  Despite the widespread use of silicon in modern technology, its peculiar
thermal expansion is not well-understood. Adapting harmonic phonons to the
specific volume at temperature, the quasiharmonic approximation, has become
accepted for simulating the thermal expansion, but has given ambiguous
interpretations for microscopic mechanisms. To test atomistic mechanisms, we
performed inelastic neutron scattering experiments from 100-1500K on a
single-crystal of silicon to measure the changes in phonon frequencies. Our
state-of-the-art ab initio calculations, which fully account for phonon
anharmonicity and nuclear quantum effects, reproduced the measured shifts of
individual phonons with temperature, whereas quasiharmonic shifts were mostly
of the wrong sign. Surprisingly, the accepted quasiharmonic model was found to
predict the thermal expansion owing to a fortuitous cancellation of
contributions from individual phonons.
