Superconductivity in the Ti-D system under pressure

The pressure dependence of the superconducting transition temperature in TiD_0.74 has been measured up to 30 GPa in a diamond high-pressure chamber. It is found that the deuteride TiD_0.74 becomes a superconductor at pressures corresponding to the transition to the high-pressure ζ phase, with a transition temperature that increases from 4.17 to 4.43 K in the interval P=14–30 GPa. The value extrapolated to atmospheric pressure T _c (0)=4.0 K is significantly lower than the superconducting transition temperature (T _c =5.0 K) measured earlier in the metastable state obtained by quenching TiD_0.74 under pressure. It is assumed that the significant difference of the extrapolated value from the superconducting transition temperature in the metastable state after quenching under pressure is caused by a phase transition on the path from the stability region of the ζ phase under pressure to the region of the metastable state at atmospheric pressure. Fiz. Tverd. Tela (St. Petersburg) 40, 2153–2155 (December 1998)     

Melting line, spinodal and the endpoint of the melting line in the system with a modified Lennard—Jones potential

A molecular dynamics method was used to calculate the pressure p* and the internal energy e* of a liquid and a crystal in stable and metastable states in a system of 2048 particles, which interaction is described by a modified Lennard—Jones potential. For the liquid phase, calculations were performed along 13 isotherms from the range of reduced temperature T* = 0.35–3.0, and for the crystal phase, along 16 isotherms from the range T* =0.1–3.0. The thermal p* = p*(ρ*,T*) and caloric e* = e*(ρ*,T*) equations of state for liquids and crystals have been constructed. The parameters of crystal-liquid phase equilibrium have been determined from the conditions of phases coexistence at positive pressures and in the region of negative pressures, where the coexistent phases are metastable. The spinodal of a stretched liquid has been approximated. It has been found that with a temperature decrease the metastable extension of the melting line meets the spinodal of the liquid phase. The point of their meeting, the endpoint of the melting curve, is the point of termination of crystal-liquid phase equilibrium without the onset of identity of the phases.     

Surface free energy of the crystal-liquid interface on the metastable extension of the melting curve

The surface free energy γ, excess surface energy e, and excess surface stress τ at the crystal-liquid interface of a Lennard-Jones system have been determined by molecular dynamics simulation. The calculations have been performed for temperatures both above and below the triple-point temperature for the region where each of the coexisting phases is metastable and is at a negative pressure. The asymptotic behavior of γ, e, and τ has been analyzed near the endpoint of the melting curve, which is a point of the contact of the metastable extension of the melting curve and the spinodal of the stretched liquid [V.G. Baidakov and S.P. Protsenko, Phys. Rev. Lett. 95, 015701 (2005)]. It has been found that γ, e, and τ at this point are finite and the excess surface entropy is zero.     

Magnetic phases in quasi-binary (Fe1−x Cox)Ge2 intermetallic compounds

Magnetic neutron diffractometry revealed the existence in (Fe_1−x Co_x)Ge₂ solid solutions (x<0.5) with C16 structure of only two magnetic phases, namely, low-temperature (AFI) and high-temperature (AFII). A third magnetic phase, AFIII, suggested by earlier magnetic measurements, has not been found. The AFI and AFII phases have a commensurate and an incommensurate antiferromagnetic structure with the wave vectors k ₀=2π/a (1,0,0) and k=k ₀+δ k, respectively. The regions of their existence are shown in the magnetic phase diagram. Neutron diffraction measurements yielded the concentration dependence of the average magnetic moment per atom in the antiferromagnetic sublattice of a 3d metal, which, similarly to the dependence of the Néel point on x, was found to be nonlinear. An analysis of these dependences suggests that substitution of cobalt for iron is accompanied, on the one hand, by a decrease of the local spin density on the iron atoms in the nearest environment of a cobalt atom and, on the other hand, by an increase of the effective exchange integral between the nearest-neighbor iron atoms located along the tetragonal axis. Fiz. Tverd. Tela (St. Petersburg) 41, 283–289 (February 1999)     

Magnetoresistance of HgSeS crystals at hydrostatic pressures of up to 1 GPa

Magnetoresistance (MR) of HgSe_1−x S_x crystals has been studied in the temperature range 4.2–300 K and in magnetic fields up to 12 T under hydrostatic pressures P exceeding the threshold P _t for the structural phase transition. Shubnikov-de Haas quantum oscillations in longitudinal and transverse MR were observed to occur in the original samples at T=4.2 K. For P>P _t, HgSeS crystals transferred to metastable states, which presumably incorporate the high-and low-pressure phases, and in which the oscillations vanished. At the same time the monotonic behavior of MR with magnetic field B, as well as the temperature dependences of resistivity ρ retained the shape characteristic of the original phases. The observed weakening of the dependences of ρ on B and T is attributed to an increase of the temperature independent contribution to ρ caused by phase inclusions and structural defects in the metastable states. It is the corresponding decrease of electron mobility that suppresses the oscillations. Fiz. Tverd. Tela (St. Petersburg) 39, 1717–1722 (October 1997)     

Pseudogap and symmetry of superconducting order parameter in cuprates

The phase diagram, nature of the normal state pseudogap, type of the Fermi surface, and behavior of the superconducting gap in various cuprates are discussed in terms of a correlated state with valence bonds. The variational correlated state, which is a band analogue of the Anderson (RVB) states, is constructed using local unitary transformations. Formation of valence bonds causes attraction between holes in the d-channel and corresponding superconductivity compatible with antiferromagnetic spin order. Our calculations indicate that there is a fairly wide range of doping with antiferromagnetic order in isolated CuO₂ planes. The shape of the Fermi surface and phase transition curve are sensitive to the value and sign of the hopping interaction t′ between diagonal neighboring sites. In underdoped samples, the dielectrization of various sections of the Fermi boundary, depending on the sign of t′, gives rise to a pseudogap detected in photoemission spectra for various quasimomentum directions. In particular, in bismuth-and yttrium-based ceramics (t′>0), the transition from the normal state of overdoped samples to the pseudogap state of underdoped samples corresponds to the onset of dielectrization on the Brillouin zone boundary near k=(0,π) and transition from “large” to “small” Fermi surfaces. The hypothesis about s-wave superconductivity of La-and Nd-based ceramics has been revised: a situation is predicted when, notwithstanding the d-wave symmetry of the superconducting order parameter, the excitation energy on the Fermi surface does not vanish at all points of the phase space owing to the dielectrization of the Fermi boundary at k _x=± k _y. The model with orthorhombic distortions and two peaks on the curve of T _c versus doping is discussed in connection with experimental data for the yttrium-based ceramic. Zh. éksp. Teor. Fiz. 115, 649–674 (February 1999)     

On the nature of the γ-α transition in cerium

In 1964 Davis and Adams established that the large increase of the thermal expansion and compressibility in the critical region of the γ-to α-Ce phase transition occurs predominantly in the α phase. This provides strong evidence that a tricritical point is realized in Ce. This also means that the aforementioned transition is not isomorphic and that α-Ce should have a distorted fcc structure. A careful examination of Jayaraman’s data (1965) shows that a second-order transition line continues beyond the tricritical point to the vicinity of a triple point on the melting curve. The phase boundary with the tricritical point and the minimum of the melting curve are reconstructed within the framework of Landau theory. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 2, 111–117 (25 January 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Molecular dynamics investigation of the size effect upon the β → α transformation in Zr nanocrystals

The stability of the β phase in cubic zirconium nanoparticles has been calculated as a function of the size r (r varies in the range from 2.5 to 11.5 nm) by the molecular dynamics method with the many-body interatomic interaction potential obtained within the embedded-atom model. It has been demonstrated that the temperature T _k at which the cubic cluster of body-centered cubic zirconium becomes structurally unstable depends nonlinearly on the particle size. The curve T _k (r) exhibits a pronounced maximum in the range r ≈ 4.3−4.7 nm. It has been established that the mechanism of the structural transition from the body-centered cubic phase to the hexagonal close-packed phase depends substantially on the particle size. For particles with sizes in the range from 2.5 to 5.0 nm, there exists a temperature range in which the transition from the body-centered cubic phase to the hexagonal close-packed phase remains incomplete for a long time. In this case, two phases coexist and the initial particle undergoes a strong deformation along the habit plane.     

Supersymmetric spin glass

The manifestly supersymmetric four-dimensional Wess-Zumino model with quenched disorder is considered at the one-loop level. The infrared fixed points of a beta function form the moduli space ℳ=RP ², where two types of phases are found: with and without replica symmetry. While the former phase possesses only a trivial fixed point, this point become unstable in the latter phase, which may be interpreted as a spin glass phase. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 8, 657–662 (25 April 1997) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Topological Berry phase and semiclassical quantization of cyclotron orbits for two dimensional electrons in coupled band models

The semiclassical quantization of cyclotron orbits for two-dimensional Bloch electrons in a coupled two band model with a particle-hole symmetric spectrum is considered. As concrete examples, we study graphene (both mono and bilayer) and boron nitride. The main focus is on wave effects – such as Berry phase and Maslov index – occurring at order (^h/_2p)\hbar in the semiclassical quantization and producing non-trivial shifts in the resulting Landau levels. Specifically, we show that the index shift appearing in the Landau levels is related to a topological part of the Berry phase – which is basically a winding number of the direction of the pseudo-spin 1/2 associated to the coupled bands – acquired by an electron during a cyclotron orbit and not to the complete Berry phase, as commonly stated. As a consequence, the Landau levels of a coupled band insulator are shifted as compared to a usual band insulator. We also study in detail the Berry curvature in the whole Brillouin zone on a specific example (boron nitride) and show that its computation requires care in defining the “k-dependent Hamiltonian” H(k), where k is the Bloch wavevector.     

Stable and metastable phases in Nd−Fe binary alloys

Melt-spinning Nd _x Fe_100-x alloys over a wide composition range: 10≤x≤90, has lead to the identification of three metastable phases. Two of these correspond to phases which are stable in late rare earth-iron alloy systems, the third is related to the fcc grain boundary phase observed in sintered Nd−Fe−B permanent magnets. Structural and magnetic data are presented.     

Oscillatory phenomena in cold matter with four-fermion interaction

The phase structure of the Nambu-Jona-Lasinio model in space-time with the topology R ³×S ¹ (spatial coordinate compactified) and chemical potential μ is investigated. Phase portraits of the model are constructed in the μλ plane (λ=1/L, where L is the size of the dimension S ¹) in the case with periodic boundary conditions. It is shown here for the first time that there exist in the model an infinite number of both chirally symmetric massless phases and asymmetric massive phases, between which (as a rule) transitions are second-order. Because of this phase structure, changes in the parameter λ induce oscillations in the particle density, fermion mass, and the critical curve on which chiral invariance is restored. Zh. éksp. Teor. Fiz. 114, 418–436 (August 1998)     

Features of the melting dynamics of a vortex lattice in a high-T c superconductor in the presence of pinning centers

The phase transition “triangular lattice-vortex liquid” in layered high-T _c superconductors in the presence of pinning centers is studied. A two-dimensional system of vortices simulating the superconducting layers in a high-T _c Shubnikov phase is calculated by the Monte Carlo method. It was found that in the presence of defects the melting of the vortex lattice proceeds in two stages: First, the ideal triangular lattice transforms at low temperature (≃3 K)into islands which are pinned to the pinning centers and rotate around them and then, at a higher temperature (≃8 K for T _c 584 K), the boundaries of the “islands” become smeared and the system transforms into a vortex liquid. As the pinning force increases, the temperatures of both phase transitions shift: The temperature of the point “triangular lattice-rotating lattice” decreases slightly (to ≃2 K)and the temperature of the phase transition “rotating lattice-vortex liquid” increases substantially (≃70 K). Pis’ma Zh. éksp. Teor. Fiz. 66, No. 4, 269–274 (25 August 1997)     

On the possibility of investigating the dispersion of the energy bands of a crystal using resonant x-ray emission spectra

It is shown that, when the dispersion of the energy bands of crystals is investigated by resonant x-ray emission (RXE), an ambiguity can arise in the determination of k _tr — the transition point in k space — as a result of the characteristic features of the band structure and the value of the matrix elements. It is proposed that calculations of the distribution of partial contributions to interband optical transitions in the Brillouin zone (BZ) be used as a means of obtaining a simplified estimate of k _tr. The basic properties of this distribution are examined for lithium hydride, which is a convenient model object having a simple band structure and interband transitions which have been studied in detail. It is shown that the k points of the general position, which form a complex figure in the BZ, make the main contribution to the interband transitions. The contribution of high-symmetry points is much smaller mainly because of their small representativeness. This make it easier to understand the reason for the possible nonmonotonic variation of k _tr in RXE measurements of the dispersion of the energy bands of crystals or the sharp changes in the resonance-fluorescence intensity. Fiz. Tverd. Tela (St. Petersburg) 41, 1597–1601 (September 1999)     

Diffuse X-ray scattering by ice in the vicinity of the melting point

The X-ray pattern of ice recorded at −10°C reveals, along with the reflexes of a hexagonal phase, intense diffuse X-ray scattering, testifying to the presence of a noncrystalline phase in the sample. Heating of ice to a temperature close to the melting point leads to almost complete decomposition of the crystalline phase. As this takes place, intense diffuse X-ray scattering with a maximum at 2Θ of 23°C appears in the diffraction pattern, which is typical for a metastable amorphous phase. The first maximums of the radial distribution function for the metastable amorphous phase of ice appear to be close in their positions to the first radii of the hexagonal phase coordination spheres.     

Textural analysis of a mesophase with banana shaped molecules

Observed under the polarizing microscope, the phase in the banana compound D14F3 [J.P. Bedel et al., Liq. Cryst. 27, 1411 (2000)] displays two types of textures of defects, namely (a): helical ribbons, that nucleate in large quantities when the samples are quenched from a sufficiently high temperature in the isotropic phase (b)- shapes with no helicity having the structure of developable domains much akin to those observed in columnar phases, either resulting from the annealing of the helical ribbons or nucleating under slow cooling processes. The existence of these two kinds of defects points toward the complex nature of the structure of the B7 phase, which is at the same time a columnar and a smectic phase. Our observations fit the model [M. Kleman, J. Phys. France 46, 1193 (1985)] according to which the geometry of a helical ribbon is that one of the central region of a screw dislocation with a giant Burgers vector, split into two helical disclination lines of strength k = 1/2 which bound the ribbon. Textures and defects, already partly documented, and growth features and annealing processes, not yet reported in the literature, are analyzed. We conclude that the helical ribbons and the developable domains with no helicity are textures of two different B7 states, namely a metastable state and the ground state respectively. Comparative textural analysis is performed for two other banana compounds exhibiting B2 phases.Received: 8 November 2003, Published online: 5 February 2004PACS: 61.30.Jf Defects in liquid crystals - 61.72.Bb Theories and models of crystal defects - 64.60.My Metastable phases     

Size effects in the exciton energy and first-order phase transitions in CuCl nanocrystals in glass

The absorption spectra and the melting and crystallization kinetics of CuCl nanocrystals in glass are investigated in the range of particle radii 1–30 nm. Three discontinuities are found on the curves representing the size dependence of the melting point T _m(R) and the crystallization point T _c(R). As the particle radius gradually decreases from 30 nm in the range R⩽12.4 nm there is a sudden 60° drop in the temperature T _c in connection with the radius of the critical CuCl nucleus in the melt. A 30° drop in T _m is observed at R=2.1 nm, and a second drop of 16° in the temperature T _c is observed for CuCl particles of radius 1.8 nm. The last two drops are associated with changes in the equilibrium shape of the nanoparticles. In the range of smaller particles, R⩽1.34 nm the T _c(R) curve is observed to merge with the T _m(R) curve, owing to the disappearance of the work of formation of the crystal surface during crystallization of the melt as a result of the zero surface tension of CuCl particles of radii commensurate with the thickness of the effective surface layer. An increase in the size shift of the exciton energy is observed in this same range of CuCl particle radii (1–1.8 nm). The size dependence of the melting and crystallization temperatures of the nanoparticles is attributed to variation of the free energy in the surface layer of a particle. Fiz. Tverd. Tela (St. Petersburg) 41, 310–318 (February 1999)     

Crystalline phase transitions and acoustic phonons behaviour of polymorphic ethanol

Ethanol shows a complex scenario of different crystalline phases in the temperature range between its glass transition at T_g = 97 K and its melting point at T_m = 159 K. Brillouin spectroscopy has revealed capable of observing and assessing acoustic phonon changes related to these phase transitions between different crystalline phases (either a plastic-crystal phase or different monoclinic phases). By combining this technique and calorimetric experimental data, we are able to corroborate the existence of at least two stable and two metastable (monoclinic) crystalline phases of pure ethanol.     

Evidence of maximum in the melting curve of hydrogen at megabar pressures

Hydrogen at high pressures of ∼400 GPa might be in a zero-temperature liquid ground state (N. Ashcroft, J. Phys.: Condens. Matter A 12, 129 (2000), E. G. Brovrnan et al., Sov. Phys. JETP 35, 783 (1972)). If metallic hydrogen is liquid, the melting T _melt(P) line should possess a maximum. Here we report on the experimental evaluation of the melting curve of hydrogen in the megabar pressure range. The melting curve of hydrogen has been shown to reach a maximum with T _melt = 1050 ± 60 K at P = 106 GPa and the melting temperature of hydrogen decreases at higher pressures so that T _melt = 880 ± 50 K at P = 146 GPa. The data were acquired with the aid of a laser heating technique where diamond anvils were not deteriorated by the hot hydrogen. Our experimental observations are in agreement with the theoretical prediction of unusual behavior of the melted hydrogen [S. Bonev et al., Nature 481, 669 (2004)]. The article is published in the original.     

Melting of polymer single crystals studied by dynamic Monte Carlo simulations

We report dynamic Monte Carlo simulations of lattice polymers melting from a metastable chain-folded lamellar single crystal. The single crystal was raised and then melted in an ultrathin film of polymers wetting on a solid substrate, mimicking the melting observations made by using Atomic Force Microscopy. We observed that the thickness distribution of the single crystal appears quite inhomogeneous and the thickness increases gradually from facetted edges to the center. Therefore, at low melting temperatures, melting stops at a certain crystal thickness, and melting-recrystallization occurs when allowing crystal thickening; at intermediate temperatures, melting maintains the crystal shape and exhibits different speeds in two stages; at high temperatures, fast melting makes a melting hole in the thinnest region, as well as a saw-tooth-like pattern at the crystal edges. In addition, the linear melting rates at low temperatures align on the curve extrapolated from the linear crystal growth rates. The temperature dependence of the melting rates exhibits a regime transition similar to crystal growth. Such kinetic symmetry persists in the melting rates with variable frictional barriers for c -slip diffusion in the crystal as well as with variable chain lengths. Visual inspections revealed highly frequent reversals upon melting of single chains at the wedge-shaped lateral front of the lamellar crystal. We concluded that the melting kinetics is dominated by the reverse process of intramolecular secondary crystal nucleation of polymers.