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.     

Bose-Einstein condensation of incommensurate solid 4He

It is pointed out that the simulation computation of energy performed so far cannot be used to decide if the ground state of solid 4He has the number of lattice sites equal to the number of atoms (commensurate state) or if it is different (incommensurate state). The best variational wave function, a shadow wave function, gives an incommensurate state, but the equilibrium concentration of vacancies remains to be determined. We have computed the one-body density matrix in solid 4He for the incommensurate state by means of an exact ground state projector method in which incommensurability occurs spontaneously. We find a vacancy induced Bose-Einstein condensation of about 0.23 atoms per vacancy at a pressure of 54 bar. This means that bulk solid 4He is supersolid at low enough temperature if the exact ground state is incommensurate.     

Off-diagonal long-range order in solid 4He

Measurements of the moment of inertia by Kim and Chan have found that solid (4)He acts like a supersolid at low temperatures. To understand the order in solid 4(He), we have used path integral Monte Carlo simulations to calculate the off-diagonal long-range order (ODLRO) [equivalent to Bose-Einstein condensation (BEC)]. We do not find ODLRO in a defect-free hcp crystal of (4)He at the melting density. We discuss these results in relation to proposed quantum solid trial functions. We conclude that the solid (4)He wave function has correlations which suppress both vacancies and BEC.     

The unambiguous identification of vacancy migration stage in resistivity recovery of irradiated metals based on trapping of vacancies at probe impurity atoms

The method of resistivity recovery is a powerful tool for studying point defects in irradiated metals. However, the method is nonspecific with respect to a type (vacancy or interstitial) of investigated defects. To overcome this shortcoming, we made use of opposite signs of excess electric charges of the vacancies and self-interstitial atoms in a lattice. Resistivity loss takes place on trapping of vacancies at impurity atoms if excess charges of the impurity atom and defect are opposite in sign. A way of selecting the impurity atoms with the excess charge opposite in sign to that of vacancies is proposed. The specific evolution of resistivity recovery spectrum induced by vacancy trapping at the selected impurity atoms (probe traps) allows one to unambiguously identify the stage of free long-range vacancy migration.     

Onset temperature of Bose-Einstein condensation in incommensurate solid (4)He

The temperature dependence of the one-body density matrix in (4)He crystals presenting vacancies is computed with path integral Monte Carlo simulations. The main purpose of this study is to estimate the onset temperature T(0) of Bose-Einstein condensation in these systems. We see that T(0) depends on the vacancy concentration X(v) of the simulated system, but not following the law T(0) ~ X(v)(2/3) obtained assuming noninteracting vacancies. For the lowest X(v) we study, that is X(v)= 1/256, we get T(0) = 0.15 ± 0.05 K, close to the temperatures at which a finite fraction of nonclassical rotational inertia is experimentally observed. Below T(0), vacancies do not act as classical point defects becoming completely delocalized entities.     

Atomic structure of the Zr–He,Zr–vac,and Zr–vac–He systems: First-principles calculation

The ab initio investigations have been performed for the atomic structure of the Zr–He, Zr–vac, and Zr–vac–He systems with concentrations of helium atoms and vacancies (vac) of ~6 at %. A heliuminduced instability of the zirconia lattice has been revealed in the Zr–He system, which disappears with the formation of vacancies. The most preferred positions of impurities in the metal lattice have been determined. The energy of helium dissolution and the excess volume introduced by helium have been calculated. It has been established that the presence of helium in the Zr lattice leads to a significant decrease in the energy of vacancy formation.     

Vacancy trapping mechanism for multiple hydrogen and helium in beryllium: a first-principles study

The microscopic mechanism for H and He trapping by vacancy defects and bubble formation in a Be host lattice is investigated using first-principles calculations. A single He atom prefers to occupy a vacancy centre while H does not. He can segregate towards the vacancy from the interstitial site much more easily than H. Both H and He exhibit lower diffusion barriers from a remote interstitial to a vacancy with regard to their diffusion barriers inside a perfect Be solid. Up to five H or 12 He atoms can be accommodated into the monovacancy space, and the Be-He interaction is much weaker than Be-H. The physical origin for aggregation of multiple H or He atoms in a vacancy is further discussed. The strong tendency of H and He trapping at vacancies provides an explanation for why H and He bubbles were experimentally observed at vacancy defects in materials. We therefore argue that vacancies provide a primary nucleation site for bubbles of H and He gases inside Be materials.     

Molecular dynamics simulations of point defects in plutonium grain boundaries

A modified analytic embedded atom method (MAEAM) potential is constructed for fcc updelta-Pu. Molecular dynamics (MD) simulations with the potential are performed to investigate the interactions between two symmetrical tilt grain boundaries (GBs) and point defects such as He atom, vacancy and self-interstitial atom (SIA) in Pu. The calculated results show that point defect formation energies are on average lower than those in the lattice but variations from site to site along the GBs are very remarkable. Both substitutional and interstitial He atoms are trapped at GBs. Interstitial He atom is more strongly bound at the GB core than the substitutional He atom. The binding energy of SIA at GB core is higher than those of He atom and vacancy. GB core can bind many He atoms and SIAs due mainly to the fact that it contains many vacancies. Compared with He atom and SIA, the vacancy far from GB core is difficult to diffuse into the core. The GBs can act as sinks and sources of He atoms and SIAs, which may be a reason for the swelling of Pu after a period of self-irradiation because of the higher concentration of vacancy in the bulk.     

Molecular dynamics simulations of He bubble nucleation at grain boundaries

The nucleation behavior of He bubbles in single-crystal (sc) and nano-grain body-centered-cubic (bcc) Mo is simulated using molecular dynamics (MD) simulations, focusing on the effects of the grain boundary (GB) structure. In sc Mo, the nucleation behavior of He bubbles depends on irradiation conditions. He bubbles nucleate by either clustering of He atoms with pre-existing vacancies or self-interstitial-atom (SIA) punching without initial vacancies. In nano-grain Mo, strong precipitation of He at the GBs is observed, and the density, size and spatial distribution of He bubbles vary with the GB structure. The corresponding He bubble density is higher in nano-grain Mo than that in sc Mo and the average bubble size is smaller. In the GB plane, He bubbles distribute along the dislocation cores for GBs consisting of GB dislocations and randomly for those without distinguishable dislocation structures. The simulation results in nano-grain Mo are in agreement with previous experiments in metal nano-layers, and they are further explained by the effect of excess volume associated with the GBs.     

Fate of vacancy-induced supersolidity in 4He

The supersolid state of matter, exhibiting nondissipative flow in solids, has been elusive for 35 years. The recent discovery of a nonclassical moment of inertia in solid 4He by Kim and Chan provided the first experimental evidence, although the interpretation in terms of supersolidity of the ideal crystal phase remains a subject to debate. Using quantum Monte Carlo methods we investigate the long-standing question of vacancy-induced superflow and find that vacancies in a 4He crystal phase separate instead of forming a supersolid. On the other hand, nonequilibrium vacancies relaxing on defects of polycrystalline samples could provide an explanation for the experimental observations.     

Exciton dispersion and electronic excitations in hcp 4He

We present first measurements of the dispersion of excitons in solid helium, taken on a single hcp 4He crystal along the c axis. In agreement with studies on helium clusters, the major energy-loss peak can be interpreted as an intermediate molecular-type exciton, as we do not observe Wannier-like excitations. The measurements are in the (0 0 2) periodic zone, with the exciton energy dispersing along the c axis with a minimum at the gamma point. A calculated conduction band minimum at 31.0 eV above the valence band at gamma is supported by our data at energies above the exciton energy, leading to an exciton binding energy of 8.4 eV.     

Quantum momentum distribution and kinetic energy in solid 4He

We present measurements of neutron scattering from solid 4He at high momentum transfer. The solid is held close to the melting line at molar volume 20.87 cm3/mol and temperature T=1.6 K. From the data, we determine the shape of the momentum distribution, n(k), of atoms in the solid and the leading final state contribution to the scattering. We show that n(k) in this highly anharmonic, quantum solid differs significantly from a Gaussian. The n(k) is more sharply peaked with larger occupation of low momentum states than in a Maxwell-Boltzmann distribution, as found in liquid 4He and predicted qualitatively by path integral Monte Carlo calculations. The atomic kinetic energy is =(24.25+/-0.30) K. If n(k) is assumed to be Gaussian, as is usually the practice, a 10% smaller is obtained.     

Possible existence of bound state Frenkel vacancies in solid 3He

The effects on the low temperature (T ? 15 mK) magnetic and thermal properties of solid ³He due to the presence of bound state Frenkel vacancies (BFV) are analyzed. The coupling of a ³He to a BFV contributes to the zero point motion of the ³He. Assuming that the BFV are strongly interacting and propagate coherently through the crystal, we find good qualitative agreement with $\text{both}$ the specific heat and magnetic susceptibility data.     

Equilibrium concentration of point defects in crystalline4He at O K

We calculate the concentrations of vacancies and intersitials in the ground state of a Bose solid which models⁴He. Because ground-state boson wave functions are nodeless, their probability densities correspond to classical Boltzmann factors, and properties of Bose solids, such as the concentration of vacancies and interstitials, can be calculated using classical statistical mechanics. We model the ground-state wave function of⁴He with the product (Jastrow) form that corresponds to a classical 1/r ^b pair potential, and use a quasiharmonic approximation to calculate the concentrations of vacancies and interstitials in an fcc lattice with this potential. We find that the fractional concentration of vacancies at the melting point is 1.60×10^–5 for 1/r ⁹ and 6.36×10^–6 for 1/r ⁶, while the interstitial fractional concentrations are 1.32×10^–3 and 1.08×10^–5, respectively; the defect concentrations decrease by 7–16 orders of magnitude when the crystal density increases by 50%. At the same density, and with the same 1/r ⁹ potential, the concentration of vacancies in an hcp lattice is essentially the same as in an fcc lattice, but the interstitial concentration is much lower, apparently because the fcc lattice contains a more favorable split-interstitial site than does hcp. Therefore, our fcc vacancy results should be directly relevant for (hcp)⁴He, providing what we think is a lower bound on the vacancy concentration, while the interstitial concentration in⁴He is probably much lower than our results.     

The Effect of Flow Ratio between Elements of Groups III and V on the Structure and Properties of InGaAs Layers Grown by Low-Temperature Molecular-Beam Epitaxy

InGaAs layers grown by low-temperature molecular-beam epitaxy on InP substrates at variable flow ratios between elements of groups III and V are investigated. Layers with a defect structure and low electrophysical parameters are shown to grow with an excess of the components of group III. Growth with high As flows gives rise to trapping of excess arsenic and generation of point defects (As_III antistructural defects and V_III vacancies). High-quality InGaAs layers at low growth temperatures are produced under near-stoichiometric conditions (V/III = 1–4).     

Lattice defects of V3Si single crystals studied by positron annihilation

The sensitivity of positrons to point defects created by the irradiation of V₃Si with neutrons is demonstrated. We found no indication of thermal vacancies by thermal equilibrium measurement up to 1273 K which indicates that the monovacancy formation enthalpy for V₃Si isH _1V ^F ≧(1.84±0.14) eV. Investigations within the range of homogeneity for excess vanadium suppot the idea that substitutional defects are the dominating defect type, whereas for excess silicon a direct confirmation of existing structural vacancies as the dominating defect type is given.     

Vacancy excitation spectrum in solid 4He and longitudinal phonons

The first microscopic ab initio calculation of the excitation spectrum of a vacancy in solid 4He is reported. The energy-wave vector dispersion relation has been obtained at melting density within a development of the shadow wave function variational technique. The calculation of the excitation spectrum of a vacancy gives a bandwidth which ranges from 6 to 10 K in the hcp solid 4He, depending on the particular direction of the wave vector of the excitation. The effective mass of the vacancy turns out to be about 0.35 4He masses. We have also computed the spectrum of longitudinal phonons and we find rather good agreement with recent experimental results.     

Positron annihilation studies of defects in helium-irradiated silicon

Positron annihilation studies have been carried out on Si-n irradiated with He⁺ ions at the V.U.B. cyclotron, to a dose of 4×10¹⁷ He/cm². No temperature dependence on the S-parameter and lifetimes is seen below the irradiation temperature. The positron lifetime associated to the created defects is 290 ps. During the isochronal annealing, this lifetime stays constant up to 700 K. It is attributed to the annihilation of positrons from large vacancy-clusters filled with He atoms. From the isochronal annealing results, only one annealing stage is seen. This annealing stage which extends over a long range of temperature 700–1000 K, is ascribed to the degassing of helium atoms from defects and the growth of vacancy-clusters. The lifetime of positrons in those defects reaches a value of about 530±30 ps at 1000 K, indicating that the vacancy-clusters formed have a mean size of more than 8 vacancies.     

Supersolid state of matter

We prove that the necessary condition for a solid to be also a superfluid is to have zero-point vacancies, or interstitial atoms, or both, as an integral part of the ground state. As a consequence, in the absence of symmetry between vacancies and interstitials, superfluidity has a zero probability to occur in commensurate solids which break continuous translation symmetry. We discuss recent 4He experiments by Kim and Chan in the context of this theorem, question its bulk supersolid interpretation, and offer an alternative explanation in terms of superfluid interfaces.     

Kernresonanz-und leitfähigkeitsmessungen zu diffusion und fehlordnung in LiBr

Electrical conductivity and nuclear magnetic relaxation rates were measured with pure and doped LiBr between 400 K and the melting point (824 K). Prevalent intrinsinc disorder was observed down to 470 K. The degree of thermal disorder is 5.10⁻⁷ at 470 K and 5.10⁻³ at the melting point. From the relaxation rates of ⁷Li, which are caused by Li-diffusion and nuclear dipole interaction, mean jump frequencies of the cations are derived. Conductivities calculated from these frequencies for a jump process via neighbouing cation vacancies are in perfect agreement with directly measured conductivities. From relaxation rates of ⁸¹Br with MgBr₂-doped crystals jump frequencies of vacancies were obtained which are again in good agreement with those derived from the conductivity data. The energies resulting from the measurements are (0.43 ± 0.03) eV for migration of cation vacancies and (1.46 ± 0.05) eV for thermal disorder. From motional narrowing of the ⁸¹Br absorption line the jump frequency of the anions is obtained, which is much smaller than for the cations. Since this motional narrowing is not influenced by any doping, it is concluded that anion transport mainly occurs via pairs of cation and anion vacancies.