Nuclear quantum effect with pure anharmonicity and the anomalous thermal expansion of silicon
Significance Silicon has a peculiar negative thermal expansion at low temperature. This behavior has been understood with a “quasiharmonic” theory where low-energy phonons decrease in frequency with volume contraction. We report inelastic neutron scattering measurements of phonon dispersions over a wide range of temperatures. These measurements cast doubt upon quasiharmonic theory, which predicts the wrong sign for most phonon shifts with temperature. Fully anharmonic ab initio calculations correctly predict the phonon shifts and thermal expansion. Crystal structure, anharmonicity, and nuclear quantum effects all play important roles in the thermal expansion of silicon, and a simple mechanical explanation is inappropriate. The quantum effect of nuclear vibrations is also expected to be important for thermophysical properties of many materials.