טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
Ph.D Thesis
Ph.D StudentSorkin Viacheslav
SubjectComputer Simulations of Excitations of a Quantum Solid and
of The Melting Transition at High Pressure
DepartmentDepartment of Physics
Supervisors Dr. Joan Adler
Professor Emeritus Emil Polturak


Abstract

The subject of the first part of the thesis is excitations in solid helium.  Solid helium is characterized by large zero-point motion and significant correlation of its atoms. The self - consistent phonon (SCP) theory, which accounts these properties, has been developed over the years.

However, the predictions of the SCP do not agree with experiment in the bcc phase. As a  complementary approach to the SCP, we decided to use Path Integral Monte Carlo to study the dynamics of solid helium.  We calculated the dynamic structure factor of solid He-4  at a molar volume of 21 cc and of solid He-3  at a molar volume of 21.5 cc at a temperature of 1.6 K.  From these we obtained the phonon spectra  and found good agreement between our results  and experimental data for He-4 and with the theoretical prediction  for He-3.

Melting at high pressure is the subject of the second part of the thesis. Systematic differences exist in experimental results on the melting temperature, measured at high pressures using the diamond anvil cell (DAC) and the shock wave technique. The  melting temperature determined by shock waves is systematically higher than that obtained by DAC measurements. Several explanations were proposed to resolve this discrepancy, but no attention was devoted to the different conditions which exist at the surface of the samples.  Therefore, we decided to study how the different types of boundary conditions may affect the melting transition at high pressures. A model system of argon atoms  was simulated using the Monte Carlo method. We examined two cases: in the first case the argon was in contact with a rigid wall and in the second case with a fluid neon layer.

Our results showed that the melting temperature  is systematically different in the two cases. In the presence of a rigid medium, melting resembles the mechanical instability. With a soft medium at the boundary, melting begins at the surface and at a lower temperature. These results are related to experiments and appear to be consistent with  systematic differences that exist between shock wave and DAC measurements.   We suggest one possible interpretation of our simulations: the results obtained with a DAC technique should be compared with thermodynamic theories, while the shock wave results should be compared with theories based on a mechanical instability.