X-ray diffraction measurements of the c -axis Debye-Waller factors of YBa 2 Cu 3 O 7 and HgBa 2 CaCu 2 O 6

We report an application of x rays to the measurement of the temperature-dependent Bragg peak intensities to obtain Debye-Waller factors on high-temperature superconductors. Intensities of $(0,0,l)$ peaks of ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7}$ and ${\mathrm{HgBa}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{6}$ thin films are measured to obtain the c-axis Debye-Waller factors. While lattice constant and some Debye-Waller factor measurements on high-${T}_{c}$ superconductors show anomalies at the transition temperature, our measurements by x-ray diffraction show a smooth transition of the c-axis Debye-Waller factors through ${T}_{c}.$ This suggests that the dynamic displacements of the heavy elements along the c-axis direction in these compounds do not have anomalies at ${T}_{c}.$ This method in combination with measurements by other techniques will give more details concerning the dynamics of the lattice.