942
F. WM. CAQLE,JR.,AND HENRYEYRING
and EtGeC13, the expected range for the skeletal bendings of all types is 150-175 cm.-'. Again, a Raman line could be too weak t o show up. The line a t 320 cm.-1 may, as was 333 cm.-' in EtGeC4, be ascribed to C-C-Ge bending. However, instead of having a single line a t 295 cm.-', as in EtGeCl8, we now have two lines, at 275 and 288 cm.-l. These may tentatively be ascribed t o symmetric and asymmetric torsions of the H-C-C-H angles in the two ethyl groups. The non-appearance of the 112 cm.-' line in Et2GeClz may be ascribed t o the hindrance of this mode by steric effects, if it indeed corresponds to the C-CGeCl torsion. The extra-skeletal frequencies for both compounds are closely similar. They fall roughly into three classes: C-C stretching and H-C-C bending, 900-1100 cm.-l, H-C-H bending, 1100-1500 cm.-' and C-H stretching, 2900-3000 cm.-L. These assignments are tabulated in Table VIII. It seems worth while t o make some comments on the interaction of the ethyl groups with the frame of the molecules. As is apparent from the discussion above, the ethyl groups have little effect on the frame vibrations, and the skeletal spectra are readily interpreted in terms of the CGeC4 and C2GeClz frames. The symmetry of the ethyl groups, however, is reduced from the D B dsymmetry of free ethane, to C,. I n consequence, the AI, species is activated, and the degenerate modes are split. This accounts for the appearance of the line a t 295 cm.-l in EtGeCL. If the assignments proposed for the lines a t 112 and 295 cm.-l in EtGeClo are correct, we may assume that there is a small interaction between the ethyl group and the frame, on one hand and, in Et2GeCl2, between the two ethyl groups on the other hand.
VOI. 57
TABLE VI11 ASSIGNMENTOF Low FREQUENCIES FOR EtzGeC12 EtGeCla Frequency, om.-'
AND
Type .of vibration
Assignment
EtGeCla v6 vb
va
v2 Y4
VI
112 136 150 174 295 333 397 425 596
T
E E A,
(C-C-Ge-C1)
6 (Cl-Ge-CI) 6
(C-Ge-CI)
6 (Cl-GeCI) T
(H-C-C-H)
6 (C-C-Ge)
Ai E A1
(Ge-Cl) (Ge-Cl) v (Ge-C) Y
Y
Et2GeC12
Vi
155 155 165 165 165 275 288 320 376 395 561
ve
(io5
Yb
v4 V? Y3
YB
Y2
Y8
A2
Ai
B1 Ai €32
Ai J32
Ai BI
Twist 6 ( CI-GeCI) Rocking 6 (C-Ge-C) Rocking T (H-C-C-H) T (H-C-C-H) 6 (C-C-Ge) Y (Ge-CI) Y (Ge-Cl) v (C-Ge) v (C-Ge)
If this is the case, the skeletal lines in EtGeCls corresponding t o the E vibrations are in reality unresolved doublets. The breadth of the line a t 425 cm.-l suggests that this might be the case. Any definite conclusion, however, must await further study with high dispersion spectrographs. The authors wish t o acknowledge financial support from the office of Naval Research Contract M 8 onr-72700.
AN APPLICATION OF THE ABSOLUTE RATE THEORY TO PHASE CHANGES IN SOLIDS1 BY F. WM. CAGLE,JR.,AND HENRY EYRING Deparlinent of Chemistry and Institute for Rate Processes, University of Utah, Salt Lake City 1 , Utah Received April 16, 1965
A theory for phase transitions in sol'ids, based on the absolute reaction rate theoryl has been developed. It has been applied quantitatively t o the transition of white to gray tin. This theory leads to the interpretation that only where growth lines for white tin cross those for grey tin can the transition occur. As might be expected, such crossing points are exceptionally rare and account for most of the slowness of the transition. The transformation of monoclinic to orthorhombic sulfur has also been discussed in terms of the theory. The effect of external constraints, especially pressure, has been considered both upon the thermodynamics and upon the kinetics of such transformations.
fully such systems, which on account of their relaIntroduction Quite aside from the enormous practical interest tive simplicity, are able t o provide information attached to phase changes in solids, one readily ob- concerning the nature of the activated complex. We consider first the p- to a-tin transition. This serves that at least in the case of pure solids, these changes permit a study of a one-component reaction system undergoes transition a t a convenient temwhich occurs a t an interface between phases. It is, perature and therefore has been the subject of numof course, of primary importance to examine care- erous investigations. While most of these investigations were undertaken t o elucidate the thermo(1) This paper was presented on July 14 at the 1952 Gordon Condynamic relationship of the system, some are conference on Physios and Chemistry of Metals, New Hampton, New cerned with the kinetics of the reaction. Hampshire.
Dec., 1953
APPLICATION OF THE ABSOLUTE RATETHEORY TO PHASE CHANGES IN SOLIDS
The enantiotropic transformation of tin occurs slightly under room temperature. White tin is the B-form and crystallizes in t$e tetragonal system (a0 = 5.822 d., co = 3.165 A.).2 The a- or grey form is stable at lower temperatures and has the diamond structure (ao = 6.46 A.).3.4 The exact temperature of transformation is uncertian but is given as 18” by Cohen and Van Eijk6 or 13.2’ by Cohen and van Lieshout.” The great disparity between the densities of atin (5.75 g./cc.) and p-tin (7.30 g./cc.) indicates that the transformation would cause the failure of any item made of tin. In fact, the name of the transformation p-tin + a-tin (tin disease) is derived from the pustules of grey tin which spread over the surface of the metal undergoing this phase change. Since tin alloys are much used as solder and are observed to undergo phase change in very cold climates, a study of this phenomenon is of practical value. Theoretical Experimental studies of the kinetics of the transformation
have been made by Cohen and Van Eijk16 Cohen and van Lieshout,e Jiinecke’ and Tammann and Dreyer.8 An equation for the rate of transformation of grey and white tin was proposed by Stepanoff.9 While the equation developed gives calculated rates in good agreement with experimental values, it does not seein possible to interpret it in terms of the molecular processes which occur. It was, therefore, decided to investigate this transformation with a view toward the application of the theory of absolute reaction rates. This treatment has the advantage of being interpretable in terms of molecular processes. Tammann and Dreyers investigated the growth of pustules of grey tin on a white tin matrix a t various temperatures. These studies were made on a tin surface in contact with the atmosphere and on a surface immersed in a solution of ammonium chlorostannate. They observed that the rate of increase of the radius of the pustule was constant a t a fixed temperature, and that when inoculated a t a point with a small crystal of grey tin, the growth occurred from the point of inoculation. In view of this and equation 1, we may write the rate of increase of radius as d- r= RX(kl‘ - k 2 ’ ) - .___.-
dl
(2) A. J. Bijl and N. I
