The temperature dependence of lattice vibrations in gold from X-ray diffraction measurements

Abstract

T_he measurements of the Debye characteristic temperatures O and mean-square vibrational amplitudes tt 2 of gold in the temperature range from 300 to 1150°K are presented. All data were determined from the X-ray integrated intensities of a gold single crystal. The room temperature value O = 188 + 4°K was found to be larger than O-values reported in the literature from X-ray data. The new value of O can be compared, however, with O= 186+ 8°K calculated from the specific heat value of OD= 178 + 8°K and Poisson's ratio for gold. The temperature dependence of O is in satisfactory agreement with the volume dependence given by Griineisen's law.The Debye characteristic temperature was determined because of an apparent anomaly in the curve of thermal vibrational amplitudes versus concentration resulting from the X-ray diffraction measurements. If the room temperature value of O = 177 + 5 °K for gold reported by Alexopoulos, Boskovits, Mourikis & Roilos [Acta Cryst. (1965) 19, 349] were employed a sharp drop of the u2 versus concentration curve would result for silver-gold alloys of high gold content. However, if the value of O = 188 + 4 °K reported in this investigation together with the valueof O = 190 + 4 °K for an Ag-94"9 atom per cent Au are plotted on the above curve a smooth curve of u2 versus gold composition is obtained.

Quasi-harmonic analysis of the thermodynamic data for gold and an estimate of ΘM(T)

“…Our results for OM (T,V~) may be compared to very recent M6ssbauer measurements and to previously published X-ray determinations of the Debye-Waller factor. We mention that Au was of special interest because relevant experiments for Au indicate that at room temperature, O M is greater than the Debye temperature determined from elastic constants, Ok; this is contrary to what is found in other studied materials, as noted by Synecek, Chessin & Simerska (1970).…”

“…This recent value of ~ is in excellent agreement with our results. Owen & Williams (1947), Alexopoulos, Boskovits, Mourikis & Roilos (1965), and Synecek et al (1970) have evaluated OU(T, VT) at high temperatures (T> 290 °K.) from X-ray scattering measurements.…”

“…Our estimated errors correspond to the quoted uncertainties in the specific-heat data and do not include possible uncertainties arising from our neglect of explicit anharmonic effects at low and moderate temperatures. Synecek et al (1970) This work, V0 This work, V300 * Method I: Computed from X-ray measurements from studies of the temperature dependence of OM(T, VT). Method II: Computed from X-ray measurements by analyzing the variation of the scattered intensity with the Bragg angle.…”

Heterogeneous to homogeneous melting transition visualized with ultrafast electron diffraction

“…(D to F) Temporal evolution of T e and T i simulated by means of TTM with different g ei at energy densities corresponding to data of (A) to (C). (G to I) Temporal evolution of Q D (±SD) derived from the experimental (220) decay (red squares) up to T nom melt , and the linear fit through individual data points as a function of T i [blue solid line with the gray area representing error bar (±SD)], which are compared with the x-ray measurements at equilibrium conditions from(31), shown by the green dots; the DFT calculations from(16),shown by the magenta line; and results adopted from(8), shown by the gray line. In (A) to (C), the solid blue lines represent the data determined below the nominal T nom melt of 1340 K, and the dashed lines represent Debye-Waller factor based on linearly extrapolated Q D as a function of T i .…”

Electron-lattice energy relaxation in laser-excited thin-film Au-insulator heterostructures studied by ultrafast MeV electron diffraction

“…We used published data on the temperature dependence of the Debye-Waller-factor of Au 32,33 to convert the experimental $\Delta 〈u^2〉false(\Delta tfalse)$ into the transient temperature rise $\Delta Tfalse(\Delta tfalse)$. The result of this conversion is shown in Fig.…”