Isobaric vacancy formation volume in bcc 3He

The value of vacancy volume formation are obtained in bcc crystall ³ He at the temperature 0.5-0.66 K, and at molar volume 24,20 - 24,72 cm ³ /mole range. This data are obtained by measuring the pressure dependence of self-diffusion coefficient. The volume of formation is in agreement with the values calculated from theory, under assuming of existing the wide-zone tunneling motion in bcc ³ He.     

NMR,optical, and plastic flow experiments in bcc3He —4 He mixture crystals — in pursuit of a vacancy fluid

We describe experiments on the properties of bcc³He —⁴ He solid mixtures on the melting curve between 0.5K and 1.9K. In this paper we focus on effects related to the presence of thermal vacancies. First, we used NMR to image the³He distribution within the solid in equilibrium with the superfluid, as well as its T₁ and t₂. The most surprising result was that above about 1K, vacancy related motion of³He atoms in the solid becomes faster than in the liquid. To check the macroscopic aspects of this motion, we used the vibrating wire technique to look at plastic flow of the bcc solid phase, by moving the wire through the crystal. The temperature dependence of the plastic flow velocity indicates that the vacancy population in the bcc solid behaves like a viscous fluid. The extent to which the vacancy population causes the solid to have liquid like properties is best demonstrated through optical observations of the distillation of³He atoms out of the crystal, which takes place via formation of fluid bubbles within the solid, which then percolate into the liquid, creating a vivid impression of boiling.     

Comparative Study of Vacancies in the b.c.c. and h.c.p. Phases of 4He using Shadow Wave Functions

We use the shadow wave function formalism (SWF) to determine the energy of formation of single and double vacancies in ⁴ He crystals at T=0 K. Data is presented for both the bcc and hcp phases. The activation energy for single vacancies in bcc ⁴ He was found to be 6.7±3.9 K, about 43% of that in the hcp ⁴ He, 15.6±3.9 K. By determining the occupation of the Voronoi regions of the crystal sites, we determined the location of vacancies in the crystal and studied the relaxation of the neighboring atoms. We also present data on the correlations between vacancies, and between vacancies and ³ He impurities. Following the position of the vacancy through successive configurations we observed the motion of the vacancy as seen in our Monte Carlo simulations. On the shorter Monte Carlo time scales, greater vacancy motion was observed in the bcc phase than in the hcp phase.     

Constant-volume pressure measurements on BCC solid3He

Measurements have been made of the pressure of the bcc phase of solid³He at molar volumes from 24.2 to 23.2 cm³ and at temperatures from 25 to 0.5 mK. The solid undergoes an unusual antiferromagnetic ordering at a temperature that depends strongly on the sample density. This ordering is due to the unusually large exchange interaction in solid³He, a factor of 10⁴ stronger than the nuclear dipole-dipole interaction. The large latent heat associated with the first-order transition has constrained the size of the sample. The pressure of 0.005 cm³ of solid³He has been measured while the volume of the experimental cell was regulated to within 15 parts in 10⁶. The results provide information on the magnitudes and molar volume dependences of the exchange rates, and suggest that a single physical process governs all aspects of the ordering transition.     

Self-Diffusion in 3He crystals

Measurements of self-diffusion in bcc ³ He 24,20-24,80 cm ³/mole were carried out by a new method in the temperature range 0.4 - 0.8 K. The vacancy diffusion coefficient was obtained by comparison of the self-diffusion data and the vacancy specific heat. It is found out that the vacancy diffusion is independent of temperature, because of spin disorder in this region. The data obtained shows that vacancies in bcc ³ He are wide-gap quasiparticles.     

Magnetic properties of solid 3He down to 0.3 mK

Nuclear magnetization of solid ³He has been studied by static magnetization measurements from 10 mK down to 0.3 mK for molar volumes ranging from V = 24.14 to 21.02 cm³/mole in the bcc phase and from V= 19.83 to 19.26 cm³/mole in the hcp phase. In the bcc phase, both the antiferromagnetic transition temperature T _N and the reciprocal of the maximum magnetization V _max ^–1 at T _N vary in proportion to V ^16.5±1, and the magnetization below T _N is constant. The magnetization reduced by M _max is found to be represented by a universal function of the reduced temperature T/T _N. In the hcp phase, the magnetization can approximately be represented by Curie's law, and the estimated Weiss temperatures are below 50 K. We also observed that the boundary magnetism of liquid ³He depends considerably on pressure. The transition temperature of solid ³He to the antiferromagnetic phase coexisting with liquid in a restricted geometry is 15% higher than that of the bulk solid on the melting curve.     

Pinning of Dislocation Motion in bcc Solid 3He

We have measured the dissipation of dislocation motion in bcc solid ³ He using the high-Q torsional oscillator technique at 1079 Hz. We observed a broad maximum in the temperature dependence of the dissipation. The maximum of the dissipation can be explained by the theory of Granato and Lucke in which the dislocation mobility depends upon the interactions of dislocations with point defects. ⁴ He impurities tend to bind to the dislocation lines at low temperatures and pin this dislocation motion. The maximum of the dissipation corresponds to the depinning of the dislocation motion. From the amplitude dependence of the depinning temperature we first obtained the activation energy of 1.03 K of the impurity ⁴ He atom trapped on the dislocations in bcc solid ³ He at a molar volume of 24.30 cm ³ /mol. The activation energy of the impurity atom in bcc ³ He was found to be larger than the value of 0.7 Kin hcp ⁴ He.     

Thermodynamic properties of4He. II. The bcc phase and theP-T and V-T phase diagrams below 2 K

The constant-volume heat capacity of ⁴He has been measured at molar volumes from 20.45 to 29.71 cm³/mole in the temperature range from 0.3 to 4 K. The entropy has been obtained as a function of volume and temperature by extrapolation of the data to 0 K. The P-T equilibrium curves below 2 K were obtained from the volume dependence of the entropy in the two-phase regions. The V-T curves were obtained above 1.25 K by observation of heat capacity discontinuities at the phase boundaries and below 1.25 K from the equilibrium pressure-temperature data and the properties of the pure phases. The minimum in the melting pressure occurs at 0.774 K and is 8.04 × 10^–3 atm below the 0 K value. The corresponding maxima in the molar volumes of the solid and liquid were also determined. In the bcc phase (S/V) _T and (C _v /V) _T are everywhere positive. Both the temperature and volume dependence of the heat capacity are similar to those of bcc ³He, in the very limited ranges of volume and temperature in which the phase could be studied. An unexpected rise in heat capacity in the 20 mK interval below the melting temperature was observed.Work supported by the U.S. Energy Research and Development Administration.     

Volume Dependence of H c1, H c2, and ΔP(H c1) in Magnetically Ordered bcc 3He

We have used constant-volume pressure measurements over the entire range of molar volumes of bcc solid ³He, 20>v>24 cm³/mole, to determine the zero-temperature critical field H _c1 and the pressure discontinuity ΔP(H _c1) between the two antiferromagnetically ordered phases. The upper critical field H _c2 has been determined for 20>v>21.75 cm³/mole. The ³He was cooled by direct (two-stage) adiabatic demagnetization from T≈100 µK and H=2.5 T where its entropy S≈0. We find the Gruneisen parameters for H _c2 and ΔP to be larger than in previous work, but still smaller than for H _c2 and other physical quantities such as the Neel temperature T _N and e ^1/2 ₂, where e ₂ is the coefficient of the second-order term in the free energy of the paramagnetic phase. These resugts are significant for testing the mugtiple-exchange model for solid ³He.     

Path-Integral Monte Carlo Study of Phonons in the bcc Phase of 3He

Using Path Integral Monte Carlo and the Maximum Entropy method, we calculate the dynamic structure factor of solid ³He in the bcc phase at a finite temperature of T = 1.6 K and a molar volume of 21.5 cm³. From the single phonon dynamic structure factor, we obtain both the longitudinal and transverse phonon branches along the main crystalline directions, [001], [011] and [111]. Our results are compared with other theoretical predictions and available experimental data.     

Solid helium. I. Ground-state energy and compressibility

The ground-state energy and the compressibility of solid helium is calculated by means of a modified Brueckner theory. The Bethe-Goldstone equation is solved to give the reaction matrix or the effective interaction in coordinate space, and the ground-state energy for the two helium isotopes³He and⁴He is calculated. Also, the compressibility is estimated from the dependence of the ground-state energy on density or molar volume. Both bcc and hcp structures are considered. The calculations are done for two different two-body potentials, an Yntema-Schneider potential given by Brueckner and Gammel, and a Frost-Musulin potential given by Bruch and McGee. Theoretical results for the ground-state energy per particle are 0.2 to 2.6 K for solid³He at a molar volume of 24 cm³/mole, and –2.4 to –5.9 K for solid⁴He at a molar volume of 20 cm³/mole. The corresponding experimental results are –1.0 and –5.6 K, respectively. Theoretical results for the compressibility are 0.0031–0.0042 atm^–1 for solid³He at a molar volume of 22 cm³/mole, and 0.0014–0.0022 atm^–1 for solid⁴He at a molar volume of 18 cm³/mole. The corresponding experimental results are 0.0032 and 0.0014 atm^–1, respectively. The agreement with experimental results is reasonably good since higher order cluster terms are not included in this first approximation.     

Spin lattice relaxation in BCC3He

Analysis is made of spin lattice relaxation measurements made at low temperature in various BCC samples of solid³He with concentrations of⁴He of 60 and 82 ppm, at Larmor frequencies of 50 and 200 MHz, and for molar volumes covering the range 23.05V24.82 cm³. From the characteristic features of the relaxation we deduce the mechanisms involved and their relative strengths. We stress the importance of a one-phonon process in relaxing the exchange energy at large molar volume and give an estimate of the bandwidth of the vacancy waves. The combination of the various mechanisms gives a coherent picture of the relaxation at low temperature.     

Umklapp region thermal conductivity of body-centered-cubic3He

The thermal conductivity of body-centered-cubic³He has been measured in isotopically pure samples. In agreement with previous measurements in impure samples, the thermal conductivity in the bcc phase of³He does not obey the simple Umklapp temperature dependence which is found in the higher density hexagonal-close-packed phase. The calculated phonon mean free paths also do not obey a simple Umklapp temperature dependence, providing evidence that the high-temperature specific heat anomaly in bcc³He is not directly responsible for the anomaly in the thermal conductivity.Work supported by grants from the National Science Foundation and the Army Research Office (Durham).     

Phase separation in solid mixtures of helium-3 and helium-4

Phase separation temperatures have been determined in bcc³He-⁴He mixtures as a function of³He concentration and melting pressure from measurements of changes in the X-ray lattice parameter and Bragg peak shape. A new rigid tail dilution refrigerator cryostat was used to study³He-⁴He crystals with³He concentrations of 0.10, 0.20, 0.30, 0.45, 0.60, and 0.70 and melting pressures between 3.0 and 4.3 MPa. The phase separation temperatures determined are in good agreement with regular solution theory and give little support for an asymmetry in the coexistence curve expected from a Nosanow-type model and reported from previous experiments using other signatures of phase separation. At a given concentration, differences in phase separation temperatures determined from slow cooling and warming data, respectively, are as much as 25 mdeg, but this is less than half the differences reported from previous experiments. A bcc-hcp transformation was seen in a crystal with 10%³He at aboutT=0.3 K for a melting pressure of3.7 MPa.     

Pressure measurement during nuclear demagnetization of BCC and HCP solid3He

Direct nuclear demagnetization is used to cool high density solid³He into the magnetically ordered phases. The pressure change in the samples is detected by a capacitive strain gauge. The entropy of the samples is removed by precooling to a temperature of 0.5 mK in a field of 2.5 T. For a bcc sample with a molar volume of 20.10 cm³/mol, two magnetic transitions have been observed. A similar experiment on an hcp sample with a molar volume of 19.65 cm³/mol is being done. Preliminary data indicates no abrupt change in the pressure as observed in the bcc sample.     

Temperature dependence of the sound velocities and elastic constants of bcc3He

High-resolution measurements of the sound velocity in 20 crystals of bcc³He at constant molar volume (24.1 cm³/mole) show a monotonic decrease of about 0.1% for longitudinal and 0.3% for transverse velocities for a temperature increase from 0.123 to 0.800 K, the change being approximately proportional toT ⁴. A low-lying transverse mode of 102 m/sec was observed for the first time. The orientation of three samples could be inferred from their absolute velocity, and the temperature dependence of all three elastic constants was calculated. The change in adiabatic bulk modulus is in good agreement with the Mie-Grüneisen equation of state. No effect from the exchange interaction on the velocities could be observed.This work was supported by the National Science Foundation.     

Phonons and thermal properties of bcc and fcc helium from a self-consistent anharmonic theory

Numerical calculations of phonon spectra, including damping, are reported for bcc³He and⁴He and for fcc⁴He. Strong damping is found for the longitudinal branches near the boundary of the Brillouin zone. In the bcc phase anomalous dispersion occurs for several directions at long wavelengths, which is most pronounced in the lowest transverse branch in (110) direction. This leads to an anomaly in the specific heat at low temperatures. In this calculation anharmonicities and short-range correlations are treated in a self-consistent way.     

The Universality of Energy Spectrum of Phonon and Vacancy Excitations in Solid Helium

The most careful measurements on the specific heat C(T) and dP/dT (P is the pressure, T is the temperature) are analysed using a model where the thermodynamic properties of ³He and ⁴He crystals are described by a sum of phonon and vacancy contributions. The analysis, in which the Debye model of phonons and the Hetherington model for wide-band vacancies are used, yields a universal molar volume depence for the Debye temperature Θ _D and the vacancy activation energy Q _V , and constant values for the Grüneisen parameters in the molar volume range of 14–24 cm³/mol. The Θ _D values are found to be in good agreement with the data obtained from the elastic moduli measurements and with Horner’s theoretical calculations. The Q _V values are in good agreement with the X-ray measurements on the temperature dependences of ³He and ⁴He crystal lattice parameters analysed in terms of the Hetherington model.     

NMR Studies of 3He Impurities in 4He in the Proposed Supersolid Phase

Preliminary results are reported for measurements of the NMR relaxation times of very dilute ³He in samples of solid ⁴He at low temperature, 0.25 K <T< 1.3 K. The results were obtained for carefully prepared samples with different ³He concentrations. The measurements of the spin-spin relaxation time, T ₂, show several interesting features. A temperature independent plateau attributed to the exchange motional narrowing is observed down to the lowest temperature studied, and the observed variation of T ₂ with ³He concentration favors the nonlinear theory suggested by Landesman. The best fit to the data is given by T ₂ ∝ x ₃ ^?1.89±0.1 rather than x ₃ ^?1 . No evidence of an exchange-phonon bottleneck for the spin-lattice relaxation is seen down to 25 mK. The vacancy activation energy is determined to be 13.5±0.3 K for a sample with x ₃=5×10^?4 and molar volume 20.9 cm³.