Study of quantum effects on atomic displacements in quartz

The crystal structure of quartz (SiO₂) was analyzed by neutron powder diffraction at several temperatures in the range of 10-250 K. The temperature dependence of the structure parameters was consistent with our previous results obtained using single-crystal X-ray diffraction above room temperature. Atomic displacements are order parameters for displacive structural phase transitions. The temperature evolution of Si atomic displacement in quartz was analyzed by studying the quantum expansion of the Landau potential. The expansion was found to accurately describe the evolution of the atomic displacement over the entire temperature interval. To the best of our knowledge, such a verification of atomic displacement is the first of its kind. A proportional relationship between spontaneous strain and the square of the atomic displacement was observed over the entire temperature interval. The validity of the obtained characteristic temperature for the quantum effect is discussed and compared with the results of previous Raman-scattering studies.