1OB4
B. 11. ABRAH.IM,D. W. OSBORNE, H. E. FLOTOW A N D R . R. ~ I A R C U S
from solution, because in concentrated H 3 0 4 the nitrate ion is converted to NOz+. Acknowledgments.-The authors wish to take this opportunity to acknowledge the support of this work by the U. S. Naval Ordnance Test Station,
VOl. F2
China Lake, California, through a research contract with the Research Foundation of the Ohio State University and to thank these organizations for permission to Publish this research. COLUMBUS
io,
OHIO
[CONTRIBUTION FROM ARCONXE NATIOXAL LABORATORP]
The Heat Capacity and Thermodynamic Functions of ,&Uranium Deuteride from 5 to 350 OK.
l l 2
BY BERNARD hf. ABRAHAM,DARRELL iv. OSBORNE,HOWARD E. FLOTOW AND ROBERT€3.
AfARCUS
RECEIVED JULY 20, 1959 The heat capacity of UD, has been measured in an adiabatic calorimeter from 5 to 35OOK. The enthalpy and entropy at 298.15"K. calculated from the data are 2577 f 5 cal. mole-' and 17.20 0.03 cal. deg.-l mole-', respectively. The entropy and free energy of formation for UDJ a t 298.15'K. as well as the heat of formation a t the absolute zero were calculated from these data and the previously reported heat of formation and have the values -46.76 cal. deg.-' mole-', - 17,080 cal. mole-' and -29,000 cal. mole-'. It was found that the calculated and observed dissociation pressures are not in agreement. A similar discrepancy was found for UHJ and i t was suggested that the source might be a particle size effect in the dissociation pressure measurements or the heat of transition of the a-form of UH3 to the 19-form. These heat capacity data were combined with the reported values for UH, t o calculate the hydrogen and deuterium vibration frequencies in the compounds. An anomaly in the heat capacity was observed which arises from the transition from the ferromagnetic state to the paramagnetic state. The maximum in the heat capacity is 11.72 cal. deg.? mole-' and occurs at 167.6 f 0.5OK. It was estimated that 1.19 cal. deg.-l mole-' is the entropy change in the transition which is less than the expected Measurements of the magnetivalue, R In 2 = 1.38 cal. deg.-l mole-', from the Heisenberg theory of ferromagnetism. zation of UD3 do not appear t o be in accord with the thermal measurements.
+
Introduction Measurements of the heat capacity of ,B-UH3from 3 to 350°K. previously have been reported from this L a b ~ r a t o r y . ~In order to observe the effect of isotopic substitution on the thermodynamic properties as well as on the ferromagnetic transition similar measurements have been made on ,B-UD3. We report here the heat capacity measurements on P-UD,, the thermodynamic functions derived from the measurements and an analysis of the data from which the vibrational frequencies of H and D in the hydride molecule were calculated and also some conclusions regarding recently reported magnetic measurements on P-CD3. The structure of P-UD3 is identical to that of ,3-UH3. The unit cell has cubic symmetry and contains eight uranium atoms arranged as in or-tungsten, ix.,2U1 a t (O,O,O) and ('/2,'/2,'/2) and 6U11 a t =t (1/4,0,1/2).4 The lattice constant a0 is equal to 0.G2 kX units; all of the U-D distances are equal to 2.32 A. as in P-UH3. The density of &UD3 is equal to 11.11 g./cc. which is to be compared to 10.92 g./ cc. for the density of /3-UH3. The deuteride has been shown to be ferromagnetic but with a saturation moment of 0.98 Bohr magnetons per atom a t 1.3'K. compared with 1.18 Bohr magnetons for UH3.5 Although the data are not presented by Henry, the statement was made : "The absolute moment of uranium deuteride seems to be less, for all equal conditions of temperature and magnetic field, than that of the hydride." (1) Based on work performed under the auspices of t h e U. S. Atomic Energy Commission. (2) Presented in part a t the 133rd meeting of t h e Am. Chem. SOC, San Francisco, -4pril 13-18, 1958. (3) H. E . Fiotorv, H. R. Lohr, B. M. Abraham and D. W. Oshorne, m r I s JOURNAL, S I , 3529 ( i g j g ) . ( 4 ) R. E. Rundle, ibid., 73, 4172 (1951). ( 2 ) W.Henry, P h y s . Rea.,109, 1976 (1958).
Karchevskii, ct have reported the Curie temperature of UH3 as 152.O"K. and of UD3 as 17S.4OK., the former in close agreement with the value lSl°K. given by Lin and Kaufmann.* Karchevsk? has in addition determined the magneto-caloric effect for both compounds and finds that the effect is 1.G times greater for UH3 a t the Curie temperature than for UD3. One might expect therefore to observe some difference between the heat capacity of ,B-UH3and ,&ED3a t low temperatures a s a result of the smaller magnetic moment and smaller magneto-caloric effect for CD3. Experimental The ED3 sample was prepared from high purity uranium in the form of rods 3 mm. in diameter, made by the Metallurgy Division of this Laboratory .g Spectroscopic analysis of the uranium showed the presence of these various elements in p.p.m.: Al, 5; Cr, 1; Cu, 1; Fe, 2; Mg, 0.5; and Si, 10; all other elements were below the limits of spectroscopic detection. Chemical analysis showed 24 p.p.m. of carbon and less than 10 p.p.m. of nitrogen. After removal of a small amount of surface oxide with nitric acid, the uranium metal was placed in a reaction vessel attached to a vacuum line. It was converted to UD3 by reaction a t 190 to 200" with deuterium gas liberated from the thermal decomposition of another sample of UDJ. Under these conditions the 6-phase is formed. The operation of transferring the sample from the reaction vessel to the calorimeter and soldering i t shut was performed in a dry-box under an atmosphere of purified helium. Two 1-gram portions were taken for analysis at the time the calorimeter was loaded. These were assayed by thermally decomposing the samples on a vacuum line and volumetrically determining the total gas evolved. The amount of gas collected corresponded to 99.65y0 of the theoretical for UD3. The isotopic composition of the gas, determined mass spec(6) A. I. Karchevskii, E. \'. Artyushkov and L. I. Rikoin, Zhur. E k s p f l . i Teovet. F i z . , 36, 630 (1959). (7) A . I. Karchevskii, ibid., 36, 638 (1959). ( 8 ) S. T. Lin and A. R. Raufmann, Phys. Rea.,102, 640 (1956). (9) B. Blumenthal and R. A. Noland, "Progress in Nuclear Energy," Vol. I, Pergamon Press, London and S e w York, 1956, Series V, pp. 62-80.
March 5, 1960
HEATCAPACITY AND THERMODYNAMIC FUNCTIONS OF &URANIUMDEUTERIDE 1065
trometrically, was 99.67 atom yo D and 0.33 atom yo H. The mass of the sample used for the calorimetric measurements was 116.6883 g. The measurements were made with the same apparatus used for B-UHs and for a number of other compounds measured and reported from this Laboratory.uJ1 Briefly, the calorimeter is of the adiabatic type. The temperature measurements were made with a platinum resistance thermometer which has been calibrated on the International Scale above 90'K. and on the scale of the National Bureau of StandardsI2 between 14 and 90'K. Below 14'K. the scale was obtained BT2 CT6 t o the reby fitting the equation R = A sistance a t the boiling point of helium, the resistance a t 14'K. and d R / d T a t 14'K. It is believed that the temperature scale agrees with the thermodynamic scale within 0.1' from 4 to 14'K., within 0.03' from 14 to 9OoK., within 0.05' from 90 to 373'K.
+
A
+
a 0 w J
Results The experimental values of the heat capacity, expressed in terms of the thermochemical calorie, defined equal to 4.1840 joules, are presented in chronological sequence in Table I. The temperaTABLE I HEATCAPACITY OF @-URANIUM DEUTERIDE (IN CAL.DEG.-*
a 0
6
0
20
y
-~
''0
50
100
MOLE-^)
T,
OK.
Mol.-wt. = 244.11;JI'C. = 273.15"K. CD T,OK. 0 T,OK. CD T,OK.
CD
4
-
I
1
0.080 ,098 .I27 .I68 .231 .315 .424 .566 .738 ,946 1.183 1.458 1.771 2.114 2.485 2.880 3.268 3.647 4.029 4.392 4.773
150
200 T.
Series I
5.95 7.72 9.70 11.64 13.59 15.55 17.47 19.45 21.49 23.66 25.94 28.45 31.23 34.27 37.68 41.51 45.61 49.94 54.76 59.77 65.64
72.09 79.28 87.08 96.72 106.25 114.85 124.45 134.23 143.96 154.21 161.98 167.02 172.16 177.27 182.25 187.20 192.18 199.66 209.48 219.38 229.29
5.141 5.536 5.964 6.386 6.888 7.440 8.048 8.732 9.490 10.39 11.18 11.72 10.85 10.32 10.31 10 44 10.62 10.93 11.37 11.84 12.31
239.15 249.11 269.20 289.17 278.99 289.03 299.21 309.19 319.05 328.93 338.89 346.94
12.80 13.28 13.77 14.24 14.89 15.13 15.58 16.00 16.41 16.81 17.20 17.51 Series 11 160.99 11.07 163.00 11.29 164.49 11.45 165.47 11.57 168.45 11.66 167.42 11.72 168.39 11.68 169.37 11.51
170.35 171.35 172.36 173.37 174.92 176.96 178.97 180.98
11.29 11.03 10.81 10.62 10.45 10.33 10.29 10.29 Series I11 6.23 0.082 8.17 .IO2 10.04 ,129 11.98 ,176 13.92 ,243 15.91 .333 17.91 .453 19.90 ,601 21.92 ,778 24.07 ,987 26.49 1.242 29.15 1.535
Fig. 1.-Heat
~1 I__-I
250
300
350
OK
capacity of UHI (top curve) and UDa (bottom curve) as a function of temperature.
in Table I1 for selected temperatures; these values are considered to have a probable error of 0.2% above 30°K., 1% a t 14'K. and 5% at 5'K. The same curve was used to obtain the heat capacity values for evaluating the thermodynamic functions given in Table 11. The entropy So was obtained by numerical integration of f C, d In T and the increment in the enthalpy, ("I - HOO), by numerical integration of J C , d T between OOK. and the temperature of interest. Below 8°K. the heat capacity was extrapolated by the equation C, = O.O126T,
(1)
which joins the experimental curve smoothly a t 8°K. Below this temperature the experimental ture differences can be estimated from the succes- values were somewhat higher than equation 1, persive mean temperatures. Smaller temperature in- haps due to the desorption of helium gas. tervals were used in Series I1 in order to establish The values in Table I1 may be combined with the shape of the heat capacity curve in the region the thermal data in the literature to obtain the free of the anomaly, near 168OK. A small correction energy and entropy of formation of UD3 a t 298.15' for the finite temperature increment has been ap- K. and the heat of formation a t OOK. Abraham plied to all values in Table I by adding - (d2Cp/ and F10tow'~have measured the heat of formation dT2) (AT)2/24to the measured mean heat capacity. of UD3 calorimetrically by the direct combination Another small correction was made for the differ- of uranium metal and deuterium gas a t 25'. ence in the amount of helium in the measurements The reaction product was not analyzed but in the on the empty and on the full calorimeter. No cor- UH3 experiment i t was found that the product was rection was applied for the presence of 0.33 atom % 25% a-UH3 and 75% P-UH3; it was assumed, H nor for the fact that the total amount of hydro- however, that the heat of transition cy --t P was gen isotopes evolved on thermal decomposition was negligible. Making the similar assumption for only 99.65% of theoretical, The heat capacities of UDB, they reported the value -31,021 cal. mole-' P-UD3 are plotted in Fig. 1 together with those for the heat of formation, AHfo2g8.1s,for the reaction previously obtained for P-UH3.3 U(Q) 3/2Dz(g) UDdB) (2) The heat capacity values read from a smooth curve through the experimental points are given Jones, Gordon and Long14 have measured the heat capacity of bulk uranium metal from 15 to 300°K.
+
(10) E. F. Westrum, Jr., J. B. Hatcher a n d D. W. Osborne, J. Chem. Phys., 21, 419 (1953). (11) D. W. Osborne and E. F. Westrum, Jr., {bid., Pi. 1884 (1953). (12) H. J. Hoge a n d F. G. Bnckwedde, J . Research Nall. Bur. Slandards, 22, 351 (1939).
(13) B. M. Abraham and H. E. Flotow, THISJOURNAL, 77, 1446 (1955). (14) W M.Jones, J Gordon and E. A. Long, J. Chem. Phys., 40, 695 (1952).
B. M. ABRAHAM, D. W. OSBORNE,H. E. FLOTOW AND R. B.
1066
Vol. 82
11.4RCUS
TABLE I1 Dissociation Pressures.-The available thermoTIIICRMODTUAMIC PROPERTIES O F P-URANIUM DEUTERIDE dynamic data may be used to calculate the disAT SELECTED TEMPERATURES sociation pressures of UD3in the temperature range CP,
T ,OK.
cal deg.-l niol?-I
0 063 131 in 1n 289 20 610 1 083 "5 30 1 631 2 191 35 40 2 728 3 212 45 3 651 50 4 408 60 5 024 70 5 576 80 6 100 90 6 605 ion 7 154 110 120 7 758 8 424 130 140 9 169 i n 01 1h0 10 96 160 11 72 167 6 ' 11 37 170 10 29 180 10 33 i9n 10 94 200 11 40 210 11 87 220 12 34 230 12 84 240 13 32 250 13 80 260 14 27 270 14 73 280 15 1s 290 15 61 300 16 03 310 16 45 330 16 65 330 17 24 340 17 63 350 14 43 273.15 15 53 288 15 +0 02 a Maximum.
5
SO caf. deg. -1 mole - 1
n ,063 .126 ,204 ,327 ,512 ,757 1.051 1.379 1.729 2.091 2.825 3.553 4.260 4.947 5.616 6.271 6.919 7,566 8.217 8.877 9.553 10.081 i n . 245 10.850 11.412 11.962 12.507 13.048 13.586 14.122 14 655 15.187 15.717 16 345 16.769 17.291 i7.m 18.325 18.837 19.347 19.552 15.bS 17.20 10.03
HO
- Hoe,
cal. mole-'
0 0 1 3
16 63 63 80 7 99 14 75 24 32 36 64 51 51 68 69 109 09 156 36 209 37 267.80 331 30 400 06 474 59 555 46 643 37 739 18 843 94 930 36 958 18 1063 9 1167 8 1275 1 1386 8 1503 1 1624 2 1750 1 1880 9 2016 5 2156 9 2301 9 2451 5 2605 4 2763 6 2926 0 3092 5 3'62 9 3437 2 2203 2577 rt5
Cdl deg -1
mole-1
0.031 063 095 137 192 265 356 463 581 717 1 007 1 319 1 643 1 971 2 303 2 634 2 964 3 293 3 621 3 949 4 278 4 j30 4 609 4 939 5 266 5 586 5 903 6 216 6 524 6 830 7 131 7 431 7 729 8 024 8 316 8 fin6 8 895 9 181 9 466 9 750 10 031 7 82 8 56 *o 02
and calculated from their data that the entropy at 2.7' has the value 12.03 0.03 cal. deg.-' mole-l. From their data we calculate that ( f P 2 9 8 . 1 5 H:) has the value 1320 f 3 cal. mole-'. The thermodynamic properties of normal deuterium were taken from the tables of Woolley, Scott and Brickvc.cdde15; however, R In 9 was subtracted from the tabulated values of the entropy and the free energy function to exclude the contribution from the nuclear spins. For reaction 2 we obtain these values
*
-
(3)
it is necessary to have the free energy function, -(P - II&')/T, for uranium, deuterium and UD3 up to 700'K. in addition to A F f o 2 9 8 1 b and AIIf,P. The free energy function for uranium was obtained from the increments in the enthalpy and entropy above 23' tabulated by K. K. Kelley,17 a n d the function for normal deuterium was taken from the LTroolley, Scott and Brickwedde tables.15 However, in order to obtain this function for UD3, it is necessary to extrapolate the heat capacity above 330°K., the temperature limit of the measmements. The experimental values between 230350'K. were fitted to the equation C, = -2.18
+ 00755T - 0.000054P cal. deg.-l
mole-' (4)
which reproduces the experimental values to better than 0.01 cal. deg.-l mole-'. It was shown in ref. 3 that the calculated values for the dissociation pressures are insensitive to the method of extrapolating the heat capacity so that only equation 4 was used, and as before it was found that the calculated pressures were higher than the observed pressures. Recalculation of the heat of formation a t 29S.15'K. yielded a value of -21,757 cal. mole-l instead of the calorimetric value of -31,02 1 cal. mole-' a difference of approximately 700 ca1. mole-l as observed with U H S . ~ Hydrogen Vibration Frequencies.-It can be seen from Fig. 1 that below 90°K. the heat capacities of UH3 and UD8 are nearly the same and that above that temperature the heat capacity of UD3 becomes appreciably higher. It-e have analyzed the heat capacity curves on the assumption that the difference arises solely from the effect of the isotopic mass on the hydrogen frequencies, except for a difference in the magnetic heat capacity near the Curie temperature. As a result of the much larger mass of the uranium atoms the optical modes can be considered, to very good approximation, to be vibrations of the individual H or D atoms in the field of stationary U atoms. The remaining vibrations, the acoustical modes, are chiefly ribrations of the uranium lattice. The contributionof the optical modes to the heat capacity should be well approximated by the sum of three Einstein functions. It is assumed that each of the three characteristic hydrogen frequencies in UH3 is reduced in UD3 by the ratio of the square root of the masses, or (D/H)'/t = 42. The heat capacities of UHs and of UD3 are then given by 3
Cp(UHa)/31< = D
= -16.76 cal. deg.-' mole-' AFro2g~.l& = - 17,080 cnl. mole-' A.Hroo = -29,000 cal. mole-' Asio?ga.16
( 1 5 ) 13. W. Wuolley, R. B. Scott and F. G. Rrickwedde, Aoll. Birr. S l n v d n r d s , 41, 379 (194X).
500-700°K. for a comparison with the experimental valuesle a s was done with UH3.3 To obtain AFfo/Tfrom which the dissociation pressures were calculated by the relation
-tc11/3R
= D 4-
Elu,) ( 5 ) r=l
J. Research
(16) F. H. Spedding, el aI., A'ucleonics, 4 , No. 1, 4 (1949). (17) K. K. Kelley, U. S. Bur. RIines Bull. -170, C. S. Goxernment Printing Office, Washington, D. C., 1949.
March 5, 1960 Cp(UD3)/3R = D
HEATCAPACITY AND THERMODYNAMIC FUNCTIONS OF 0-URANIUM DEUTERIDE 1067
+ C D / ~ R= D +
3
180-
E(Ui/dS)
rI ---
I
~
--
(6)
/
i-1
where CH and CDare the contributions of the hydrogen and deuterium vibrations, respectively, E is the Einstein heat capacity function, and Ui = hcFi/kT. D is a function of T representing the sum of the contribution of the uranium vibrations, the electronic contribution, and the magnetic part of the heat capacity, and this function is assumed to be the same for the two compounds, except near the Curie temperatures. The difference in the heat capacities is then Cp(UD8)
- Cp(U13a)
3 (E(Ui)
-E(Ui/fi))
(7)
i=l
A relation between the characteristic frequencies can be obtained from the difference in the zero point energies of UH3and UD3. The heat of formation of UD3 a t absolute zero (vide supra) may be combined with the published value for UHS3 = -27,945 cal. mole-') and the zero point energy difference for hydrogen and deuterium'5 to obtain the difference in zero point energy between UH3 and UD3; i.e. AEo'(CH3
- UDa) = A(AHro") (3/2)AE8(H*
30
120
200
30 I
- Dz) = 3769 cal. mole-'
(8)
Since the uranium contributions to the zero point energy are assumed to be the same in both compounds then AEoo(UH4- UD3) = (3/2)Nhc
:-
3
i,(l
-
1/
