3130
DALEE. WORKAND HARRY A. EICK bC(z,s)
D---bx where d is the thickness of the salt-free layer of water created a t the electrode surface at time t = O+, and Co is the concentration of reactant in the bulk of the solution. A full solution of eq A1 is not required for the present purpose. It suffices to obtain [bC(x,t)/bx],,o, because the charge consumed per unit area by the diffusing reactant is given by
The Laplace transform of the derivative needed can be obtained by standard methods.gJ1 I n the region 0 5 x < d the result is
d-{
co zi
=2
s exp[&
(x - d ) ]
+
where s is the Laplace transform variable. Since the Laplace transform of
is l/s [bC(x,s)/bxJX=o we set x = ply the result by l/s to obtain
l
[bC(x,t’)/bx],,o dt’ 0 in eq A6 and multi-
The inversion of the right-hand side of eq A7 yields eq 2 in the main text. (11) H. S. Carslaw and J. C. Jaeger in “Conduction of Heat in Solida,” 2nd ed, Oxford University Press, 1959,Chapter XII.
The Vaporization Thermodynamics of Samarium Oxide Fluoride by Dale E. Work and Harry A. Eick Department of Chemistry, Michigan State University, East Lansing, Michigan 48883
(Received March 18, 1970)
Samarium oxide fluoride has been studied at high temperatures by X-ray diffraction and target collection Knudsen effusion techniques and found to vaporize over the temperature range 1614-2017’K to the sesquioxide and gaseous trifluoride. At 1815’K, AH’, = 101.5 i 1.1 kcal/gfw and AS’, = 34.73 i 0.63 eu. Combination of these values with estimated and measured heat capacity data yields for SmOF(s)AHt0z9s= -274.6 =!z 2.5 kcal/gfw, and ASr0z9s = -42.6 * 4.0 eu. Second- and third-law vaporization enthalpies are presented and discussed.
Introduction Samarium oxide fluoride has been known for many years and several of its physical properties have been investigated,’ but its high-temperature decomposition mode has never been characterized. Indeed, aside from the vaporization mode of NdOF2 (for which no thermodynamic data were given), the high-temperature decomposition modes of MOF and the corresponding thermodynamic studies constitute a virtually unexplored area, Thermodynamic data have not been reported for either the lanthanide oxide fluorides or, aside from a few recent s t u d i e ~ ,for ~ . ~the other lanthanide oxide halide systems. This dearth of thermodynamic experimental data probably stems from a scarcity of thermodynamic and spectroscopic data for the corresponding trihalides. The purposes of this investigation were: (1) to characterize the vaporiaation mode of SmOF(s) and thus to define more clearly the phase diagram of Sm0,Fe-2a at n = 1; and (2) to The Journal of Physical Chemistry, Vol. 74, No. 16, 1970
determine the thermodynamics of vaporization, thus providing a predictive tool for decomposition reactions of related species.
Experimental Section Preparative. Samarium oxide fluoride was prepared as described by Shinn and Eick.2 The trifluoride, prepared from a mixture of Smz03 (>99.9% pure, Michigan Chemical Corp., St. Louis, Mich.) and excess ammonium fluoride (reagent grade, J. T. Baker Chemical Co.), and sesquioxide were mixed in a mortar with a pestle and were placed in a Pt boat inside a Vycor tube. They reacted according to eq 1. Heating the mixture (1) L. Mazza and A. Iandelli, Atti. Acad. Ligure Sci. Lett., Genoa, 7, 44 (1961). (2) D. B.Shinn and H. A. Eick, Inorg. Chem., 8 , 232 (1969). (3) J. M. Haachke and H. A. Eick, J. Amer. Chem. SOC.,92, 4550 (1970). (4) A. K.Baev and G. I. Novikov, Zh. Neorgan. Khim., 10, 2467 (1965).
3131
VAPORIZATION THERMODYNAMICS OF SAMARIUM OXIDEFLUORIDE
Results The diffraction pattern of the air-insensitive product gradually to 1050" in an inert atmosphere and maintaining it a t that temperature for 5 hr yielded the white crystalline oxide fluoride. The products from two such preparations and a samarium oxide fluoride sample prepared 42 months earlier by Shinn and Eick5 were studied. Analytical. The various crystalline species involved in this study were identified by X-ray powder diffraction (Haegg-type Guinier camera Cu Kal radiation, ha1 = 1.54051 A, T = 24 f lo,internal standard KC1, a = 6.29300 k 0.OOOOg A). Vaporization. The thermal decomposition of SmOF(s) under vacuum was traced by a series of X-ray diffraction patterns obtained as the decomposition progressed. The net weight loss of each of the three oxide ff uoride preparations used was also determined. I n each case, a weighed specimen was heated by induction under vacuum Torr) in an outgassed molybdenum effusion cell to a temperature above 1500" for several hours until the weight of the solid residue was invariant. The vapor pressure was measured over the temperature range 1614-2017'K, using the Knudsen effusion target collection apparatus and technique as described elsewhere.6 I n experimental run 11, in which exceptionally long exposure times were required, a Latronics Coloratio pyrometer-analog controller system was used to improve temperature stability and these data points were assigned double weight in the corresponding thermodynamic calculations. The one other data point which involved a similarly long exposure time was also assigned double weight. Calculated fractions of the effusate' were collected on liquid nitrogen-chilled aluminum targets which were then analyzed for samarium by an X-ray fluorescence procedure using a previously determined calibration graph. Power settings and electronic circuitry were adjusted to provide maximum sensitivity to Sm L-/% radiation according to the method suggested by Neff,s and the analysis was standardized as described elsewhere. Symmetrical molybdenum effusion cells previously outgassed a t 1900" under vacuum Torr) were used for the vaporization measurements and no crucible-sample interaction was observed either visually or by X-ray diffraction. Circular knife-edged orifices with areas to 120 X cm2 were used ranging from 9 X without apparent effect on the equilibrium pressure measurements. The sticking coefficient of the oxide fluoride on the aluminum collection targets was determined by a bouncing experiment in which a thin aluminum disk was exposed to the effusate over the temperature range 1600-1700' via a 6.0 mm diameter hole in the disk. The disk was mounted 5.0 mm from the face of a chilled aluminum collection target.
of reaction 1 matched that of the SmOF sample5 prepared by Shinn and Eick and stored in a desiccator 42 months earlier, and is in good agreement with that calculated from published lattice parameters for SrnOF.'O Metal analysis for the phase is consistent with the formula SmOlF1.6 X-Ray diffraction results showed clearly the solid product of the oxide fluoride decomposition was monoclinic B-Smz03. The diffraction pattern of the reaction product matched that of reagent grade Smz03heated to >1200". The successive X-ray diffraction patterns obtained as the decomposition progressed revealed no intermediate crystalline phase between the oxide fluoride and the sesquioxide for the temperature and pressure ranges studied. This observation suggested that SmOF decomposes incongruently according to reaction 2. Further evidence that this is the decomposition 3SmOF(s) = Smz03(s)
+ SmFa(g)
(2)
mode was obtained by net weight loss experiments in which the observed weight losses of the three oxide fluoride preparations used were 99.7 k 1.0, 96.5 f 1.0, and 100.5 k 1.0% of the theoretical loss expected according to reaction 2. The rapidity with which the initial equilibration was attained for the second sample was taken as additional evidence that the sample yielding 96.5% of the theoretical weight loss contained excess SmtO3. The sticking coefficient determination revealed that no detectable trifluoride had been reflected by the chilled aluminum target to the back of the disk, even though approximately 18 pg was collected on the chilled target. Accordingly, the sticking coefficient was taken to be 20.95. Six independent vaporization experiments were performed, the last two on the oxide fluoride sample prepared by Shinn and Eick. The linear least-squares fit of the 34 log P s m s g US. 1/T data points (R = 1.987 eu) presented in Figure 1, is described with standard deviation as
R In P S r n F s ( s t m ) = - [(lOl.5 * 1.1) X 103]/T
+ (34.73
f
0.63)
From this equation the thermodynamic data for reaction 2 a t the median temperature, together with their (5) D. B. Shinn, Ph.D. Thesis, Michigan State University, East Lansing, Mich., 1968. (6) J. M. Haschke and H. A . Eick, J . Phys. Chem., 7 2 , 4235 (1968). (7) J. L. Margrave in Bockris, White, and Mackenzie, "Physicochemical Measurements a t High Temperatures," Butterworths Scientific Publications, London, 1959,p 225 ff. (8) H.Neff, Arch. Bisenheuttenw., 34, 903 (1963). (9) J. M. Haschke, R. L. Seiver, and H. A. Eick, U. S. Atomic Energy Commission Report, COO-716-033,1968. (10) N.C.Baenziger, J. R. Holden, G. E. Knudsen, and A. I. Popov, J . Amer. Chem. SOC.,76, 4734 (1954).
The J O U T Wof~ Physical Chemistry, Vol. 74,No. 18,1070
3132
DALEE. WORKAND HARRY A. EICK these average values, and because the heat capacity of AsF3(g) agrees well with an independent estimate for SmFa(g) at lower temperature^,'^ the heat capacity of SmFa(g) was taken to be that of AsF3(g): C, [AsF3(g)] = 19.04 0.52 X 10-3T - 3.12 X 105T-2(298" 5 T 5 2000°K). Combining these data according to reaction 2 yields
+
E
c 0
b
AH"T
- AH"11gj =
3.12 X 105T-l
-8.35T
+ 9346
+ 0.26 X 10-3T2 (1195"
2000°K)
+
AH", - AH"2g8 = -5.275T - 0.9 X 10-8T2 0.97 X 105T-l - 2424 (298" 5 T 5 1195°K)
E v)
e
AS',
E
\
-
AX"1196
=
-8.35 In T
0.52 X 10-3T
I
+
+ 1.56 X 106T-2 + 58.44 (1195" < T
APT
- AS"298
=
standard deviations, are: AH"181j = 101.5 f 1.1 kcal/gfw of SmFB(g) and AS"1815 = 34.73 f 0.63 eu. To reduce these second-law data to 298"K, published heat capacities were used for B-Sm20311~12and a Kopp's rule appro~imationl~ was employed for the heat capacity of SmOF: C,[SmOF(s)] = 18.355 2.32 X 10-3T - 2.15 X lO5TP2(298 5 T 5 1195'K)) and C,[SmOF(s)] = 21.43 (1195 < T 5 2000°K). The enthalpy of transition of SmOF at 52402was estimated as 1.25 kcal/gfw (AS,, = 1.57 eu), and the enthalpy of transition of B-SmzOa at 922" was taken to be 0.25 kcal/gfw (As,, = 0.21 eu)." The heat capacity of SmFB(g) also had to be approximated. Heat capacity data for 16 gaseous NIX3 species1* (X = halogen) with masses ranging from 71 to 456 amu, ten of which are pyramidal, four of which are trigonal planar, and two of which are T-shaped, were examined. Above lOOO", these data showed the heat capacity of R4X3(g) to be surprisingly invariant and virtually mass independent, but a t lower tempera.tures the magnitude of the heat capacity became decisively mass dependent. The four BX3(g) species exhibj+,ed exceptionally low heat capacities at lower temperatures with respect to the other twelve compounds, and were disregarded. For the remaining compounds the heat capacities, when given, were averaged at 1000, 1500, and 2000" and were found with their standard deviations to be 19.46 f 0.42, 19.79 f 0.07, and 19.91 f 0.08, respectively. Because of the close agreement of the heat capacity of AsFa(g) with
+
2000°K)
+ 0.485 X 105T-2 + 25.33 (298"
Figure 1. Graph of the h g a r i t h m of the partial pressure of SmF3(g)in equilibrium with condensed S m p 0 3and SmOF as a function of reciprocal temperature.
5
-5.275 In T -
1.80 X 10-3T
The Journal of Physical Chemistry, Vol. 7q9 No. 16, 1970
