Kinetics of Polymorphic Transitions in Tetrahedral Structures Part 1.-Experimental Methods and the Transition y + fi Li2ZnSiO4

BY MARIA E. VILLAFUERTE-CASTREJON Division Estudios Superiores, Facultad de Quimica,

U.N.A.M., Mexico 20 DF, Mexico

ANTHONY R. WEST* Department of Chemistry, University of Aberdeen, Meston Walk, Old Aberdeen AB9 2UE, Scotland

AND

Received 30th June, 1978

Possible methods are discussed for studying the kinetics of polymorphic transformations in oxides that have tetrahedral structures. Quantitative powder X-ray diffraction methods have been developed for analysing the amounts of 8- and y-polymorphs in samples of Li2ZnSi04 and these methods applied to determine the kinetics of the y + /3 transformation. The kinetics were studied isothermally between 572 and 855°C and at each temperature are deceleratory throughout. The reaction approximates to first order kinetics at several temperatures (734-802°C) but orders as low as 0.5 were observed at other temperatures.

Compounds such as Li2ZnSi04, Li,P04 and NaAIOz are polymorphic and have crystal structures that belong to the family of " tetrahedral structures ".l The polymorphs fall into two main groups, the p- and y-structures. Both groups contain an approximately hexagonal close packed arrangement of oxide ions with the cations variously distributed over the available tetrahedral sites. During the + y transition, the oxygen arrangement is probably unchanged and the transition is accomplished by the cations jumping between adjacent tetrahedral sites.

+ y transitions has been commenced with a view to obtaining two kinds of possible information. (1) The slow step in the transition is likely to be the movement of Si (in silicates), P (in phosphates), A1 (in aluminates), etc. Measurement of the kinetics of the transition may give us a novel way to study the movement in crystals of these " immobile " atoms (or ions). (2) Phase changes and reactions are commonly slow at temperatures that are close to the equilibrium transition temperatures, because the difference in free energy between the two polymorphs or phase assemblages is small. A study of the temperature dependence of the /3 + y kinetics may give quantitative information about the relative importance of kinetic and thermodynamic control in the reactions of solids.

From an experimental point of view, the /3 + y transitions have several attractive features : (a) they are sluggish and may be studied over a wide temperature range, often tn both forward and back directions. (b) Quantitative powder X-ray diffraction may be used to measure the kinetics. (c) The transition occurs in a variety of oxide phases.

For the first stage of this project, a study of the transition kinetics in Li,ZnSi04 has been made. Part 1 describes the various experimental methods that were tried and developed and gives the methods used to analyse the kinetic data.

A kinetic study of the

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M . E . VILLAFUERTE-CASTREJON A N D A . R . WEST 375

POLYMORPHISM OF Li2ZnSi04 Li2ZnSi04 is a stable phase melting at - 1475"C.2 Its polymorphism is complex

but to a first approximation, all of the polymorphs belong to one or other of two families, the #? and y families. The equilibrium p $ 7 transition temperature is -870°C. At lower temperatures /3 is stable and at higher temperatures, y is the equilibrium phase. The feasibility of this whole project rests on the observation that, on cooling the y form from high temperatures, its conversion to P is sluggish and may be suppressed entirely by using a fairly rapid cooling rate. Thus, samples of y may be retained to room temperature where they are kinetically stable although thermodynamically metastable (relative to the equilibrium P form). These relative energy relationships are shown schematically in fig. 1 . The equilibrium phase at any temperature is the one of lowest free energy and is represented by the solid curves. Dashed curves represent metastable extensions of stable states. To determine the kinetics of the P + y transition, in either direction, the material must first be obtained in a metastable condition, from which it can slowly convert back to its equilibrium state. The arrows indicate how it may be possible to do this for the two directions.

In practice, conversion of metastable, undercooled y to f l occurs at measurably fast rates above -500°C and so it should be possible to study the kinetics for this direction between -500 and 870°C. For the reverse direction, #I + y, it may also be possible to follow the kinetics if superheated P changes to y only slowly. An upper limit to the temperature range over which the kinetics may be studied occurs for reaction times of < 10-20 min since samples take at least 2-3 min to equilibrate at the temperature of the furnace.

The polymorphism of Li2ZnSi04 is more complicated than indicated in fig. 1 because there are structural variants within both p and y Both families undergo polymorphic changes in the range 630-670°C and, although the different forms have not been well-characterised, the transitions are probably minor and displacive and do not involve any cation migration steps. With increasing tempera- ture, the following sequences of changes have been identified :

Y o + (YI) + 711

PI + (B1! + PIP) + P1I.

From the work of HedvallY4 it is known that phases are often more reactive in the vicinity of a phase transition. It will, therefore, be interesting to see if any anomalous speeding-up of the kinetics occurs around 650°C. It could be, for instance, that the changes which occur in the y structure at temperatures close to, or at the y o + y I r transition, may facilitate the conversion of y to P.

CRYSTALLOGRAPHY OF Li2ZnSi04 AND PROPOSED #? + y TRANSITION MECHANISM

The crystal structures of the B- and y-polymorphs of Li2ZnSi04 have not been solved directly but from a comparison of unit cells, space groups and X-ray powder patterns, they appear to be derived from the crystal structures of #?- and y-Li3PO4.l' The relation between Li2ZnSi04 and Li3P04 is given by the replacement mechanism :

Si + P and

Zn + Li.

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376 KINETICS OF POLYMORPHIC TRANSITIONS

metastable 'b ̂\ \ \

\ temperature

FXG. 1 .-Schematic free energy relationships for the 8- and y-polymorphs of Li2ZnSi04.

- / ' 0 oxygenat 50. ' ' oxygen at 0 e L i O S i 4 Zn \ - '

FIG. 2.-Idealised crystal structure of (i) y11 and (ii) /311 Li2ZnSi04.

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M. E. VILLAFUERTE-CASTREJON AND A. R. W E S T 377

The high temperature PII and yII forms of Li,ZnSiO, appear to be directly related to p- and y-Li3P04. The structures of the other P- and y-Li,ZnSi04 polymorphs are not known but are probably slight variants of the parent BII and yII structures and involve small distortions such as deformation or partial rotation of the MO, tetrahedra.

The structures of yI1 and pII Li,ZnSi04 are shown in an idealised projection in fig. 2 and as a schematic oblique projection in fig. 3. Full crystallographic details of the Li3P04 structures may be obtained from ref. (5) and (6). Here, it is more important to have a clear overview of the structure of the two polymorphs and especially, their similarities and differences.

One way to describe the PII and yII structures is in terms of close packed layers of oxide ions with the cations distributed over the tetrahedral interstices. These oxide layers may be seen in fig. 2 ; the unit cell contains two such layers, parallel to the xy plane and at z heights of 0 and 3 (i.e., the oxygens at 0 and 50) within the unit cell. The layer stacking sequence is hexagonal close packing ( . . ABABA . . ). The same oxygen arrangement is present in pI1 and yIr, although in yrI, the layers are buckled (not shown). Each cation is tetrahedrally coordinated by four oxygens, three of which are in one layer and one in the next, either above or below. These tetrahedral

A

(a) (b) FIG. 3.-Schematic oblique projection of the structures of (a) y11 and (6) fir1 Li2ZnSi04.

sites occur at four heights, 13, 37, 63 and 87, but there are twice as many tetrahedral sites as there are cations. The #IIr and yII structures differ only in the manner of their occupancy. To be specific, in BII the sites at 13 and 63 are fully occupied and those at 37 and 87 are empty ; in yII, half of all sets are 0ccupied.l

Another way to describe both structures is as a network of linked (MO,) tetrahedra. In BII, each tetrahedron shares each corner with three other tetrahedra and all tetrahedra point in the same direction, fig. 3(b). In yIr, half the tetrahedra point in the opposite direction to the other half, fig. 3(a). The relation between BII and yII is very simple; if those tetrahedra which point down in yII could be inverted through their bases, but without moving any oxygens, then the prI structure would be generated. This gives a simple mechanism for the BII + yII transiti0n.l

The atomic movements that are necessary to accomplish the transition may be seen from fig. 2. The oxide ions and half the cations do not need to move ; whereas the other cations move by 4 4 , e.g., Si at c-height 37 in yII moves to 63 in PII ; Li at 87 in yII moves to 13 (= 113) in BII. Each of these movements involves sur- mounting a considerable potential barrier. A Si moving from 37 to 63 has to pass through a triangle of three oxygens at 50; the bond from Si to oxygen at 0 must first break and a new bond to oxygen at 100 forms. These moves cause an apparent inversion of tetrahedra which is emphasised by the manner of presentation in a. 3.

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378 KINETICS O F POLYMORPHIC TRANSITIONS

The reality is that the tetrahedra are present all the time and all that happens is that tetrahedra become occupied or empty.

There seems to be no other simple alternative mechanism to the one described above. Possibly, cations could take a more roundabout pathway than the single, direct jump but there seems to be no reason why this should happen. Any mechanism which involves movement of oxygens, such as complete inversion of the whole M 0 4 tetrahedron, would involve the breaking of many more bonds. As the structures contain approximately close packed oxide ions, the oxide ions would not be able to move easily and without considerable disruption of the rest of the structure.

Some experimental support for the simple cation migration model has been obtained. From optical microscopy, crystals of Li3P04 retain their continuity after undergoing the pII 4 yII transition.' Similarly, single crystal X-ray diffraction experiments showed that the y + p transition in Li,BeSi04 occurs topotactically and that a definite orientation relationship exists between the starting crystal and the product.

POSSIBLE METHODS OF STUDYING KINETICS

Two general methods were considered initially, differential thermal analysis (d.t.a.) and quantitative X-ray powder diffraction. There seemed to be several possible ways in which d.t.a. might be of use. Some involved analysis of partially transformed material by measuring peak areas corresponding to PI 7 pit, yo -+ yIr, and/or Prr + yII transitions. From these data and with the aid of calibration curves, the percentage transformation could, in theory, be determined. These experiments were unsuccessful however, because (i) poor resolution of PI -+ PII and y o -+ yII peaks was obtained and (ii) further transformation of unreacted y occurred during the d.t.a. experiment.

d-spacing E t a 4.- X-ray powder pattern of a mixture of PI- and yo-Li2ZnSi0,.

In addition to these essentially static analyses of partially transformed material, possible dynamic methods of analysis were considered. In these, starting with pure y-Li2ZnSi04, the heating rate would be adjusted so that the y 4 /3 transition occurred during the heating cycle and appeared as a d.t.a. exotherm. These experiments were unsuccessful because, although it was possib€e to adjust the conditions so as to observe a y + B exotherm on d.t.a., this exotherm overlapped partially with endo- thermic transitions such as #Jx 4 PIr. Consequently the base line for the y 3

transition was completely unknown and peak shape analysis was not feasible. The method that was finally adopted was quantitative X-ray powder diffraction

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M. E. VILLAFUERTE-CASTREJON A N D A. R. WEST 379

at room temperature on material which had been previously heated at high temperature and " frozen in " by rapid quenching. The X-ray patterns of yo and /II (the two forms commonly obtained at room temperature) are fairly similar with many lines in common but have characteristic differences. A microdensitometer trace taken from a Guinier powder X-ray film (it closely resembles a conventional diffractometer trace) is shown in fig. 4 for a 50 : 50 mixture of yo-and p1-Li,ZnSi04. The peaks with Miller indices (101) and (002) are characteristic of the two phases and from their relative intensities a method was developed for the analysis of ply contents.

EXPERIMENTAL

Reagents used were Li2C03, ZnO (both reagent grade) and high purity crushed quartz crystaI. The ZnO was dried at 900°C prior to weighing. Equimolar mixtures of the three oxides totalling 10-100 g were ground together under acetone in an agate mortar and grinding continued until all the acetone had evaporated. For the larger scale preparations, several mixings of different portions were necessary to achieve homogenisation. The mixtures were fired in Pt crucibles in electric muffle furnaces, initially at -600°C to drive off C02 and finally at lo00-1100"C for 1-3 days to complete the reaction. After cooling to room temperature in air (1-5 min), the product was analysed by powder diffractometry (Philips 1390 goniometer, CUKa radiation) to be pure yo-Li2ZnSi04. Thus, the cooling rates were sufficiently fast to prevent any conversion to the equilibrium p form occurring. For calibration purposes, a quantity of yo-Li2ZnSiOl was converted to B1-Li2ZnSi04 by heating for - 1 day at 750OC.

For the kinetic experiments, samples of y-Li2ZnSi04 (2-5 g) were suspended in small Pt crucibles at the hot zone of a vertical tube furnace. Temperatures were controlled to +2"C using a Eurotherm controller and a Pt/Pt 13 % Rh thermocouple was placed just over the crucible in order to measure the sample temperature. The transformation was stopped at various stages by removing the crucible and allowing it to cool in air (2-3 min). Sufficient Li2ZnSi04 for X-ray analysis was sampled from the crucible and the crucible returned to the furnace for further heat treatment. The furnace operated in the normal laboratory atmosphere. Since the sample takes 2-3 min to equilibrate at the temperature of the furnace, heat treatment times were never < 10 min and were usually much longer. Runs were timed from when the crucible was placed in the furnace; the errors incurred by not allowing for the dead time during which the sample was raised to temperature were small or insignificant.

The samples which were usually used for the kinetic runs were lightly crushed powders of Li2ZnSi04.

Two X-ray techniques for measuring the kinetics were tried and both found to be successful. In one, a powder diffractometer was used to scan at slow speeds (1 18' 28 min-I) the angular range which included the (101) p- and y-peaks. The intensities were determined from the peak areas by cutting out and weighing the peaks and latterly, by planimetry. The percentage transformation was then read off a calibration graph. Similar experiments were tried with the (002) peaks of /? and y but as the results showed more scatter than for the (101) peaks, these were discontinued. The manner of preparation of the diffractometer sample, pressing a finely powdered flake onto a glass slide, probably introduced preferred crystal orientation and this affected the intensities of the (002) peaks.

In the second X-ray method, Guinier powder photographs were taken with a Philips Hagg camera and the photographs analysed by microdensitometry using equipment designed and built by Brian Cooksley in Aberdeen. The microdensitometer output could be in the form of a chart record, in which w e the pattern resembled a diffractometer trace or as an oscilloscope trace. For this work, the (101) and (002) intensities of j? and y were taken as the peak heights measured from the oscilloscope. Samples for the Guinier camera were prepared by swirling the powder in acetone and, with a capillary tube, spotting a small amount onto a piece of cellotape which covered the window in the sample holder. This method of pre- paration did not appear to cause problems of preferred orientation and both (101) and (002) pairs of reflections could be used satisfactorily.

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380 K I N E T I C S OF POLYMORPHIC TRANSITIONS

For the d.t.a. experiments, a Du Pont 990 thermal analyser, 1600" cell, was used with heating rates between 5 and 100°C min-I.

RESULTS

Two sets of experiments were carried out. In the first, samples were heated in a muffle furnace whose temperature could be controlled and measured only to +30°C. Results were analysed by diffractometry. In the second, a tube furnace was used, which gave control and measurement of temperature to +2"C, and the results were analysed by the Guinier method and microdensitometry. Because of the much larger errors in temperature in the first experiments, only results for the second set are reported here. After allowing for the very different errors limits, however, the two sets of experiments gave comparable results.

CALIBRATION CURVE

Standard, mechanical mixtures of /3- and y-Li,ZnSi04 of known composition were prepared, Guinier photographs taken and the films analysed by two methods. Results are shown in fig. 5 for the (101) reflections method 1, in which log,, (YIP) is plotted against composition. Most data points are the average of results from up to four films and vertical bars indicate the scatter generally encountered. The agreement between results obtained from the same film was very good and it was necessary to

20 LO 60 80 100

%Y

log (y//3) are plotted against composition. FIG. 5.-Calibration curve for the (101) reflections method 1. Measured peak heights, given as

carry out each oscilloscope reading only once. The calibration curve is linear over almost all the composition range studied. At the two compositional extremes, gross departures from linearity must occur as the curve becomes asymptotic to the log(y//3) axis. At these compositions however, the X-ray method is insensitive anyway and departures from linearity in the calibration graph are not too important.

In method 2, the intensities of fi and y (101) reflections are measured relative to a reference line within the powder pattern, the (120) reflection at 4.09A. This line

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M . E. VILLAFUERTE-CASTREJON A N D A . R . WEST 38 1

appears as a singlet in P l y mixtures although it is a doublet and contains the (120) reflection of both #?- and y-Li2ZnSi04. The advantage of using an internal reference peak such as this is that the method is rapid, can be used on small samples and should be free from errors due to sample inhomogeneity. In more conventional quantitative

1 4 0

a 2 80 x

LO

0 20 40 60 80 100

%Y

relative to the (120) peak whose intensity is set equal to 100. FIG. 6.-Calibration curve for the (101) reflections, method 2. fi and y intensities are measured

X-ray methods, it is necessary to add a known weight of standard material to the sample and use one of the peaks of the standard as the reference intensity. The method is lengthy, can only be used on larger samples and is subject to a variety of errors (e.g., see C~ll i ty) .~

100

80

60 aQ x

LO

20 I

. 0 20 40 60 0

tlmin 7.-Percentage transformation against time at 734°C.

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382 KINETICS OF POLYMORPHIC TRANSITIONS

The caIibration curve for method 2 is given in fig, 6. The ordinate gives the heights of the (101) peaks relative to a value of 100 for the combined (120) intensity. The curve giving the y composition is linear over the whole composition range but this appears not to be so for jl.

Similar calibration curves were constructed using methods I and 2 for the (002) reflections. For method 2, the internal reference peak used was the combined (040) reflection at 2.69 A.

ANALYSIS OF KINETIC D A T A

Results for two temperatures, 734 and 572°C are given in fig. 7 and 8. These data are chosen as being representative of the behaviour commonly encountered. For both, the kinetics are deceleratory throughout and there is no sign of any induction

0 0 0 2 4 6 8 10 12 14 16

m FIG. 8.-Percentage transformation against time at 572°C.

period. Each data point is the average of four results, namely from (101) and (002) peak intensities, using methods 1 and 2 for both. A commonly used equation for fitting solid state reaction kinetic data is the Avrami-Erofeyev equation :lo

log (L) = (kt)". 1 -a

TABLE l.-VAcuEs OF EXPONENT, n, IN THE AVRAMI EQUATION

temperaturel'c n+

536 0.52 572 0.50 603 0.57 655 0.69 734 0.97 745 1.18 802 1.11 839 0.76 855 not constant

* Errors in n are - f 0.06.

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M. E. VILLAFUERTE-CASTREJON A N D A. R. WEST 383

a is the extent of reaction, which in the present case is equal to the amount of /3 and so the equation may be rewritten as :

log ('> = log (t> = (kt)". 1 -B

The value of the exponent, n, may be obtained from graphs of log . log (l/y) against log t, as shown in fig. 9 ; each data point is again the average of results from the four methods : n = 0.97 at 734°C and n = 0.5 at 572OC. The values of n for a range of temperatures are given in table 1.

At 734"C, n x 1 and the transformation obeys first order kinetics : -log(l-a) = -logy = kt.

- 2 6 / 2.5

1.0 7.2 7.4 76 T8 0 0.2 0.4 0.6 0.8 1.0 1.2

log t FIG. 9.-Determ€nation of reacfion order, n. Upper: 734OC, slope = 0.97; lower: 572°C

slope = 0.5.

0 0.2 0.4 0.6 0.8 1.0

tlh FIG. lO.-Fkst order kinetics observed at 734"C, slope = 2.18.

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384 KINETICS OF POLYMORPHIC T R A N S I T I O N S

To show this, the data are replotted in the form log (l/y) against t , fig. 10, and give a straight line of slope k = 2.18. The line intercepts the time axis at a small positive value (-2 min) which may correspond to the time taken for the sample to heat up once it has been placed in the furnace.

DISCUSSION

An X-ray method has been developed for studying the kinetics of polymorphic transitions such as y-+ p-Li2ZnSi04. Many of the problems inherent in quantitative powder diffractometry have been avoided because it has not been necessary to add an internal standard. Also, there is no problem of differential absorption of X-rays by different phases present in the samples because both phases present, y- and p- Li2ZnSi04, have the same composition. With recent advances in microdensitometry, intensities of lines on X-ray films may be measured accurately and rapidly and this provides a real alternative method to conventional powder diffractometry . Pre- liminary results at several temperatures show that the kinetics may be followed satisfactorily by the X-ray method.

The results have been analysed using the Avrami-Erofeyev equation and the order of the reaction, n, has been found to be temperature dependent. The data obey first order kinetics at 734°C and approximately first order kinetics at two other temperatures. A common reason for first order kinetics in reactions involving powdered solids is that the kinetics are nucleation controlled. A single nucleation site is sufficient for the transformation or reaction of each grain and so the reaction rate depends on the number of unreacted grains. It remains to be seen, however, whether the present kinetics are nucleation controlled and the occurrence of reaction orders lower than 1 also awaits explanation.

A. R. W. thanks the S.R.C. for financial support and the British Council for travel assistance. We thank Kathleen McKenzie for experimental assistance.

A. R. West, 2. Gist . , 1975,141,422 and references therein. A. R. West and F. P. Glasser, J. Mat. Sci., 1970, 5, 557. A. R. West and F. P. Glasser, J. Mat. Sci., 1970, 5, 676. J. A. Hedvall, Solid State Chemistry (Elsevier, Amsterdam, 1966). J. Zemann, Acta Cryst., 1960, 13, 863. C. Keffer, A. Mighell, F. Mauer, H. Swanson and S. Block, Inorg. Chem., 1969, 6, 119. A. R. West and F. P. Glasser, N.B.S. Spec. Publ. 364, Solid State Chemistry, 1972, 457. A. R. West, unpublished results. B. D. Cullity, Elements of X-ray Difraction (Addison Wesley, 1978).

lo A. K. Galwey, Chemistry of Solids (Chapman and Hall, London, 1967).

(PAPER 8/1200)

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