  In semiconductors almost all heat is conducted by phonons (lattice
vibrations), which is limited by their quasi-particle lifetimes. Phonon-phonon
interactions represent scattering mechanisms that produce thermal resistance.
In thermoelectric materials, this resistance due to anharmonicity should be
maximised for optimal performance. We use a first-principles lattice-dynamics
approach to explore the changes in lattice dynamics across an isostructural
series where the average atomic mass is conserved: ZnS to CuGaS$_2$ to
Cu$_2$ZnGeS$_4$. Our results demonstrate an enhancement of phonon interactions
in the multernary materials, and confirm that lattice thermal conductivity can
be controlled independently of the average mass and local coordination
environments.
