Lattice-dynamics of the intermediate oxide of tin

The lattice-dynamical properties of the intermediate oxide of tin (IO) have been investigated over the temperature range 80-295 K. The logarithm of the recoil-free fraction varied linearly with temperature. However, a Debye model does not give a good account of this dependence. By comparison with the other oxides of the Sn-O system, the recoil-free fraction for tin atoms with 2+ and 4+ oxidation states of the IO were estimated. At room temperature, they are 0.463 and 0,323 for 4+ and 2+ states respectively.


Lattice-dynamics of the intermediate oxide of tin
The lattice-dynamical properties of the intermediate oxide of tin (IO) have been investigated over the temperature range 80-295 K.The logarithm of the recoil-free fraction varied linearly with temperature.However, a Debye model does not give a good account of this dependence.By comparison with the other oxides of the Sn-O system, the recoil-free fraction for tin atoms with 2+ and 4+ oxidation states of the IO were estimated.At room temperature, they are 0.463 and 0,323 for 4+ and 2+ states respectively.

I n t r o d u c t i o n
It is well known that at increasing temperatures the SnO becomes thermodyna-micaUy unstable and undergoes a disproportionation reaction.Depending on the temperature, SnO2, 13-Sn and an IO displaying 2+ and 4+ oxidation states are formed irrespectively of the atmosphere: air, Ar or vacuum.The composition and mechanisms of formation of the IO is still an open question [1].
An insight into the composition, structure and mechanisms of formation of the IO is possible using MS.For these purposes it is necessary to determine the recoilfree fractions of each oxidation state, and characterize the hyperfine interactions of tin atoms in the IO.In previous studies [2] this was successfully done for the 2+ oxidation state but the impossibility of separating at room temperature (RT) the interactions of SnO2 and those of Sn 4+ in the IO was also evident.
In this paper we have determined t h e f factors of tin atoms at sites with the two (hereafter 2+ and 4+) IO oxidation states and give account of some dynamical properties of the crystal lattice.

Experimental
MS measurements were performed on the products of disproportionation of SnO heated in Ar (10 Torr) at 450°C, namely SnO2, IO and 13-Sn.A variable temperature cryostat operating in the range 80-295 K (4-0.1 K) was used for the Mtssbauer spectra acquisition.The spectra were recorded in a conventional con-stant acceleration apparatus with a transmission geometry.The data were fitted with a non-linear least-squares program with constraints to Lorentzian line shapes.

Results and discussion
A simple way to study lattice-dynamical properties of solids is to normalize the absorption area A(T) to a particular temperature To, and plot In A(T)/A(To) versus T. If the absorber is thin the temperature behaviour of A(T) is the same as that of the absorber recoilless fraction fa (T).Its knowledge permits the evaluation of characteristic temperatures which are functions of the frequency moments of the phonon frequency spectrum.
The relevant parameters extracted from the temperature-dependent M6ssbauer experiments are summarized in table 1.The spectra taken at extreme temperatures are displayed in fig. 1.The spectra were fitted with two quadrupole doublets and a single line.The quadrupole doublets correspond to the 4+ oxidation state (unresolved doublet centered at about 0.0 mm s -1) and to the 2+ oxidation state (doublet centered at about 2.5 mm s-l).The single line stems from 13-Sn.
The linewidth of the 2+ and 4+ oxidation states subspectra were constant in the temperature range observed.The effective thickness was estimated to ta ~ 1 which justifies the thin absorber approximation used.The linewidth of the subspectrum corresponding to the 2+ oxidation state of IO is narrower than the values previously reported at RT [3,4].The evolution of the hyperfine parameters indicates that there is a unique environment for Sn 2+ in the IO.The absence of a distribution of hyperfine fields at the 2+ sites indicates that the IO is a well defined phase, with a narrow composition range.With respect to the line corresponding to the 4+ oxidation state in fig. 1, there are no noticeable differences between Taken from ref. [8].b Taken from ref. [9].c Taken from ref. [7].a Values proposed from comparison with those of SnO and SnO2.• M6ssbauer lattice temperature calculated from A(T) dependence and using the atomic mass of ll9Sn" the interactions of SnO2 and those of IO.This means that the nearest neighborhood oxygen coordination for Sn 4+ in IO must be very similar to that of SnO2, as confirmed by EXAFS [5].
The IS and quadrupole splitting (A) varied linearly with temperature.This dependence and the fact that A 2+ was weakly dependent, with a slope of ~ 1.35 10 -4 mm s -1 K -1, are evidences that a phase change did not take place in the IO over this range.states.The data are well fitted by linear relationships.This seems to indicate that anharmonic effects are not present in the investigated temperature range.However, the rates of variation offa are lower than predicted by a Debye model, a fact also known for SnO2.In this system the existence of a low-temperature anharmonicity has to be discarded because of the high f value at low temperatures 0c(4.2K ) = 0.89).This behaviour was explained qualitatively by Kagan and Maslov [6], who concluded that the optical branch contributes significantly to the phonon spectrum and that it is difficult to attribute the smaller slope to any mechanism other than to the activation of optical modes in this system formed by very unlike atoms.This seems likely to be also the reason for the temperature dependence observed for the IO.
It is worth mentioning that thefa(T) versus T plot does not supply absolute f values, a fact not taken into account by Herber [7] in his study of SnO, where he gave absolute f factors fa(80 K) = 0.78 and fa(295 K) = 0.37.These were values obtained relative to those at 0 K. Table 1 shows the f factors for SnO and SnO2 obtained from a survey in the literature.In spite of their different crystalline structures and characteristic temperatures, the respective f at 80 K are nearly equal.Assuming t h e f factor of Sn 4+ (IO) equal to that of SnO2 and of Sn 2+ (IO) equal to that of SnO at 80 K we could get at RT the values shown in table 1 for the IO.

Fig. 2 Fig. 2 .
Fig. 2. Temperature dependence of the normalized areas of the oxidation states of the IO.That of SnO was taken from ref. [7].

Table 1
Summary of llgSn M6ssbauer data for tin oxides.