Path integral calculations of vacancies in solid Helium
We study properties of vacancies in solid 4He using Path Integral Monte Carlo. We find, in agreement with other calculations, that the energy to create a single vacancy is 11.5 K and is monotonic with the number of vacancies. If more then a few percent of the system becomes vacant, we find the system becomes unstable to melting. We show the number of exchanges in the system is increased by vacancies and how the underlying lattice is altered by the presence of a vacancy. We also examine the efficacy of using a tight binding Hamiltonian to describe the vacancy in the crystal, show that vacancies are attractive, and find values for the effective mass and inter-vacancy attraction.
Quantum dislocations: the fate of multiple vacancies in two-dimensional solid 4He
Defects are believed to play a fundamental role in the supersolid state of 4He. We have studied solid 4He in two dimensions (2D) as a function of the number of vacancies nv, up to 30, inserted in the initial configuration at ρ = 0.0765 Å − 2, close to the melting density, with the exact zero-temperature shadow path integral ground state method. The crystalline order is found to be stable also in the presence of many vacancies and we observe two completely different regimes. For small nv, up to about 6, vacancies form a bound state and cause a decrease of the crystalline order. At larger nv, the formation energy of an extra vacancy at fixed density decreases by one order of magnitude to about 0.6 K. It is no longer possible to recognize vacancies in the equilibrated state because they mainly transform into quantum dislocations and crystalline order is found almost independently of how many vacancies have been inserted in the initial configuration. The one-body density matrix in this latter regime shows a non-decaying large distance tail: dislocations, that in 2D are point defects, turn out to be mobile, their number is fluctuating, and they are able to induce exchanges of particles across the system mainly triggered by the dislocation cores. These results indicate that the notion of the incommensurate versus the commensurate state loses meaning for solid 4He in 2D, because the number of lattice sites becomes ill defined when the system is not commensurate. Crystalline order is found to be stable also in 3D in the presence of up to 100 vacancies.
Chemical Metallurgy: Principles and Practice
Foreword. Preface. Acknowledgements. Appreciation. 1. Acquaintance. 2. Mineral Processing. 3. Thermodynamics and Kinetics. 4. Pyrometallurgy. 5. Hydrometallurgy. 6. Electrometallurgy. 7. Energy and Environment. Subject Index.