Heat capacity, entropy, and Gibbs energy of technetium hexafluoride between 2.23 and350 K; magnetic anomaly at 3.12 K; mean energy of 99TcDarrell W. Osborne, Felix Schreiner, Klaus Otto, John G. Malm, and Henry Selig

Citation: The Journal of Chemical Physics 68, 1108 (1978); doi: 10.1063/1.435789 View online: http://dx.doi.org/10.1063/1.435789 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/68/3?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Radiation Exposure Levels in Diagnostic Patients Injected with 99mTc, 67Ga and 131I at the Mexican NationalInstitute of Cancerology Nuclear Medicine Department AIP Conf. Proc. 854, 233 (2006); 10.1063/1.2356458 Determination of the 99Tc(thermal n,)100Tc Reaction Cross Section from the Prompt Ray Yields AIP Conf. Proc. 769, 1454 (2005); 10.1063/1.1945278 Transmutation of 99 Tc in a low lethargy medium as a function of the neutron energy AIP Conf. Proc. 447, 35 (1998); 10.1063/1.56731 Heat capacity and thermodynamic functions of 242Pu2O3 from 8 to 350 K. Contributions to the excess entropy J. Chem. Phys. 74, 5269 (1981); 10.1063/1.441691 Heat capacity, entropy, enthalpy, and Gibbs energy of 242PuF4 from 10 to 350°K J. Chem. Phys. 63, 4613 (1975); 10.1063/1.431271

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Heat capacity, entropy, and Gibbs energy of technetium hexafluoride between 2.23 and 350 K; magnetic anomaly at 3.12 K; mean f3 energy of 99Tca)

Darrell W. Osborne, Felix Schreiner, Klaus Otto, b) John G. Maim, and Henry Selig C)

Chemistry Division, Argonne National Laboratory, Argonne, Illinois 60439 (Received 4 October 1977)

The heat capacity of solid and liquid technetium hexafluoride has been measured between 2.3 and 350 K. The standard entropy, S, the enthalpy increment. (If" - Iro), and the Gibbs energy function, (Go-Iro)!T, have been calculated. At T=298.15 K, the thermodynamic functions have the following values: C'p = 157.84 JK-I.mol- I, S = 253.52±0.25 JK -I.mol-I, (Ir - Iro) = 38331 ±38 J mol-I, and (Go - Iro)! T = -124.95 ±0.12 J K -I.mol-I. TcF. has a solid-solid transition at 268.335 K associated with an enthalpy change AIr" = 8024.9 ± 5.0 J mol I. It melts at 31L14±0.05 K and has an enthalpy of fusion of AIrf =4618.86±1.60 lmol- I. TcF. has a lambda-shaped anomaly in the heat capacity with a peak at 3.12 K, probably caused by a transition to a ferromagnetic state. A similar lambda-shaped transition was observed for rhenium hexafluoride at 1.30±0.05 K. The magnetic entropy of TcF. is estimated to be 5.823 lK I·moll The third law value for the standard entropy of TcF. vapor at 320 K was calculated to be S (TcF" g) = 371.278 ±0.750 1 K' I·mol' I Molecular data for TcF6 lead to a lower value of S (TcFo• g, 320 K) = 367.53 1 K,I·mol-l. The entropy from molecular data can be made to agree with the calorimetric value if the frequency for the inactive vibrational mode V6 is lowered to 131 cm ,I from the reported value of 145 cm -I. The average energy of the /3 decay of 90Tc was evaluated from the radioactive self-heating of the sample and was found to be 97.2 ± 1.2 keY. This number exceeds the literature value but agrees with a more recent integration of the /3 spectrum.

INTRODUCTION

Technetium hexafluoride is similar in its structure and many of its properties to the other hexafluorides of the 3d and 4d transition metal series. All of these com­pounds have a high volatility which permits the study of their molecular properties in the vapor phase. Accord­ingly, a considerable amount of spectroscopic and elec­tron diffraction work has been done with the objective of determining their molecular structure. But even though all of the transition metal hexafluorides were found to have comparatively simple molecular spectra because of their regular octahedral structure, thermodynami.c information, notably the standard entropy of the vapor, proved to be indispensable for the complete interpreta­tion of the spectroscopic data. In the present article we are presenting the results of measurements of the heat capacity and related thermal properties for the temperature region 2.23 to 350 K of technetium hexaflu­oride, and furnish the value for the standard entropy of the vapor calculated from our thermal measurements.

In the case of the technetium hexafluoride the calori­metric measurements were particularly rewarding. Beyond providing the raw data for the calculation of the entropy and the Gibbs energy as functions of the tem­perature, the measurements uncovered a magnetic tran­sition at 3.12 Kl and a solid-solid transition at 268.314 K, and furthermore permitted an accurate determination

alBased on work performed under the auspices of the Division of PhYSical Research of the U. S. Energy Research and Development Administration.

blPresent address: Ford Motor Company Scientific Laboratory, Dearborn, Michigan.

elpresent address: Department of Inorganic and Analytical Chemistry, The Hebrew University, Jerusalem, Israel.

of the energy released in the radioactive decay of tech­netium.

EXPERIMENTAL

The work with technetium hexafluoride requires spe­cial attention to the radioactivity of the compound. Technetium is an element for which no stable isotopes exist. The isotope with the longest half life of 105 years is 99Tc , which decays via beta decay into stable 99Ru. H was this isotope that was used for the preparation of the calorimetric sample. The maximum beta energy is 0.291 MeV and the radiation is therefore very soft. H is not necessary to use special shielding when handling the element or its compounds in the laboratory. Care must be taken, however, to avoid leakages and spills. To make sure that no avoidable contamination occurred, sensitive monitors were used during the preparation and purification of the sample, and during the loading and the subsequent unloading of the calorimeter.

The radioactivity of the technetium affected the calo­rimetric measurements in two ways, viz., by causing a certain amount of decomposition of the compound es­pecially in the condensed phases, and by producing a certain amount of heating which made it impossible to cool the sample below 2 K in our cryostat and which made it necessary to adopt a special technique of mea­surement during the heat capacity determinations below 11 K.

The heat capacity measurements in the 5-350 K range preceded the low temperature measurements between 2-25 K. After evaluation of the data obtained in the higher temperature region it was found that the heat capacity curve could not be extrapolated smoothly to absolute zero on the assumption of a T3 temperature dependence. With some effort measurements were ex-

1108 J. Chern. Phys. 68(3), 1 Feb. 1978 0021-9606/78/6803·1108$01.00 © 1978 American I nstitute of Physics

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Osborne, Schreiner, Otto, Maim, and Selig: Heat capacity of technetium hexafluoride 1109

tended to about 3.5 K in the high temperature cryostat and evidence was obtained for a minimlm in the heat capacity curve near 5 K. In order to trace the true shape of the heat capacity curve in this low temperature region a separate series of measurements was under­taken with a new sample and in a cryostat more suitable for the low temperature region.

Preparation of the sample

The calorimetric samples of technetium hexafluoride were taken from a stock amount of the substance that had been prepared in the following way: Approximately 24 g of pure 99Tc metal obtained from Oak Ridge Na­tional Laboratory was divided into four batches and each batch was reduced in a stream of hydrogen in a fused silica tube at 1020 uC for 2 h. The original material was black2

; after reduction the product was gray. 1

23.618 g (= 0.239 mol) of this material was trans­ferred to a 1588 cm3 prefluorinated Monel reaction ves­sel. 1. 09 mol of pure fluorine (99.85% Fa) was con­densed in the reactor and the mixture was heated at 400 'c for 16 h. The reaction vessel was cooled to - 78 °C and the excess fluorine was removed. The TcFs was warmed to 25C and distilled to another large ves­sel at - 78 C and pumped upon until a vacuum of 10-4

mm Hg could be maintained. This procedure was re­peated several timi~s to free the product from the last traces of volatile impurities (HF, SiF4), The infrared spectrum of the purified compound showed only the bands characteristic for TcFs. The yield as determined by PVT measurement was 49.8 g of TcFs or 97.8%.

Heat capacity measurements were carried out with three different samples taken from the original prepara­tion of technetium hexafluoride: The first sample of 49.9591 g (= 0.23466 mol) was used for the measure­ments of series 1 through series 13. During the time it took to complete the measurements of the first thir­teen series radiation decomposition had led to the for­mation of a small amount of impurity. The technetium hexafluoride was therefore removed from the calorim­eter and purified before a second sample was trans­ferred back into the calorimeter for the measurements of series 14 through 19. The purification procedure was the same as that described for the preparation of the sample, viz., sublimation of the hexafluoride and pump­ing at - 78 "C. The amount of TcFs in the second sample was 51.1882 g (=0.24044 mol). (The second sample in­cluded an additional amount of TcFs made independently for density measurements).

A third calorimetric sample was used for the mea­surements in the isoperibolic cryostat. Because of the radioactive self-heating and because the heat capacity of the empty sample container is sufficiently small a lesser amount of technetium hexafluoride was adequate. The quantity of TcFs in the third sample was 39.0708 g (=0.18352 mol).

Calorimetric apparatus and technique

Two different containers were used to hold the sam­ples of technetium hexafluoride during the calorimetric

measurements in the 5-350 K and in the 2-25 K ranges. The two containers were made as nearly alike as pos­sible and were identical in construction to a calorimeter described in earlier publications. 2 They were made of nickel and had an internal volume of approximately 23 cm3. Each had a re-entrant well to accommodate the heater-thermometer assembly, and one of them was provided with three eyelets at the top for mounting in the low-temperature cryostat. Samples were loaded and removed through a valve at the top that could be operated by means of a screwdriver while the calorim­eter was connected to the transfer line. The seal was made by a small copper-gasketed valve sc rew.

The cryostat for adiabatic measurements of the heat capacity in the temperature range from 5-350 K is de­scribed in two earlier publications. 3.4 The technique of measurement involves observations of the temperature drifts before and after each heating period of 5 or 10 min. The data from the drift observations were used to correct for deviations from truly adiabatic conditions. Temperatures were determined with an encapsulated platinum resistance thermometer (laboratory designa­tion A-t). This thermometer was calibrated to give temperatures on the 1948 international practical tem­perature scale (IPTS) above 90 K. At lower tempera­tures a calibration point had been obtained at the normal boiling point of helium, and between 14-90 K a compari­son with an NBS-calibrated resistance thermometer was used to establish the resistance vs temperature curve for A-1. To convert the resistance readings to tem­peratures a table of quotients R/ Ro as a function of tem­perature was used. This table had been worked out in this laboratory and was designated as temperature scale A-17.5

A description of the apparatus that was used for the measurement of heat capacities between 2 and 25 K is found in Refs. 6 and 7. The cryostat consisted of two concentric glass Dewar vessels and was operated with liquid helium in the inner and liquid nitrogen in the out­er vessel. The sample container was mounted inside a copper can which was immersed in the liquid helium. Temperatures in this apparatus were measured with a germanium resistance thermometer that was located on the heater-thermometer support on which the calorim­eter was mounted. This thermometer was a four lead platinum-encapsulated germanium resistor of type CG-1 as furnished by Radiation Research Corporation, West Palm Beach, Florida. The calibration of the germa­nium resistance thermometer has been described else­where. 8 Briefly, the calibration between 0.85-2.3 K was done by comparison with the vapor pressure of liquid 3He, between 2.1-4.2 K by comparison with the vapor pressure of 4He, and between 4.2-25 K by gas thermometry with ~e. An additional calibration point was obtained near 20 K from a measurement of the vapor pressure of liquid hydrogen. The T 62 and the TS8 scales were used to correlate the vapor pressure data of 3He and of 4He, respectively, with the temperature.9• IO

The hydrogen calibration point was based on a value of 20.384 K for the normjl-l boiling point of 25% para-, 75% ortho-hydrogen.

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1110 Osborne, Schreiner, Otto, Maim, and Selig: Heat capacity of technetium hexafluoride

TABLE 1. Molal heat capacity of technetium hexafluoride. Molecular weight: 212.8968. 0 °C= 273.15 K.

11K CP!(J· K-1

'mor l )

First sample Series 1

6.188 8.023 9.715

11.540 13.570 15.701 17.813 19.859 21. 910 24.100 26.463 29.130 32.034 35.308 38.932 42.715

1. 45a

1. 98 3.15 5.03 7.78

11.12 14.59 17.90 21. 06 24.25 27.46 30.80 34.04 37.31 40.61 43.82

46.953 47.25

6.168 8.034 9.888

11. 757 13.682 15.694 17.758 19.724 21. 677 23.800 26.145 28.794 31. 813 35.176 38.903 42.936 47.371 52.359 57.916 63.945

Series 2

Series 3

1. 43 a

2.00 3.30 5.29 7.95

11.10 14.50 17.68 20.70 23.82 27.05 30.39 33.80 37.20 40.58 43.99 47.56 51. 45 55.67 60.18

54.164 52.86 59.757 57.09 65.591 61.42 72.020 66.09 79.148 71.04 87.097 76.42 95.863 81. 92

Series 4 105.441 87.49 115.026 92.89 124.736 98.05 134.957 103.28 144.995 155.064 165.143 175.107 185.089 195.085 205.028 215.060 225.071

108.10 112.73 117.29 121.64 125.94 130.30 134.51 138.82 143.26

TIK CP/(J· K-1

. mol-I)

Series lOb

236.784 148.99 241.881 246.764 251. 447 256.109 265.494

151. 43 153.83 156.22 159.81 164.15

Series 11 b

273.802 150.72 278.611 152.72 283.378 288.075 292.720 297.394 302.061 306.573

153.78 156.43 156.49 158.05 161.47 173.17

Series 12b

315.824 173.35 320.785 325.715 330.616 335.127 339.391 343.754 347.937

174.15 174.63 175.52 175.81 176.48 176.91 177.45

Series 13b

314.192 172.99 319.036 173.78 323.845 328.620 333.365 338.111 342.897 347.669

174.40 175.24 175.83 176.59 177.01 177.65

Second sample Series 14

226.360 143.94 231.593 236.626 241.639 246.660

146.19 148.59 150.92 153.58

251.650 156.98 256.632 160.83 261.556 164.88 265.858 167.93

Series 15f

270.865 150.07 275.816 151.42 280.878 152.84 285.977 154.46 291.096 155.76 296.213 301.200 306.025

157.29 159.07c

162.40c

Series 16 228.794 145.12 233.888 147.51 238.975 244.183

149.90 152.78

TABLE I (Continued)

r/K

235.043 245.043 254.999

Series 4

CP/(J· K-I

. mol-I)

147.59 152.85 160.11

Series 5f

272.368 150.39 276.993 151.68 281. 636 286.653 291. 727 296.870 302.052 307.164

Series 6

153.03 154.67 155.92 157.49 159.50c

168.01c

316.338 173.33 321. 417 326.650 331. 927 337.293 342.482

174.21 174.92 175.63 176.53 177.25

347.471 178.14

Series 7 290.682 156.07d

Series 8 313.198 172.98"

Series 9 240.442 151.03 250.188 260.043

156.34 164.04

C/(J' K- J

r/K . mol-I)

Series 16

249.450 254.622 259.774 264.912

155.37 159.15 163.20 167.25

Series 17 315.535 173.33 320.335 325.065 329.724 334.269 338.746 343.239 347.719

174.17 174.78 175.41 176.01 176.69 177.5U 177.11

Series 18 3.862 2.76 a

5.089 1. 56a

7.111 9.150

10.962

Series 19

1.61a

2.68 4.39

4.048 2.50a

5.950 1.46a

8.048 2.01 9.856

11. 791 13.805 15.882

3.27 5.33 8.11

11.41

aData points from the adiabatic cryostat with average tempera­tures belcw 8 K were not included in the calculation of thermo­dynamic functions.

hnata of this series were not used to calculate thermodynamic functions because of the build up of impurities from radiation decomposi tion in the sample.

cRun affected by premelting. dLlT= 30. 973 K. "LlT=4.181 K. fNo curvature correction applied.

HEAT CAPACITY RESULTS

The measured data for the heat capacity of technetium hexafluoride are given in Tables I and II, and in Fig. 1. The calculation of molal heat capacities was based on a molecular weight of 212.8968 for TcFa in accordance with a value of 98.9064 for the atomic weight of 99Tc listed in the tables of nuclidic masses compiled by Ever­ling et al. 11

Table I lists the data obtained from measurements with the adiabatic cryostat. After the measurements of series 13 the technetium hexafluoride was taken out of the calorimeter and repurified by sublimation and pump­ing. It was then combined with a small additional amount of TcFs previously used for density determina­tions and filled back into the calorimeter. The data points of series 14 through series 19 were obtained on

J. Chern. Phys., Vol. 68, No.3, 1 February 1978

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Osborne, Schreiner, Otto, Maim, and Selig: Heat capacity of technetium hexafluoride 1111

TABLE II. Molal heat capacity of technetium hexafluoride; data points for the region from 5. 8-23.7 K obtained by iso­peribolic calorimetry. (Molecular weight: 212.8968; 0°C=273.15 K) ..

CP/(J • K-t

"T/K CP/(J 'K-!

"T/K . mol-I) . mol-i)

Series 1 Series 3 8.681 2.361 16.278 12.05 9.478 2.955 17.869 14.64

10.344 3.761 19.542 17.35 11.626 5.200 21. 524 20.47 13.003 7.027 14.530 9.256

Series 2 5.809 1. 370 7.660 1.757 8.710 2.382 9.665 3.125

10.813 4.268 12.012 5.681 13.300 7.451 14.607 9.383 16.276 12.00

this second sample. The additional measurements were considered necessary because the effects of radiation decomposition led to spuriously high heat capacity val­ues in the region around 285 K. Repeated measurements indicated the gradual accumulation of impurities, while measurements taken shortly after loading of the repuri­fied sample into the calorimeter showed the heat capac­ity curve to be smooth in this region.

The measurements of series 18 and 19 were under­taken in order to confirm the observation that the slope of the heat capacity curve at the lowest temperatures appeared to approach zero and made it impossible to extrapolate the curve smoothly. The data of series 18 and 19 were the first evidence for the presence of a lambda-shaped anomaly near 3 K. It was because of this evidence that measurements were undertaken in the low-temperature cryostat which permitted a more accu­rate mapping of the heat capacity curve below 5 K.

The probable error of the heat capacities listed in Table I is O. 1 % for temperatures above 25 K. A t lower temperatures the error increases to 1% at 10K and to 10% at 3 K because of the uncertainty in the measure­ment of the temperature interval. In calculating the molal heat capacities of Table I, allowance was made for the presence of 32x 10-s mol of 4He in the calorim­eter as a heat exchange gas. Adjustments were also made for changes in the amounts of the Apiezon T grease which was used as thermal contacting medium between the heater-thermometer assembly and the cal­orimeter. The heat capacity of the empty sample con­tainer itself had been determined in a separate series of measurements. It was subtracted from the measured gross heat capacity before conversion to molal heat ca­pacity and it accounted for 10 to 40% of the gross heat capacity. The tabulated data also include a correction for curvature equal to - (d2C/ dT2 ) (a T)2 /24 deriv~d from polynomials fitted to the experimental data, and

a correction for vaporization of small amounts of the sample into the vapor space in the calorimeter during each run.

The experimental data obtained from measurements in the isoperibolic low-temperature apparatus are com­piled in Table II and in Fig. 1. The sample size was 0.18352 mol TcFs. This was approximately 25% less than the amounts used for the measurements in the adiabatic cryostat. It was still large enough, however, to cause considerable self-heating on account of the radioactive decay of 99Tc . In consequence, it was not possible to follow the regular routine of measurement by discrete heating runs with drift observations before and after the heating period at temperatures below 5 K. The procedure adopted for the measurements at the low­est temperatures including the region of the lambda­shaped anomaly consisted effectively in following the warm up of the sample by observing the temperature in suitably short time intervals of approximately 1 min. These observations were extended up to 12 K and over­lap the series of discrete runs which span the region from 5-25K. In the overlapping region the conventional heat capacity measurements provide the reference da­tum for the interpretation of the temperature drift ob­servations that extend to 2 K. Table II contains the heat capacity data from the conventional discrete method of measurement. Figure 1 is a graphical representation of the heat capacities obtained from the temperature drift measurements, which include the region of the lambda-shaped anomaly. The error of the entries in Table II is 0.3%. In converting the raw data to molal heat capacities the same corrections were applied as those described for the adiabatic measurements. The heat capacity of the empty calorimeter had been mea­sured in the same cryostat prior to loading the sample. Its contribution to the gross heat capacity varied from 10% to 16%. Since the measurements extended substan­tially below the normal boiling point of 4He, 3He was used as a heat exchange gas. The amount of 3He above the sample was 12. 8 x lO-s mol. The individual data points depicted in Fig. 1 are molal heat capacities that were calculated from the temperature drift observations according to the equation

30~--~----~--~----.---~

25

..!! 20 o E = 15 " .. 0.10 u

5

3

TcFS

8 ,

"--4 5 6 7

T, I<

FIG. 1. Experimental molal heat capacity of technetium hexa­fluoride between 2.23-7 K.

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1112 Osborne, Schreiner, Otto, Maim, and Selig: Heat capacity of technetium hexafluoride

C 1 Qrad+BN(Trlng-T)+2Enln_c -124715 TcF6 =;; t/60 MT' X n3He

(1 ) in which the symbols have the following meaning: CTCF 6 is the molal heat capacity of technetium hexafluoride, J. K-1 • mol-I, n is the sample size (mol), Qrad is the power of radioactive self-heating of the sample owing to the decay of 99Tc (W), BN is the constant of Newton's cooling law describing the heat interchange of the calo­rimeter with its surroundings (W /K), En and In is the voltage and current, respectively, of the germanium resistance thermometer, V and A, respectively. (The heat generated in the germanium resistance thermom­eter is very nearly twice the power calculated from the product of voltage and current. This is a consequence of the design of the thermometer in which the potential leads are located at points where they measure approxi­mately one-half of the total voltage drop across the thermometer.) i is the observed temperature drift (K/min), CMT is the heat capacity of the empty calorim­eter (J/K), n 3He is the number of moles of 3He in the calorimeter (mol), Trlng is the temperature of the so­called "ring", K. The ring is the mechanical structure between the submarine and the sample container to which all electrical leads and mechanical supports of the con­tainer are anchored. Its temperature can be controlled at an intermediate value between the sample tempera­ture and the temperature of the bath, and T is the tem­perature of the sample. The heat capacity of the empty calorimeter was calculated from a polynomial of degree 16 that had been least-squares fitted to measured data points. The cooling constant, BN , was evaluated from observations of the temperature drift of the empty calo­rimeter while the ring was controlled at a temperature very close to the one maintained during measurements on the sample. Under these conditions the heat inter­change characteristics of the apparatus can be assumed to be nearly identical to those prevailing during the mea­surements on the sample, except for slight differences of the ring temperature for which allowance was made. A quadratic interpolation function was used to represent the variation of BN with temperature. The probable er­ror of the points plotted in Fig. 1 is estimated to be 1%.

Mean energy of beta radiation of ~9Tc

The energy liberated in the radioactive decay of 99Tc is almost completely absorbed by the sample and the calorimeter and is converted into heat. Below 12 Kit is the most important term in Eq. 1. The evaluation of the power of radioactive heating, QradJ was made in the region between 5-12 K in which the observations of the temperature drift overlapped the series of discrete heat capacity runs. There were eight of the discrete data points in the overlap region and for each of them the radioactive heating was calculated with the equation:

(2)

In this equation the symbols have the same meaning as in Eq. (1) and CgreSS is the observed heat capacity of calorimeter' and sample in J/K. Since the radioactive heating does not vary with temperature the arithmetic mean of the eight independent numbers was accepted as

the best value for Qrad' The result of the calculation yielded the value of Qrad, avg = (1. 767 ± O. 016) x 10-4 W.

From this number the average energy of the beta ra­diation of 99Tc is readily calculated. The kinetic energy of the electrons emitted by the technetium i.s entirely converted into heat in the sample except for a small fraction that escapes from the calorimeter as x rays. These x rays originate as bremsstrahlung from the stoppage of the electrons in the sample and in the mate­rial of the calorimeter. It is estimated that the fraction of the total radioactive energy that leaves the calorim­eter in this fashion is less than 0.1%.12 Given the half­life of (2.14± O. 04)x 105 years of 99Tc (The value of 2.14 x 105 years for the half-life of 99Tc is the average of three values reported in the literature. 13-15), the sample size of O. 18352 mol, and the radioactive heating power of 1. 767 W, the calorimetric measurement shows the mean energy of the beta particles to be 97.2 ± 1. 2 keV. This number is Significantly higher than the value of 85 keY reported by Hogan et al. 16 It is in accord, how­ever, with a mean energy of 94± 2 keY which was ob­tained by integration of the beta ray spectrum to ener­gies as low as 19 keY and extrapolation to zero energy Y

Evaluation of additional thermodynamic data

Though the heat capacity provides the essential basis for the establishment of the thermodynamic functions, additional information is needed before the entropy and the Gibbs energy can be calculated as functions of the temperature. In the case of technetium hexafluoride, the following quantities had to be obtained from calori­metrIC and othe:r;- independent physicochemical measure­ments or were derived from existing data: The tem­peratures for the solid-solid and for the solid-liquid tranSitions, the enthalpies of transition and of fUSion, the entropy of vaporization, and the densities of TcF6 in the solid, the liquid, and the gaseous states.

Solid-solid transition

A feature that is common to all known hexafluorides of the 4d and 5d transition metal series is the existence of two solid modifications. X-ray diffraction studies have shown the high-temperature modification (solid 1) to have a body-centered cubic crystal lattice and the low-temperature modification (solid II) to be most likely orthorhombic in structure. 17 For technetium hexafluo­ride the transition from the orthorhombic to the bee modification occurs isothermally at 268.314 K. This transition temperature was obtained in the calorimetric apparatus and is the average of three values measured after conversion of 26.2%, 48.5%, and 71. 4% of the sample to the high-temperature form. The spread of the observed temperatures was ± O. 002 K. A correc­tion of - 0.002 K was applied to the experimentally ob­served temperatures to obtain the transition tempera­ture of pure TcF6 in the absence of helium exchange gas. In the standard state, i. e., under a total pressure of 1 atm, the transition temperature is higher by 0.019 K, viz., 268.335 K.

The enthalpy of the solid-solid transition was deter­mined in three independent measurements in the calo­rimeter. The sample was heated from a temperature

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Osborne, Schreiner, Otto, Maim, and Selig: Heat capacity of technetium hexafluoride 1113

TABLE III. Enthalpy of transition of technetium hexafluoride.

Total {2CdT

Heat heata

Tl leak

T/K T2/K J. mol-t J 0 mol-! J'mol-!

259.9594 269.8247 10762.9 2734.1 +1.4

264.9324 271.2980 9759.7 1740.0 -3.2

267.7956 271. 8404 9099.7 1076.5 -4.1

Average value of the entl1alpy of transition at 268.314 K:

Standard enthalpy of transition at 268.335 K and 1 atm:

Vaporization correction J'mol-!

t1.4

+1.4

d.4

/lil b t

J o mort

8030.2

8021.1

8024.6

8025.3±5.0 J • mol-l

8024.9±5.0J 0 mar!

aIn calculating the heat supplied per mole of the sample allowance was made for the change of the number of moles in the calorimeter with time owing 10 radiation decomposition.

bA correction of f 0.1 J. mol-1 is included in /lilt to obtain the enthalpy of transition in the absence of he­lium in the calorimeter.

slightly below the transition to a temperature slightly above it. The temperature increase was corrected for by evaluating the integral fH edt, where C is the heat capacity of calorimeter and sample, and by subtracting this quantity from the total heat supplied during the measurement. Corrections were also applied for con­densation of a small amount of sample because of the volume increase during the tranSition, and for the ef­fect of the presence of the helium exchange gas in the calorimeter. The results of the three enthalpy mea­surements are summarized in Table III.

Melting point and enthalpy of fusion

The melting point temperature of technetium hexa­fluoride was determined in the calorimeter by observ­ing the equilibrium temperatures of the sample with progressively larger fractions in the molten state. Be­cause of radiation decomposition and the attendant grad­ual increase of impurity in the sample, a slow tempera­ture drift was observed even after long waiting periods. In order to evaluate the melting point temperature for the pure compound, the experimental temperatures were first corrected to a constant amount of impurity by re-

T ABLE IV. Melting temperature of technetium hexafluoride.

Temperature Time Fraction Experimental corrected hours melted temperature, K to 0 hours, Ka

- 90.46 0.0646 310.649 310.121 -75.16 0.1455 310.792 310.603 -42.36 0.3645 310.933 310.889 -25.48 0.4494 310.955 310.933

0 0.6158 310.984 310.984

Triple point temperature for fusion of pure TcF 6 : 311.12±0.05 K

~he corrected temperatures were obtained under the assump­tion that the rate of radiation decomposition is 0.0026% per hour and that the products of the decomposition are liquid­soluble, solid-insoluble TcF5, and F 2• The corrected tem­peratures then refer to a sample of the same constant impur­ity content as that at time zero. The corrected temperatures are accurately represented by the linear equation (T corr ~ 311.122 - O. 0849/(fraction melted) the constant term of which is the triple point temperature of pure TcF6• The effect of helium pressure in the calorimeter is less than 0.005 K and has been neglected in the calculation.

fer ring them to the time of the last temperature mea­surement. This was done under the assumption that the sample decomposed at the rate of O. 0026% per hour and that the products of the radiation decomposition were liquid-soluble, solid-insoluble TCFs, and elemental fluorine. Table IV summarizes the experimental data.

The corrected temperatures are linearly dependent on the reciprocal of the fraction melted and are well represented by the equation

T = 311 122 _ 0.0849 corr • fraction melted (3)

It follows that T = 311. 122 K is the melting temperature of pure technetium hexafluoride under the conditions of the calorimetric experiment, i. e., in the presence of helium gas at a pressure of 162.43 mm Hg. The tem­perature of the melting point under a total pressure of 1 atm is 311. 136 K. The probable error of these tem­peratures is estimated to be ± O. 050 K and arises chiefly from the uncertainty of the extrapolation of Eq. (3).

The variation of the melting temperature with various fractions of the sample in the liquid state is caused by the presence of impurities that are soluble in the liquid but insoluble in the solid. Presumably the TcFs formed by radiation decomposition constitutes the bulk of the impurity. Its concentration as calculated from the slope of Eq. (3) was 0.0486 mol % at the end of the melting point measul'ements, i. e., 14 days after loading of the calorimeter. An independent estimate of the TcFs formed by radiation decomposition was obtained at the time when the technetium hexafluoride was transferred out of the calorimeter. This occurred 37.9 days after the first loading and at that time the sample container showed a weight gain of 0.0450 g. On the assumption that the weight gain reflected the amount of TcFs, the rate of radiation decomposition was calculated to be 0.00260% of the sample per day. This number leads to an impurity concentration of 0.036 mol % at the time of the melting point measurements, in good agreement with the concentration derived from Eq. (3).

The enthalpy of fusion of TcF6 was determined in three independent calorimetric runs. A summary of the ex­perimental data and of the results of the calculation of the enthalpy of fusion is presented in Table V. The

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1114 Osborne, Schreiner, Otto, Maim, and Selig: Heat capacity of technetium hexafluoride

TABLE V. Enthalpy of fusion of technetium hexafluoride.

Number of days elapsed after Energy Heat leak loading T/K T2/K J J

9.06 304.6485 313.8733 1695.75 - 1.74

16.08 304.2694 314.0111 1730.98 -5.01

24.10 304.3515 313.3378 1678.22 -4.98

{2CdT Tl Premelting J J

613.01 0.92

647.19 2.24

595.62 3.57

Sample size molesa

0.234609

0.234566

0.234517

Molal enthalpy of fusion b

J/mol

4620.80

4617.81

4619.49

Average of molal enthalpy of fusion of the sample at 311.120 K, AH m: 4619.37 ± 1. 60°

4618.99 ± 1. 60 d Enthalpy of fusion, at 311.107 K, A Hm:

Standard enthalpy of fusion at 311.136 K, and 1 atm pressure, AH~: 4618.86 ± 1. 60

"To allow for radiation decomposition the amount of technetium hexafluoride present at the time of the measure­ment was calculated from the equation n ~ O. 234664 (1-2.60 x 10-5t), where n is the sample size in moles at t days days after loading the calorimeter.

":InclUdes a correction for vaporization of + 8.62 J/ mol and an adjustment for expansion of the solid with rising temperature, fit"' VdP~ +0.59.

°Enthalpy of fusion of the sample with 408.8 mm Hg of He in the calorimeter. dEnthalpy of fusion of the pure sample without He in the calorimeter.

starting temperature for each of the three runs was sev­eral degrees below the melting point temperature to minimize the effects of premelting. The heat of fusion of the sample was obtained from the gross energy sup­plied during each run after correction for the heat leak of the calorimeter to the surroundings, after subtraction of fH Cdt, the amount of heat required to raise the temperature of the calorimeter and sample from Ti to T2 , and after allowing for premelting at the starting temperature. The premelting correction was based on the observed excess of the experimental heat capacity over the constant slope extrapolation of the heat capacity curve from temperatures well below the melting point. The sample size at the time of the measurement was calculated from the equation

n=0.234664 (1-2.6xlO-5t) mol (4)

to allow for the cha.nges caused by radiation decomposi­tion (t = elapsed time in days). The values for the molal enthalpy of fusion listed in Table V also include a va­porization correction arising from condensation of part of the sample because of a reduction of the volume of the vapor phase during the melting process, and a term equal to n~ VdP representing the enthalpy change of the solid hexafluoride. The result obtained for the standard enthalpy of fusion of pure technetium hexafluoride under a total pressure of 1 atm and at 311.14 K is /lH~ =4618. 86± 1.60 J. mol-i.

Densities

Solid TcF6 , high-temperature modification (solid IJ:

The density of the body-centered-cubic high-tempera­ture modification of technetium hexafluoride was re­ported to be 3.02 g/cm3 at 283.2 K by Siegel and Nor­throp.17 For the purpose of calculating vaporization cor­rections and other corrective terms for the thermody­namic functions, the x-ray density was combined with

an estimated value of the temperature coefficient to give the following linear equation for the denSity:

p = (0.01703 - O. 00001 T) mol· cm·3 • (5)

Solid TcF6, low-temperature modification (solid II):

By assuming the low-temperature modification of TcFs to be isostructural with orthorhombic UFs• Siegel and Northrop calculated a density of 3. 38± O. 03 g/cm3

for TcFs at 254.2 K from x-ray crystallographic data. 17

In addition, two independent measurements of the den­sity were made by helium displacement on the calori­metric sample. Accordingly. the denSity of TcFs was found to be 3.633 g/cm3 at 77.18 K and 3.478 g/cm3 at 194.27 K. The three measured values are adequately represented by the linear relationship:

p = (0.017545 - O. 00000622 T) mol· cm-3 , (6)

which was used in the thermodynamic calculations.

Liquid TcF6:

The density of liquid TcFs was determined pycnomet­ric ally on samples of approximately 3.5 g. The pycnom­eter itself was a small bulb made of Pyrex glass with a capillary extension. It was attached to a brass bellows valve by means of a copper to Pyrex graded seal (Housekeeper seal), The volume had been calibrated with water for varying heights of the liquid meniscus in the capillary neck. Prior to loading samples of TcFs the pycnometer was thoroughly dried and outgassed by heating and evacuating. With a known amount of TcFs in the pyconometer measurements of the meniscus height were made in the temperature range 311. 5-352.7 K. The measured heights were converted to volumes in ac­cordance with the earlier calibration, and densities were calculated after an adjustment had been made for the small amount of the hexafluoride in the vapor phase. A least-squares fit to the experimental data resulted in the following equation for the density of liquid TcFs be-

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Osborne, Schreiner, Otto, Maim, and Selig: Heat capacity of technetium hexafluoride 1115

tween 311-352 K:

p = (0.017599 - O. 0000169 T) mol· cm-3

liapor density

(7)

For the purpose of evaluating the entropy of techne­tium hexafluoride vapor it was important to determine an accurate value of the vapor density. A significant fraction of the vapor entropy is contributed by the en­tropy of vaporization which was calculated from the slope of the vapor pressure curve since no direct ca­lorimetric value for the heat of vaporization was avail­able. The calculation makes use of Eq. (10) and re­quires accurate knowledge of the molal volume of the vapor.

The vapor density was determined at 298. 15 K by measuring the amount of technetium hexafluoride con­tained in a nickel can of known volume at a pressure just below the vapor pressure. The can was made of heavy nickel pipe with bell-shaped top and bottom plates so that the volume change upon evacuation was negligible. Its volume was calibrated with water and was 2021. 0 cm3

• After passivation of the interior surface with some technetium hexafluoride two determinations of the vapor density were made. Pressures were measured with a mercury manometer and a fused silica spoon gauge serving as pressure transducer. The tempera­ture was ma.intained by keeping the calibrated can in a thermostated bath the temperature of which was mea­sured with a platinum resistance thermometer. When temperature equilibrium had been reached, the techne­tium hexafluoride was transferred from the 2 1 can to a weighing can and weighed. The results of the vapor den­sity measurements were used to calculate the value of the second virial coefficient B in the equation of state

PV=RT+BP . (8)

The average number obtained for B was - 895 cm3 /mol. Its temperature dependence was assumed to follow the inverse square relationship of the leading term in the Berthelot equation of state. Accordingly, the equation

PV=RT-79.6 r-2 p (9)

was adopted as the equation of state for technetium hexa­fluoride vapor. (In SI units: B( T) = - 79. 6 T-2m 3K-2

mol-I).

Entropy of vaporization

As was mentioned before, no calorimetrically deter­mined value for the enthalpy of vaporization of TcF6 is available. This number is needed, however, for the calculation of the entropy of the vapor, of which the en­tropy of vaporization accounts for approximately 25%. An indirect way of arriving at the entropy of vaporiza­tion, ~Sva., is afforded by the thermodynamic relation­ship

(10)

The slope of the vapor pressure curve, dPldT, was calculated from the vapor pressures published by selig and MaIm, 18 who report the following equation repre-

senting the experimental data in the temperature range between 310.11-324.83 K:

2404.9 loglOPmmHg = ---T-- 5. 8036 10glOT+ 24.8087 (11)

Equation (11) was obtained by least-squares fitting and will represent the slope of the vapor pressure curve most reliably near the middle of the temperature range for which it is valid. For this reason the temperature chosen for the evaluation of ~S,"" is T = 320 K. With dPldT derived from Eq. (11), and V,,,,, and Vl\q calcu­lated from Eqs. (9) and (7), respectively, the result obtained for the entropy of vaporization is ~Sv"" = 93.285 x J . K-1 • mol-I. The probable error of this number is estimated to be O. 5%. The corresponding value for the enthalpy of vaporization at 320 K is ~Hv"" = 29.851 ± 0.150 kJ· mol-I.

Thermodynamic functions

The calorimetric data presented in the previous sec­tions form the basis for the computation of the standard entropy, So, the enthalpy increment, (HO - H~), and the Gibbs energy function, (Go - H~)/ T. These quantities were evaluated by integration of C; I T and C p as func­tions of the temperature, and by making use of the equa­tion

(12)

For integration the heat capacity curve of the low-tem­perature solid was represented by two polynomials of degree 10 and 16, respectively, with a changeover point at 25 K. The heat capacity of the high temperature solid and of the liquid was taken to vary linearly with the tem­perature. Numerical values of the thermodynamic func­tions of technetium hexafluoride for selected tempera­tures are listed in Table VI. The tabulated values in­clude the entropy and enthalpy changes accompanying the solid-solid and the solid-liquid transitions. In order to obtain the entries of So and (H 0 - H ~) at 5 K the heat capacity points shown in Fig. 1 were integrated numerically between 2.23-5 K, and it was assumed that below 2.23 K the heat capacity follows the Debye T3 law. The latter assumption may not be fully justified in view of the proximity of the starting temperature to the lambda-shaped peak. Most likely the extrapolation in accordance with the T3 proportionality leads to high values for SO and (H 0 - H ~) at 2. 23 K as explained in the last section.

It is estimated that the probable error of the tabulated functions is 0.1% at temperatures above 25 K, and rises to 1% below that temperature.

Standard entropy of the vapor

An independent value for the standard entropy of the vapor is among the most important numbers resulting from the evaluation of the thermal data. Comparison with the same quantity calculated from the molecular characteristics of TcFs shows no gross discrepancy but indicates that further refinement of the data is neces­sary in order to achieve overall consistency within the limits of experimental error.

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1116 Osborne, Schreiner, Otto, Maim, and Selig: Heat capacity of technetium hexafluoride

T ABLE VI. Thermodynamic functions of solid and liquid tech­netium hexafluoride in the standard state.

L K

10 15 ~U

30 35 40 45 50 60 70 80 ~o

100

110 120

130

140 150 160

170 180 l~)O

~(I()

~1(l

2~U

~:10

240 25(J

~60

268.335

268.335 ~70

273.15 280 290 298.15 300 310 311.J36

311.136 320

330 340

350

.J' K- t • mol- t

1. 598 3.410 9.985

lB. 117 25.501 31. 802 37.024 41. 539 45.675 49.625 57.2.61 64.626

71.656 78.253 84.381

90.110 95.551

100.76

105.73

11U.45 114.97 119.40 12:),77

128. on 132. :33 1:16.65 H1.()G

145.3;1 13u, :2J

1.35. tln !G3,38 170,15

14!L27 149.75 150.65 152.62 155.5U 157.8·1 158.38 161. 25 161.58

172.65

173.97 175.45 176.94

178.43

SO

J' !("t . mol-t

Low temperature solid

5.683a

6.960 9.477

13,463 1B.316 23.540 28.847 34.091 39.225 44. ~43 53.970 G3. ~s53 72.446 81.2n 89.838 98.151

JUG. ~3

114. OS

121.7:1

129.19 136,·W

143.57 150.52

157. :32 1(54.00

170.56 177.02 183, :39 1119.oS

I D5. D2

20L.IH 207.44

High temperature solirl

237.35 2:1H.27 240.01 243,77 249.18 253.52 234.50

25D.74 2GO. :~:~

27fi.17 280.04

285.41 290.67

~95. 8:~

15.51' 25.25 57.40

127.65 237,09 380.85 553.29 749.92 968.06

1206.36 1741.02 ~350, 7()

3032.44 3782,4

4595.9 0<:l6H.7 G:~97. 2 7378,9

8411. " U49~.7

U)62l1.0

1179~ . 130uH. 142G7. IG:)()9.

16~1l·L

1 ~:i():1.

IH7:J1j.

~l~l·L

22744,

~433H.

~57~!).

33754, 34UU2. 34475, 33514. 37055. :lH3:H. 38G24.

'10222. -10405.

·1::)(12·1. 4G5Gl.

-l630H. :;UU7U.

51846.

-(CO-Ho)!T J . K-t . mol- t

2.581 4.435 5.650 7.080 8,832

10.846 13.038 15.343 17.713 20.116 24.953

~9.77'2

34. ::'41 39.2'l5 43. H78 4H, ,136

5'2. n17 57.321

G 1. 650

Li5.905

70. UR9

7-l,203 7S. '250 ,y~. 23:)

KG.153

90.0l!)

93.Sn 97.3Ha

lUI. :.:!9 10 .. L 93

tOH.37 Ill.3£)

111. 5G 112. :14 113.80 110.93 121. 40 124.93 125.75 129.99 1:JO.4G

1:10.4(; 134. ,,4

139,03

14:L 41

H7.6~

aThe entropy and enthalpy increment at T~ 5 K were obtained by numerical integration of the heat capacities shown in Fig. 1 between 2.23-5.00 K, and by extrapolation from 2.23-0 K with the assumption that the heat capacity is proportional to T 3.

The overwhelming term by which the entropy of the vapor differs from that of the liquid is the entropy of vaporization. In the thermal calculation it contributes 25% to the total vapor entropy and in the absence of a calorimetric value for the enthalpy of vaporization it had to be evaluated from the slope of the vapor pres­sure curve. The calculation is described in a previous section. There it was pointed out that the temperature chosen for the evaluation of the slope was 320 K near the center of the range over which the vapor pressure of the liquid had been measured. It is about the center of the range that the least-squares fitted vapor pressure equa­tion is expected to reflect the slope most accurately.

In addition to the entropy of vaporization several other minor terms enter into the calculation of the standard entropy of the vapor. First, the standard entropy of the liquid has to be corrected to obtain the entropy of liquid TcFe at the vapor pressure by adding the integral ff:J47e(as/ap)TdP=fr:6476(av/aT)pdP. There follows the addition of the entropy of vaporization giving the entropy of real TcFs vapor at the vapor pressure. To this is added a correction for nonideality of the vaporcalcu­lated as fg· 7476(dB/dT)dP, and finally allowance is made for the entropy change of the ideal vapor upon compres­sion to one atmosphere. The complete calculation of the standard entropy of TcFe vapor is summarized in Table VII. The number obtained from the thermodynam­ic calculation is S C (320) = 371. 278 ± 0.75 J . K-1 • mol-!.

For the statistical calculation of the standard entropy it is necessary that a complete set of the appropriate molecular constants be available. The information has to include the frequencies for the molecular modes of vibration, the moment of inertia or the bond distances and the symmetry of the molecule, and the electronic angular momentum of the ground state. The molecular spectra of technetium hexafluoride show the 'molecule to be of regular octahedral symmetry, the corresponding group symbol being 0,. It follows that the symmetry number for the calculation of the rotational partition function is 24. In this case one bond distance is suffi­cient for the calculation of the product of the principal moments of inertia. This distance was taken to be 1. 84x 10-10 m, i. e., the same bond distance as the one of molybdenum hexafluoride which was determined by electron diffraction measurements. 19

The symmetrical configuration of the molecule leads to six different normal modes of vibration the frequen­cies of which were assigned on the basis of infrared and Raman spectroscopic observations. 20,21 The six fre­quencies for TcFe are as follows with their respective degeneracies given in parentheses: v! = 712. 9 cm-! (1), V2 = 639 cm-! (2), V3 = 748 cm-1 (3), v4 = 265 cm-1 (3), Vs = 297 cm-1 (3), and VB = 145 cm-1 (3). This assignment is that given by Claassen, et al. 21 It is based on the direct observation of the fundamental VI in the Raman spectrum and of the fundamentals V3 and v4 in the infra­red spectrum of the vapor. The frequencies for V2 and Vs follow the assignment of Weinstock and Goodman. 22

The inactive frequency ve was inferred from an analYSis of the combination bands and overtones of the Raman spectrum. 22

The electronic degeneracy of the ground state of TcFe is 4 in accordance with the effective angular momentum J' = 3/2. 22 The result of the entropy calculation with the molecular data listed above is a value of 367.53 J. K-1

. mol-1 for So at T=320 K. The uncertainty of this num· ber estimated from the uncertainty of the measured fre­quencies is ± 0.5 J. K-1 • mol-I. It is obvious that the calculated entropy is 1% lower than the calorimetric en­tropy and that the disagreement is outside the estimated limits of error. The statistical entropy can be made to agree with the calorimetric one within the estimated un­certainties of both numbers by assuming a frequency of 131 cm-1 for the lowest and inactive vibrational mode,

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Osborne, Schreiner, Otto, Maim, and Selig: Heat capacity of technetium hexafluoride 1117

TABLE VII. Standard entropy of technetium hexafluoride va­por at 320 K from thermal data.

S" of liquid Tc F 6' from Table VI 280. 040 ± O. 28 J' K-I • mol-I

Correction to vapor pressure, (aV/ aP)/>(P' - p v• p ) 0.003 J' K-I . mor l

Entropy of vaporization, (dP/dTiv•p • • (VV'll> - VueJ 93.285 ± O. 47 J' K-I • mol-I

Correction for non ide ality , (aE/aTI' p v• P

Compression to 1 atm, R'lnP /r v.P.

SO of TcFs vapor at 1'~320 K

0.368 J K-!' mol-!

- 2. 41 R .T • K-! • mol-!

371. 278 ± O. 75 J' K-1 • mol-!

VS' Table VIII lists the thermodynamic functions of gaseous TcFs with this low value for Vs and the remain­ing molecular data as given before.

Magnetic transition at 3.12 K

The lambda-shaped peak in the heat capacity curve near 3 K is ascribed to a magnetic ordering transition in TcFs' Technetium has seven valence electrons in a 4d 5 5s2 configuration. In TcFs six of the electrons par­ticipate in bond formation with fluorine atoms. This leaves the seventh electron with an unpaired spin. As a consequence technetium hexafluoride is paramagnetic.

Measurements of the magnetic susceptibility show a linear variation with 1/ r between 295-14K in accordance with the equation23

XM ~ (0.2541 r + 0.000439) mol-l .

The magnetic moment calculated from Eq. (13) is 0.45 /lB'

(13)

An attempt was made to extend the measurements to lower temperatures and a single data point was obtained at 4.2 K. At this low temperature the susceptibility was found to be 120% larger than the number calculated from Eq. (13). Even though the experimental error was com­paratively large, Selig et al. 23 felt the result to be sig­nificant enough to consider a ferromagnetic transition as a cause for the enhancement of the susceptibility.

The dlta plotted in Fig. 1 show the existence of a transition very clearly. The heat capacity increases from .1. value of 4.07 J. K-l . mol-l at 2.23 K, the lowest temperature attained during the measurement, to a maximum Observed value of 27.0 J. K"l • mol-l at 3.12 K. Thereafter it drops sharply and reaches a shallow minimum of 1. 34 J. K"l • mol-l near 5.8 K.

When viewed together with the results of the suscep­tibility measurements the heat capacity data suggest that technetium hexafluoride becomes ferromagnetic below 3.12 K. This behavior has to be verified, how­ever, by magnetic measurements.

As described in an earlier section, the entropy, So, and the enthalpy increment, (H ° - H ~), between 2. 23-10 K were computed by numerical integration of the ex­perimental data points. Below 2.23 K the heat capacity curve had to be extrapolated. The extrapolation intro-

duces an uncertainty in the thermodynamic functions, in particular in the standard entropy, which is difficult to estimate. For the calculation of the entries in Table VI it was assumed that a cubic temperature function adequately describes the heat capacity at low tempera­tures. In the limit near absolute zero proportionality with r 3 is expected to be the correct representation of the lattice heat capac ity.

In the case of the technetium hexafluoride, however, the heat capacity at 2.23 K appears to incorporate a predominant magnetic contribution. Comparison of the heat capacities of molybdenum hexafluoride5 and tech­netium hexafluoride in the region 230-250 K indicates that the heat capacity of molybdenum hexafluoride can be taken as a reasonable estimate of the lattice heat capacity of TcFs' At 2.23 K the heat capacity of MoFs has the value C = 0.027 J . K- l . mol,l, and is less than 1% of the heat capacity value observed for TcFs'

We may conclude that at 2.23 K the magnetic contribu­tion outweighs the lattice heat capacity of TcFs substan­tially. The assumption of proportionality with r3 in this temperature region can therefore not be supported on theoretical grounds.

It is possible to fit the branch of the heat capacity curve between 2.23-3 K by an expression of the type

(14)

With a value of 4 for the exponent b very close agree­ment between experimental and calculated heat capaci­ties can be achieved. If it is assumed that the heat ca­pacity curve is proportional to r4 below 2.23 K, too, the previously calculated values for the entropy and for the enthalpy increment are seen to be too large. The standard entropy, So, would have to be reduced by 0.339 J . K 1 • mol-l and the enthalpy increment, (HO -H~) by 0.454 J/mol. However, the assumption of a r4 temperature dependence is entirely empirical and based solely on the behavior of the curve above 2.23 K. Its validity for extrapolation is clearly limited because ultimately the Debye r3 law must be followed

TABLE VIII. Thermodynamic functions calculated from mo­lecular data for TcF s vapor in the ideal state at 1 atm pres­sure. a

L Cp S H'-He - (Go -HIJ)!..T K J. K-1 • 010l-1 J ·K-1 • mol-1 (.]/moli J. K'!· mol'!

50 42.883 222.01 1780.6 186.40 100 67.101 259.23 4535.3 213.87 150 86.087 290.23 8390.1 234.29 200 100.58 317.06 13071. 251.70 250 112.13 340.79 18400. 267.19 273.15 116.60 350.92 21048. 273.86 298.15 120.88 361. 32 24018. 280.76 300 121.17 362.07 24242. 281. 26 320 124.19 369.99 26696. 286.56 400 133.32 :l98.77 37U30. 306. "0 500 140.91 429.43 50782 327.87 600 145.52 455.56 65120. :l47.02 700 148.53 478.2:) 79833. 364.19 800 150.59 498.21 94795. 379.71 900 152.06 516.04 109930. 393.89

1000 153.13 532.11 125190. 406.92

"calculated with the set of molecular constants given in the text except for the frequency of V6 which was taken to be 131 cm-t to obtain agreement of the thermal and the statistical entropy values at T ~ 320 K within the limits of error.

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1118 Osborne, Schreiner, Otto, Maim, and Selig: Heat capacity of technetium hexafluoride

as 0 K is approached.

The lack of knowledge with regard to the true shape of the heat capacity curve at the lowest temperature intro­duces an uncertainty into the values for the entropy and for the Gibbs energy function that is of the order of the experimental error itself. In order to improve this situation additional measurements in the low-tempera­ture range are necessary.

It is of interest to estimate the excess or magnetic entropy associated with this transition. We assume that 10 K is a sufficiently high temperature for the heat ca­pacity no longer to be affected by the transition, and furthermore we assume that an estimate for the entropy in the absence of the magnetic transition can be obtained by taking the heat capacity to vary as T3 between 0-10 K. The estimate for the lattice entropy obtained in this fashion leads to a value of Slat (10) =1.137 J. K'l . mol-I. By subtracting this number from the tabulated entropy at 10 K we arrive at an estimate for the magnetic en­tropy: Smog = S 0 (10) - Slat (10) = 5. 823 J . K'I . mol'l. This result is in very satisfactory agreement with the expected value of R In2 = 5, 763 J. K'I . mol-I.

The electronic configuration which is responsible for the magnetic transition is not a unique feature of tech­netium hexafluoride. A similar configuration exists in the closely related sister compound rhenium hexafluo­ride. Rhenium hexafluoride, too, is characterized by the presence of a spin-unpaired electron that causes the compound to be paramagnetic. 23 Between 4.2-300 K the molar susceptibility follows the Curie law expres­sion

(15)

Because of stronger spin-orbit coupling the magnetic moment of ReF6 calculated from the coefficient of Eq. (15) is significantly smaller than that of TcF6 , viz., 0.25/-LB' This, in turn, leads to a weaker magnetic interaction between molecules and a lower expected tem­perature for the cooperative magnetic ordering transi­tion. Measurements of the heat capacity of ReF6 be­tween 1-20 K substantiate this expectation. (The heat capacity measurements on ReF6 were carried out on a 16.844 g sample in the isoperibol cryostat). A peak similar to the lambda-shaped anomaly of TcF6 is ob­served in the heat capacity curve of ReFs, The tempera­ture at which the maximum heat capacity is observed is 1.3 K, The preliminary character of the data for rhe­nium hexafluoride does not yet permit an evaluation of the magnetic entropy, nor is the temperature of the maximum known to better than ± 0.05 K. The existence of the peak, however, has been demonstrated, but here

as in the case of the technetium compound further mea­surements are required in order to establish the pre­cise shape of the heat capacity curve at the very lowest temperatures.

ACKNOWLEDGMENT

The authors gratefully acknowledge Mr. Joseph Tague's assistance with some of the calorimetric mea­surements.

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