Mean‐Square Ionic Displacements and Force Constants of Crystals with the CsCl Type Structure

Abstract

Mean-square vibrational amplitudes of ions in the diatomic lattices of crystals with the CsCl type structure have recently been determined in the high temperature region by elastic scattering of neutrons. An evaluation of mean-square displacements in terms of frequency moments is derived and connections with the force constants of the crystals are worked out. The difference of the vibrational amplitudes of the two ions is calculated from the experimental data and by means of force constants derived from phonon measurements.Vor kurzem wurden die mittleren Schwingungsamplitudenquadrate zweiatomarer Gitter mit CsC1-Struktur im Bereich hoher Temperaturen aus Experimenten mit elastisch gestreuten Neutronen bestimmt. Zur Interpretation der Daten wird eine Entwicklung nach Frequenzmomenten angegeben und der Zusammenhang mit den Kraftekonstanten des Schalenmodells aufgezeigt. Am Beispiel einer linearen Kette werden die allgemeinen Resultate erlautert und die Differenz der mittleren Schwingungsamplituden berechnet.

Thermal vibration amplitudes of TlCl between 296 and 534 K

“…Nevertheless, it is clear that the thallium ions undergo much larger vibrations than the chlorine ions, and the difference seems to increase with temperature. This is in qualitative agreement with an earlier measurement [20], and a similar, although less pronounced behaviour has been observed in TlBr [5,211. Within a rigid-ion model this would imply a much larger force constant between the Clk-Cl-pairs than between TI+-TI+.…”

Debye-Waller factors of alkali halides

“…This supports claims by Huiszoon and Groenewegen 29 and Jex et al 30 that, for temperatures greater than the Debye temperature and in the harmonic approximation, the mean-square displacements of ions are independent of their masses.…”

“…For temperatures above the Debye temperature, this is expected. 25,29,30 The bulk of our measurements were taken at high temperatures, as we were primarily inter-ested in anharmonic effects. The amount and quality of data taken below the Debye temperature of each sample were insufficient to allow any conclusions to be drawn about the relative DWF's of the two ion types at low temperatures.…”