where S is the Seebeck coefficient, σ is the electrical conductivity, S 2 σ is the power factor (PF), and κ is the thermal conductivity given by the sum of the electronic and lattice (phonon) components κ elec + κ latt . The electronic transport coefficients in Eq. 1, viz. S, σ , and κ elec , are interrelated through the carrier concentration n such that ZT is generally optimised in the range of n = 10 19 -10 20 cm -3 typical of doped semiconductors. The lattice thermal conductivity κ latt , on the other hand, can in theory be optimised independently, and minimising κ latt is therefore an important avenue of research for improving ZT . While the structure-property relationships that underpin low κ latt are not well understood at present, low κ latt is typical of materials with large/complex unit cells containing many atoms, made of heavy elements, and/or with weak chemical bonding. Other structural features such as "active" lone pairs and layering are also known to reduce κ latt , by increasing phonon anharmonicity and introducing discontinuities in the bonding network, respectively. The IV-VI chalcogenides show a good balance of favourable electrical transport properties and low κ latt , and as such are among the most widely-studied TEs for mid-to-high-temperature applications. The lead chalcogenides PbS, PbSe and PbTe have been widely studied, and nanostructured PbTe, with a maximum ZT max of 2.2 at 915 K, is a current industry-standard hightemperature TEG. The high thermoelectric performance of PbTe arises from a low κ latt due to strong phonon anharmonicity and favourable electronic transport due to "band convergence" at elevated temperature. Both phenomena are thought to be linked to the high-symmetry cubic rocksalt (Fm 3m) structure adopted by these materials, although the extent of the phonon anharmonicity is disputed. However, the toxicity of Pb and the low abundance of Te prevent widespread deployment of PbTebased TEGs. Given the high performance of PbTe, SnTe and GeTe have been explored as alternatives. These systems both adopt a rhombohedral (R3m) structure, related to the rocksalt structure by a cation off-centering along the [111] direction, below ≈ 100 and 700 K respectively. GeTe shows large intrinsic cation vacancy concentrations, resulting in high carrier concentrations and good electrical conductivity. Co-doping with group V elements such as Sb, In and Bi, and also alloying with PbTe, has been shown to enhance the electrical properties of GeTe to yield ZT > 2. (We note however that alloying with Pb raises the same environmental issues as the Pb chalcogenides.) Cu-and Mn-doped SnTe also show good thermoelectric performance, with a reported ZT max = 1.6 at 925 K. However, a working TEG requires both p-type and n-type materials to form a complete device, and to date n-type conduction has only been demonstrated in GeTe 1-x (AgBiSe 2 ) x alloys with a large x > 20%. The rarity of Te has also motivated research into the group IV sulphides and selenides. In particular, SnSe has become one of the benchmark chalcogenide TEs following reports of an unprecedented bulk ZT of 2.6 and a potential ZT > 3 in polycrystalline samples. Unlike the Pb chalcogenides and the tellurides, SnSe adopts an orthorhombic Pnma structure at low temperature and transforms to a higher-symmetry orthorhombic Cmcm phase on heating. As for PbTe, the record thermoelectric performance of Cmcm SnSe 31 has been attributed to a combination of strong phonon anharmonicity, leading to low κ latt , and a multi-valley band structure that results in favourable electronic transport. The layered structure of SnSe also results in anisotropic transport, such that along the out-of-plane direction the thermal conductivity approaches the amorphous limit while facile electronic transport is retained. This effect is somewhat diminished in polycrystalline samples, but is offset by improved mechanical properties. Due to its chemical similarity to SnSe and the isostructural low-temperature Pnma phase, GeSe has also seen renewed interest, but the predicted ZT max ≈ 2. 5 has not yet been realised in experiments. This is attributed to the difficulty of forming Ge vacancies leading to a low intrinsic charge-carrier concentration of n ≈ 10 16 cm -3 , and the detrimental effect on the power factor is difficult to counteract with single-atom doping due to the low solubility of typical dopants such as Ag and Na in GeSe. GeTe and SnTe are both also reported to undergo a pressure-induced transition to the Pnma phase, and therefore analogous telluride phases may be synthetically accessible.