Calculation Of The Pressure And Finite Temperature Elastic Constants Of The Cubic Metal

The elastic constants of bcc Li, Na and fcc Al crystals have been evaluated as functions of pressure and temperature by using a new model together with Ab initio electronic structure and total-energy calculations. In the model it is considered that the elastic constants of crystals at a given temperature and pressure can be calculated using a conventional density functional method but modified by a new set lattice constants due to the isobaric volumetric thermal expansion when temperature rise from absolute zero to the given one. The isobaric volumetric thermal expansion with rising temperature is determined according to the Classic Statistic Dynamics theory.We use two methods to calculate volumetric thermal expansion. One is called effective pair potential method and the other is called effective mean potential method. In the first method the pair potential is deduce from the total energy. In the second method the nuclear or ion is considered to vibrate in a mean potential field, which can be calculated using the Ab initio electronic structure and total-energy calculations.In this study we used the accurate full-potential linear muffin-tin orbital method to calculate the total energy. Comparison of the calculated elastic moduli with the experiment ones for fcc Al and bcc Li and Na it shows they are in perfect agreement with each other. This shows that the calculating scheme and approach to the elastic constants at high pressure simultaneously at finite temperature is advisable.The calculation results also show that the elastic constants of Li, Na, Al elevates with the increasing pressure value and decline with the increasing temperature value, which illuminate the soften effect of these metals with rising temperature.