A THEORETICAL MODEL FOR THE CONTINUOUS ORDER-DISORDER TRANSITION AT 703 K IN SUPERIONIC α-AgI

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A THEORETICAL MODEL FOR THE CONTINUOUS ORDER-DISORDER TRANSITION AT 703 K IN

SUPERIONIC α-AgI

V. Mazzacurati, G. Ruocco, G. Signorelli, E. Cazzanelli, A. Fontana, G.

Mariotto

To cite this version:

V. Mazzacurati, G. Ruocco, G. Signorelli, E. Cazzanelli, A. Fontana, et al.. A THEO- RETICAL MODEL FOR THE CONTINUOUS ORDER-DISORDER TRANSITION AT 703 K IN SUPERIONIC α-AgI. Journal de Physique Colloques, 1981, 42 (C6), pp.C6-196-C6-198.

�10.1051/jphyscol:1981658�. �jpa-00221594�

JOURNAL DE PHYSIQUE

CoZZoque C6, suppldment au n O 2 2, Tome 42, de'cembre 1981 page C6-I96

A THEORETICAL MODEL FOR THE CONTINUOUS ORDER-DISORDER TRANSITION AT

703 K IN SUPERIONIC a-AgI

4 4

V. Mazzacurati, G. Ruocco, G. Signorelli, E. Cazzanelli , A. Fontana and G. Mariotto*

Istituto di Fisica e Unitd GNSM-CNR, Roma, Italy

*Dipartimento di Fisica e Unitd GNSM-CNR, Trento, Italy

Abstract.- We interpret the Raman intensity behaviour and the depolarization ratio in superionic a-AgI on the basis of a theoretical model.

A great deal of theoretical and experimental work has been devoted to study of solid electrolytes and especially A g I both in the superconducting "phase" (a) and in the normal one ( 8 ) . Recent experiments show that the Baman spectrum of a-AgI is essentially characterized by two broad bands, which are assigned to the acoustic and optical phonon density of states of the crystal respectively. The Ag+ ions (4 per unit.cell) are randomly distributed and therefore their movements are essential- ly uncorrelated with I- oscillations ( 3 ) . Furthermore the polarization ratio of the Raman spectrum is frequency independent and below 320'~ has a value f = 1i/III ^{= 1.05.}

As a matter of fact if a liquid like distribution of ~ g + ions has t; be expected, the depolarization ratio should not, in any case, exceed 0.75: only a model in which A ~ + ions are distributed randomly in a defined sublattice can in principle explain this value. An other peculiar result is that increasing the temperature both intensi- ty and depolarization ratio decrease reaching above 430°C respectively a factor 12 less and the value of 0.68. In principle the p = 0.68 value suggest that the disor- der is increasing, while the decrease in intensity of the disorder allowed Raman spectrum can be interpreted only by supposing that the overall distribution of the A ~ + ions is more isotropic.

Following these considerations we will assume a very simple picture for our c r y stal (using mostly the same approximation adopted by Andreoni and Phillips in their recent paper (4?), in order to attempt an explanation of the experimental data. We suppose that the A ~ + ions can be located essentially

in the d-sites obtained with the aid of a 3 interpene- trating bcc sublattices (see fig. 1). Around a given I- we will have therefore 8 I- ions in a bcc lattice and 24 d sites that should allocate an average of 4 A ~ + ions. We shall consider hereafter this 24 sites as

constituting the "cage" relative to the central I-ion Each cage has 8 neighbouring cages, each having in common the hexagonal face evidentiated in Fig. 1.

The disorder in polarizability whichgives raise to the Raman spectrum is introduced by deformation of the symmetric electronic cloud of each I- ion by means

of a randomly oriented electric field acting on this -. sig. 1 : The cage with the 24 point polarizable charge due to the occupied sites of

d-sites.The sketched the cage. A given configuration of the Ag+ distribu-

fase is that in comnon tion in the crystal has a total energy, which is the

with the near cage.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1981658

sum of the covalent part of the bonds, the I-Ag' Coulomb attraction, and the I--1- and Ag+-Ag+~oulomb repulsion. ----I- Supposing that both the covalent part and the screening of the electric field do not depend on the distribution considered, the only part of this energy that depends on the configuration is the Ag+-Ag+ repulsion, depending on the mutual distances of the distribution. The simplest

form is to assume for the induced polarizability a trace- ^{2 . 9 5} less tensor, which is diagonal in any cartesian frame ha-

vgng the z axis parallel to the resulting electric field p lied in the central I- ion, the components bei-

::Ot FP ^{+ )}

in a first approximation, B a Etot. On the basis of such 2

, , ,

, , ,

hypotheses, we may develope the induced polarizability in

Tab. 1 : Energy in eV unit power series of atomic displacements and then obtain the

corresponding to Raman spectrum by Fourier transforming the correlation

the various con- functions of these derivatives (5). We can write:

figurations of N

1,

Ap

4

where y , ~ ' are the I- ions, the polarizability derivatives of which have to be corre- lated, 1' and 1" are Ag+ ions in two cages and 6xa are a cartesian component of the

1 v

relative displacements. Iii is the 90" scattered Intensity with incoming radiation polarized in the i directi0n.a d the outcoming radiation polarized in the j direc- tion. The average

a

6 q . 2 x;J

~ g + ion in the cages centered around p,~'. Assuming complete disorder in the orienta- tion of the polarizability tensor, so to have only self correlation functions we ha- ve calculated the average as follows (each configuration has been chosen calculating repulsive interaction between A$ ions). Using the stoichiometric distribution (4 in a given cage) the lowest configuration

~ 0 4

sotropic polarizability and one related to the change in direction of the induced tensor. The expressions are identical to the two first terms in the polarizability modulation adopted in the paper of Alben and Burns (6). Of course both term have the effective charge again as a parameter. While for the change in direction we can pre- sumably use the same value adopted in the repulsive energy calculation, related to the Phillips ionicity, we have to use the Szigeti charge in calculating the modula- tion of the electric field value. This gives in our case a fixed number to the ratio of the two coefficients limiting the choice of this polarizability expansion.

means of this number the polarization ratio calculated averaging over the 24 C; con- ?y figuration becomes p = 0.68. The basic idea is to consider also cages with only three or five Ag+. Of course, if a cage has 3 Ag+, there must be elsewhere some other with 5 in order to achieve electrical neutrality. If we calculate the distribution of 3 and 5 Ag on the cage we obtain that 1) the lowest energy configuration C? and C0 are

1 1 3

widely separated from the C3 and C5, '2) the sum of the energies of isolated C'₃

!

C6- 198 JOURNAL DE PHYSIQUE

is greater than 2 x c,: but not so much _I different. 3) the depolarization ratio is always p = 1.08 for all the diffe- ^1.0 rent realizations of the C; and C$ con- figurations, and the same valcle is ob-

1 1

tained also for the C3 and C5. 4) Being each cage not at the stoichiometric va- _0.5 lue, if two cages with distributions C: and CO are close together, there is an addit~onal 5 attractive term which can be evaluated.

Of course the distribution of nea- 0.1

100 200 300

rest neighbour cages influence one each

other, so that, as an example at least Fig. 2 : The points are the integrated Raman two cages out of eight around a given intensity. The solid line is the be- C

: must be either :C or c?. Of course haviour of n(T) by experimental da- the idea of cages out of the stoichio- ta.

metric population does not contraddict I I

can assume "cage" structure of the crystal to be essentially that of neighbouring C3 and C2 configuration. The fraction of :C and C4 is only a small part, and the par- .'

tial correlation between C3 and Cg consti-

tute an interconnected path, as if the sy-

1 ^'k 1

200 300 400 1 TIC)

stem is beyond same percolation thereshold.Fig. 3 : The points are the experimental the charge neutrality principle. Simply it

states out that the correlation lenght of A ~ + is greater than the edge of the bcc I- lattice.

At low temperature in the a-phase we .9

Increasing the temperature the number of data of depolarization ratio p.

CZ

CZ

.

.

' '3

other) becomes more and more important and ned by 17 (T).

at a "critical" temperature of 430°C the number of CZ and C: will be dominant, so that no interconnected paths can be found. With this picture we will have of course a decrease in the Raman intensity, connected to increasing number of C: which do not contribute to the scattering process and a progressive decreases of the polarization ratio from the p '3 5' value of 1.08 to the p 4' value of 0.68. Our model has as p a rameter the fraction of cages C4, q(T) at every temperature. It is possible, however, to have such parameter by the Raman intensity behaviour I(T); in such manner the va- lues of p(T) are determined without any other parameter. Fig. 2 shows I(T) and the corresponding parameter n(T), while Fig. 3 shows the experimental p(T) and the value obtained with our model. The very good agreement gives us confidence in the validity of the proposed model and we shall try to use it to explain other experimental data, such as ionic conductivity, specific heat, etc.

1) A. Fontana, G. Mariotto, M.P. Fontana, Phys. Rev. B g , 1102 (1980) G. Burns, F.H. Dacol, H.W. Shafer, Phys. Rev. B g , 14LO (1977)

2) G. Mariotto, A. Fontana, E. Cazzanelli, F. Rocca, M.P. Fontana, V. Mazzacurati, G. Signorelli, Phys. Rev. B 2, 4782 (1981)

3) E. Cazzanelli, A. Fontana, G. Mariotto, I?. Rocca, V. Mazzacurati, G. Ruocco, G.

Sienorelli, Solid State Ionics

4) V. Andreoni, J.C. Phillips, Phys. Rev. B 3 (1981) 5) To be published

6) P.C. Alben, G. Burns, Phys. Rev. B 16, 3746 (1977)