OBSERVATION OF PRETRANSITIONAL EFFECTS ON THE SHAPE OF THE E2 (17 cm-1 ) OPTICAL MODE IN β-Ag1 BY RAMAN SPECTROSCOPY

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OBSERVATION OF PRETRANSITIONAL EFFECTS ON THE SHAPE OF THE E2 (17 cm-1 ) OPTICAL

MODE IN β -Ag1 BY RAMAN SPECTROSCOPY

E. Cazzanelli, A. Fontana, G. Mariotto, F. Rocca, M. Fontana

To cite this version:

E. Cazzanelli, A. Fontana, G. Mariotto, F. Rocca, M. Fontana. OBSERVATION OF PRETRAN- SITIONAL EFFECTS ON THE SHAPE OF THE E2 (17 cm-1 ) OPTICAL MODE IN β-Ag1 BY RAMAN SPECTROSCOPY. Journal de Physique Colloques, 1981, 42 (C6), pp.C6-776-C6-778.

�10.1051/jphyscol:19816229�. �jpa-00221313�

JOURNAL DE PHYSIQUE

Colloque C6, suppl&ment au n o 12, Tome 4 2 , de'cembre 1981 page C6-776

OBSERVATION OF PRETRANSITIONAL EFFECTS ON THE SHAPE OF THE E 2

-

¹

(1 7 cm ) OPTICAL MODE I N

6

- A g I BY RAMAN SPECTROSCOPY

E. Cazzanelli, A. Fontana

,

^{G. Mariotto,} F. ~occa* and M.P. ~ontana**

Dipartimento d i Fisica e Unitd G.N.S.M.

-

^{C.N. R.,} Trento, I t a l y

*

I s t i t u t o per l a Ricerca S c i e n t i f i c a e TecnoZogica, Trento, I t a l y

**

I s t i t u t o d i Fisica e Unitd G.N.S.M.

-

C.N.R., Parma, I t a l y

Abstract.- Resonance interference between the E2(17 c m l ) optical mode and the continuum of one-phonon density of state has been observed in E-AgI. From a fitting of the E2 optical node shape with a "Fano" formula ve have obtained the temperature behaviour of the coupling parameter c, and the true half-wid t h which show substantial change near the B-ta transition temperature.

The lattice dynamics of AgI has been extensively studied in recent years('). On par- ticular interest is to understand the vibrational dynamics near the superionic tran- sition. Since the ionic conductivity jump at To 2 1 4 7 O ~ is coupled with a change in the crystal structure(l) it is reasonable to assune that phonons play an impor- tant role in driving the transition. However no detectable pre-transitional effects have been observed in R m a n spectra upon approaching To.

The nature of the Raman spectra in AgI and its change with temperature is clearly a- nomalous and has been the subject of some controversy. Recently we have shown that the anomalous features in the Raman spectra and their temperature dependence were connected with a first order phonon partial density of states, activated in the 6-phase by a local low temperature desordering

of the A ~ +

ion^(^-^).

In Fig. 1 we show the tern perature dependence of Raman spectra in 6-AgI.

It is clear from the figure that the perfectly 1

normal spectrum due to zone center optical modes

-

V changes continuously into a continuum of vibra-

tional states, as temperature is increased, with

e

= o the sole exception of the E2(17 cm-1) optical 2

mode. Thus such optical mode is barely affected >

by the local disordering of ~ g + ions: this is I:

probably due to the extreme flatness of disper-

$

sion curve(4). Biihrer and ~ruesch(~) argue that 5 the sharp E2 optical mode induce the phase tran- o . sition by favouring of Frenkel pairs in the Ag

5

sublattice. In fact the E2 mode has the appro- priate eigenmode structure and disappears dis- continuously at 147'~. However the "coupling"

of such mode to jumping cations does not appear to produce important effects on the mode dynamic

-

1

^-.--

A['(- ^-

I 12 K

i2d!bd,

5 0 100 150 ^{, -}

structure factor as the phase transition is ap- ^O R A M A N SHIFT I C ~ - ' I

proached. One reason for apparent insensitivity

7ig. 1: Experimental Raman spectra of E2 mode may be that overall vibrational re-

at various Temperature from to sponse of AgI is similar in two fi and a-phase

150 cm-l.

(395). However, a finer experimental analysis of

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19816229

1

-

the E2 mode damping increases considerably;

2

-

the shape of E2 line is visibly asymmetric;

3

-

there is a slight shift towards low frequencies;

4 - the total Raman Intensity devided by the Bose- Eistein factor remains constant.

-

>

In order to interpret these data we hypothize a Fano b interference(6) between the 17 cm-I peak and the un- V)

iz

derlying continuum of vibrational states. From ine-

5

lastic neutron scattering we can assume that such

- _z

continuum is due to the phonon density of states as- sociated with an acoustical branch: such branch has,

2

at zone edge, the same sinmetry and nearly the same

d

energy as the almost flat branch of the E2 optical

mode. For a given temperature the Fano spectral sha 10 15 20

pe can be written as(7) RAMAN SHIFT (cm-'1

2 Fig. 2: Experimental E2 optical

mode at various temperature near E2 mode spectral region does show some pretransiti~

where 0' is the cross section for the underlying transition. a = 3 0 3 " ~ ; b = 380'~;

continuum which does not interact with the discrete ⁼ 4170K.

state, and

<I la1

10> -

= n<l]w12><2[a2[0> m ?

2)

-

E

-

^El

E

-

n1<21a210>1T

'

^{= Eq +}

where Eq is the eigenvalue of the uncoupled one-phon state (i.e. the energy of the E2 mc

-

de) and F is the slight shift from Eq due to c

z

admixture of states. A simple scheme of Fano _, ... . . . . ,-.-.

interference is to view the like shape of a ...

discrete mode interacting with a continuum

as due to interference between two coherent -

scattering channels into the same heavely 7 12 17 2 2 damped final state: the first is a direct R a m a n Shift (crn-'1 channel <21a210> coupling the ground state Fig. 3: The E2 line at 4030K.

10,

^to ,.he continuum 12,; the second is an Dots: experimental data; solid line: fit indirect one, coupling states lo> and [2> using eq. (1). Lower solid line: true li via the discrete state

I

I > and is given by ne

a second order matrix element <2[wll><lla [0> where <2[w[l> describes a non radiative nal effects as To is approached (fig. 2). From the-

se experimental data we see that:

transition from the discrete level into the continuum degenerate with it. Such non radiative transition is connected with the true width of the line

A

r

⁼ 2n]<21wll>l 2

In the figure 3 we show a typical fit of the spectra for T = 403'~ together with the calculated

true

experimental band shape.

If the reasonable assumption that <llal 10> and <21a210> are independent or weakly de- pendent on temperature is also made, then we have that 3) q ?.

T-4

and thus the main contribution to the temperature dependence in the Fano fitting of the E2 mode

lineshape will be connected with the behaviour of the true linewidth. We have veri- fied the assumptions leading to (3) by fitting the E2 lineshape using (1) with both

C6-778 JOURNAL DE PHYSIQUE

q and

r

as free parameters. We have found that the product q

l'-1

was independent temperature q within our 10.Z estimated error.

In fig. 4 we show separately the behaviour of

I

the coupling parameter q and the halfwidth

r 20.

temperature.

Prom inelastic neutron scattering data (4) we found that the E2 opticai mode and the density of states associated with the acoustical branch change little with temperature. Thus the change in the <llwl2> matrix elements as To is approa-

,rm8,ip

ched cannot be due to changes in the vibrational dynamics. Rather the increase in the coupling must be connected with a "static" property of the system, such as an order parameter.

In the framework of our interpretation of the anomalous features in the Raman spectrum of I3 and a-AgT, we are led to associate the behaviour of q (or l') to the jump motion of the ~ g + ions and

to the associated degree of disorder. Thus the 0.4 I appropriate order parameter could be the concen-. 180 300 420 7 tration of Frenkel pairs, itself connected with Fig. 4: Behaviour of the q and macroscopic ionic conductivity. parameters versus temperature.

Work supported in part by CNR contract N. 80.00816.11.

References

1) G.D. Mahan, W.L. Roth, Editors, "superionic Conductors", Plenum Press,N.Y. (1976) P. Vashista, J.N. tlund-{, Editors, "Fast ion transport in solids", North Holland, Amsterdam (1979)

2) A. Fontana, G. tlariotto, If. Montagna, V. Capozzi, E. Cazzanelli, bi.F. Fontana Solid State Cornmun.

28,

35 (1978)

3) G. llariotto, A. Fontana, E. Cazzanelli, 1I.P. Fontana, Phys. Stat. Sol. (b)

101,

341 (1980)

4) ^11. Bchrer, R.H. Nicklow, P. Briesch, Phys. Rev.

Bx,

3362 (1978) 5) A. Fontana, G. PIariotto, M.P. Fontana, Phys. Rev. B z , 1102 (1980) 6) U. Fano, Phys. Rev.

124,

1866 (1961)

U. Fano, J.!J. Cooper, Phys. Rev.

137,

1364 (1965) 7) J.F. Scott, Rev. Modern Phys.

46,

^{86 (1974)}

P.L. Rousseau, S.P.S. Porto, Phys. Rev. Lett.

2,

1354 (1968)