V. A. Maidanov

Contribution of phonon and vacancion excitations to the thermodynamic properties of solid helium

Precision measurements of the temperature dependence of the pressure are made on high-quality crystals of He4 and He3–He4 solutions grown at a constant volume. The phonon and vacancion contributions to the pressure are separated on the basis of the Debye model for the phonons and the model of wide-band vacancion excitations. This approach is also used to analyze all the other available thermodynamic data for the solid pure isotopes of helium and their solutions. This yields information about the Debye temperature and vacancy activation energy, and a universal dependence of these parameters on the molar volume is found for He3, He4, and He3–He4 solutions. The values found for the corresponding Gruneisen parameters turn out to be independent of the molar volume.

Observation of Andreev-Pushkarov vacancy clusters in phase-separated solid solutions of 4He in 3He

New features are observed for the pressure in a phase-separated dilute solid solution of 4He in 3He subjected to multiple temperature cycling within the phase-separation region. The results are explained within the framework of the hypothesis of A.F. Andreev and D.I. Pushkarov that the vacancies in a crystal without ideal periodicity are surrounded by clusters with a periodic structure. The equation for determining the radius of a cluster of pure 4He in a solution of 4He in 3He is refined. This hypothesis is shown to provide quantitative agreement between the calculated and experimental data under the assumption that the homogenization of the phase-separated solution is accompanied by the formation of metastable vacancies with a concentration of ∼(4–5)×10−5.

Giant asymmetry of the processes of separation and homogenization of 3He–4He solid mixtures

A comparison of the kinetics of the separation processes and homogenization of 3He–4He solid mixtures is made with the use of precision barometry for samples of three types—dilute mixtures of 3He in 4He and of 4He in 3He and concentrated 3He–4He mixtures. It is found that in all types of mixtures studied the rate of the initial stage of homogenization can exceed the rate of separation by more than 500 times. An appreciable rate of phase separation in the concentrated mixtures, where, according to existing ideas, the impurity atoms in quantum crystals should be localized, attests to a new, unknown mechanism of mass transfer under those conditions, while the fast homogenization indicates that this process is nondiffusional in nature.

Kinetics of the phase transition in solid solutions of 4He in 3He at different degrees of supersaturation

Precision measurements of the pressure during phase separation in samples of solid solutions of 4He in 3He have been used to obtain data on the characteristic times of the phase transition. A processing of the results gives additional evidence supporting the view that homogeneous nucleation is realized in 3He–4He solid solutions at significant supercoolings and heterogeneous nucleation at the smallest supercoolings. Two different ways are proposed for comparing the results with a theoretical calculation taking into account the processes at the boundary of a nucleus of the new phase. Both give roughly similar values of the coefficient of surface tension at the nucleus–matrix boundary, and those values agree with those obtained in other studies. It is conjectured that the bcc–hcp transition has a substantial influence on the kinetics of separation at the lowest supersaturations.

Detection of fluctuation effects near the phase separation temperature of concentrated 3He-4He solid solutions

A precision barometric study has revealed unusual behavior of the pressure of 3He−4He solid solutions with a concentration of around 30% 3He: in the pre-separation region the pressure increases with decreasing temperature long before the start of the phase transition. It is established that such an anomaly is due to correlation effects in the impurity subsystem which give rise to large-scale fluctuations of the impurity concentration, and the fluctuation contribution to the pressure is much greater than the phonon contribution. Quantitative agreement between the experimental data and the proposed theory is obtained, and it is shown that the observed temperature dependence of the pressure in the pre-separation and metastable regions can be explained only when the long-range character of the interaction between impurities is taken into account.

Formation of a disordered (Glassy) phase in deformed solid 4He in the region of supersolid state

A method has been proposed to create disorder in helium crystals by their deformation immediately during the experiment. Precise measurements of the pressure have been performed at a constant volume in samples of various qualities. It has been revealed that excess pressure, which is characterized by the quadratic temperature dependence typical of the disordered glassy phase and of the dislocation contribution to the pressure, is observed in the deformed crystals along with the phonon contribution to the pressure. The effect is observed in the supersolid-state region and disappears after the careful annealing of the crystals. The ultraslow relaxation of the pressure also characteristic of the glassy phase has been observed in the process of annealing of the crystals. The obtained experimental results have been analyzed in the framework of the dislocation model and the model of two-level tunneling states.

Spin–lattice relaxation in the bcc phase of phase-separated 3He–4He solid mixtures

The spin–lattice relaxation time in two samples of 3He–4He solid mixtures with initial concentrations of 0.5% 3He in 4He and 0.5% 4He in 3He is measured by the pulsed NMR method. As a result of phase separation, in both cases two-phase crystals form, having the same helium concentration in the concentrated bcc phase. However, in the first sample the bcc phase forms as small inclusions in an hcp matrix, while in the second sample the bcc phase is the matrix. It is established that in the second case the spin–lattice relaxation occurs in the same way as in pure bulk 3He, while in the first case one observes anomalous behavior of the spin–lattice relaxation time at low temperatures. Experiments have shown that this anomaly is due not to the possible influence of the small 4He impurity but to the small dimensions of the inclusions of the of the bcc phase. In this case the main contribution to the relaxation is apparently due to defects formed at the boundaries of the bcc inclusions and the hcp matrix.

Phase separation and diffusion processes in concentrated He3–He4 solid mixtures

The kinetics of phase separation in quantum crystals of concentrated He3–He4 mixtures containing 34.0, 61.3, and 89.9% He3 are investigated experimentally by the method of precision barometry. The variation of the pressure P(T) of the system upon stepwise cooling and heating is registered. The P(T) curves observed in the experiment are compared with a theory based on a diffusion description of the kinetics of isotropic phase separation. This yields the first information about the mass diffusion coefficient in the whole concentration range. It is shown that in concentrated mixtures the mass diffusion coefficient is several orders of magnitude lower than in dilute mixtures, owing to the interaction of impurities and the presence of elastic strains in the crystal. At the same time, because of the high concentration of new-phase nuclei and the small diffusion length, the phase transition process takes place over a comparatively short time.

Multi-echo in phase-separated 3He–4He solid solutions under NMR conditions

A pulsed NMR method is used to make the first observation and study of the multi-echo in a phase-separated 3He–4He solid solution. Analysis of the behavior of the second echo under these conditions in comparison with the results obtained in samples of liquid and solid 3He reveals the presence of a significant amount of liquid 3He in a fine-grained 3He phase and offers a new explanation of the origin of the unusual damping of the first echo observed previously under these conditions.

Effect of phase separation kinetics on the homogenization kinetics of solid solution of 4He in 3He

New features of the kinetics of phase separation and the subsequent homogenization of solid solutions of 4He in 3He are observed at temperatures of 0.1–0.5 K. Separation was initiated by rapid cooling of a uniform solution, as well as by cooling it in small temperature steps. Information on the kinetics of the phase transitions was obtained using precision measurements of the pressure of the solid helium at constant volume. The homogenization kinetics are found to depend substantially on the kinetics of the preceding separation. The time constants for homogenization in the separation region are smaller by more than a factor of 5 with rapid cooling, than with slow cooling. These results are consistent with a model of homogeneous nucleation.