Aims of this study

The general aim of this study is to understand the influence of the preferred Se incor-poration on the lattice dynamics and the bonding properties, especially with respect to the postulated metavalent bonding, of the tetradymite structure type. Moreover, up to now, the vibrational properties of Sb₂Se₃ have been studied mostly by first-principles calculations and an experimental confirmation of the predicted phonon

5.2. Lattice dynamics of the Sb₂Te₃−xSex solid solution 83 spectra and heat capacity data is missing and will be provided here. This will allow an evaluation of the theoretical data reported previously [19, 146, 145].

Five Sb₂Te₃−xSe_x (x=0, 0.6, 1.2, 1.8, 3) mixed crystals have been selected, where the samples Sb₂Se_0.6Te_2.4, Sb₂Se_1.2Te_1.8 and Sb₂Se_1.8Te_1.2are isostructural to Sb₂Te₃. As the lattice dynamics of Sb2Te3 was studied intensively in the past, the endmember serves as a benchmark. For the sample Sb₂Se_0.6Te_2.4, the A1 site is partially filled with Se, whereas the A2 site is exclusively occupied by Te. In contrast to this, the A1 site of the samples Sb₂Se_1.2Te_1.8and Sb₂Se_1.8Te_1.2is completely filled by Se and there is a smaller and larger excess of Se also on the A2 site, respectively.

The phonon density of states in the energy range of the modesA_2u(3) and A_1g(2) is correlated with vibrations of the Sb-A2 bonding (figure 5.21) and thus, this energy range is expected to reflect composition-induced changes on this bonding. As the el-emental contribution of Sb to the total phonon density of states is dominating in this energy range (figure 5.21), an analysis of the¹²¹Sb partial phonon density of states is most promising to obtain information of the Sb-A2 bonding.

For Sb2Te3, the modesEu(3) andA2u(2) are correlated with vibrations of the atoms in the A1 and A2 site of the tetradymite structure [140] and the elemental contribution of Te to the total phonon density of states is dominating (figure 5.21). Thus, analysis of the¹²⁵Te partial phonon density of states of the Sb₂Te₃−xSe_x (x=0, 0.6, 1.2, 1.8) mixed crystals are expected to provide information on the Sb-A1 bonding. The¹²¹Sb contribution to the total density of states in the energy range of the modes E_u(3), A_2u(2) and Eg(2) is considered to reflect the reaction of the Sb atoms to vibrations of the A1 and A2 atoms. Thus, it is expected that composition-induced changes on the A1 (and A2) site also influence the¹²¹Sb partial phonon density of states in this energy range.

In this study, a macroscopic analysis of the vibrational properties is provided from low-temperature heat capacity measurements and temperature-dependent inelastic neutron scattering experiments. Further low-temperature¹²¹Sb and ¹²⁵Te nuclear inelastic scattering experiments give access to the partial phonon density of states from which atom-specific information on the lattice dynamics are obtained. The Se partial phonon density of states of the Sb₂Te₃−xSex (x=0.6, 1.8, 3) mixed crystals are determined as described in section 4.3.5.

Finally, for a future high-pressure nuclear inelastic scattering experiment, a diffrac-tion experiment up to about 18 GPa on polycrystalline Sb2Te3 was performed to determine the transition-pressure and stability fields of the different high-pressure polymorphs of Sb2Te3. As the high-pressure nuclear inelastic scattering experiment using the currently existing setup at the beamline P01 can only be performed un-der non-hydrostatic conditions [149], also the diffraction experiment was performed under non-hydrostatic conditions.

84 Chapter 5. Results 5.2.2 Sample characterization

For all Sb₂Te₃−xSe_x(x= 0, 0.6, 1.2, 1.8, 3) samples, powder diffraction data were mea-sured at ambient conditions (figure 5.22). For the isostructural compounds Sb₂Te₃,

FIGURE5.22: Powder pattern of the Sb2Te3−xSex(x= 0, 0.6, 1.2, 1.8, 3) samples.

Sb₂Se_0.6Te_2.4, Sb₂Se_1.2Te_1.8and Sb₂Se_1.8Te_1.2, all detected peaks could be indexed with the structural data reported earlier for Sb2Te3[97] and there was no evidence for any impurities (figure 5.22). The powder pattern of Sb₂Se₃were indexed using the lattice parameter reported in [134] (appendix D.3) and there is also no indication for any impurities.

In figure 5.23, the lattice parameter a and c and the unit cell volumes, V, of the compounds from the stability field of the tetradymite structure type studied in this work are shown in dependence of the Se content, x(Se). While for the compound Sb₂Se_0.6Te_2.4 a deviation from Vegard’s law clearly can been seen in all parameters, Sb₂Se_1.2Te_1.8 shows an ideal mixing behavior. Lostak et al.[66] found a deviation from Vegard’s law in theclattice parameter of compounds with Se contents up to x(Se)=0.38, whereas they reported an ideal mixing behavior for mixed crystals with larger Se contents. Thus, the results from this study and the one from the literature [66] seem to indicate that the non-ideal mixing behavior is limited to compounds with small Se contents. In contrast to this, Molodkinet al.[137] reported a non-ideal

5.2. Lattice dynamics of the Sb₂Te₃−xSex solid solution 85

FIGURE5.23:Thelatticeparameteraandbandtheunitcellvolumeofthesampleswithtetradymitestructuretypeindependenceof theSecontent.Theexperimentallydeterminedvaluesarecomparedtotheresulsofpreviousstudies[66,137].Errosaresmallerthan thesymbols.

86 Chapter 5. Results mixing behavior over the entire compositional range of the tetradymite structure type (exception: aofx(Se)=0.6;cofx(Se)=1). It is noteworthy that the samples stud-ied here and by Lostaket al.[66] were synthesized from stoichiometrically weighted amounts of the elements and at temperatures above the melting points of the start-ing materials and the products, whereas the samples in [137] were synthesized from stoichiometric mixtures of Sb₂Te₃and Sb₂Se₃and at temperatures below the melting points of the reactants. As no chemical analysis of the samples is provided in [137], it is very difficult to evaluate the influence of the route of sample preparation on the properties of the Sb2Te3−xSexmixed crystals.

For the isostructural compounds Sb₂Te₃, Sb₂Se_0.6Te_2.4 and Sb₂Se_1.2Te_1.8, the experi-mentally determinedc/a ratios are in good agreement with the literature data [97, 66, 134] (table 5.7) and only small deviations are observed which might be due to slight differences in the chemical compositions. Thec/aratios reported in [137] are

TABLE5.7: The lattice parameter ratios of the Sb2Te3−xSex(x=0, 0.6, 1.2, 1.8, 3) samples. For the samples x=0, 0.6, 1.2, 3 the ratios deter-mined in this study are compared to the corresponding ones from the

literature. Sb2Se3 0.9872(1) 2.9625(3) 2.9246(3) this study

0.9876(1) 2.9590(5) 2.9223(5) [134]

significantly smaller than the ones found in this study which might be a consequence of the above-mentioned differences in the sample preparation.

For Sb2Se3, lattice parameter of a=11.7795(8) Å, b=3.9762(3) Å and c=11.6289(7) Å and a unit cell volume ofV=544.67(8) ų were determined (table 5.7). The lattice parameter are in very good agreement with literature data [134].