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:

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. Organic liquids and mercury were used as calorimetric media for the study of materials which react with water. Later, metal cups were installed to catch the sample, the liquids (or ice) being used merely to increase the calorimeter heat capacity. Many of the newest instruments make use of massive metal blocks (20,29,37,60) to absorb the heat of the sample. This provides a much cleaner system and re­ quires fewer corrections. Drop calorimeters may be classified as isothermal (ice calorimeters), which are almost perfectly adiabatic, or temperature rise types, (metal block and liquid calorimeters), which are usually operated in a thermo­ stat and require the data to be corrected for heat ex­ change with the environment. These latter calorimeters can be made adiabatic by adding a shield which is heated to match the calorimeter temperature very closely.

(b-l) Ice Calorimeters Several ice calorimeters (17,4-1,4-3) were constructed within the period surveyed (31). Ginnings (17) and others give an excellent description of one used at the National Bureau of Standards, Washington, D. C. -9- This calorimeter consists of a vaned tube surrounded with a closed glass jacket completely filled with water and mercury. Prior to making a run, a sheath or mantle of ice is frozen about the vaned tube. During the run, the sample is dropped inside the tube and allowed to cool. This causes the ice mantle to melt, reducing the volume of the two phases of water, and drawing mercury in from a weighed reservoir. The weight change of the mercury reservoir permits the very precise cal­ culation of the volume of ice melted by the heat of the sample. Since the heat of fusion of the ice i§ accur­ ately known, the heat content of the sample can be calculated. This design is a great improvement over the first ice calorimeter, which consisted of a hole drilled into a massive block of ice. The sample was dropped into this hole after it had been wiped dry, and the water which formed was carefully absorbed in a tared sponge. Reweighing of the sponge, of course, gave the weight of ice melted, and the heat content could be then calculated.

(b*&) Metal Block and Liquid Calorimeters Most of the modern drop calorimeters are of the metal block type. Since these instruments require a temperature rise and the measurement of sensible rather than latent heat, they require corrections for heat leak, -10- unless operated in an adiabatic shield. Since a metal t block instrument was used in this research, we will discuss the technique of its operation in some detail in the apparatus section of Part I, in which the high- temperature work is reported,

(2) INCREMENT CALORIMETERS As was mentioned above, the drop method is not satis­ factory for low temperature measurements. The excellent low temperature increment instrument developed by Eucken, Nernst, and others (1,14,15,24.) has permitted such ac­ curate and rapid work, that it is now standard for low temperature measurements. This type of instrument was used to measure the low temperature data on titanium and will be discussed in more detail in the apparatus section of Part II. Some workers have claimed that the drop method is unsuited to the study of slow transformations (28), since the rapid cooling of the sample may result in the incomplete transformation to the low-temperature modifi­ cation. Also, the increment method is oftfcn faster than the drop method. For these reasons, the increment method has been adapted to relatively high temperatures. (34,44). In this method, the sample is maintained near the temperature being studied so that equilibrium is more readily attained between the modifications or phases Involved in sluggish processes. The specific -11- heat Is measured directly by introducing a measured amount of electrical energy to the calorimeter and measur­ ing the temperature rise. It is necessary to keep the calorimeter within an oven (56) which is maintained at a temperature as close as plssible to that of the calorimeter during measure­ ments. This reduces losses by conduction and radiation by providing approximately adiabatic conditions. It would be futile to try to use an increment calorimeter without such shielding, since even the data obtained from the shielded calorimeters is less accurate than that obtainable from drop calorimetry after the tem­ perature reaches a few hundred degrees. None of the increment methods described in the literature was considered accurate above 1273°K. Lapp (34-) studied iron up to 1233°K, but the precision was only 1 or 2 per cent. This fact is of great importance when one wishes to select an accurate method for making extreme temperature studies.

(3) COOLING AND HEATING RATE METHODS The cooling rate methods are related to the in­ cremental methods in that the heat capacity is directly calculated. The fact that several assumptions must be made increases the uncertainty of these methods. The method of Sykes (52) is the most refined of these and -12- o has been used to obtain acceptable data up to 1073 K. Brown and Furnas (5), and Newman and Brown (39) have also used a cooling rate method, but their results are less reliable than those obtained by other methods. Studies on incandescent fallments by several authors (2,7,12,25,4-2,4-7,57,61) have provided data in the ex­ treme ranges above 2300°K. The method is limited to refractory conductors of electricity. The data are neither precise nor accurate by lower temperature or drop calorimetric standards because of the difficulties involved in the measurement of the variables required with precision. £AR£ .1 THE HIGH-TEMPERATURE HEAT CONTENTS OF MOLYBDENUM AND TITANIUM

INTRODUCTION The heat capacity of molybedenum has been measured by Simon and Zeidler (45) (150^''275°K). Several in­ vestigations (3,4*6,9,22,50,51) were made between room temperature and about 1000°K. Only two studies (22,58) were made above this temperature, and none was made o above 1828 K. This research includes measurements of o the heat content between 305 K and the range between i 1103 and 2623°E. The heat capacity of titanium has been measured at low temperatures by Kelley (27) (53°-296°K) and by the author (Part II, this dissertation) (15°-305°K). High temperature data have been obtained by several authors (21,40 ), but only one (21) reported data above the transition (1150°K) and no data are available above 1476°K. Further, some hyteresls was found in the highest temperature data reported, indicating possible contamination of the sample. This research includes measurements of the heat content between 305°K and the range between 1067 and 1856°K. - u -

AEEA M Vft The drop calorimetric method was chosen for the high temperature research for the reasons discussed in the historical section. Since the second calorimeter described by Ziegler (60) was intact, this instrument was used after the necessary modifications had been made to put it in operating condition. The calorimetric apparatus consists of a vacuum furnace and calorimeter, a thermostat, a General Elec­ tric radio-frequency induction heater, and the necessary vacuum pumps and gages, and electrical circuits for precision thermometry in a high vacuum system. A Leeds and Northrup optical pyrometer was used to measure the upper sample temperatures*

The Furnace The furnace shell (Figure l) is identical to the one described by Ziegler. It consists of a brass tube 14 inches in diameter and 20 inches tall. Brass plates, 3/8 inch thick are soldered over each end. The top plate contains two ports. A 7/8 inch hole in the center is machined to receive the dropping mechanism, forming a vacuum tight seal with this part by means of an 11 on- rlng gasket. The same hole and a similar one in the bottom plate permit the opening of the radiation shield and recovery of the sample from the calorimeter. A VACUUM FURNACE h

FIGURE I second hole, one inch In diameter, near one side of the top plate serves as an observation port. This hole is sealed with an optically flat window and a rubber gasket. The optical pyrometer can be mounted above this hole to measure the upper sample temperature. The shield, (P) can be closed to cover this window and reduce the amount of metal deposited on it from the hot sample. A third hole receives the two inch vacuum line. In addition, there are six small holes sealed with Stupakoff seals for introducing electrical leads. The side of the furnace is drilled with a hole for the observation port shutter, sealed with an Ho"- ring gasketed shaft when under vacuum, and cut out for a large (10H x 12") port for entrance when preparing for a run. Two holes provide inlets for the r.f. leads to the heating colls (b). These are sealed with housekeeper metal to glass seals and lava plugs instead of the black wax and red fiber seals (c) shown in the drawing. The bottom has two holes. The 7/8 inch hole in the center allows the hot sample to fall through into the calorimeter. The small one provides access for an non-ring sealed shaft with which a radiation shield is moved over the large hole. The radiation shield pre­ vents hot sample radiation from reaching the calori­ meter before the sample is dropped. It is opened immediately before the sample is dropped. All gaskets in the furnace are lubricated with Dow- Corning silicone high vacuum grease. This material is used because it does not drop from the gaskets when the furnace is heated to 80°C to degas. Heating the grease in high vacuum also reduces its vapor pressure by distilling off volatile components. The degassing heaters are four chromel coils, mounted on the inside of the furnace. Application of 50 to 80 - volts heats the furnace to the corresponding centigrade temperature. This procedure is necessary for proper degassing to study reactive metals. The brace (n, m) reduces the swinging of the sample when the r.f. heater is turned on. This keeps the sample from touching the coils and grounding out the high voltage. The parts (d - j) have been replaced.

The Dropping Mechanism The "exploding" wire method, involving the electri­ cal fusion of the wire which supports the sample, is commonly used with the ordinary air type calorimeters. It is bad practice to employ this technique in vacuum calorimeters since adsorbed and dissolved gasses of questionable composition are suddenly released. This caused the vacuum to go bad for several minutes during the first few runs attempted and it is conceivable that the gases could contaminate reactive substances* An additional fault was that the sudden evolution of heat often cracked the glass or melted the solder of the Stupakoff seals which insulated the leads. This caused several leaks* In addition to this, the mechanism occasionally failed to operate. A new dropping mechanism (Figure 2) was devised, therefore, which operates on purely mechanical prin­ ciples. It has never failed and holds a very good va­ cuum. It consists of a 0.010-inch jeweller's lathe collet, a vise and a releasing shaft which can be turned from outside of the furnace by a conventional handle. The sample is threaded with a 0.010-inch tantalum support wire which is held in the top end by the collet* The sample can be released by one turn of the handle* The turning shaft is made vacuum tight by three nott-ring gaskets. The spaoe between the dropping mechan­ ism and the furnace is sealed by an wo"-ring which is forced into place by a gland nut.

The Calorimeter The oalorlmeter proper consists of three separate metal parts (l) the copper block, (2) the heater plug and (3) the gassing gate assembly (W,V,K,C) in the first system (Figure 3) or the cavity liner and shield housing in the second (Figure 4). Two calorimetric assemblies were actually used. The first two parts described by -19

FIG.Z DROP CALORIMETER DROPPING MECHANISM - 20-

2 6 0 - e>5

IMPROVED CALORIMETER

OIL LEVEL

TOP VIEW

£

SECTION AA

Fig* 3 21-

_^H 1

-MG -T

\° /-X z 1

I

F^vVv\\v\v\v\vv\v\\\\^3 FIG.4 MODIFIED CALORIMETER TL - 22- Ziegler was discarded after making the molybdenum runs. The design Skinner (4-6) used for the zirconium data, consisting of a tube to isolate the calorimeter atmos­ phere from the blbck cavity and furnace, was retained in a modified form. This syBtem is much more certain of success, since two isolated vacuum systems are used, and the furnace and cavity can be gassed without ruining the insulating vacuum between the block and the environ­ ment. The copper-block (B) is a cylinder 4- inches in diameter and 9 inches long. A hole, 2 inches in diameter and 6 inches deep, was bored into the top to receive the heater plug. The side of the block was wrapped with number 40 formex coated copper wire to be used as a strain-free resistance thermometer. The block is sus­ pended from the lid of the calorimeter container, des­ cribed below, by three number 20 piano wire supports (S). The heater plug (H) is a copper cylinder 2 inches in diameter and 4 inches long. It is bored 3 inches deep with a hole 1 inch in diameter at the top and 3/4 inches at the bottom* The outside is double chased to receive a non-inductively wound, number 36 manganin wire heater. The conductivity gas retention gate (Figure 3) was used for the runs on molybdenum. Its action was not very dependable and the system was later discarded. It con­ sisted of a sliding valve (V) which was lapped to a seat which in turn was sealed to the calorimeter with Apiezon (W). Helium was automatically Introduced into the cavity beneath the gate as the gate was closed (C through K). However the helium capillary was so small and the system had to be opened so often for maintenance, that this feature proved faulty. It was more satisfactory to gas the entire furnace and to seal the calorimeter vacuum off from the furnace vacuum. The last run on zirconium had ruined the radiation shield (G) (Figure 3). Since this shield could not be made to work satisfactorily thereafter, a complete revamping of the shield and the system for separating the furnace vacuum from the calorimeter vacuum was made. The new shield is of massive construction and designed primarily for dependability of operation. A cavity liner is sus­ pended beneath the shield housing to make a vacuum seal which completely eliminates organic materials from the caeity of the calorimeter. The entire assembly is then Inserted into the cavity and waxed in with Apiezon (W). This system was devised after considerable thought and care and has justified the extra effort by its depend­ ability.

The Calorimeter Container The Calorimeter container is also essentially un­ changed. It is a brass "can" 6 inches in diameter and 18 inches high. The lid is perforated with 2 holes to admit electrical leads, (J), one for helium capillary, one for the entrance of the gate activating rod, and one for the sample tube (T), Three studs (S) provide support for the three piano wire suspensions for the copper block. The lid was originally sealed to the can with "Cerrobend" solder, but the container was evidently too large to permit satisfactory sealing or the lid was not rigid enough to prevent the "Cerrobend" from working and cracking under the strain. After the second failure, this seal was replaced by flanges bearing against a double "©"-ring seal. This arrangement has never leaked even though the system has been opened several times for repairs and alterations. The openings in the lid now serve different pur­ poses in two cases. The helium gassing capillary has been drilled out and serves as the take-out for the con­ tainer vacuum McLeod gage. The tube used to admit the gate actuating rod now serves as the outlet to the container vacuum pump system.

The Vacuum Systems The furnace and dropping tube vacuum system is very important and provision is made for very rapid pumping, A 2 inch line from the furnace is oonnected through a large monel liquid nitrogen trap to a 20-liter per second (at 10~4 mm. of mercury pressure) Distillation -25- Products Incorporated oil diffusion pump using Dow Corning 703 Silicone fluid. This pump is backed with a Welch Duo—seal mechanical fore—pump. The system can be pumped down to pressures better than 10“-* mm. of mer­ cury as read on a McLeod gage. This system uses silicone greases which have been baked-out in place for at least one hour at 75 to 80°C while the system is under high vacuum. The large liquid nitrogen trap efficiently retains the condensable vapors from the oil pump. The pressure is measured by a Mc­ Leod gage system which is taken off from the 2 inch vacuum tube between the trap and the furnace. The fur­ nace is protected from the mercury of the McLeod gage by a liquid nitrogen trap. This system has given accurate pressure readings as was Indicated by an HG-200 ioniza­ tion gage. The calorimeter container is separately evacuated through a 3/16 - 3/8 inch copper tube by a 10-liter per second (at 10 ^ mm. of mercury pressure) Distillation Products Incorporated oil diffusion pump using Dow Corning 703 silicone fluid. This pump is backed by the same Welch Duo-seal pump as is the furnace system. The system can be evacuated to a pressure of 10“-* mm. of mercury, which is adequate for an insulating vacuum. The pressure here is also measured with a McLeod gage separated from the system by a liquid nitrogen trap. - 26- A stopcock, separating the furnace fore-pump line from the container fore-pump line, can be closed so that the entire furnace and dropping tube can be gassed with helium to facilitate cooling of the sample.

The Helium Gassing System After it falls into the calorimeter, the hot sample cools rapidly by radiation at first, but soon it cools chiefly by the conduction of heat through the point contacts on which it rests on the bottom of the calori­ meter cavity. To hasten this final cooling and the equilibrium between sample and block temperatures, it is necessary to increase the effective area for heat transfer by introducing an inert gas. To do this a helium gassing system has been set up by which a small amount of pure helium can be introduced to the calori­ meter during each run. This system consists of a one- liter glass reservoir filled with pure helium at about atmospheric pressure. A small volume of this gas is trapped between two stopcocks and allowed to bleed into the furnace after the sample has cooled somewhat and the furnace stopcock has been closed. The pure helium is prepared from the commercial grade material by passing the impure gas slowly over activated charcoal at liquid nitrogen temperature. The charcoal is activated by heating any good commercial active car­ bon to 450°C under vacuum, until the pressure has reached the 10“-* mm. of mercury range. After a trap filled with this material has been cooled to liquid air tem­ peratures, it will remove practically all traces of gases other than helium.

The Induction Heater A General Electric radio-frequency generator was used to provide the current for the work ooil in the furnace. This type of generator allows for only six temperature settings as originally designed. The internal circuits were modified by L. Bollonger at this laboratory to permit twelve settings to be select­ ed. Since the efficiency of heating varies from sub­ stance to substance and also with the size and shape of the sample, provision was made in the original design to permit five adjustments in the frequency by changing the inductance of the tank coil. The "variometer" used by Ziegler (4-9) permits the attainment of temperatures ordinarily lying between the tap settings of the oscillator. This device changes the inductance of the load circuit by the action of two concentric oolls, one being moved into the other, and works in connection with servo-mechanism actuated by the oscillator output voltage to regulate the sample temperature. - 28- The Thermostat The thermostat^consists of a cubic sheet metal box in which 30 gallons of transformer oil serves as the fluid. Two 1/4 horsepower motors drive two agitators which circulate the oil past a Fisher-Surfass mereury- switch temperature regulator and an electric resistance heater. The agitation also serves to maintain a uni­ form temperature within the bath. This temperature is measured with a thermocouple soldered to the calori­ meter container with "Cerrobend'1 . The system holds the temperature constant within * 0.005°C.

The Electrical Circuits Three types of electrical measurements are re­ quired: (1) the resistance of the resistance thermometer, (2) the energy supplied to the calibrating heater and (3) the electro-motive force of the thermocouples. These measurements were made with a White double (1,2, 3) and a Rubicon potentiometer (3) in conjunction with two Leeds and Northrup reflecting galvanometers. An ordinary "wet" cell battery is used as the working battery in the Rubicon potentiometer and seven Nicad cells joined in parallel serve the White. (l) The Resistance Thermometer The resistance thermometer consists of about 1000 feet of formex coated number 40 copper wire wrapped around the copper block. The block is first covered -29- with an insulating coating of General Electric adhesive, and after winding the thermometer, Kaufmann-Lattimer lens tissue is pasted on with the same adhesive and wrapped with gold foil. This arrangement gives a strain-free resistance thermometer. A battery of 14-Edison cells supplies the current for the resistance thermometer. A 200,000 ohm Mbuffer" resistor in series with the resistance thermometer re­ duces the voltage across the resistance thermometer (about 1285 ohmB) to about 80,000 microvolts. This voltage is measured across the terminals of the ther­ mometer at the block. The current is determined by measuring the voltage drop across a standard 1000.00 ohm resistor which is in series with the resistance thermometer. Since the current through the system is so small (about 62 microamperes^ its heating of the calorimeter is negligible. Both the current and voltage for the resistance thermometer are measured on the Vhite potentiometer.

(2) The Calibrating Heater The calibrating heater consists of a length of manganin wire (210 ohms resistance) wrapped non-induc- tively around a copper plug which fits snugly within a cavity drilled in the block. The wire, coated with formex and wrapped with cotton, is saturated with General Electric adhesive to improve the insulation. - 3.0-

P

RESISTANCE THERMOMETER

D^4B S2

CALIBRATION HEATER

FIG.^T ELECTRICAL CIRCUITS -31- The heater plug is soldered into the block with "Cerro- bend M solder prior to winding the resistance thermometer. A set of Id "wet" cell storage batteries provides direct current at 4# volts, which is applied directly to the resistance heater. The voltage and current a re measured across the low voltage side of a voltage di­ vider and across a 10 ohm standard resistor, respectively. The actual current passing through the heater must be calculated according to Kirchhoff’s law for parallel circuits, since some of the total current measured bypasses the heater via the voltage divider. Both the current and the voltage for the heater energy are measured on the White potentiometer.

(3) The Thermocouples Copper-constantan thermocouples are used to measure the thermostat temperature and to check the block tem­ perature. The electromotive force of each can be measured on either the Rubicon or the fl QM portion of the White potentiometer. -32

MEASUREMENTS AMD CALCULATIONS

Calibration The block calibration is made by adding an ac­ curately measured amount of electrical energy and accurate­ ly measuring the resistance rise. In a typical run, the resistance drift of the resistance thermometer is followed for a half-hour or more, before the heating is started. Since the heating period is 30 minutes or more, it is possible to time the heating period with a negligible error, and follow the energy input very carefully. Enough data can be obtained to establish the drift for current and voltage for the entire run. The basic equation for calculating the energy is: Energy = Voltage x Current x Time. In the circuit diagram (Figure 5), a s't;an<*ar<* resistor of 9*999j ohms. The total current can be measured directly across this resistor. According to Kirchhofffs laws for parallel circuits,

St - ♦ Ih* where the subscripts refer to the total, volt-box and heater currents. To calculate the size of 1^, the resistances of the parallel circuits must be known. Let E v be the voltage actually measured across P R be the resistance of that portion of the volt- box across the terminals, P. R^ be the total resistance in the volt-box circuit from 1 to 2. From above, 1^ ** 1^ - Iy Rv can be conveniently measured by comparison with a

standard resistor. Since I„ v» E„/R V' v is known, 9

If the values of E and I are not linear with time, the power can be calculated as a function of time and graphically integrated to give the energy* The voltage across the heater is E^ = Ey x R,j./Rv or Ev, where is the volt-box rati The energy applied is

dt where t refers to time* Since the voltage, Ey, can be measured to within a microvolt and E§2> the e*m.f. across the standard re­ sistor, as well, the energy can be measured with an accuracy of about 1 0*005 per cent. The resistance of the resistance thermometer can be measured to + 0.001 ohms. Since the usual change of resistance for a cali- bration run is about 16 ohms, this quantity is known with a precision of 1 0.02 per cent. The error of measuring time for such a run is less than Z 0.01 per cent. The heat leak correction can be made very small because the thermostat can be set accurately at the mean temperature. (In the case of a heat content run this cannot be done, since the time required for equilibration between sample and block is not known). The calibration data made for Ziegler's system gave 289.73 calories per ohm with a precision of Z 0 .04. per cent. Since all runs were made in a small resistance region, the dependence of the factor on total resistance could not be measured. However, be­ fore making the . titanium runs, the block was calibrated over a wide resistance interval and the following polynomial was derived: Q 2&1*. m 251.75 + 0.034688R} Z 0.035 per cent *■* ohm where^O.035 is the mean deviation.

Heat Content Runs In making a heat content run, the most important preliminary operation is that of regulating the thermo­ stat in such a way that the average temperature of the block over the time of the warming and final drift is as close to that of the thermostat as possible. This minimises the heat leak correction and insures the maxi­ mum accuracy for the run. The initial drift is followed for 30 to 60 minutes and the data are extrapolated to the time of the drop. -35- During this initial drift, the sample is brought to the required temperature and held there. As soon as suffi­ cient data have been taken to assure a successful run, the radiation shield on the furnace floor( which covers the dropping tube) is opened momentarily (one second, for example) and the sample is released. The sample falls a measured distance and strikes the trigger for the calorimeter radiation shield, causing it to fall and cover the top of the calorimeter, trapping the sample inside. At this time the gassing gate was quickly closed when the older system was used. With the new system, the shield usually makes a perfectly light-tight seal, and so the only speed required is to get back to the potentiometers. It is possible to gas the sample al­ most immediately, but it is convenient to wait for the sample to cool a little bit by radiation. The e.m.f. across the resistance thermometer rises rapidly immediately after the sample is dropped, and does not slow down for several minutes. When this happens, a convenient time is chosen and hel.ium is let into the system. This causes a further rapid rise which con­ tinues until the sample is almost in thermal equili­ brium with the block. The Correction for Heat Leak The course of the calorimeter block temperature with time is shown in Figure 6. The slow initial rise is due to heat leak by conduction along the supports and leads and radiation from the walls of the calori­ meter case. The rapid rise at t^ (time of drop) is due to the sudden heating of the block by the hot sample when it suddenly enters the calorimeter and loses heat at decreasing rates as it cools. The temperature rises until the sample approaches the temperature of the block. When this occurs, the block cools by New­ ton* s law of cooling, viz.,

- $ = *(*-*,) which states that the heat transfer between two objects depends on the temperature difference when the tempera­ ture difference is small. By changing the units of k, Q and T, we get _ dfi „ _ CpdT and dX ■ JsdK dt ~dt~ dt If we substitute, it is possible to get an equation which permits the use of resistance without the explicit use of and conversion to temperature. This saves much time in the calculations. Thus,

- at R By following the drift of R with time, the derivative can be determined. The environment temperature equivalent -37

R cCT

TIME

FIG. 6 TEMPERATURE TIME CURVE FOR HEAT CONTENT RUNS or R, viz,, Rq, can be calculated from an analytical expression (R = a + bV) relating R to the environment thermocouple e.m.f. ThenAR can be calculated aft

A R = R - Ro where R is some instantaneous value of the resistance. After the slope and the constant, k, have been determined the following algebra can be applied to calculate the heat leak: The block is either losing heat to or receiving heat from the environment at all times, except for the instant at which the glock temperature passes through the temperature qf the environment. This heat leak is proportional to the difference between the block and calorimeter temperatures. If we consider the course of this temperature difference with time, it is possible to use the cooling law in the form - dT = K A Tdt where dT is the instantaneous temperature change due to heat leak. We know the resistance equivalent of AT, viz.,AR, as a function of the time. Integrating this expression over the time between dropping and the end of the run,

td 39 Since the temperature need not be solved for explicitly, this becomes, in terms of the resistance,

But the integral is equal to the difference in areas under the R^ curve between t, and t„ and the block ° d f temperature curve f(R) between t^ and t^. It is seen at once that if these two areas are equal, the correction term, /^R^, vanishes. Since the uncertainty in deter­ mining A Is relatively large, the careless choice of the environment temperature for a run precludes good precision. It is possible to predict the best value for this temperature very closely from the atomic heat (at the temperature to be studied) of a substance simi­ lar to that being studied, the block calibration factor and the approximate time required for a run. One merely tries to get a curve similar to that in the illustra­ tion, such that the two areas A^ and A^ are equal.

Temperature Corrections Two corrections must be made concerning the upper sample temperature. Some of the radiation from the sample is absorbed by the window through which the temperature is observed, causing temperature readings to be low. Also, the sample cools a small amount while falling from the furnace to the calorimeter. The first correction is made by calibrating the pyrometer and window against a standard lamp after each run. This also takes into account the film of metal usually de­ posited from the hot sample. The standard lamp was calibrated at the Pyrometry Laboratory of the National Bureau of Standards and the maximum uncertainties are: about 5°C at 800°C, 3°C at 1063°0 and 7°C at 2300°C. These uncertainties are the greatest in all the measure­ ments . The correction for cooling of the sample during the drop is made with the aid of cooling data which are measured before the heat content runs are made. These data are obtained by heating the sample to various tem­ peratures and measuring the time required for the sample to cool to some predetermined reference temperature. The instantaneous loss of temperature can be found by measuring the slope of the temperature-time curve at several temperatures, plotting these data against time and then reading the correction for a given run from the smoothed curve. The data are somewhat uncertain o above 2150 C, but most of the data show a good fit to a curve, and valid extrapolation of the data for the higher temperatures is easily made. The rate of cool­ ing varies from about 2°C at 800°C to 30°C per second at 2300°C. The time of fall is about 0.2 seconds and the correction lies between 0.4°C at 800°C and 12°C at o 2300 G, The maximum uncertainty in the lower temperature correction is negligible. For the high temperature correction, the effective temperature loss from the o law would be 24. C, but it seems unlikely that the sample conductivity can hold the surface temperature up, so the true loss must be less than 24°C. However, if we o o accept the difference between 24 0 and 12 C as the maxi­ mum possible uncertainty in the cooling correction, then the contribution is only 0.5 per cent, which, when added to the uncertainty in the standard lamp calibration of 7°C, gives a total of 0.8 per cent uncertainty. Skinner (4 6 ) studied cooling rates for zirconium at two holes at different distances from the center of the sample and found no great difference between the two cooling rate curves up to 1600°G. The author used two different methods to study the data (fixed upper temperature to variable lower and variable upper to fixed lower) and again found no great difference in the two curves. An additional correction was made for the molybde­ num when it was found that the shallow (l/4 inch deep x number 60 drill) hohlraums were giving low readings when compared to a deep hohlraum (5/S inch). This correction amounted to twenty degrees at 2600°K but fell rapidly (by T^ law) at lower temperatures. The correction - 4.2- o was measured with a precision of + 2 C, -43

3 0

2 8

26

24 22 20

18

16

14

12

10 8 6

4 2

0 I ) 1000 1400 1800 2200 TEMPERATURE, °K

FIG.7 MOLYBDENUM COOLING DATA -44-

15

14

13

12

II

10

9

8

7

6

5

4

3 2

I

0 1300 1400 1500 1600 7 0 0 TEMPERATURE, °K FIG.8 TITANIUM COOLING DATA -45- m g as, The errors previously mentioned serve to indicate the uncertainty of some of the steps of the work. The purpose of this section is to summarize all experimental errors in the high-temperature work.

(a) Calibrations The energy can be measured to + 0.1 parts in 48,000 and £ 0*05 parts in 23,000 for the voltage and current, respectively, a precision of about ± 0.002 per cent or about as precise as the standard resistors have been calibrated. The time is known to within 0,005 per cent, the resistance to + 0.01 ohms, or + 0.002 ohms uncertainty for a 16 ohm rise, giving + 0.01 per cent. The error in correcting for heat leak is about 0.05 per cent. Two sets of block calibration data have shown probable errors of (1 ) ± 0.03 per cent over a range of 20 ohms (for the molybdenum data), and (2 ) + 0.02 5 for a polynomial describing four calibration points over a 50 ohm range of resistance thermometer resistance.

(b) Heat Content Huns In addition to the fractional uncertainty due to the block calibration which appears in all the calcula­ tions for heat content, the uncertainty of resistance change reappears, 0.01 per cent, as does the heat leak correction error, about 0.1 per cent for heat content -46- runs. There is also an error of about 0.1 per cent of the absolute temperature for the precision of the pyro­ meter readings. This error appears twice in enthalpy runs: once, in the sample temperature measurement and once in the window and pyrometer calibrations. For the molybdenum data, the error appears for a third time in the hohlraum correction. The error in the lamp temperature scale (maximum) is 5°C at 800°C, 3°C at 1063 C and 7°C at 2300°C. The error in reading the pyrometer is actually somewhat larger at the top and bottom of each range. The probable error is about 1 to 1.5°C for both sample and calibration readings, with a slightly greater uncertainty for sample tempera­ ture readings at the higher temperatures. The cooling correction error is not very large until about 2100 or 2200°C. The uncertainties can be estimated by varying the conditions under which the data are measured. Thus, Skinner studied the cooling rates at hohlraums drilled at different radii from the center of his sample and found an essential difference for data up to 1600°C. The author has varied the studies so that data were taken from fixed upper temperatures to varied lower temperatures and also from varied upper

i temperatures to fixed lower temperatures. The data I i i -47- agreed within the experimental error up to about 1500°C, as high as the data were measured. The cooling data at the extreme temperatures for molybdenum are probably not greatly in error. Calculation of radiation losses by the Steffan—Boltzmann law indicate an increasing system­ atic error, becoming 12°C at 2300°C. This value is probably high, but even assuming it is correct, it is not greatly beyond the limits of error for the other measurements• The White potentiometer readings are corrected for battery drift and dial autoc&libration. The first correction is small (0.3 V) and can be made with good precision (10 per cent). The second may be 7 or 8 V, but can be made with even greater precision. The figure + 0.1 V for the uncertainty in readings is reached from the examination of curves of V versus time. The experimental accuracy seems to be within 0.5 per cent, as estimated by Ziegjer.

(3) Uncertainty of Derived Functions The uncertainty in the heat capacity seems to be quite large, when checked against the data of other workers, even when the heat content data are in good agreement. This is not serious, however, since the heat capacity is not used to calculate other functions. The probable error in the heat content is 0.26 per cent for -48- molybdenum and about 0.2 per cent for titanium. The uncertainty in the entropy of molybdenum is about 0.03 units at 800 C and 0.09 at 2300°C. The uncertainty is slightly less for titanium. -49-

EXFERIMENTAL RESULTS Molybdenum The heat content data for molybdenum are In good agreement with the data of Jaeger and Veenetra (22) below 1800°K, but increase with temperature somewhat faster at higher temperatures. The molybdenum used in this research was a cylinder, 3/4 inches in diameter and 1 inch long, weighing 72 grams. The material was obtained from the Fansteel Metallurgical Corporation, North Chicago, Illinois and was 99.9 per cent pure. The sample was bored 5/3 inch deep with a number 60 drill to provide a hohlraum and the bottom of this hole was covered with molybdenum powder to improve the black body conditions. The enthalpy data were taken in a sequence which showed that no hysteresis was pre­ sent. The contamination of the sample was very slight (0.005 gms. in 70 gm. No, corresponding to 0.05 atom per cent as carbon) and no correction was made. The data obtained fit the polynomial aT“H298 16s -1'719 + 5.6471T+0.000372bT2 +1.197xl0“7T3 with a probable error of 0.24 per cent. The heat capacity is given by Cp = 5.6471 + 0.000744T + 3*590xlO“7T2 The thermal data calculated with the aid of these equations are presented in Table 50

TABLE I

The High Temperature Heat Content of Molybdenum

T, HT"H298.16 cal* atom*"1 Observed Calculated 1103 5075 5123 1177 5684 5638 1281 6356 6377 13*5 7149 7134 1474 7857 7796 1564 8493 8481 1655 9225 9189 1770 10090 10105 1864 10915 10875 1966 11725 11730 2068 12600 12610 2175 13495 13550 2269 14300 14410 2379 15500 15430 2482 16490 16420 2623 17800 17810 CAL GATOM 20,000 15,000 10,000 5,000 300

500

700

900

I. HA CNET F MOLYBDENUM OF CONTENT HEAT FIG.9 1100

TEMPERATURE,°K 1300

1500

1700 ~THIS AGR VEENSTRA a JAEGER

1900 RESEARCH

2100

2300

2500

'2700 Titanium The sample of iodide-process (53) titanium was generously donated by the New Jersey Zinc Co., Falmer- ton, Pa. Analysis revealed 99*96 per cent purity, the principal contaminants being Mn, 0*0082 per centj Si, 0.007 per cent and AL, 0.0066 per cent with smaller amounts of N, Te, Pb and Cu. A large piece of the rough rod (2 inches long, 7/8 inches approximate dia­ meter) was machined to give a fairly smooth cylinder, 5/8 inches in diameter and 1-1/4 inches long. Two hohlraums were made, 5/8 inches deep with a number 60 drill and titanium powder was dropped in to increase emission from the bottom. One hohlraum was parallel to the axis of the cylinder and the other made an angle of 20° with this axis. The purpose was to give the best conditions for observation from directly above in the glass furnace (see/ below; \ and from an angle of 20 o as is done in the metal furnace. The cooling data for titanium were taken in a glass vapor pressure cell which was capable of giving an ex­ cellent vacuum and rapidly removing gases given off by the sample on heating. This permitted measurements and sample clean-up to be done simultaneously. The transition temperature was measured by heating the sample with the oscillator set to give a final tempera­ ture of about 1000°C, and tt'easiiriligrthe< temperature; -53- as a function of time (Figure ID). This gave fairly slow heating so that the transition could be observed easily. The transition point was checked by cooling data • The heat content data are in fair agreement with Jaeger, Rosenbohm and Fonteyne (21) Their data gave a transition over a range of temperature which might indicate a second order transition. The data reported here indicate a much sharper transition however. The low temperature points are significantly below the data of Jaeger and fall nicely cm a smooth curve extra­ polated from Jaeger's lower temperature data. The higher temperature data lie somewhat above Jaeger's, (one per cent at the transition, falling to 0.5 per cent and then increasing above their extrapolated data). The high temperature deviations are just be­ yond the experimental error, but seem difficult to explain unless Jaeger over-corrected for impurities. Our sample picked up 0.5 atom per cent of oxygen during the runs and the data were corrected for this. Our vacuum was better than 10 -5 mm. of mercury. Since Jaeger's data show a smeared out transition and ours show a much sharper one, their sample was evidently more heavily contaminated. The lower range data consist of two points which were used along with the lower temperature data of O o TEMPERATURE, 0 9 8 0 4 9 0 0 9 I.O IAIM ETN DATA HEATING TITANIUM FIG.JO -54- T IM E , SEC. , E IM T 150

200 -55- Jaeger et al. to establish the best smooth curve below the transitioh. This curve was fitted to the polynomial

HT“H298.16 = 5.091T .+ 0.00H32T - 1656 with a probable error of + 0.1 per cent for the range 1000° to 1154-°K. The experimental points had a mean

deviation of + 0.3 per cent, the lower point falling nicely on the smooth curve and the higher one being 0.5 per cent high. There may have been a trace of pretransition heat in the second point. This equation gives a heat capacity value of 5.94 cal, deg.™^ g. atom"^ at 298.16°K, which is essentially in agreement with the value of 5.98, obtained from the low tempera­ ture data. In general, the equation seems adequate for the representation of data between 298.16° and 1000°K, although the precision is somewhat less. The data above the transition were plotted on large scale graph paper and a smooth curve drawn. This curve was fitted by the method of least squares to the function: Ht*H298>i6 = -8807+24.164T-0.012690T2 +3.19x10*6T3 with a probably error of + 0.03 per cent for the smooth curve and + 0.06 for the experimental points. However, the polynomial did not give heat capacity values which were consistent with the shape of the curve between 1154° and 1400°K, The data describe a straight line which i•s h6 s" the formula '

HT-H298.16 ’ 7-410T - 1 4 6 8 i calories g. atom”1 in the range 1154. to 1400°K with a standard deviation of + 0.04 for the experimental data, and was used to obtain thermal functions in this range. Above 1400°K the cubic polynomial was valid and was used to calculate the thermodynamic functions. (Table IV.) The heat content change associated with the trans- -1 ition is 943 cal. g. atom .

Calculation of the Thermodynamic Functions (2£) The heat capacity was calculated merely by sub­ stituting values of T°K into differentiated equations for the enthalpy. The entropy was calculated from the following:

3T— 290.16 * l,jf ^ ' J « * ’> T J ~ ----

Integrating by parts

^ ^ M-r ^ I jrp — =f=------J —

Thus, 1 6 ^ T was calcula'fced and (— was plotted against log T and graphically integrated from 298° to T°K for even temperature intervals. The High Temperature Heat Content of Titanium (Atomic Wt. 4-7.90)

n. HT~H293.16 ®K Observed Calculated

1067 5393 5394 1132 5978 5948 1156 6538 — 1211 7501 7506 1319 8312 8306 1391 8835 8839 1477 9478 9472 1559 10098 10102 1667 10977 10978 1750 11723 11702 1856 12720 12710 x <\i CAL G ATOM" 12,000 10,000 6,000 2,000 4,000 300 500 I.2 ET OTN O TITANIUM OF CONTENT HEAT FIG.32 900 700 TEMPERATURE,°K 1100 AGR VEENSTRA a JAEGER — HS RESEARCH THIS — 301500 1300 1700

1900 -59-

gii w L m The Thermodynamic Functions of Molybdenum at High Temperatures

cal* dag."*1 h °p h T~H298.16 ST~S298.16_ °K g. atom*"^ cal. cal. dag."1- g. atom“-L g. atom”!

298*16 5.90 0 - 0 400 6.00 607 1.75 500 6.11 1213 3.10 600 6.22 1829 4.22 700 6.34 2457 5.19 800 6.47 3098 6.05 900 6.61 3752 6.82 1000 6.75 442 0 7.52 1100 6.90 5102 8.16 1200 7.06 5800 8.77 1300 7.22 ' 6515 9.34 1400 7.39 7245 9.88 1500 7i57 7995 10.39 1600 7.76 8760 10.89 1700 7.95 9545 11.36 1800 8.15 10350 11.82 1900 8.36 11175 12.27 2000 8.57 12020 12.70 2100 8.79 12890 13.13 2200 9.02 13780 13.54 2300 9.26 14695 13.95 2400 9.50 15630 14.35 2500 9.75 16595 14.74 2600 10.01 17580 15.13 2650 10.14 18085 15.32 TABLE IV The Thermodynamic Functions of Titanium at High Temperatures

ll Cp T“ 298 . 16 I 298.16 OK g. atoi.1 eal. * oal. de?. - g«atom g.atom-1

298.16 5.94 0 0 300 5.95 11 .04 4-00 6.24 596 1.79 500 6.52 1248 3.21 600 6.81 1924 4.42 700 7.10 2605 5.5 0 800 7^38 3333 6.46 900 7.67 4083 7.35 1000 7.96 4853 8.17 1050 8.10 5258 8.56 1100 8.24 ■ 5677 8.94 1154 8.40 6140 9.34 1154 7.14 7083 10.16 1200 7.14 7424 10.45 1300 7.14 8165 11.04 1400 7.14 8906 11. 59 1500 7.61 9646 12.10 1600 8.04 10425 12.61 1700 8.66 11260 13.11 1800 9.47 12165 13.63 1900 10.47 13160 14.17 -61- JBABI II

LOW TEMPERATURE HEAT CAPACITY OF TITANIUM imflMffiClQff The low temperature heat capacity data are required for the calculation of the entropy and the correlation of heat content data with the free energy and equili­ brium constants. Titanium is a very important metal in that it is the strongest light metal and has a rather high melting point, 1800°C. It is the fourth most abun­ dant metal useful as a structural material and any data which pertain to its metallurgy and reactivity are of great value. An additional importance of low temperature heat capacity data is that titanium is a super conductor. With the aid of Debye’s law, low temperature (to 15°K) heat capacity data reveal the amount by which lattice vibrations contribute to the heat-capacity near absolute zero. This information is needed to assign thermal energy into the superconductive range and also to evaluate the electronic specific heat. The only previous low temperature heat capacity measurements were those made by Kelley (26) on relatively impure metal (98.75 per cent pure). These data were mea­ sured down to 53°K, only. To obtain more reliable data, we have measured the heat capacity of pure iodide-process titanium between 15 and 350°K, 4£f-MAXUS The heat capacity measurements were made with calorimeter number three of the Nernst type increment calorimeters built at this laboratory (24). The calori­ meter is a copper can 4 cm. in diameter and 8 cm. long. Twelve radial vanes of copper are inserted to facilitate the transfer of heat. The end pieces are stamped cups with a short cylindrical riser (for filling) in the top and a short copper tube soldered against the bottom face to serve as a thermocouple well. The pieces are soldered vacuum-tight when the calorimeter is assembled. After assembly, a resistance thermometer is wrapped around the side and covered.with gold foil. This thermometer is a nylon wrapped No. 40 B. and S. gage gold wire containing 0.15 per cent silver. This wire has about 200 ohms re­ sistance at room temperature. The silver reduces the rate of loss of resistance with temperature at low tem­ peratures. The thermometer also serves as a resistance heater during the energy input. Standard thermocouple number 139 was used to calibrate the resistance ther­ mometer. For the titanium runs, the calorimeter was filled with 2.5 gram atoms of iodide-titanium, which had been degassed and cut from a crystalline rod (iodide process) with a shaper, and annealed in a very high vacuum furnacd for several hours. The calorimeter was gassed with pure -63- helium in the apparatus shown and the filling tube sealed with a copper disc and "Cerrobend". The cryostat, container and blocks at junction-box numbfv S were used. The calorimeter is suspended in the vacuum system as described below. Suspended from the lid of the calorimeter container is a lead auxiliary block. Beneath this is hung the upper block, consisting of a lead filled copper tube, and the calorimeter is hung below this block from three cotton threads. The resis­ tance thermometer, heater leads, the upper block thermo­ couple and the standard (calorimeter) thermocouples pass through the upper block and are sealed in with wax. This gives good thermal contact between the block and the wires and reduces the heat leak to the environment. The lower block fits around the calorimeter and serves as a radiation shield as well as a temperature buffer. It is made of lead filled copper, also. Both the upper and lower blocks are wrapped with No. 30 B. and S. con- stantan wire to serve as a heater. These heaters and the resistance thermometer are saturated with the same insulating adhesive as was described in the drop-calori- meter section (General Electric No. 7031 adhesive). The upper and lower blocks are each equipped with thermocouples to follow their temperature course during a run. After the calorimeter and blocks have been put to­ gether, the assembly is lowered into the container and -64- the lid is sealed with !lCerrobend" solder. A monel tube, soldered into the container lid, provides a vacuum sealed take-out for the electrical leads. This tube passes through and is soldered to the lid of the cryostat. After the container has been solder sealed the container thermocouple and heater leads are soldered in place, and the whole assembly is lowered into the cryostat. The electrical leads are taken out of the vacuum system through slots along the side of a lucite plug machined to fit a standard taper ground glass joint. The leads are worked over with hot Apiezon 11W" until a vacuum tight seal is produced. The cryostat can be sealed vacuum tight. It is thus possible to cool the system with liquids as far as possible and then pump them with an efficient vacuum pump to go severalcbgrees lower. We have thus been able to cool to about 55°K with solid nitrogen and to 13 or

14°K with solid hydrogen. The calorimeter container can be gassed with helium to facilitate cooling with refrigerants. This transfer gas is pumped out before runs are made. -65-

LUCITE PLUG

TAPE

APIEZON WAX

KOVAR PYREX SEAL

SOLDERED

TO OUTER CONTAINER OF CALORIMETER ASSEMBLY

METHOD OF SEALING LEAD WIRES 8 THERMOCOUPLES TO CALORIMETER SYSTEM FIGURE 12 LAPPED FACE

TO VACUUM SYSTEM & HELIUM SUPPLY I 0 O' KOVAR PYREX 1 SEAL

APPARATUS FOR FILLING CALORIMETER WITH HELIUM GAS t v m * 13 FIG. W SOLID CALORIMETER ASSEMBLY -68

CALORIMETER AND CRYOSTAT

ELECTRICAL LEADS VACUUM TAKEOUT

ELECTRICAL LEADS

I -T O VACUUM SYSTEM If

TRANSFER TUBE BLOW-OFF TUBE

'I T "'f

'■ w 5! l">-V ' I !IO. J itI BRASS CRYOSTAT Oj II LUCITE WINDOW

DEWAR

MONEL TUBE

AUXILIARY BLOCK -UPPER BLOCK

HEATMG COILS OUTER CONTAINER

LOWER BLOCK

STANDARD CALORIMETER THERMOCOUPLE

WOODEN BLOCK ::Z3 ritunc 15 -69- Electrical Circuits The electrical leads are run into potentiometer station number 2. At this station, a 10,000 microvolt Wanner potentiometer is used to measure the thermocouple e.m.f.’s. A White double potentiometer of 100,000 micro­ volt capacity is used to measure the resistance thermometer and heater voltages and currents. This is accomplished in precisely the same way as for the drop calorimeter. All standard resistors were calibrated at the Bureau of Standards. The Wenner potentiometer uses a lead storage battery as a working battery and the White uses Nicad cells. The current for the resistance thermometer is supplied by Edison cells. The energy for the runs is supplied by four banks of Edison cells. The input of energy for the short runs made with the low temperature calorimeter is timed and switched on and off by a Johnston timer (23) which is activated by a standard clock by means of a photoelectric relay system* This device times the heating period to ± 0.002 seconds. EC

Bal ast

^ Resistance Thermometer^ RTC (Set) i ^

V t (Sprung)

Timer Master Switch Potential Selector Switch EC Energy Cells with Selector Switch (20 Cells) RTC Resistance Thermometer Cells (21 Cells) TRS Timer Reversing Switch MA Milliammeter (0— 150 ma) R| Voltage Divider: High Resistance Arm (500 Ohms) R2 Voltage Divider: Low Resistance Arm (60 Ohms) R6 Standard Resistance (I Ohm) R7 Energy: Current Limiting Resistance (0-50 Ohms) R8 Energy: Ballast Resistance (0-400 Ohms) R9 Standard Resistor (100 Ohms) (0-120,000 R,0 Resistance Thermometer: Current-Limiting Resistance Ohms) R(i Resistance Thermometer: Ballast Resistance (0-50,000 Ohms) E Potential Leads to Calorimeter via Switch Panel I Current Leads to Calorimeter via Switch Panel 0 To Q Dials of White Potentiometer via Reversing Switch P To P Dials of White Potentiometer via Reversing Switch

Fi gl6 Schematic Energy, Resistance Thermometer, and Timer Circuits. MEASUREMENTS AND CALCULATIONS (a) Runs The calculations are similar to those for cali­ bration runs for the drop calorimeter with a few addi­ tional corrections for the superheating of the heater- resistance thermometer wire which is at the surface of the low temperature calorimeters. The details of the calculations have been discussed elsewhere (16,19), and so only the salient points will be mentioned here. The resistance is followed to establish an initial drift and to locate the resistance at the initial heating time. During the heating period, the heater current is followed and read at 0.21tj1 and 0.79tj1, where t is the heating interval. The heater voltage is followed for several minutes through 0 .5^ to enable extrapolation to 0.79tj1. These considerations permit a simple calcu­ lation of energy even if the current is quadratic with time. After the heating is stopped, the final drift is followed to establish the rate and permit extrapolation back to the time heating was stopped. Battery unbalance, and block and container thermocouples and the resistance <9 thermometer current are read only at the beginning and the ends of the runs. The standard thermocouple is read during the initial and final drifts. After battery balance and autocalibration corrections have been calculated, the initial and final resistances -72- are calculated. An approximate correction is made for heat leak by averaging the initial and final drifts (including the slg$) and subtracting the resulting quantity from the resistance change. Corrections are made for the fact that the surface is sujber heated during the energy input and these are made as fractional corrections to the energy. The heater current is calculated in precisely the same way as in the drop calorimeter calibrations. The temperature scale is established by plotting the thermocouple readings versus resistance. A linear equation is established which gives the value Ro, the resistance as calculated from the equation. Ro is cal­ culated at each thermometer intercomparison point and subtracted from the true value of R, This data (R-Ro) is plotted against the temperature and a smooth curve is drawn. From the readings, a precise, smoothed table of resistance versus temperature is prepared. This permits rapid calculation of temperatures and the final heat capacity on the Kelvin scale. (b) Debye Theta The lowest temperature points of the data were used in conjunction with Debye tables of Cy to establish the Debye 0 as about 352°. (c) Thermodynamic Functions The thermodynamic functions were obtained by graphical integration of the heat capacity curve. A smooth curve was plotted through the heat capacity data and read at every degree up to 29S°K. The heat content function was calculated as follows: H° - H° = P CpdT o » o since Cp * aT^,

H° - K° = a T^dT » = CP*T ° ^ 4L L4 Thus at 15°K, Cp = 0.040 and » 0.150 cal. g. atom"-1-

The heat content function was then evaluated at every o , 0 25 interval up to 298,16 K by Simpson’s rule integration of the heat capacity table. The entropy was calculated by integration of a table of C /T for every degree. Extrapolation below to Sr 0°K was done in a similar way as for the heat content function. S° = X ° P dT = - f- Thus, at 15 K, Cp = 0.040, S?- - 0.013 15 /pO xj O \ The free energy function, - ^7, ^ , 0 ^» was calculated as follows: F° a H° - TS° F° = H° - TS® =

(g° ,r. JttS) so CH° - Hq - ( T ) “ ( T The heat content function was divided by the temperature and subtracted from the entropy. -74-

The resistance thermometer current and voltage can be read to * .05 microvolts. This means that the resis­ tance is known to about * 0.0001 V. The resistances of all circuits and resistors are known with a similar accuracy. The resistance change is known to about * 0.002 per cent. The heater currents and voltages are known with equal precision as the resistance. Errors of appreciable size do not appear until the energy corrections become large (at high and low temperatures) and the resistance thermometer intercomparison with the standard thermometer becomes uncertain (at low temperatures). The error in measuring time is * 0.002 seconds in several hundred seconds and so insignificant. The heat capacity data show a mean deviation of 0.2 per cent from a smooth curve or a probable error of about 0.17 per cent. The errors in the thermodynamic functions were cal­ culated in the usual manner (4&) and indicate a maximum uncertainty of 0.5 calories g. atom"^ in the heat content, 0.02 entropy units for the entropy and 0.02 calories g. atom"^ for the free energy function at 29S.l6°K. -75- EXPERIMENTAL RESULTS The experimental results are summarized in Table ,V. The data of Kelley (26) are somewhat lower than those of this research below 180°K and slightly higher above 220°K. This sort of minor discrepancy was also observed by Skinner (46) in the case of zirconium, when comparing his data with those of Todd at Kelley’s labora­ tory. Since both Kelley and Todd used less pure metals than were used at this laboratory, it might be that the oxide or soluble oxygen in the Bureau of Mines laboratory material does not obey the law of the additivity of heat capacities. The thermodynamic functions derived from the smoothed heat capacity data are also presented. The entropy at 29S.16°K is 7.33 of which 0.01 E.U. was obtained by a 3 o Debye T extrapolation below 150 K. The entropy value is 0.09 E.U. higher than that of Kelley. The Debye theta (Table VII) has the same form as has been reported for some other elements and some in­ dication of the influence of electronic specific heat seems to be present. -76- TABLE V Titanium Heat Capacity Run No. Mean T. 6 1 Cp 93 15.439 2.312 0.0457 94 17.362 1.777 .0559 95 18.754 1.475 .0670 96 20.045 1.444 g0812 97 21.311 1.686 .0898 98 22.872 1.748 .1168 99 24.600 1.945 .1488 100 26.708 2.232 .1919 101 29.323 2.952 .2600 102 32.232 2.908 .3493 103 35.264 3.185 .4557 104 38.666 3. 585 .5898 105 43.540 6.193 .8079 106 49.044 4.888 1.0848 107 53.890 4.832 1.3496 108 57.999 3.428 1.5719 59 63.946 6 .265 1.8734 60 ; 63.946 6.265 1.8734 61 70.273 6 . 368 2.1731 62 76.999 7.013 2.4888 63 85.618 10.040 2.8796 64 94.758 8.335 3.2519 65 104.492 11.070 3.583 66 114.763 9.562 3.887 67 127.074 10.621 4.215 68 137.652 10.536 4.439 69 148.701 >11.578 4.654 10 160.373 11.638 4.855 * 71 172.744 13.804 5.020 72 185.705 12.372 5.161 73 198.459 13.280 5.305 74 212.404 13.671 5.427 89 215.286 9.238 5.532 90 2 2 4 ,524 9.305 5. 536 91 234.026 9.612 5.602 77 248.048 11.905 5.682 78 259.296 12.096 5.768 79 271.726 12.683 5.865 80 283.322 10.368 5.913 81 293.571 9.132 5.950 82 299.576 3.990 5.958 83 305.510 6.063 6.005 O O C

l , CAL DEG'1 G ATOM" 2 0 550 25 75 FIG. HEAT 17 CAPACITY TITANIUM OF 2 5 175 150 125 TEMPERATURE.°K

200100 KELLEY • TI RESEARCH THIS 6 225 250

275 300 -78

BLE vr

The Thermodynamic F ^ k:tionsoof Titanium at Lou Temperatures

J, 0® S ° H°_H® -(P»-H® K cL.deg.-i ~i; _i - r * g.atom-1 g.atom g.atom A cal.deg, g.atom”! 15 0.040 0.013 0.15 0.003 25 .157 .054 .94 .017 50 1.136 .414 15.31 .108 75 2.402 1.123 50.1 .322 100 3.434 1.963 133.7 .626 125 4.155 2.811 229.0 .979 150 4.684 3.652 339.9 1.386 175 5.043 4.403 461.9 1.764 200 5.321 5.095 591.5 2.137 225 5.539 5.735 727.3 2.502 250 5.713 6.328 868.0 2.856 275 5.864 6.879 1012.8 3.196 298.16 5.976 7.334 1149.9 3.478 79- TABftTLJgl Tabulation of ihe Debye Theta for Titanium

T°K Theta °p 15.439 0.0447 337.02 17.362 .0559 352.01 18.754 .0670 357.36 20.045 .0812 358.59 21.311 .0898 368.94 22.872 .1168 362.25 24.600 .1488 359.16 26.708 .1919 358.39 29.323 .2600 355.92 32.232 .3493 352.71 35.264 .4557 351.51 38.666 .5898 351.28 43.540 .8079 350.85 49.044 1.085 350.27 53.890 ' 1.3496 349.15 57.999 1. 572 349.04 59.329 1.652 347.96 63.946 1.873 350.94 70.273 2.173 353.61 76.996 2.489 354.80 85.618 2. 880 353.77 94.758 3.252 352.31 104.492 3.583 3 52.14 114.763 3.887 351.06 127.074 4.215 346.40 137.653 4.439 344.41 148.701 4.654 339.19 160.373 4.855 331.33 -80- ACKNOWLEDGMENT

The author would like to express his thanks to Professor Herrick L. Johnston for inviting him to come to Ohio State to undertake this research and for his continued encouragement and interest in its progress. He wishes to thank Drs. J. W. Edwards, J. H. Hu, and G. B. Skinner; Messrs. P. E. Blackburn, W. E. Dit- mars, N. C. Hallett and R. N. White for their sugges­ tions and assistance in the experimental work. He is indebted to Dr. C. W. Beckett for his training in certain theoretical aspects of thermodynamics. Mr. L. E. Cox and his staff and the Messrs. Laverack and Stinnett were helpful in the design, construction and maintenance of the apparatus and the author wishes to thank these gentlemen. Finally, the author thanks the Office of Naval Research for the financial support given to this re­ search and for the fellowship which enabled him to devote his full time to it. APPENDIX I

Physical Constants 0°C = 273.16 t 0.1°K 1 calorie = 4.1840 absolute joules = 4*1833 int. joules Atomic Weights: Molybdenum, 95.95> Titanium, 47.90

Drop Calorimeter Data (a) Improved Calorimeter-AS289.73 1 0.15 cal. ohm*"'*' (b) Modified Calorimeter JL^Sl. 75 + 0.034£9R 1 0.08 cal. ohm Voltbox Ratios (a) 1001.0 (b) 1001.22 Standard Resistances (International Ohms):

RS1 = i000-°o r S2 = °-°99997 Environment Thermocouple (V^):

t°C = 0 .0 8 8 2 7 + 0.025723V2 - 4.209Sxlo“? V2 Block Thermocouple (V-^) : t°C = -0.0409 + 0.026182V1 - 7.6906x10“7 Intercomparison of R versus R = 1158.133 + 0*118771V2 APPENDIX II

Low Temperature Calorimeter Data Calorimeter: No. 3 Terminal Box: No. 8 Potentiometer Station: No. 2 Volt Box Ratio: 501.167 Resistances: Short Arm of Volt Box, 59*94 ohms Upper Block to Terminal Box, 1.964 ohms Terminal Box to Main Panel Board, 1.829 Main Panel Box to Volt Box, 0.400 Energy E.M.F. Factor, 0.99882 Corrected Volt Box Ratio: ^ * 501.241

Ra,' 100.00 o ohms Standard Thermocouple: No. 139 -83- APPENDIX III

The following page is a reproduction of the standard lamp certification of calibration from the Bureau of Standards. This lamp was used to calibrate pyrometers and windows in the high temperature work. -34- UNITED STATES DEPARTMENT OF COMMERCE, WASHINGTON NATIONAL BUREAU OF STANDARDS CERTIFICATE FOR Tungsten Ribbon-Filament Lamp (NBS 1099 B) Furnished to Ohio State University, Cryogenic Laboratory Columbus, Ohio Corresponding Values of Brightness Temperature ( = 0.65 ) and Lamp Current Degrees Degrees Centigrade Ampere s Centigrade Amperes 800 9.88 1600 21.01 900 10.68 1700 22.98 1000 11.68 1800 25.05 1100 12.85 1900 27.21 1200 14.19 2000 29.45 1300 15.69 2100 31.76 1400 17.35 2200 34.15 1500 19.13 2300 36.63 The values in the above table apply when the observer sights at the center of the filament at the level of the notch and about 1 millimeter above the pointer and when the lamp is operated with the envelope in a vertical posi­ tion with base down and with the center contact of the base at positive potential. The maximum uncertainties In the values reported decrease from about 5 degreeB C at 800°C to about 3 degrees C at 1063°C and then increase to about 7 degrees C at 2300°C. For the Director by R. J, Corruccini

R. J. Corruccini, In Charge, Pyrometry Laboratory 3.1/117936 Division of Heat and Power P. 0. No. RF 22109 8 /2 7 /4.8 JL:AM APPENDIX IV BIBLIOGRAPHX (1) Bauer, T. W., Beckett, C. W. and Johnston, H. L. "Calorimetry at Low Temperatures," The Ohio State University: Air Materiel Command Technical Report, (1949), pp. 4-11. (2) Bockstahler, L. I., Phys. Rev.f 25, 677 (1925) (3) Bronson, H. L.' and Chisholm, H. M,, Proc. Nova Scotia Inst. Sci.f 17, 44 (1929). (4 ) Bronson, H. L,, Chisholm, H. M. and Dockerty, S, M., Can. J. Research,. 8, 282 (1933).

(5) Brown, G. G. and Furnas, C. C., Trans. Am. Inst. Eftg», 13, 309 (1926). (6) Cooper D. and Langstroth, G. 0., Phys. Rev.f 33, 243 (1929). (7) Corbino, -0. M. Attiaccad. Lineal. 21, I, 188, Ibid.. 22, I, 430; Phvslk. Z.. 13, 375 (1912). (8) Debye, P., Ann. Physik. 39 (4), 789 (1912). (9) Defacqz, E. and Guichard, M., Ann, chim. phys. 24 (7), 139 (1901). (10) Dulong, and Petit, , Ann, ohim._ et._nhra.. 10, (2), 395 (1819). (11) Einsteih, A., Ann. Physik. 22, 180 (1907). (12) Gaehr, P. F., Phys. Rev.. 12, 396 (1918). (13) Giauque, W. F., J. Am. Chem. S_og.. 52, 48O8 (1930). (14) Giauque, W. F., and Johnston, H. L., J. Am. CfaftJIU Sflffi., 51, 2300 (1929). (15) Giauque, W. F. and Weibe, R., J. Am. Chem. 50, 101 (1928). (16) Gibson, G. E. and Giauque, W. F., J. Am.Chem. 45, 93 (1923). -86-

(17) Glnnlngs, D. C. and Corruccini, R. J., £&£• Standards J. Research, 38, 583 (19*7); Ibid.f 38, 593 (1947); Ibid-f 39, 309 (1947). (IS) Glasstone, S. "Thermodynamics for Chemists," New York: D, Van Nostrand Co., 1947, Ch. VI. (19) Hersh, Herbert N. "Thermodynamic Properties of Some Solid Compounds of Boron." Ph.D. Dissertation, The Ohio State University (1950)* (20) Jaeger, F. M. and Rosenbohm, E., Proc. Acad. Scl. Amsterdam. 30, 905 (1927)* (21) Jaeger, F. M., Rosenbohm, E. and Fonteyne, R., Proc. Acad. Sci. A&filSXdflJfl, 39, 442 (1936); fieg. Arflj. chim., 55, 615 (1926). (22) Jaeger, F. M. and Veenstra, W. A., Proc. Acad. Sci. Amsterdam. 37 , 61 (1934); Reff-.- tr.fly. g Mffl» * 53, 677 (1934). (23) Johnston, H. L., J. Ont. Soc. and Rev._ Sci. Instr., 17, 3S1 (1928). (24) Johnston, H. L. and Kerr, E. C., J. Am. Chem. S^., 72, 4733 (1950), (25) Jones, H. A. and Langmuir, I., Gen. Elec. Res. Lab., No. 419, Sept., 1927. (26) Kelley, K. K., Ind. Ene. Chem.. 36, 865 (1944). (27) Kelley, K. K., "Contributions to the Data on Theoretical Metallurgy. XI. Entropies of Inorganic Substances. Revision (194&) ot Data and Methods of Calculation" U. S. Dept, of Interior, Bur. Mines Bulle­ tin 477. (28) Kelley, K, K., "Contributions to the Data on Theoretical Metallurgy. X. High Temperature Heat Con­ tent, Heat Capacity and Entropy Data for Inorganic Compounds" U. S. Dept, of Interior, Bur. Mines Bulle­ tin 476 (1949). (29) Kelley, K. K., Naylor, B. F. and Shomate, C. H., U. S. Dept, of Interior, Bur. Mines Tech. Paper 686 (1946). -87-

(30) Knudsen, M., Ann. Physik. 29, 179 (1909)* (31) Kothen, C. W., Beckett, C. If. and Johnston, H. L., "Experimental High Temperature Heat Capacity of Solids." The Ohio State University: Air Material Command Technical Report (1950), pp. 4-11. (32) Kothen, C. W., Beckett, C. W. and Johnston, H. L. "Bibliography on High Temperature Heat Capacities of Solids, Liquids and Gases." The Ohio State University: Air Materiel Command Technical Report (1950)* (33) Langmuir, I., Phys. Rev.. 2, 329 (1913). (34) Lapp, C., Compt. rend.f 186, 1104 (1923); Ann, phys., 12 (10), 422 (1929); 6, 826 (1936). (35) Latimer, W. M. J. Am. Chem. Soc.f 44, 2136 (1922). (36) Lewis, G. N., J. Am. Chem. Soc.f 29, 1165, 1516 (1907). (37) Magnus,- A., Ann. Physik. 31, 597 (1910); Phzai]s*__£., 14, 5 (1913). (38) Marshall, A. L., Dornte, R. W. and Norton, P. J. J. Am. Chem. Soc.f 59, 1161 (1937). (39) Newman, A. B. and Brown, G. G., Ind. Eng. Chem. 22, 995 (1930). (40) Nilson, L. F. and Petterson, 0., Ber.. 13, 1459 (1880). (41) Oberhoffer, P., Metallurgies 4, 427 (1907).

(42) Pirani, M. V., Ber. phys. Gob.. 1912, 1037 (43) Sato, S., Bull. Inst. Phys. Chem. Research (Tokyo), 13, 716 (1934)7 (44) Seekamp, H., Z. anore. Chem.. 195, 345 (1931). (45) Simon, F. and Zeidler, W., Z. phys. Chem.. 123, 383 (1926). (4 6 ) Skinner, Gordon B., "Thermodynamic and S ructural Properties of Zieconlum" Ph.D. Dissertation, The Ohio State University (1951). - 88 -

(4-7) Smith, K. K. and Bigler, P. W., Phrs. Rev.. 19, 268 (1922)* (48) Southard, J. C., J. Am. Chem. Soc.f 63, 3142 (1941). (49) Speiser, R., Ziegler, G. W. and Johnston, H. L., Rev. Sci. Instr.. 20, 385 (1949). (50) Stern, T. E., Phys. Rev. f 32 (2), 298 (1929). (51) Stttcker, N., Sjtgb^ W 3-P £■*.,. HASH* 114, 657 (1905). (52) Sykes, C., Proc. Roy. Soc. (London), A148, 422 (1935). (53) Van Arkel, A. E. and DeBoer, J. H., Z. anorg. allgem. Chem.f 148, 345 (1950); MgtalltflrtflShaft, 13, 405 (1934). (54) Weber, H. F., Ann. Physik. (2) 154, 367, 552 (1875); Phil. Mag.P (5) 49, 161, 276 (1875). (55)White, W. P. "The Modern Calorimeter" New York: The Chemical Catalog Co., 1928. (56) White, W. P. J. Phys. Chem.. 34, 1121 (1930)* (57) Worthing, A. G., J. Franklin Inst.. 185, 707 (1918); Phys. Rev.r 12, 199 (1918)s Bull. Nela.Hes. Lab. 1, 349 (1922); Physik. Ber.. 5, 67 (1924). (58) Wiist, F., Meuthen, A, and Durrer, R., Forsch. Arb. Ver. deut. Ing.. 204, (1918). (59) Zeise, H., Z. Elektrochem.. 39, 758, 895 (1933); ibid.f 4 0 , 6 62, 885 (1934); JJaid., A7, 38 0 , 595 (1941); liid., 48, 425, 693 (1942). (60) Ziegler, George W., "High Temperature Enthalpies of Tantalum and Columblust" Ph.D. dissertation, The Ohio State University, 1950. (61) Zwikker, C. and Schmidt, G., PhvsicA. 8, 329; Z. Physik. 52, 668 (1928). -89-

AUTOBIOGRAPHY

I, Charles W. Kothen, was born September 25, 1921, in Buffalo, New York. I received my secondary school education at the Buffalo Riverside High School, gradu­ ating in June, 1939. I received my undergraduate training at the University of Buffalo and the Georgia School of Technology, Atlanta. My education was inter­ rupted by thre? years of military service during World War II. I received my B. A. degree from the University of Buffalo in June, 1943. In September, 194-3, I entered the Graduate School of The Ohio State University, where I have held a Research Fellowship during the four years while completing the requirements for the degree Doctor of Philosophy.