https://doi.org/10.1007/s10051-001-8682-5
Unified description of elastic and acoustic properties of cubic media: elastic instabilities, phase transitions and soft modes
1
Institute of Physics, University of Rzeszów, ul. Rejtana 16 A, 35-310 Rzeszów, Poland
2
Institute of Theoretical Physics, University of Wrocław pl. Maxa Borna 9, 50-204 Wrocław, Poland
3
Institute of Nuclear Physics, ul. Radzikowskiego 152, 31-342 Kraków, Poland
Corresponding author: a zielinsk@alf.ifj.edu.pl
Received:
21
June
2001
Published online: 15 December 2001
Elastic properties of all cubic materials are classified
with the use of a stability triangle in a 2D subspace of elastic
parameters. The behavior of bulk modulus (B), shear modulus
(Cs), Poisson's ratio (
) and anisotropy
parameter (
) is studied in the vicinity of characteristic
lines of this triangle -mechanical stability borders and lines
of acoustic anomalies. The low symmetry phases, the ferroelastic
domains and the related soft modes are found for symmetry breaking
phase transitions (
, 
). The corresponding
slowness surfaces are presented. The existence of the only
possible longitudinal soft modes is predicted in two corners of
the stability triangle. Anomalous behavior of the Debye velocity
is found at the symmetry breaking borders of the stability
triangle. The phase velocities of soft modes are expressed by
eigenvalues of the tensor of elastic constants. Examples of the
predicted behavior are given for intermediate valent compounds
and for alloys undergoing the martensitic phase transitions.
PACS: 61.50.Ks – Crystallographic aspects of phase transformations; pressure effects / 64.60.-i – General studies of phase transitions / 64.70.Kb – Solid-solid transitions
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2001
