Détermination théorique des courbes de fusion à haute pression pour des solides non cubiques. Application au cadmium et au magnésium

Temperature dependence of elastic moduli for non-cubic solids: application to cadmium, magnesium and zinc

“…Moreover, it is well known that G! : ) and Hij$ are related to thermal effects and consequently to the temperature derivatives of the C$:)s at constant pressure [8,3]. Thus, for ijkl = 1111, 1122, 1133, 3333, 2323 one obtains by evaluation at initial state where al and a3 are the linear thermal expansion coefficients and a, is the volume coefficient of thermal expansion, with a, = 2 a l + a3 for the considered symmetry.…”

“…;&,, , which are not directly related to experimentally available quantities, can be calculated from C@,, using (8) (i.e. 1 + 2Eii = (1 -2eji)") and expanding E,, in terms of e,, to the second order [8].…”

“…m n p q q k i q m n q p q + ' ' 1 (i, j not summed). This relationship gives the following two independent equations for a crystal of hexagonal symmetry [8] expressed in the Voigt notation:…”