Effect of High Pressure on the Solidification of Al–Ni Alloy

The effect of high pressure on the microstructure of hypo-peritectic Al–38wt.%Ni alloy was studied. The results show that Al3Ni and Al3Ni2 phases coexist at ambient pressure. However, it becomes a typical hyper-eutectic microstructure when synthesized at 2 GPa and 4 GPa. Meanwhile, the interface temperature of Al3Ni and Al3Ni2 phases was calculated with the combination of the BCT dendrite growth model, which is suitable for the Al3Ni2 phase. According to the highest interface temperature principle, the result shows that the Al3Ni phase dominates over 1–5 GPa. Finally, the Debye temperature and potential energy of the hypo-peritectic Al–38wt.%Ni alloy under different pressures were researched. Based on the low temperature specific heat-capacity curve. The Debye temperatures at ambient pressure, 2 GPa, and 4 GPa are 504.4 K, 508.71 K and 515.36 K, respectively, and the potential energy in the lowest point decreases with the increase of pressure.

Fermi–Dirac Statistics

The main application of Fermi–Dirac Statistics is to calculate the properties of electrons. This chapter explains how the properties of fermions account for the behavior of metals. The Fermi energy is introduced and shown to correspond to a very high temperature, so that most properties can be obtained from low-temperature expansions. Both discrete and continuous densities of states are discussed. The Sommerfeld expansion is derived explicitly. The low-temperature specific heat and compressibility are derived. The most important fermions are electrons, and understanding the properties of electrons is central to understanding the properties of all materials. In this chapter we will study the ideal Fermi gas, which turns out to explain many of the properties of electrons in metals.