Thermal decomposition of materials with layered structures

Reactivity of Solids, 2 (1987) 359-372 Elsevier Science Publishers B.V., Amsterdam

THERMAL DECOMPOSITION WITH LAYERED STRUCTURES DEHYDRATION CRYSTALS

OF CALCIUM

V.B. OKHOTNIKOV

*, S.E. PETROV,

359 - Printed

OF MATERIALS

SULPHATE

B.I. YAKOBSON

Institute of Solid State Chemisty, Siberian Derzhavina 18, Novosibirsk 630091 (U.S.S.R.) (Received

January

20th, 1986; accepted

in The Netherlands

DII-IYDRATE

and N.Z. LYAKHOV

Branch of the U.S.S.R.

August

SINGLE

Academ_v of Sciences,

12th, 1986)

ABSTRACT The kinetics of the thermal dehydration of CaS0.,.2Hz0 single crystals, which have a layered structure, has been studied in vacua by means of a quartz crystal microbalance. It has been found that the rate of the reaction interface advance in the crystallographic [OlO] direction is controlled by diffusion of water molecules through the layer of the solid product, whereas in the [OOl] direction it is controlled by the chemical step. To explain the experimental results, a topochemical model has been suggested. The kinetic parameters for the [OOl] direction are: activation energy (E) = (19.8 + 0.4) kcal/mol and frequency factor (v) = (1.5 f 0.9). 10'4 s-l.

INTRODUCTION

Thermal decomposition of materials with layered structures is often characterized by anisotropy in the reaction interface advance. For example, during thermal decomposition of CU(HCO,)~ .4H,O [l], Mn(HCO,), . 2H,O [2,3], K,Fe(CN)6 - 3H,O [4], Na,H(CO,), .2H,O [5] and NiPt(CN), - 2NH, [6] the reaction interface moves into the bulk of the reactant exclusively parallel to the layers of H,O and NH,. Similar geometric control by a “contracting parallelogram” [1,2] may also be expected in the dehydration of a gypsum single crystal in which water molecules are packed in layers parallel to the (010) [7]. The products of gypsum dehydration are controlled both by temperature, T, and water vapour pressure, PHzO. It was known that the following products are formed: hexagonal calcium sulphate ( y-CaSO,, soluble anhydrite), orthorhombic calcium sulphate (,&CaSO,, insoluble anhydrite) and two polymorphous forms of calcium sulphate hemihydrate a-CaSO, . 0168-7336/87/$03.50

0 1987 Elsevier

Science Publishers

B.V.

360

0.5Hz0 and P-CaSO,. 0.5H,O [S]. Recently, however, it has been shown that (Y-and P-modifications are not polymorphous forms of one compound, but belong to CaSO, .0.67H,O and CaSO, . 0.5H20 with monoclinic and trigonal crystal lattices, respectively [9]. Under atmospheric pressure a-form transforms into p-form in the temperature range 346 to 353 K. In addition, an unknown compound with the formula CaSO, .0.8H,O has recently been found [lo]. It is also known that y-CaSO, transforms into /?-CaSO, at T = 473 K [8]. Such a variety of gypsum dehydration products, of course, presents difficulties for investigation of the kinetics and reaction mechanism. The formation (after removal of crystal water) of zeolite-like channels in the crystallographic [loll direction [7] may be responsible for this. Gypsum dehydration in a reactor proceeds according to the following equation: CaSO, .2H,O

--, y-CaSO,‘+

2H,O

(1)

After taking anhydrous y-CaSO, out of the reactor it will become saturated with atmospheric water vapour due to the presence of such zeolite-like channels, to yield any form of the hydrate with the content 0.5H,O, 0.67H,O and 0.8H,O per CaSO, formula unit. This rehydration proceeds very rapidly as shown in ref. 11. At T<425 K and P H,O < 1.3 . 10e3 Pa gypsum dehydration proceeds exclusively according to reaction 1 [12-141. The activation energy of this process (E) = 19.1 kcal/ mol [14] and the value of frequency factor, v, is not reported since kinetic studies were made with powders. Therefore, it is of interest to study dehydration of CaSO, - 2H,O single crystals under the conditions of reaction 1 with the aim of obtaining Arrhenius parameters E and v and revealing the reaction interface propagation anisotropy as in the case of analogous compounds with layered structures.

EXPERIMENTAL

A natural gypsum single crystal * with chemical composition Ca2+, 23.20%; SO:-, 54.48%; H,O, 20.34%; SiO,, Mg2+ and A13+ ca. 2% (theoretical composition: Ca2+, 23.28%; SO:-, 55.79%; H,O, 20.93%) was used to cut out 0.1 cm thick disks, 0.6 cm in diameter. Since water molecules are packed in layers in CaSO, .2H,O, it is of interest to investigate two extreme cases: when the reaction interface “product-reactant” moved parallel and when it moved perpendicular to these layers. Reasoning from this, the samples were cut with a disk plane parallel to either the (001) or (010) face. It is known [15] that gypsum dehydration proceeds through formation and growth of nuclei. Therefore, in order to eliminate the nucleation stage, one

The gypsum single crystal was given to us by the Museum Branch of the USSR Academy of Sciences. l

of Geology

of the Siberian

361

Fig. 1. Scanning electron micrograph of a cross section of partially single crystal (X 1000). Left, reactant; right, product.

dehydrated

CaSO, .2H 2O

of the larger faces of each sample was activated with fine abrasive (artificial nucleation). As a result of such a treatment, instantaneous nucleation takes place. The reaction interface has a planar geometry and moves into the bulk of the crystal parallel to the initial face (Fig. 1). The reaction on the opposite and lateral faces of the sample were eliminated by covering these faces with an indium-gallium eutectic. The samples thus obtained make it possible to study the kinetics of the advance of a reaction interface in a given crystallographic direction. Kinetic studies along the [OlO] and [OOl] directions were carried out by means of a quartz crystal microbalance 1161 under conditions of dynamic vacuum of ca. 6.7. 10e5 Pa in the temperature range 292.7-357.4 K. Such experimental conditions make it possible to suggest that the reaction proceeds according to reaction 1. For the purpose of testing this assumption, the samples were completely decomposed in the reactor. Weight loss corresponded to the formation of the anhydrous product.

KINETIC

STUDIES

Kinetic studies have shown that the reaction interface moves in the crystallographic [OOl] direction (parallel to the layers of H,O) at a constant rate V (as well as during dehydration of Cu(HC0,) 2 .4H,O [l] and Mn(HCO,), * 2H,O [2,3]), whereas if the reaction interface moves in the crystallographic [OlO] direction (normal to the water molecule layers), a decrease of V is observed. Typical kinetic curves are shown in Fig. 2.

362

0

100

200

300

TIME , mln Fig. 2. The thickness of the CaSO,.2H,O crystal reacting vs. time. For the [OlO] direction: v = 370.6 K; + = 353.9 K; 0 = 343.7 K; A = 339.9 K; n = 337.6 K; A = 323.6 K; for the [OOl] direction: 0 = 342.9 K.

It may be suggested that in such compounds with a high crystal structure anisotropy as in gypsum, variable conditions of topotaxical growth of the product layer are realized depending upon the crystallographic face [17] and determining the morphology and, ultimately, anisotropy of gas permeability in the solid product layer. In the present case, the morphology of the solid product appears to be such that the rate of the reaction interface advance in the crystallographic [OlO] direction is controlled by diffusion of the gaseous product through the solid product layer. Scanning electron microscopy (SEM) studies (Jeol T-20) of the solid product morphology on the (001) and (010) faces do show a significant difference (Fig. 3). The product on the (001) face is porous (Fig. 3A), whereas no pores and cracks were observed on the (010) face at the same magnification; only at greater magnification was it possible to locate a net of fine cracks (Fig. 3B). It should be noted that SEM studies (Fig. 3) were performed on the solid product, already rehydrated to hemihydrate since this process readily occurs in air [ll]. This was confirmed by IR studies (spectrometer UR-20). According to very similar values of lattice parameters found for both y-CaSO, and hemihydrate [9], it may be considered that no essential change in morphology occurs during rehydration. The retardation of the reaction, as the thickness of the solid product layer on the (010) face increases (Fig. 2), may be considered as being a common feature for reactions of the type AB(solid)

+ A(solid)

The steady-state

+ B(gas)

reaction

interface

(2) advance

into

the reactant

bulk is ob-

363

Fig. 3. Scanning electron micrographs of morphology of the solid product (001) face (X 380) and (B) on the (010) face (X 3500).

formet d (A) on the

served only for the solid product layer with a high gas per ,meabili tYConsider a simple model which allows the results obtained to be quanti tatively interpreted.

364 MODEL OF THE REACTION INTERFACE

The solid product becomes porous due to a gap between its specific volume and the specific volume of the reactant, and removal of the gaseous product, water molecules, occurs by its diffusion through this porous layer. If C, is the concentration of chemically bonded H,O molecules in the starting reactant, and C(x) is the gaseous phase concentration of H,O molecules in the pores of the product, boundary conditions for C(x) are: on the interface “solid product-reactant” C(I) = C,; on the interface “solid product-vacuum” C(0) = C,. The flow of water molecules from the starting reactant is proportional to C,, the inverse process of capture of molecules also being possible, and the rate is proportional to C,. Using corresponding phenomenological rates of the direct and reverse reaction U, and U,, respectively, one can write down the continuity condition at the reaction interface for the flux of the gaseous product Wx) UICo - U,C, - D* . ax

=

0

(3)

where D* is the coefficient of gas diffusion librium C, = C, and eqn. 3 gives

c

-L=-L

u

co u,

= exp( -AH/RT)

through

pores.

Under

equi-

+x 1

where AH is the heat of the reaction, and R is the gas constant. The estimate obtained, C, < C,, enables one to avoid solving the general equation of non-stationary diffusion through the solid product with a moving interface and to restrict oneself to approximation of a constant gradient [18]:

where p is the shrinkage factor of the product relations 3 and 5 and the obvious equation a1 C,,.at=D*‘ax

(0 < p < 1). On the basis of

w-4

one may easily obtain advance

(6) the expression

for the rate of the reaction

interface

(7)

365

where D = D*/y.

This equation

combined

with eqn. 4 becomes

The equation obtained predicts in particular an obvious result: increasing C, concentration of the gaseous reaction product in the reactor leads to the decreased rate of the reaction interface advance I/. The linear dependence of V and C_, will take place in a limited range of C, variations since, with increasing C, catalytic influence of water vapour on the recrystallization of the solid product [19], a rise in the rate of the reverse reaction is observed. The porosity of the layer of the solid product will change correspondingly; this is equivalent to the appearance of latent dependence of D on C,. For example, in the case of thermal decomposition of CaCO, for which the catalytic influence of CO, on recrystallization of CaO is known [20], a linear relationship between V and C, only takes place within the range P, - 1O-5 < Pco, G PO. lo-*, where P, is the equilibrium pressure of CO, [21]. When the inequality (C,/C,)

exp(AH/RT)

holds, the vacuum

(9)

is called “ultimate”

[22], and eqn. 8 will take the form

u,

v=

(10)

1 + &I/D

When v=

+Z 1

V is not dependent

on 1, eqn. 10 transforms

to

u,

(11)

If one assumes that the removal of water molecules from the starting reactant is described by the model of Polani-Wigner, then the reaction rate constant is as follows [23] U, = 8~ exp( -E/RT) where 8 is the distance

(12) between

neighbouring

H,O molecules

in the lattice.

ESTIMATION OF THE VALUE OF “ULTIMATE VACUUM”

There is some evidence [24,25] that, for the reversible reaction of type 2 the Arrhenius activation energy increases with the pressure of gaseous product. Neglect of this factor may lead to unreproducible results. Therefore, in the preparatory stage of the experiment, evaluations of “ultimate vacuum” are necessary. As was mentioned above, the dynamic vacuum in the reactor is ca. 6.7 . lops Pa. Gas analysis of residual atmosphere was not performed. The

366

availability of cold trap in the reactor, however, allows one to assume that the partial pressure of water vapour does not exceed 1.3 . 10-l’ Pa [26]. To obtain an upper estimation let us assume that Puo is only an order of magnitude less than the residual pressure, i.e. PHzO IS ca. 6.7 * 10e6 Pa. The approximation of ideal gas P H,O = GkT

03)

where k is the Boltzmann constant and T = 300 K (since the external walls of reactor are at room temperature) gives C, = 1.6 * 1015 rnp3. Since for reaction 1 AH = 14.15 kcal/mol [27] and C, = 16.3 - lo*’ me3 [7], then for the temperature range 292.7 to 357.4 K being studied the value is variable from 3.7. 10d3 to 4.5 . 10p5. Thus, dy(C,/C,) exp(AH/R*) namic vacuum in the reactor is “ultimate” and therefore eqn. 10 is applicable in the scope of the model being considered.

DEHYDRATION

OF CaSO,.2H,O

IN THE [OlO] CRYSTALLOGRAPHIC

DIRECTION

Let us consider the initial curves ,( t) (Fig. 2) plotted on the ( I/ - t) coordinates. The values of the instantaneous rate of the reaction interface advance V, were calculated from the approximate formula I

-I;_,

vi= t’+l_t 1+1

(14) 1-l

where (t,+l - t,_, ) = 60 s. The corresponding

curves V(t) are represented in Fig. 4. The initial part of the curves (up to the maximum) is difficult to interpret since it corresponds to the heating of samples up to the temperature of the reaction, formation of the steady reaction interface and also, probably, transition from kinetic to diffusion control. Let us consider only the monotonically decreasing part of the curves (V-t). Eqn. 10 can be rearranged as follows 1 -= v

&.i+& 1

1

The experimental curves (Fig. 2) were plotted on the (l/V-1) coordinates (Fig. 5). The initial parts of the curves are analogous to the curves V(t) in Fig. 4. Assuming that the linear part of the curves (Fig. 5) are given by the eqn. 15, then the statistical refinement of the linear part by least-squares method gives numerical values of U,/U, D and l/U, (Table 1). On the basis of eqn. 4 and taking into account the general case that D = Do exp( -E,/RT)

(16)

367

0

100

200

300

TIME , Ill,”

Fig. 4. The instantaneous rate of the reaction interface advance vs. time. For the [OlO] direction: v = 370.6 K; + = 353.9 K; 0 = 343.7 K; A = 339.9 K; A = 323.6 K; for the [OOl] direction: 0 = 342.9 K.

where E, is the activation factor, we have

energy of diffusion,

and DO is the preexponential

07)

Fig. 5. The reciprocal instantaneous rate of the reaction interface advance vs. the thickness of the solid product for the direction [OlO]: v = 370.6 K; + = 353.9 K; l = 343.7 K; A = 339.9 K; n = 337.6 K; A = 323.6 K.

36% TABLE

1

U,/U,D,

l/U,

and D numerical

370.6 353.9 343.7 339.9 337.6 323.6

values

U*/U,D

l/Y

(lo7 s/cm*)

(10’ s/cm)

D (cm’/s)

4.3 _t 0.1 6.6 f 0.1 11.9 kO.2 15.0fO.l 17.5 _e0.4 63+3

0.76 + 0.06 1.6*0.1 2.6 rt 0.2 5.1+ 0.1 7.3 * 0.3 33.6 + 0.7

5.2 * 0.1 8.4*0.1 8.5 * 0.1 8.5 _t 0.1 8.450.2 5.8kO.3

-

The slope of the straight line, drawn through the experimental points in the coordinates [ln( U,/U,D)-l/T], is (AH + En). The corresponding refinement by least-squares method gives a value of (AH + En) = (14 k 2) kcal/ mol. A comparison of this value with the experimental value AH = 14.15 kcal/mol [27] gives En = (0.15 + 2) kcal/mol. The values of D calculated from U,/U,D subject to eqn. 4 are presented in Table 1. It is clear that D values do not depend in practice on temperature. These facts indicate that gas diffusion of water molecules through the pores of the solid product is in operation. We have no clear explanation of nonmonotonic behaviour of D values with temperature. These weak deviations may be related to pore structure dependance on the temperature or some other complex process which remains beyond the scope of our kinetic model. Integration of eqn. 10 gives (I+R)2=A(r-t,)+(f,+B)” where

B = D/U,

I

0 TIME,

100

(18)

and

A = 2U, D/ U,. The numerical

/

200

I

I

values

of 1, and

t,

1

300

mtn

Fig. 6. Straight line plot of the square of the product thickness vs. the reaction time indicates that in the [OlO] direction a diffusion process is in operation. v = 370.6 K; + = 353.9 K; 0 = 343.7 K: A = 339.9 K; n = 337.6 K; A = 323.6 K.

369

correspond to the origin of the linear part experimental points (Fig. 2) presented according to eqn. 18 are shown in Fig. 6. plots that the rate of the reaction interface [OlO] direction is controlled by diffusion pores of the solid product.

DEHYDRATION

OF CaSO,.2H,O

of the curves (Fig. 5). The initial in the coordinates [(,+ B)‘-t] It is clear from the straight line advance in the crystallographic of water molecules through the

IN THE [OOl] CRYSTALLOGRAPHIC

DIRECTION

It follows from the preliminary studies that the rate of the reaction interface advance in the crystallographic [OOl] direction does not depend on the thickness of the solid product (Figs. 2 and 4). Based on this, experimental studies of V(t) were made by the procedure described in ref. 16. The experimental results are presented in Fig. 7. Assuming that the temperature dependence V(T) is given by eqn. 12 where 6 = 3.26. lOA8cm [7] is the distance between water molecules in the [OOl] crystallographic direction and having made the corresponding refinement by the method of least squares, we obtain the following kinetic parameters: v = (1.5 &-0.9) * 1014 s-l, E = (19.8 + 0.4) kcal/mol. The value of activation energy obtained is in agreement with the literature (E = 19.1 kcal/mol) [14]. Since the value of U, for the [OOl] direction is obtained by means of direct experimental measurement, and those for the [OlO] direction are calculated from the data V according to eqn. 15 (see Table l), it is of interest to compare these data (Fig. 7). The activation energy calculated from the data l/U, is (19 _+ 2) kcal/mol and satisfactorily agrees with the corresponding value for the [OOl] direction.

-13

-15

28 TEMPERATURE

30

32

34

ClOJ/T,

Fig. 7. Dependence of the rate of the reaction interface advance vs. temperature in the directions: [OOl], A and n ; [OlO], +

370

The straight line drawn through the points represented by a plus sign is practically parallel to the straight line drawn through the points represented by closed triangles and closed squares, but the former lies above. This difference appears to be associated with values of 6 being different in the [OOl] and [OlO] direction. To verify this assumption it is necessary to calculate the values of 6 in the [OlO] direction from the data l/U, (Table 1). Assuming that U, in the [OlO] direction is defined by the same Arrhenius parameters as in the [OOl] direction, from eqn. 12 we obtain 6 = (7 f 2) . lo-’ cm. This value is in good agreement with the distance between neighbouring water molecules in the [OlO] direction 6 = 7.6 . 10-s cm [7]. The mechanism for dehydration of crystalline hydrate has been previously suggested [28,29], and accordingly the rate constant is K= (or + v2) exp[ -(E,

+&)/RT]

(19)

Where v1 and E, are the Arrhenius parameters of the flip motion of water molecules in the crystal lattice; v2 and E, are the frequency of stretching and the energy of the Ca2+ -OH, coordination bond, respectively. It is known [7] that all water molecules in CaSO, .2H,O are crystallographically equivalent and lone-pair coordination of the water molecules belongs to the D type: the bisector of the lone pairs is directed toward the Ca’+ ion [30]. From this it is assumed that the rate constant is given by eqn. 19. It is known that for chemically bonded water molecules in CaSO, .2H,O. vi = 1.56 - 1Or3 s-l, E, = (5.8 k 0.2) kcal/mol [31], and v2 = 8.4 - 10” s-r [32]. Simple comparison shows that the value (vi + v2) = 2.4. lOi sP1 agrees well with the experimental value v = (1.5 + 0.9) . 1014 s-r.

DISCUSSION

Various models of a reaction interface for the reactions of type 2 have been suggested [33-391. The main difference of the model considered here from those mentioned above is in consideration of the “vacancy structure”, for which the loss of water molecules is yet reversible (the reverse process is taken into account by the member U,C, in eqn. 8), and “impedance” [40] (the term U,l/D in eqn. 8). This enables one to obtain an analytical expression (eqn. 8) for the rate of the reaction interface advance, to estimate the “ultimate vacuum” and to account for the kinetics of CaSO, - 2H,O dehydration in the crystallographic [OlO] direction. According to the results obtained it is clear that the term “degree of conversion” should be used cautiously. Thus, it is noted in refs. 1 and 41 that up to (Y= 0.85 and in the range 0.05 < (Y< 0.5, the rate of the reaction interface advance is constant. The numerical values of (Ysupply no information. In. fact, if one takes two plate-like samples with a thickness of 1 cm and 0.1 cm and decompose them up to CY= 0.5, then in the first case the

371

maximum thickness of the solid product layer will be 0.5 cm and in the second 0.05 cm. It is possible that, for equal values of gas permeability, the member U,I/D in eqn. 8 can not be neglected in the first case even if in the second case the rate of the reaction interface advance is independent of the solid product layer thickness. The interpretation of “impedance” suggested in this paper is not the only one. An idea of the sufficient permeability of the solid product layer is provided by the solid-phase diffusion of water molecules. In this case, there is no abrupt change of concentration at the “reactant-solid product” interface, i.e. C, = C, in eqn. 4, and the relation V- D/I must hold for large time values. From this, the estimation D = 1O-9cm’ s-l follows, which seems to be quite a reasonable value. As far as the “vacancy structure” is concerned, its existence in a number of cases was shown experimentally [42-441 and attempts are currently being undertaken to use this experimental fact in classification of a reaction interface [45]. At present, there is uncertainty about “ vacancy structure”. For the crystalline hydrates, for example, it is known [46] that water molecules play an important role in stabilization of the crystal lattice. Therefore, the “vacancy structure” will collapse at a certain critical concentration of vacancies C*. Determination of c* values, an effect of elastic stresses and temperature on stability of “ vacancy structure”, requires special study. Consequently, it is premature to propose quantitative models of a reaction interface considering all the above factors and without reliable experimental support.

ACKNOWLEDGEMENTS

The authors are thankful to L.F. Kuznetsova SEM photos and to 0.1. Lomovski for discussion

for assistance in obtaining of the experimental results.

REFERENCES 1 2 3 4 5 6 7 8 9 10

P.M. Fichte and T.B. Flanagan, Trans. Faraday Sot., 67 (1971) 1467. R.C. Eckhardt and T.B. Flanagan, Trans. Faraday Sot., 60 (1964) 1289. T.A. Clarke and J.M. Thomas, J. Chem. Sot. A, (1969) 2227. T.P. Schachtschneider, E.Yu. Ivanov, V.V. Boldyrev and V.A. Logvinenko. Izv. Sib. Otd. Akad. Nauk SSSR, 12 (1981) 17 (in Russian). E.A. Prodan, M.M. Pavluchenko and S.A. Prodan, Zakonomemosty Topochimicheskich Reakziy, Nauka i Technika, Minsk, 1976, p. 93 (in Russian). A. Reller and H.R. Oswald, Proc. 6th Int. Conf. Therm. Anal., Bayreuth. July 6-12. 1980, Birkhauser Verlag, Basel, 1980, p. 63. B.F. Pedersen and D. Semmingsen, Acta Crystallogr., Sect. B, 38 (1982) 1074. M.J. Ridge and J. Beretka, Rev. Pure and Appl. Chem.. 19 (1969) 17. N.N. Bushuev, Zh. Neorg. Khim., 27 (1982) 610 (in Russian). W. Abriel, Acta Crystallogr., Sect. C, 39 (1983) 956.

11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 3X 39 40 41 42 43 44 45 46

R.F. Razouk, A.Sh. Salem and R.Sh. Mikhail, J. Phys. Chem., 64 (1960) 1350. H.G. Wiedemann and G. Bayer, Z. Anal. Chem., 276 (1975) 21. B. Molony and M.J. Ridge, Aust. J. Chem., 21 (1968) 1063. M.C. Ball and L.S. Norwood, J. Chem. Sot. A, (1969) 1633. J.E. Bright and M.J. Ridge, Philos. Mag., 6 (1961) 441. V.B. Okhotnikov and N.Z. Lyakhov, J. Solid State Chem., 53 (1984) 161. J.R. Gi.inter and N.R. Oswald, Bull. Inst. Chem. Res. Kyoto Univ., 53 (1975) 252. H. Eyring, S.H. Lin and S.M. Lin. Basic Chemical Kinetics, Wiley, New York. 1980, Ch. 9. M. Volmer and G. Seydell. Z. Phys. Chem., 179 (1937) 133. J. Ewing, D. Beruto and A.W. Searcy. J. Am. Ceram. Sot., 62 (1979) 580. T. Darroudi and A.W. Searcy, J Phys. Chem., 85 (1981) 3971. E.A. Prodan, M.M. Pavluchenko and S.A. Prodan, Zakonomernosty Topochimicheskich Reakziy. Nauka i Technika, Minsk, 1976, p. 8 (in Russian). M. Polyani and K. Wigner, Z. Phys. Chem. Abt. A, 139 (1928) 439. J. Zawadski and S. BretsznaJder. Z. Electrochem.. 41 (1935) 721. J. Zsako and H.E. Arz, J. Therm. Anal., 6 (1974) 651. R.E. Honig and H.O. Hook, RCA Rev.. 21 (1960) 360. K. Heide, Silikattechnik, 20 (1969) 232. V.B. Okhotnikov, B.I. Yakobson and N.Z. Lyakhov, React. Kinet. Catal. Lett., 23 (1983) 125. V.B. Okhotnikov and B.I. Yakobson, React. Solids, Proc. Int. Symp. lOth, 1984, Part A (1985) 150. G. Ferrans and N. Fran&u-&Angela, Acta Crystallogr.. Sect. B. 28 (1972) 3572. D.C Look and I.J. Lowe, J. Chem. Phys., 44 (1966) 2995. K. Ishii. Phys. Chem. Miner.. 4 (1979) 341. B. Topley. Proc. R. Sot. London, Ser. A, 136 (1932) 431. J.A. Cooper and W.E. Garner, Proc. R. Sot. London, Ser. A, 174 (1940) 487. W.E. Garner. Chemistry of the Solid State, Butterworth, London. 1955, Ch. 8 A.W. Searcy and D. Beruto, J Phys. Chem., 80 (1976) 425. A.W. Searcy and D. Beruto. J. Phys. Chem., 82 (1978) 163. G Bertrand, J. Phys. Chem.. 82 (1978)2536. A.K. Galwey. R. Spinicci and G.G.T. Guarini, Proc. R. Sot. London, Ser. A, 378 (1981) 417. E.S. Vorontzov. Usp. Khim., 37 (1968) 167 (in Russian). G Flor, V. Berbenni and A. Marini. Z. Naturforsch. A, 34 (1979) 1113. A.1 Zagrai, V.V Zyryanov, N.Z. Lyakhov. A.P. Chupakhin and V.V. Boldyrev, Dokl. Akad. Nauk SSSR, 239 (1978) 872. J.C. Mutin. G Watelle and Y I. Dusausoy, J. Solid State Chem., 27 (1979) 407. V.V. Zyryanov and N.Z. Lyakhov. React. Solids, Proc. Int. Symp. lOth, 1984. Part A (1985) 233. A.K. Galwey. React. Solids. Proc. Int. Symp. lOth, 1984, Part A (1985) 231. W.C. Hamilton and J.A. Ibers. Hydrogen Bonding in Solids, W.A. Beqamin Inc., New York, 1968, p. 204.