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KINETICSAND MECHANISM OF PHASE TRANSFORMATION OF SILVERIODIDE
yield would then depend rather on the radical-molecule reaction cited or the hydride ion transfer than on the hydrogen abstraction reaction. The extent of ion-molecule reactions in the liquid state is uncertain but it seems that ion dissociation reactions, which are competitive, are quite important.ls The mean lifetime of the allowed reactant fragment ions with respect to their reaction with the molecule, CbH12, is l / k c , where 12 for hydride ion transfer in pentane is 0.5 X 10-lo cc. molecule-' sets.-'. If the concentration of pentane molecules is approximately 5.2 X
1021 molecules cm.-a, then the mean lifetime with respect to the ion-molecule reaction is 4 X 10-l2 sec. If this is compared to the smallest estimates of the time for neutralization, which according to Samuel and Magee19 is to 10-14 sec., then it is obvious that the hydride ion transfer reaction competes unfavorably with neutralization processes and reactions of neutral species. ~~~~
~
~
(18) T. F. Williams, Trans. Faraday SOC.,57, 755 (1961). (19) A . H. Samuel and J. L. Magee, J . Chem. Phys., 21, 1080 (1953).
Kinetics antd Mechanism of the Low-Cubbic to Hexagonal Phase Transformation of Silver Iodide'
by Gordon Burley National Bureau 0.t Standards, Washington, D . C .
(Received November 18, 1969)
The transformation rates for the low-cubic to hexagonal irreversible phase change of silver iodide have been determined a t three temperatures by a powder X-ray diffraction technique. The reaction obeys first-order kinetics, with an activation energy of 10.3 f 0.8 kcal./niole. This is interpreted in terms of a mechanism where the silver atoms initiate the transition by movement to interstitial sites and the iodine lattice then moves to attain the lowest lattice energy.
Introduction Silver iodide is trimorphic a t atmospheric pressure. 2a Below 147' bo1;h a wurtzite-type hexagonal and a zincblende-type cubic structure can exist, but only the former is the stable modification in this temperature range. The cubic to 'hexagonal phase change is irreversible under ordinary conditions.2b At 147' both of these phases tiransform reversibly to a bodycentered cubic phase, where the silver atoms exhibit high mobility. The speed of any polymorphic transformation depends primarily on the energy barriers opposing the process, and the energy change during a transformation corresponds to a change in bonding type or geom-
etry of the atoms. Structurally the least drastic kind of transformation involves no change in the coordination of nearest neighbor atoms, but a change only in the coordination of atoms further removed than the nearest neighbors is possible. Because of the greater distances involved the bond interactions are then weaker. Two mechanisms for a change in secondary coordination are possible. In a displacive-type transformation the structure is only distorted system(1) Research supported by the Atmospheric Sciences Program of the National Science Foundation, NSF Grant G19648. (2) (a) R. B. Wilsey, Phil. Mag., 46, 487 (1923); (b) G. Burley, Dissertation, Georgetown University, Washington, D. C., 1962. (3) L. W. Strock, 2. physik. Chem. (Leipzig), B25,441 (1934).
Volume 68, Numbey 6 M a y , 1964
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GORDON BURLEY
atically. This is opposed by no energy barrier and consequently proceeds at high speed. I n a reconstructive type of transformation the entire network is broken and then reconstructed to form a new and different network. A very high energy barrier exists for this mechanism and the transformation generally proceeds very sluggishly. The phase change involving the zincblende- and wurtzite-type structures of silver iodide is of this reconstructive form. The magnitude of the energy barrier for silver iodide can be approximately determined from the kinetics of transformation. This follows directly from the Arrhenius rate equation iC =
A~-AE/RT
when values of the rate constant IC are available a t two or more different temperatures.
Table I : Experimental Data for the Face-Centered Cubic to Hexagonal Phase Transformation of Silver Iodide Time, hr.
Hex., %
0 2 4 8 15 24
30 32 34 37 41 45
0 2
30 34 40 45 49 56 30 45 53 55 57 59
5 8 12 20
Procedure Samples of the low-cubic phase with greater than 90% conversion were made from the hexagonal phase by (1) heating to just above the melting point and quenching in water and (2) compacting the material under a pressure of several hundred bars. A hightemperature powder X-ray diffraction apparatus, attached to a Norelco high-angle diffractometer, was used to obtain all data. The polycrystalline material was packed into the rectangular depression of an alumina sample holder, heated rapidly to a specific temperature, and maintained there for a number of hours. A frequent record of the diffraction pattern in the 28 range from 20 to 40°, using copper radiation, was obtained on an attached recorder. Several different samples were run a t each temperature.
Results The phase transformation occurred irreversibly and at a reproducibly finite rate a t all temperatures above 120'. The fraction of silver iodide converted to the hexagonal phase was estimated from the ratio of the integrated areas of the (100) and (101) reflections to that of the (110) reflection. The rate of conversion was determined a t 120, 137, and 146', and the experimentally determined values as a function of time are shown in Table I. The initial value of the fraction of the cubic phase was 0.70 in all cases, due to the difficulty of obtaining total conversion from the hexagonal phase as well as slight transformation during preliminary annealing a t 100'. The transformation was determined to be first order, in accordance with the k = l / t In [ a / ( a - s ) ] relation. The values of the three rate constants IC, were then determined graphically a t each experimental temperaThe Journal of Physical Chemistry
0 2'/4 4'/2 5 5 a/4 6'/4
F.C.G.,%
120" 70 68 66 63 59 55
a/(a
-
5)
log Ia/(a
- 511
1.oo 1.04 1.07 1.11 1.20 1.30
0.000 0.017 0,028 0.048 0.080 0.115
55 50 44
1.oo 1.06 1.16 1.26 1.37 1.59
0.000 0.026 0.066 0.104 0.136 0.200
146' 70 55 47 45 43 41
1.00 1.30 1.49 1.55 1.63 1.71
0.000 0.114 0.173 0.190 0.212 0.233
137' 70 66
60
ture. From the slope of a graph of the logarithms of these calculated rate constants against the reciprocal absolute temperatures the activation energy is estimated to be 10.3 f 0.8 kcal./mole (1 kcal. = 4.184 X lo3 joules), the uncertainty indicating the mean deviation of the result.
Discussion The low-cubic to hexagonal phase transformation for silver iodide has been shown to be irreversible. However, the low-cubic form can be prepared and kept for extended periods a t room temperature. Only above 120' does the conversion rate even approach a measurable rate, but nowhere is the transformation extremely rapid. This phase change is thus very sluggish, irreversible, and does not readily go to conclusion. The low-cubic phase of silver iodide, of the zincblende-type, and the hexagonal phase, of the wurtzitetype, may both be considered as layer structures and differ only in the stacking repeat. If only the iodine atoms are considered, this is analogous to the model close-packed cubic and hexagonal structures. The transition mechanism then must introduce one-dimensional stacking disorder. The relation of both the low-cubic and hexagonal phases to each other and to the high-cubic phase is shown in Fig. 1.
1113
KINETICSAND MECHANISM OF PHASE TRANSFORMATION OF SILVERIODIDE
0
v STRUCTURE.
bcc
PROJECTION: (101)
0
e
hex
tcc
(0011
(Ill1
Figure 1. Structural relationship of the three phases of silver iodide in projection, indicatcng required atomic shifts for transition. Open circles represent the A layer, filled circles the B layer, and half-filled circles the C layer.
differentiate between a model where the iodine atoms shift as layers and the silver atoms follow, and one where the silver atoms initiate the shift and the iodine lattice follows. No explanation of the specific mechanism of the low-cubic to hexagonal phase transformation has yet been proposed. An attempt will therefore be made to correlate other known properties with the kinetic results presented here. Activation energies have also been previously derived from electrical conductivity and specific heat measurements of silver iodide. These can be associated almost entirely with the known rapid creation of thermally generated defects in the temperature region between 100’ and the transition to the partially disordered high-temperature structure at 147O, and other effects can be neglected over this limited range. The conductivity has been found to be purely ionic, with B temperature dependence
The mechanism is similar to that of the diffusionless martensite-type transformation, with shear on the (111) cubic planes initiating the transition to the hexagonal lattice by a succession of identical glides on u = uo exp( -(Er/2 V)/RT)) ohm-’ tin.-' alternate parallel planes in the [Ti21 cubic directions. The dislocation node theory, developed by S e e g e ~ , ~ where Er is the energy required for the creation of one mole of defects and U is the energy barrier for transfer. suggests that the transformation begins from extended From measurements a t 100’ and 1 atm. pressure an dislocations (Shockley partials), which are anchored activation energy Er/2 U = 11.2 kcal./mole has at a screw dislocation extending into the hexagonal been r e p ~ r t e d . ~ region along the c-axis. Rotation of the half dislocaThe deviation of the specific heat in this temperation about the point of emergence of the screw advances ture region from the extrapolated low temperature the hexagonal region by two planes for each t h n . value has been equated to the rate of creation of thermal The dislocation lines would have a screw component defects by twice that of the (111) cubic interplanar distance and represent the nuclei of the hexagonal phase. de Experimentally it has been determined that slow AC, = Ei d T cooling through the transition temperature at 147’ yields the hexagonal phase, while rapid cooling proand, combined with the temperature dependence of duces the low-cubic phase.2b The latter probably indefect concentrattion, yielded a literature value for volves the formaition of a transition tetragonal strucEr/2 = 8 kcal./mole. The value of W is essentially ture, which then rearranges to the low-cubic form.3 temperature independent and was estimated as 2-4 The kinetics determined from the X-ray diffraction kcal./mole.6 The total activation energies measured results represent an average transition rate for the by the conductivity, specific heat, and kinetic methods system and cannot differentiate local inhomogeneity. are thus is excellent agreement. The transformation may occur either a t random A t this point the type of defects must be considered. sites or may be initiated a t preferred sites and progress It has been determined experimentally that the transto neighboring areas. However, the range over which port number of the Ag+ in silver iodide is near unity, the transition occurs seems to preclude a purely homoso that the entire current is carried by the cations.’ geneous nucleation process. The observed isothermal The thermal creation of defects in the temperature transformation process can then be attributed either range of interest here has been shown to lead predomito the presence of structural heterogeneities leading nately to the formation of Frenkel-type defects. This to lower interfacial energies a t specific sites, or to the refers to the creation of interstitials, leaving a positive creation of defect sites by thermal activation. For silver iodide, the silver atoms are in tetrahedral (4) A. Seeger, 2. Metnllk., 47, 653 (1956). coordination in both low-temperature structures, (5) K. H. Lieser, 2 . Physik. Chem., 9, 302 (1956). and the phase trainsformation involves a change of the (6) K. H. Lieser, Fortschr. Min., 36, 96 (1958). relative positions of these atoms as well as that of the (7) F. 9. Stone, “Chemistry of the Solid State,” W. E. Garner, Ed., iodine atoms. A transition mechanism must therefore Butterworths Scientific Publications, London, 1955, Chapter 2.
+
+
Volume 68, Number 6
May, 1964
GORDON BURLEY
1114
Figure 2. Schematic representation of the close-packed atomic arrangement. Dashed lines represent the first layer, and solid lines the second layer of iodine atoms. The arrangement of silver atoms required for the low-cubic progression is shown by triangles, and that for the hexagonal progression by small solid circles.
hole. The lattice of iodine atoms is thus essentially fixed and only the silver atoms are relatively mobile. This mobility of the silver atoms, together with the similarities of the activation energies obtained from the kinetics and ionic conductivity experiments, suggests a more detailed picture for the transition mechanism in silver iodide than any proposed previously. The layer stiucture in the cubic (111) direction is shown in Fig. 2. The arrangement of the silver atoms between the second and third iodine layers is shown by circles for the low-cubic and triangles for the hexagonal structure. The required shift is 1/& the distance between centers of iodine atoms and into an available interstitial site. The creation of one interstitial silver site leads to a local lattice instability and two factors then favor its propagation. First, the repulsive iriteractions of neighboring cation force fields favor their separation and, second, the creation of a number of adjacent identical defects is equivalent to a lattice
The Journal of Physical Chemistry
glide. These silver atoms will tend to move the adjacent iodine atoms of the next successive layer into the tetrahedral configuration. The tendency is toward the phase of lowest lattice energy, which in the case of silver iodide is the hexagonal form. The energy barrier measured by the kinetics experiments must thus be the sum of the energy required for the creation of an interstitial Frenkel-type defect and the energy to move a silver atom from its lattice site to the interstitial site. The transformation rate is temperature dependent, in agreement with the measured increase of defects a t higher temperatures. The iodine atoms then move only in order to minimize the silver coordination number and no appreciable energy barrier exists for this.
Conclusions The kinetic measurements for the irreversible lowcubic to hexagonal phase transformation of silver iodide have been interpreted in terms of a transition mechanism. An activation energy of 10.3 h 0.8 kcal./mole was derived from the rate equation in the temperature range from 120 to 146'. By analogy with the results from conductance and heat capacity experiments this leads to the conclusion that the iodine lattice remains essentially stationary and the transition is initiated by the movement of silver atoms to interstitial sites. When a sufficient number have migrated to positions required for the hexagonal progression the adjacent iodine atoms of the next succeeding layer then shift. The transformation is regional and stepwise, since only local conditions are of importance, a.nd the trend is always toward the more stable hexagonal phase. The specific mechanism may be analogous to that of the martensitic-type transition.
