Sensitivity of extended X-ray-absorption fine structure to thermal expansion

The sensitivity of extended x-ray-absorption fine structure (EXAFS) to thermal expansion has been studied by temperature-dependent measurements on germanium. The first cumulant does not reproduce the thermal expansion owing to vibrations normal to the bond. The perpendicular relative displacement ⟨Δu²₁⟩ has been for the first time experimentally obtained; the ratio ⟨Δu²₁⟩/⟨Δu²_|is in agreement with vibrational model calculations. Low-temperature quantum effects on the 3rd cumulant have been for the first time observed. The possibility of measuring thermal expansion from the 3rd cumulant is demonstrated, provided that quantum effects are taken into account.