Disorder-driven glasslike thermal conductivity in colusite $\mathrm{C}{\mathrm{u}}_{26}{\mathrm{V}}_2\mathrm{S}{\mathrm{n}}_6{\mathrm{S}}_{32}$ investigated by Mössbauer spectroscopy and inelastic neutron scattering

The influence of structural disorder on the thermal transport in the colusite $\mathrm{C}{\mathrm{u}}_{26}{\mathrm{V}}_2\mathrm{S}{\mathrm{n}}_6{\mathrm{S}}_{32}$ has been investigated by means of low-temperature thermal conductivity and specific heat measurements (2–300 K), ${}^{119}\mathrm{Sn}$ Mössbauer spectroscopy and temperature-dependent powder inelastic neutron scattering (INS). Variations in the high-temperature synthesis conditions act as a key parameter for tuning the degree of disorder in colusite compounds. Intriguingly, we find that all synthesized samples are disordered, the degree of which varies with the synthesis conditions used. Mössbauer data clearly evidence that Sn atoms do not solely occupy the $6c$ site of the crystal lattice but are present on possibly both the Cu and V sites, leading to a random distribution of these three cations within the unit cell. Increasing the disorder in these materials tends to lead to a smearing out of the main features in the phonon density of states measured by INS. Although the evolution of the inelastic signal upon warming is well described by a quasiharmonic approximation, elastic properties calculations indicate large average Grüneisen parameters, consistent with those determined experimentally from thermodynamic data. Increasing the level of disorder results in a decreased average Grüneisen parameter suggesting that the lowered lattice thermal conductivity is not driven by enhanced anharmonicity. These results provide experimental evidence to support that the remarkable changeover in the lattice thermal conductivity from crystalline to glasslike is solely driven by enhanced disorder accompanied by local lattice distortions.

Figure 1

Rietveld refinements of the PXRD data collected at 300 K for the L and H samples. All the reflections can be indexed to the cubic crystal structure of colusites described in the $P\overline{4}3n$ space group. Inset: Perspective view of the crystal structure of the colusite $\mathrm{C}{\mathrm{u}}_{26}{\mathrm{V}}_2\mathrm{S}{\mathrm{n}}_6{\mathrm{S}}_{32}$. The Cu atoms on the $8e,6d$, and $12f$ sites are shown in dark green, light green, and light blue, respectively. The Sn atoms on the $6c$ site are in dark blue, while the S atoms on the $8e$ and $24i$ sites are shown in light orange and yellow, respectively. The V atoms on the $2a$ site are shown in red.

Figure 2

(Upper panels) ${}^{119}\mathrm{Sn}$ Mössbauer spectra collected at $T=4.2\mathrm{K}$ of the L and H samples sintered at 873 and 1023 K, respectively. The experimental data are shown by the black crosses while the solid red curve stands for the best fit to the data. In the left panel, the two dotted curves correspond to the two contributions (singlet and doublet) used in the fitting procedure. (Lower panels) Spectra obtained by the sharpening procedure highlighting the presence of the two contributions to the Mössbauer signal in both samples.

Figure 3

Temperature dependence of the lattice thermal conductivity ${\kappa }_L$ of the L and H samples.

Figure 4

Lattice contribution to the specific heat $C_{ph}$ plotted as $C_{ph}/T^3$ versus temperature on a logarithmic scale for the $L$ and $H$ samples.

Figure 5

(a) Generalized vibrational density of states $G\left(\omega \right)$ of the L and H samples determined from INS measurements at 300 K. For both compounds, the spectra were normalized so that the integral of $G\left(\omega \right)$ corresponds to 198 phonon modes. (b) Debye plots $G\left(\omega \right)/{\omega }^2$ for both samples that stress the low-energy region of the $G\left(\omega \right)$ spectra. The color-coded symbols are similar in both panels.

Figure 6

Temperature dependence of the generalized vibrational density of states $G\left(\omega \right)$ of the (a) $L$ and (b) $H$ samples. The corresponding Debye plots $G\left(\omega \right)/{\omega }^2$ are shown in panels (c) and (d) for the L and H samples, respectively. The temperature- and color-coded symbols are reported in the figures.

Figure 7

Temperature dependence of the characteristic energy (filled circle symbols) of the low-energy peak at 7 meV obtained from fits to the $G\left(\omega \right)/{\omega }^2$ data with Gaussian functions. The solid lines correspond to the quasiharmonic prediction of the temperature dependence of the low-energy peak using thermodynamic average Grüneisen parameters of 1.96 and 1.45 for the L and H samples, respectively.