A STUDY OF POLARITONS AND PHONON PECULIARITIES IN CuCl1-xBrx

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A STUDY OF POLARITONS AND PHONON PECULIARITIES IN CuCl1-xBrx

O. Brafman, G. Livescu

To cite this version:

O. Brafman, G. Livescu. A STUDY OF POLARITONS AND PHONON PECULIARITIES IN CuCl1- xBrx. Journal de Physique Colloques, 1981, 42 (C6), pp.C6-96-C6-98. �10.1051/jphyscol:1981630�.

�jpa-00221566�

JOURNAL DE PHYSIQUE

Colloque C6, suppl6ment au n012, Tome 42, de'cembre 1981 page ~ 6 - 9 6

A STUDY OF POLARITONS AND PHONON PECULIARITIES IN CuCll-,BrXf

0. Brafman and G. Livescu

Department of Physics and Solid S t a t e I n s t i t u t e , Technion-Israel I n s t i t u t e o f Techno logy, Haifa 32 000, I s r a e l

Abstract.- The optic phonon anomalies found in CuCl Br by means of Raman scattering and polariton measurement are presented. 'TfiesE irregularities are explained in terms of a model which accounts for the phonon and other

anomalies in pure Cu-halides.

The optic phonon modes in CuCl Br show an irregular behavior even at low temper- 1-x x

atures. This is true with respect to concentration dependent phonon frequencies, their Raman intensities and especially their oscillator strengths. The oscillator strengths were deduced from fitting the calculated polariton dispersion to that measured by means of Raman forward scattering. Figure 1 shows the frequencies of the three oscillators so obtained. The notation (1) and (2) relates to the main oscillators, while d stands for disorder induced lines"). In fig. 2 the three oscillator strengths are presented as function of the anion concentration. The oscillator strength in a crystal is proportional to the number of oscillators participating in a given mode. Therefore both oscillator strengths in a two mode solid solution decrease gradually with mixing. This is obviously not the case in C U C ~ ~ - ~ B ~ as shown in fig. 2 and it can not have a simple and straight forward

X

explanation. On the other hand this behavior of C U C ~ ~ - ~ B ~ optic phonons is not

X

totally surprising. Even at low temperatures where CuBr phonons are well behaved, the phonon spectrum of CuCl shows numerous anomalies and those were widely dis- cussed earlier(2). The main feature is the appearance of two polar modes instead of a single expected one mode. The two polar modes, labeled B and y, exhibit the same synimetry but differ considerably in linewidth and in the effect of temperature on the lines regarding intensity, frequency and width.

We shall interpret the present results with the help of a model which successfully explains the anomalies in pure CUC~'~). It is assumed that Cu may occupy off

+

center sites in CuCl giving rise to the B mode while those in ideal sites

participate in the y mode. Microscopically can be de~cribed(~)as being composed of five types of tetrahedra with n chlorine ions and 4-n bromine ions, o<n<4, with x dependent probability. The main assumption in the present work is that Cu may occupy off center positions, only in tetrahedra built exclusively on

+

chlorine ions (n=4), and that it should then occur with the same probability as in pure CuC1. On the other hand in all tetrahedra with n#4, Cu occupy solely

+

*Work supported by the Israel commision for Basic Research and by the Fund for the Promotion of Research at the Technion.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1981630

1201 I I I I I

0 0.2 0.4 0.6 0.8 1.0

cuce x CuBr c ~ c e X CuBr

Fig. 1: The frequencies of TO(1)-LO(l), Fig. 2: The three oscillator strengths TO(d) -LO(d) and TO(2)-LO(2) , at various S1, S and Sd (triangles, crosses and ₂ concentrations. circles respectively) for the various

concentrations. The lines serve only as a guide to the eye.

Fig. 3: A layout of the functions used for deducing the Sl (x) and S2(x) (heavy lines)

.

e (XI

The dashed line is (SCuC1

-

2 d

deduced from polariton data and are the same as in fig. 2.

cuce x CuBr

JOURNAL DE PHYSIQUE

central positions. Fig. 3 presents the principal features of the calculated oscillator strengths (S) of the various modes as function of concentration, which result in S (x) and S2(x)

-

1

heavy lines in the figure. The total oscillator strength of each compound is assumed to vary linearly with x(SC C1 , SCuBr). S (x)=1.7(1-x) ⁴ where S (0)=1.7

X

is the S of pure CuCl and f=(l-x) is the probability of tetrahedra with n=4. The B

mode of CuCl and the mode of CuBr exhibit a one mode behavior thus S (x)+SCuBr(x)

B

add to S (x), which is the lower frequency polar mode. The contribution of B-CuC1 1

to S (x) decays very fast with x, corresponding to the decrease in the concentration 1

of "all chlorine" tetrahedra in the mixed crystal.

Scucl (x)

-

S2(x). The S is small compared to the other two oscillators at all concentrations.

d

S is the result of disorder and is affected also by the ability of CU+ to occupy d

off center as well as central sites. Triangles and crosses are the experimental values of S (x) and S (x) obtained from the polariton measurements (the same as in

1 2

fig. 2). Considering the fact that the only parameters we used were those employed in fitting the polariton data, the fit is self consistent and in addition it gives reasonable solutions to the problems which were presented earlier.

References

1. 2. Vardeny and 0. Brafman, Phys. Rev.

=,

2. 2. Vardeny and 0. Brafman; Phys. Rev.

e,

3. H.V. Verleur and A.S. Barker, Jr. Phys.

149 ,