Paper 2.8

A simple approach to pressure dependence, examplified in the Al-Mg-Si system

Hallstedt Bengt and Schneider Jochen M.

Materials Chemistry, RWTH Aachen, Germany

In metallurgical processes relatively high pressure (a few kbar maximum) is sometimes applied. Normally this is not considered in phase diagram calculations. In semisolid processing, pressures up to 1 kbar (100 MPa) are applied. In such processes even relatively small changes in phase equilibria may lead to a considerable change in the fraction of  liquid phase, which in turn may lead to large changes in the rheological properties of the material.

A very simple way to include a pressure dependence for condensed phases is to add a PV term with a constant molar volume to the Gibbs energy expression for each phase. For most crystalline phases the molar volume is known with high accuracy from lattice parameter determinations at room temperature and ambient pressure. The major difficulty is to estimate the molar volume of the liquid phase (at room temperature). The most reliable way is probably to use data on volume change during melting. This is also the property, together with the enthalpy of melting, that determines the pressure dependence of the melting temperature.

In this work we will explore the possibilities and limitations of this approach by applying it to the Al-Mg-Si system. For pure Al it appears that reasonable melting points can be predicted up to about 100 to 200 kbar, which is surprisingly high and far above pressures that can be appplied in metallurgical processing. Below is a part of the Al-Si phase diagram at 1 bar, 1 kbar and 10 kbar.