On the martensitic transformation in f.c.c. manganese alloys. - II. Phenomenological analysis

Abstract

A phenomenological analysis is given of our lattice vibration data of the preceding paper (I), taken as a function of temperature through the martensitic transformation of a single crystal of Mn 85 Ni 9 C 6 . Computations for a nearest-neighbour-forces-only model fitting the measured elastic stiffness constants are presented to show how anomalously ‘soft’ vibrations develop for propagation vectors near the [110] direction as the conditions for a structure transition are approached. It is shown that the acoustic energy flux vector can suffer severe refraction at interfaces where sound enters the crystal. In this material, phonon ‘softening’ is restricted essentially to wavevectors q so close to the origin of the Brillouin zone that the principal effects occur almost wholly in the region of long wave propagation where the dispersion curves of the ‘normal’ state (far from the transition) are for all practical purposes straight. In these circumstances the wavevector dependence of the squared phonon frequencies ω 2 ( q ) departs from normal by a factor which may be expressed quite simply as ( λ 2 + q 2 )/ μ ( 2 + q 2 ). Values are presented for our fitted λ ( T ), μ ( T ) and the intrinsic phonon line width Γ( T ). The phonon line-width peaks near the temperature of structure transformation, but otherwise tends to decrease with increasing temperature; as a function of wavevector it increases in a manner consistent with q 2 but saturating at roughly 0.1 q max , the wavevector region at which the propagation of sound ceases to be anomalous. General arguments show the anomalies to be due to long-range effective interplanar forces extending in the [110] direction out to several interplanar distances - for exponentially declining forces the 1 /e distance would be seven interplanar spacings.