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.
3 0 A ug 2 01 8 Temperature Dependence of the Vacancy Formation Energy in Solid
We studied the thermal effects on the behavior of incommensurate solid He at low temperatures using the path integral Monte Carlo method. Below a certain temperature, depending on the density and the structure of the crystal, the vacancies delocalize and a finite condensate fraction appears. We calculated the vacancy formation energy as a function of the temperature and observed a behavior compatible with a two-step structure, with a gap of few K appearing at the onset temperature of off-diagonal long-range order. Estimation of the energy cost of creating two vacancies seems to indicate an effective attractive interaction among the vacancies but the large error inherent to its numerical estimation precludes a definitive statement.
X-ray measurements of thermal vacancies in hcp 4He.
Changes in the x-ray lattice parameter have been used to measure directly the thermal generation of vacant substitutional atomic sites in hcp /sup 4/He crystals held at constant macroscopic volume, for samples with molar volumes in the range 20.2 to 20.9 cm/sup 3/. A progressive decrease of the apparent formation energy, from 12.6 to 8.6 K, with increase of molar volume, is seen. This variation is consistent with variations observed in the NMR diffusion activation energy for small concentrations of /sup 3/He in /sup 4/He. The magnitudes are also similar, with some exceptions, which suggests that, unlike hcp /sup 3/He, the vacancy in low-density hcp /sup 4/He moves by tunneling. By various means, values for the monovacancy free volume are deduced. Comparisons with other studies of defects in hcp /sup 4/He, such as ion transport, recovery of ultrasonic attenuation, and calorimetry, are less direct and less unambiguous.