Forbidden (222) Neutron Reflection in Silicon: Anharmonicity and the Bonding Electrons

Using neutrons, the "forbidden" (222) reflection in silicon was detected and measured between 15 and 1353 ^∘{}C. At 1001 ^∘{}C the Dawson and Willis anharmonic-force constant was evaluated as β=2.99×10^-12 ergs/³ which is close to that derived from the thermal expansion of silicon. We have used these neutron measurements to correct the x-ray (222) structure factor for the anharmonic atomic motion. The scattering from the anticentrosymmetric valence-charge density obtained in this way is found to be less temperature dependent than that from the core electrons. We take this as evidence in support of the shell model and of the failure of the rigid ion model.