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Submitted on 1 Jan 1974
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DEBYE-WALLER FACTOR OF TIN-ANTIMONY SOLID SOLUTIONS
J. Sitek, J. Cirak, J. Lipka
To cite this version:
J. Sitek, J. Cirak, J. Lipka. DEBYE-WALLER FACTOR OF TIN-ANTIMONY SOLID SOLUTIONS.
Journal de Physique Colloques, 1974, 35 (C6), pp.C6-379-C6-380. �10.1051/jphyscol:1974669�. �jpa- 00215826�
JOURNAL DE PHYSIQUE Colloque C6, supplément au no 12, Tome 35, Décembre 1974, page C6-379
DEBYE-WALLER FACTOR OF TIN-ANTIMONY SOLID SOLUTIONS
J. SITEK, J. CIRAK and J. LIPKA
Slovak Technical University, Department of Nuclear Physics and Technics, Bratislava, Czechoslovakia
Résumé. - La fraction de résonance Mossbauer a été mesurée sur "9Sn dans des solutions solides SnSb entre 80 et 500 K. La validité de l'approximation harmonique a été discutée pour des solutions solides de 3 et de 10 at % d'étain dans l'antimoine. Des valeurs du rapport des constantes de force ont été obtenues.
Abstract. - The recoilless fraction of the resonance line of Mossbauer transition has been measured on "9Sn as a component in SnSb solid solutions in the temperature range 80-500 K. The applicability of the harmonic approximation has been discussed for solid solutions of 3 at % and 10 at % tin in antimony. Values of the force constant ratio have been obtained.
The Mossbauer effect provides a very good tool for the study of the lattice dynamics of the solid solutions containing a Mossbauer nuclide. The probability of the Mossbauer resonance absorption f (Debye-Waller factor) depends upon the interatomic forces of the atoms in the crystal. In the harmonic approximation, assuming a Debye model of the lattice, the following condition had to be fulfilled [1]
2 kT
- ln f ( T ) 2 -o [ln f (O)]
*
where k is the Boltzmann constant, Er is the recoil energy and Tis the temperature.
This inequality can be used to estimate the degree of applicability of the harmonic approximation to solid solutions. This can be done by measuring f at liquid helium temperature and at higher temperature.
The general problem of the dynamical behaviour of impurities in monoatomic host lattices is difficult to treat because the symmetry of the lattice is destroyed.
Assuming nearest neighboiir central forces various approximation have been made [2, 31. For instance, Marshall's approximation assumes that the frequency spectrum is similar to that of the host lattice with such a change that for a Debye model the Debye temperature of the impurity 0; is related to the host 0, according to
been used for the measurement. The Mossbauer spectra were singlet lines. The recoilless fraction of the absor- bers has been obtained from the measurement of the area of the absorption line.
We have measured the recoilless fraction in the temperature range from 80 K to 500 K. It is evident that by increasing the temperature the value o f f is decreased. However, the differences between recoilless fraction for the sample with 3 at % (sample 1) and 10 at % (sample 2) of tin in antimony became smaller towards higher temperatures (Fig. 1). The recoilless fraction for the sample 1 over the temperature range 80-500 K has been higher than for sample 2.
where M , M' are the masses of the host and impurity o.i
atoms and 1, 1' are the corresponding force constants for host-host and host-impurity atoms respectively.
The samples of Sn in Sb were prepared as an absor-
1-
l , A U 1--ber by melting and then grinding into powder form. The 100 200 300 400 500 s tin in an timon^ were at % and FIG. 1. - Temperature dependence of the Debye-Waller factor 10 at % respectively. The source of Ba '19Sn0, has in solid solutions of SnSb for 3 at % Sn and 10 at % Sn.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1974669
C6-380 J. SITEK, J. CLRAK AND J. LIPKA There is slight difference between the masses of tin
and antimony. Thus we can assume that the impurity atoms of tin vibrate at the frequency of resonance modes. By increasing the concentration of tin, the frequency of resonance modes shifts to lower fre- quences and the recoilless fraction is lower for sample 2 than for sample 1.
We have made the test at the anharmonicity using formula (l), where we inserted for fo the value f, = 0.663 and f, = 0.476, respectively, which were obtained from the measurements at the temperature 5 K. The results of the anharmonicity test are given on figure 2. The dashed line shows the limit of the harmonic approximation.
harmonie approximation is better for the sample with lower impurity concentration. When the differences between p and the harmonic limit are getting smaller at lower temperatures, the harmonic approximation of the crystal lattice vibrations is better at these tempe- ratures. Both these phenomena indicate that the Debye mode1 for the crystal lattice is not exactly valid at higher temperatures and higher tin concentrations in antimony.
We have obtained the force constant ratio Â'/Â from formula (2) using the Debye temperature, for the tin component which was calculated from the value of the recoilless fraction. For both samples the ratio h ' / A shows a weakening of the bond between tin-antimony atoms. The temperature dependence of ,l'/A is shown on figure 3. The weakening towards lower temperature can be explained by temperature shifting of the reso- nance modes and probably slightly also by influence of the low temperature anharmonicity. Weakening of the bonds towards higher temperatures can occur under the influence of the high temperature anharmo- nicity.
FIG. 3. - Temperature dependence of the force constant ratio FIG. 2. - Dependence of p = - --- In ( T ) on the temperature in l ' / A in solid solutions of SnSb.
[ i n f (0)12 solid solutions of SnSb.
Measuring of the Mossbauer line shift has shown a The values of p , (for sample 1) are closer to the small decreasing by increasing of the temperature but harmonic limit over the entire temperature range than in this case it was not possible to distinguish the the values of p, (for sample 2). It is evident that the temperature shift from the isomer shift.
References
[Il HOUSLEY, R. M . , HESS, F . , Phys. Rev. 146 (1966) 517.
[2] MANNHEIM, P. D., Phys. Rev. 165 (1968) 1011.
[3] ~'CONNOR, D. A. et al., J, Phys. F, 2 (1972) 1179.
