate the specific heats down to 0.1 K with lattice, electronic, and Schottky equations for the respective samples. The resultant specific heat values at 0.1 K for 6 −4 −4 −1 −1 −9 −9 TiB2 and LiF are 4.08×10 ±0.27×10 J·K ·mol and 9.19×10 ±0.15 ×10 J·K−1·mol−1, respectively. ACKNOWLEDGEMENTS During my studies at Brigham Young University, I have been assisted and guided by many people, and I owe them my gratitude. To Brian Woodfield, I offer my thanks for his endless hours of direction, editing, and the occasional push in the right direction. I also thank Juliana Boerio-Goates for her continual encouragement, mentorship, and willingness to share her theoretical and practical expertise. I would also like to thank all of the members of my graduate committee for their willingness to participate in the many review sessions that have accompanied my graduate studies. Special thanks is also owed to the other graduate and undergraduate students I have worked with over the past several years in the Woodfield/Boerio-Goates lab group. Jason Lashley has been a strong collaborator since his graduation, and he has provided many samples for us to work with. Rebecca Stevens provided a lot of insight, knowledge, and skill around the lab, and she helped tremendously with data collection. I have also been assisted by Marcus Donaldson, Jamon Holzhouser, Sarah Hopkins, Tyler Meldrum, Tom Parry, and Trent Walker, and I owe them my great appreciation for their many hours of data collection and assistance. I wish to thank Bart Whitehead for his help in designing many of the electronics used in our new apparatus. I would also like to thank the Precision Machine Shop for their excellent craftsmanship in producing the parts necessary in completing the apparatus. I also need to thank Dr. Matthew Asplund and Lonette Stoddard for their help in troubleshooting LATEX during the process of writing this dissertation. Finally, I wish to thank my wife, Renee, for her love and support over the past several years, for helping me get through my graduate program, and for her patience through the long nights while I was working late at the laboratory. I also thank my children, Kylie and Jaden, for endless hours of entertainment and distraction, and for their understanding when I couldn’t be home to play with them because I needed to be at school and work. My family and friends have been my biggest cheerleaders throughout the graduate school process, and I owe them my undying gratitude. Contents List of Figures xiii List of Tables xvii 1 Introduction 1 1.1 Specific Heat Contributions to Thermodynamic Properties . 2 1.2 Physical Origins of the Specific Heat . 5 1.3 Principles of Specific Heat Measurements . 19 1.4 Scope . 38 References . 41 2 Instrumentation: Apparatus and Electronics 43 2.1 The Adiabatic Calorimeter . 43 2.2 The Semi-Adiabatic Calorimeter . 46 2.3 The Small-Scale Apparatus . 48 References . 72 3 Instrumentation: Data Collection & Temperature Control 73 3.1 Fundamentals of PID Control . 73 3.2 Small-Scale Apparatus PID Control System . 81 3.3 Data collection program . 90 References . 106 4 Measurement of Copper, Sapphire, and Benzoic Acid Reference Ma- terials 107 ix 4.1 Empty Measurements . 108 4.2 Copper . 112 4.3 Sapphire . 118 4.4 Benzoic Acid . 120 4.5 Conclusions and Recommendations . 121 References . 126 5 Specific Heat Measurements of Akagan´eite: β-FeOOH 127 5.1 Introduction . 127 5.2 Experimental . 131 5.3 Results and Discussion . 134 5.4 Conclusions . 153 References . 154 6 α-Uranium 157 6.1 Introduction . 157 6.2 Experimental . 160 6.3 Results . 162 6.4 Discussion . 164 References . 193 7 TiB2 and LiF 197 7.1 Introduction . 197 7.2 Experimental . 201 7.3 Results and Discussion . 203 7.4 Conclusion . 214 References . 217 A Derivations of Various Thermodynamic Relationships 219 A.1 Derivation of equation 6.9 . 219 A.2 Derivation of lattice microstrain specific heat from the change in vol- ume from basic thermodynamic relationships. 220 x B Additional Information on Data Collection and Analysis Programs223 B.1 The Autocal Program . 223 B.2 Autocalc Program . 235 B.3 PID Control Program . 239 B.4 Miscellaneous Programs . 246 xi xii List of Figures 1.1 The vibrational density of state of copper . 10 1.2 Debye low-temperature extrapolation . 14 1.3 Representative Schottky specific heats . 15 1.4 Specific heat of the magnetic transition in CoO . 17 1.5 A schematic representation of calorimetric systems . 20 1.6 Adiabatic pulse method . 22 1.7 The isothermal technique . 25 1.8 The AC technique . 27 1.9 The relaxation technique . 29 1.10 Schematic diagram for a resistance thermometer . 34 1.11 Heater schematic diagram . 37 2.1 The current large-scale adiabatic apparatus used for measuring specific heat. 45 2.2 The semi-adiabatic apparatus used for measuring specific heat . 47 2.3 The microcalorimeter cryostat . 50 2.4 The adiabatic shields . 53 2.5 The microcalorimeter .
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