Lattice Dynamics of Rubidium

The frequency/wave-vector dispersion relation for the normal modes of vibration in the major symmetry directions of body-centred cubic rubidium has been measured at 120° K. The large (∼ 75 cm3) single crystal was aligned with either a [110] or a [100] axis vertical, and constant incident frequencies between 3.8 and 5.5 x 1012 c,s were employed. The measurements were taken with the McMaster University triple-axis spectrometer at Chalk River in the constant-Q mode of operation. The dispersion curves are similar in shape to those of sodium and potassium. The ratio for a set of 104 values of q common to both sets of data, is 1.667 ± 0.005 with a standard deviation for an individual ratio from the mean of 0.05. The homology of the lattice vibrations for Na and Rb is poorer than for K and Rb. A Born-von Kármán analysis of the measurements has been made, and it is found that third nearest neighbour forces must be included to obtain reasonable agreement. More distant neighbour forces improve the fit relatively little. Axially symmetric constraints do not change the force constants significantly. As expected, the force constant 1XY is larger than 1XX, which suggests that the forces between nearest neighbours are repulsive. The initial slopes of the dispersion curves are considerably larger than the slopes deduced from ultrasonic measurements. The errors, mainly in the ultrasonic measurements, are barely sufficient to account for the differences. (author)