T E M P E R a T U

THE HIGH TEMPERATURE HEAT CONTENTS OP 0 MOLYBDENUM AND TITANIUM AND THE LOW TEMPERATURE HEAT CAPACITIES OP TITANIUM DISSERTATION Presented In Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By CHARLES WILLIAM KOTHEN, B.A. // The Ohio State University 1952 Approved By: Adviser i TABLE OF CONTENTS E&gft INTRODUCTION ............................ 1 THEORETICAL ............................. 3 HISTORICAL .............................. 6 PART I The High Temperature Heat Contents of Molybdenum and Titahium ................... 13 Introduction ...................... 13 Apparatus .......................... 14 Measurements and Calculations ........ 32 Errors ... ......................... 45 Experimental Results ............... 49 PART II Low Temperature Heat Capacity of Titanium.. 61 Introduction ...................... 61 Apparatus ........................... 62 Measurements and Calculations ....... 71 Errors ................... 74 Experimental Results ............... 75 ACKNOWLEDGMENTS .......................... 80 APPENDIX I Physical Constants, Drop Calorimeter Data .... 61 APPENDIX II Low Temperature Calorimeter Data ..... 82 APPENDIX III Standard Lamp Calibration ............ 83 3182G G TABLE OF CONTENTS, (cont.) Page APPENDIX IV Bibliography ................. 85 AUTOBIOGRAPHY .......................... 89 iii LIST OF ILLUSTRATIONS 1 Vacuum Furnace 15 2 Dropping Mechanism 19 3 Improved Calorimeter 20 4. Modified Calorimeter, II 21 5 Drop Calorimeter Electrical Circuits 30 6 Heat Content Run Temperature Curve 37 7 Molybdenum Cooling Data 4-3 8 Titanium Cooling Data 4-4- 9 High Temperature Heat Content of Molybdenum 51 10 Titanium Heating Data 54- 11 High Temperature Heat Content of Titanium 58 12 Low Temperature Calorimeter Elec trical Lead Vacuum Outlet 65 13 Calorimeter Gassing Apparatus 66 14. Low Temperature Calorimeter 67 15 Low Temperature Calorimeter and Cryostat 68 16 Low Temperature Calorimeter Elec trical Circuits 70 17 Low Temperature Heat Capacity of Titanium 77 THE HIGH TEMPERATURE HEAT CONTENTS OF MOLYBDENUM AND TITANIUM AND THE LOW TEMPERATURE HEAT CAPACITIES OF TITANIUM The knowledge of heat capacity as a function of the temperature from very low to high temperatures is of great scientific and technical importance, since other thermal functions can be calculated from this data. For example, a complete set of thermal properties for the reactants and products of a given reaction en ables the thermochemist to calculate thermal changes, equilibrium constants and maximum yields obtainable over temperature ranges in which direct experimental measurement may not be feasible. The statistical treatment of spectroscopic data (13,28,59) is a powerful tool for the accurate calcula tion of the thermodynamic properties of perfect gases over all temperature ranges. Data of state (pressure, volume and temperature data) permit the calculation of corrections for the application to real gases. How ever, many thermodynamic problems require the closure of thermal cycles involving condensed materials, and this requires low temperature heat capacity data for the solid, heats of transitions and phase changes, and the heat capacity of each phase through the temperature range of its existence. The measurement of the properties of the refractory metals is an especially challenging problem. Low tem perature heat capacity measurements can be made by the use of established methods. Data for the perfect gas can be obtained by the statistical methods mentioned above. The heat of sublimation may be calculated qc- dording to the methods of Langmuir (33,38) or Knudsen (30), based on the loss of weight from a sample heated to very high temperatures in a high vacuum. The high temperature heat capacity, however, has not been experi mentally measurable for many substances until the recent application of induction heating in high vacuum furnaces at this laboratory. This dissertation describes the measurement of the heat content of molybdenum between 298.16°K and the range between 1103° and 2623°K, and of titanium between 298.16°K and the range between 1067 and 1856°K. The low temperature heat capacity was also measured (15-305°K) to obtain the entropy at 298.16°K and the contribution of the lattice vibrational heat capacity at very low temperatures by the Debye law. Derived thermal functions are also presented. Ifl&QBPTWE According to the law of Dulong and Petit (10,18,36), the heat capacity of a solid element is 6,4 calories at ordinary temperatures. After he reviewed the low temperature heat capacity work prior to 1875, Weber (1, 54) noted a definite dependence of heat capacity on the temperature. Further research at lower temperatures established the familiar heat capacity curves wherein the value becomes very small at low temperatures. To explain the shape of this curve, Einstein (11) assumed that solids consist of 3N uncoupled oscillators per gram-atom, dll vibrating at the same frequency. Applying Planck*s quantum hypothesis, he derived the following expression for the heat capacity at constant volume: ■ U / K T z c » ' 3 R Debye (8) refined this theory by assuming solids to consist of a continuum behaving as 3N coupled os cillators per gram-atom which could vibrate over a range of frequencies up to some maximum frequency which was a characteristic of each solid. He concluded that the heat capacity at constant volume can be expressed as follows: <X,. o € -I . h = Planck*s constant where fL s. QjZ k = Boltzmann's constant , k T i? = frequency of oscillation (cm. ) N = Avogadro's number rn3 At very low temperatures this becomes Cy » CL ■ This relationship is used to extrapolate low temperature data to absolute zero. The characteristic constant, ^ can be evaluated from tables of heat capacity versus 4&/T, once the heat capacity has been measured. How ever, the theory holds best for cubic crystals and may be somewhat in Srror for other crystals. The Debye, Einstein, and classical treatments of heat capacity indicate a high temperature limit of 3R cal. g. atom."‘I, However, high-temperature data show a considerable increase above this value, especial ly for metals. This effect has been attributed to the weakening of the forces binding the electrons to the atoms so that they effectively increase the number of particles per gram-atom to a value greater than N, the Avogadro number, with a subsequent increase in the number of ways the assembly can absorb heat. The forma tion of this electron ’"gas" causes the heat capacity to increase with temperature in a linear manner (18,35). The fact that quadratic polynomials are required to fit the highest temperature data indicates that this effect does not remain linear, but may be exponential* -6- raxopifiAft The literature on the methods of measurement of heat capacity and heat contents has been surveyed by T. W. Bauer (l) for low temperatures, and by the author (31,32), for high temperatures. Three experi mental techniques have been used: (l) the drop method, (2) the increment method, and (3) indirect methods wherein properties, such as rates of cooling, which are related to the heat capacity, are measured and the heat capacity derived. The methods are not restricted to temperature ranges in principle, but experience (27, 28,55,56) has shown that Increment methods are best suited to low temperature work or other temperature regions wherein the heat capacity changes rapidly with temperature (transitions), and that the drop method is to be preferred above room temperatures* (1) DROP CALORIMETERS Drop calorimetry is the oldest and most widely used technique for measuring heat contents of solids. It has been used for both high and low temperature work, but recently, it has been restricted almost exclusively to studies above room temperature. For the earliest low-temperature work (1), the sample was cooled to various temperatures with refrigerants and then dropped into liquid air or nitrogen. The volume of gas formed was a measure of the heat content of the sample. The -7- data measured by this method were not very accurate, however, and more precise increment methods were develop ed. However, the increment method loses its advantage as temperatures increase and drop calorimetry is the most accurate method for measuring heat content data above 1000°K. The precision is between 0,1 and 0.2 per cent for heat content data with the better instru ments (17,20,29,4^) at temperatures up to 1873°K. A high temperature drop calorimeter consists of an oven for heating the sample, and the calorimeter proper, which absorbs and measures the heat of the sample. (a) Heating Elements The maximum operating temperature of a given instru ment is determined by the design of the heating element and the properties of its structural materials. Resis tance furnaces are usually employed. Platinum wound furnaces are used in some of the best assemblies, but the maximum temperature is limited to about 1600°C., since above this temperature, the platinum begins to sublime rather fast. To get higher temperatures, carbon or silicon carbide resistance furnaces or induction heating in high vacuum must be used. (b) Calorimeters The calorimeter may employ any of several media to measure the heat content of the sample. As mentioned -a- before, the quantity of nitrogen gas evaporated was once used to measure low temperature heat contents. The early high-temperature calorimeters (31) used water or ice and the sample was allowed to fall directly into the material.

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