Measurement of the lattice parameter of sodium by neutron-back-scattering

We report high precision results (δa/a ≈ 3 x 10^-6) of the lattice parameter of high purity sodium (99.99%) in the temperature region from 32°C up to the melting point. Data of the crystal quality are also given: the half width of the angular mosaic spread amounts to about 4'. Preliminary results on vacancy formation energy and entropy, using literature data of volume expansion, are 0.35 ± 0.02 eV and (3.7 ± 0.5) k_B resp. for a single vacancy.     

Equilibrium vacancy concentration measurements on aluminum

Thermal expansion on high purity aluminum has been measured to study defects in thermal equilibrium by the (ΔL/L ₀?Δa/a ₀) method. Measurements of the changes in macroscopic length ΔL and lattice parameter Δa were made from room temperature to 637° C. Length changes were measured by a laser interferometer and lattice parameter changes by a X-ray diffractometer technique on the same crystal at identical temperatures. At temperatures above 400° C ΔL/L ₀ becomes greater than Δa/a ₀, indicating the generation of a noticeable amount of new lattice sites due to vacancy formation. Extrapolation gives a vacancy concentration ΔN/N ₀=9.8·10^?4 at the melting point (660° C). The experimental findings can be explained by assuming formation of monovacancies and divacancies. Values for the enthalpy and entropy of formation for mono- and divacancies are given.     

Intermediate asymptotic expressions for high-order spin correlation functions in a two-dimensional classical ferromagnet

Different-point spin correlation functions are calculated for a two-dimensional classical ferromagnet in a pacerturbative range of distances r: a<r?m ^?1, where a is the lattice parameter and m ^?1 is the correlation length. The expressions for the four-and higher-order correlation functions are presented.     

Enhancement of L10 ordered FePt by Pt buffer layer

L₁₀-ordered FePt thin films prepared by molecular-beam epitaxy on MgO (0 0 1) substrate at 320 °C with different thickness of Pt buffer layer have been investigated. The out-of-plane coercivity increases with increasing thickness of Pt buffer. The maximum values of the long-range order parameter and uniaxial magnetic anisotropy energy are 0.72 and 1.78×10⁷ erg/cm³, respectively, for films with 12 nm thick Pt buffer layer, where the c/a ratio (0.976) shows the minimum value. The reason for the enhancement in ordering is due to the proper lattice strains Pt buffer bestows on FePt layer, these strains are equal to the contraction in lattice parameter c and the expansion in a. Studies of angular-dependent coercivity revealed that the magnetization reversal behaviour shifts from a domain-wall motion dominated case towards a near rotational mode with increasing thickness of Pt buffer layer.     

Defect melting as an SO(3) lattice gauge theory

We show that defect melting is closely related to SO(3) lattice gauge theory. The phase transition of this system corresponds to a Lindemann melting parameter L≈50γ where γ≈2 is a parameter characterizing the unharmonic content in the elastic forces. This is in rough agreement with experiment. The equivalence may help in visualizing the crucial rule of defects in quark confinement.     

Role of beryllium doping in strain changes in II-type InAs/GaSb superlattice investigated by high resolution X-ray diffraction method

We have studied the influence of the beryllium doping on strain in the II-type InAs/GaSb superlattices (SLs) by means of high-resolution X-ray diffraction (HRXRD). Three analyzed superlattices were grown by molecular beam epitaxy. One of the examined superlattices was undoped. Two others structures, called doped SLs, composed of two superlattices: Be-doped and undoped which were grown one on the top of each other. The doping concentration was determined by secondary ion mass spectroscopy. The doping level was 1×10¹⁷ cm^?3 and 2×10¹⁹ cm^?3. For doped superlattices, the HRXRD measurements showed splitting of satellite (ST) peaks. Furthermore, the separation of ST peaks increase with doping level. In contrast, for undoped superlattice, the splitting of the ST peaks was not observed. Sometimes the separation of ST peaks can be caused by change of thickness period of superlattice or partial relaxation of the structure. However, we claim that in our experiment the splitting is caused by another mechanism: The presence of Be atoms in SL causes the change of average lattice constant of the superlattice. The influence of Be dopant on lattice parameter of superlattice was confirmed by theoretical simulations. Furthermore, the change of the lattice constant (Δa/a) of the GaSb:Be buffer was examined. The reduction of lattice parameter of GaSb was noticed. It was caused by the presence of Be doping and unintentionally incorporated As-atoms in the GaSb layer. It is very important to know that even very small Be concentration (1×10¹⁷ cm^?3) causes the change of average lattice parameter of SL.     

Improved continuum limit lattice action for QCD with wilson fermions

Two possible ways of extending Symanzik's improvement programme to lattice fermions namely improvement to first and second order in the lattice sppacing a are discussed. The corresponding lattice actions for fermions are constructed and tree-level improvement conditions are derived by considering “classical” improvement. The concept of “on-shell” improvement is generalized to the lattice fermions studied here and the free parameters are determined for O(a) and O(a²) on-shell improved actions to all orders of perturbation theory. No evidence is found that the complicated structure of the O(a²) on-shell improved action, especially thearising fermion contact terms can be removed beyond tree level. The effect of terms in the action that explicitly break chiral symmetry and therefore remove the phenomenon of species doubling are investigated by considering the energy-momentum relations of the arising tree-level improved actions. Our main result is that the O(a) improved action is a slightly modified Wilson fermion action can still be written with only nearest-neighbour fermion interactions.     

Thermal expansion op NbSe2 and TaS2

The lattice parameters a₀ and c₀ of the hexagonal 2H polytype of NbSe₂; have been measured over the temperature range 156–478 K for a₀, and 138–482 K for c₀. The lattice parameter c₀ of the hexagonal 2H polytype of TaS₂ has been measured between 151 and 472 K. The lattice parameters a₀ and c₀ for the octahedral 1T polytype of TaS₂ been measured between 165 and 488 K. Over these temperature ranges, the following average coefficients of thermal expansion have been measured; 2H-NbSe₂, 6.6 × 10^?6K^?1 along the a-axis, 19.9 × 10^?6 K^?1 along the c-axis; 2H-TaS₂, 15.6 × 10^?6 K^?1 along the c-axis; IT-TaS₂, 12.7 × 10^?6 K^?1 along the c-axis. The parameter c₀ of 1T-TaS₂ undergoes two transitions which may be explained in terms of charge density waves.     

Crystallographic study of the phase transition in (Me4P)2ZnBr4

The compound (Me₄P)₂ZnBr₄, a member of the β-K₂SO₄ structure class, undergoes a phase transition at 84°C from the room temperature space group P12₁/c1 to the parent Pmcn structure. The room temperature structure corresponds to a ferrodistortive transition of B_1g symmetry at the zone center. At room temperature, the compound has lattice constants a=9.501(1), b=16.055(2), c=13.127(2) Å and β=90.43(1)°. For the high temperature phase, the orthorhombic cell has dimensions a=9.466(2), b=16.351(3) and c=13.284(2) Å. The structures consist of two crystallographically independent Me₄P⁺ cations and the ZnBr₄²⁻ anions. In the room temperature phase, all three ionic species show substantial displacement from the mirror plane perpendicular to the a-axis that exists in the high temperature phase, as well as rotations out of that plane. The thermal parameters of the cations are indicative of substantial librational motion. Measurements of lattice parameters have been made at 2-5°C intervals over the temperature range 40-140°C. The changes in the lattice constants appear continuous at T_c (within experimental limits) indicating that the phase transition is likely second-order. The a lattice constant shows an anomalous shortening as T_c is approached. Thermal expansion coefficients are calculated from this data. An application of Landau theory is used to derive the temperature dependencies of spontaneous shear strain and corresponding elastic stiffness constants associated with the primary order parameter.     

Lindemann's criterion and the melting of solids at high pressures

The generalized Lindemann's criterion is utilized to derive the variation of the melting temperature T_m with compression. The result incorporates the basic features of the lattice potential as well as the volume dependence of the frequency distribution through the first two moments of the mode Grüneisen parameter. This melting relation predicts that when T_m is plotted against the volume of the melting solid, the fusion curves of solids bonded by Van der Waals forces are concave to the temperature axis and in accordance with the predictions of the Simon equation. On the other hand, the predicted melting curves of ionic compounds, as the alkali-halides, are concave to the volume axis and exhibit a maxima at higher pressures. Since silicates generally possess an ionic contribution to the lattice energy, this melting relation should give a more accurate estimate of the high pressure melting temperature for these compounds than Simon's and theoretically similar equations.     

Infrared exponents and the strong-coupling limit in lattice Landau gauge

We study the gluon and ghost propagators of lattice Landau gauge in the strong-coupling limit β=0 in pure SU(2) lattice gauge theory to find evidence of the conformal infrared behavior of these propagators as predicted by a variety of functional continuum methods for asymptotically small momenta $q^{2}\ll\varLambda_{\mathrm{QCD}}^{2}$ . In the strong-coupling limit, this same behavior is obtained for the larger values of a ² q ² (in units of the lattice spacing a), where it is otherwise swamped by the gauge-field dynamics. Deviations for a ² q ²<1 are well parameterized by a transverse gluon mass ∝1/a. Perhaps unexpectedly, these deviations are thus no finite-volume effect but persist in the infinite-volume limit. They furthermore depend on the definition of gauge fields on the lattice, while the asymptotic conformal behavior does not. We also comment on a misinterpretation of our results by Cucchieri and Mendes (Phys. Rev. D 81:016005, 2010).     

Structure and magneto-transport parameters of partially relaxed and coherently grown La0.67Ba0.33MnO3 films

X-ray diffraction (XRD) and medium-energy ion scattering (MEIS) have been used to reveal distortions in the crystal lattice of La_0.67Ba_0.33MnO₃ (LBMO) films formed in relaxation of mechanical stresses. The LBMO films 25 nm thick have been prepared by laser deposition. The XRD and MEIS data obtained suggest that biaxially and mechanically elastically stressed LBMO layers grow coherently on LSATO substrates, whose crystal lattice parameter differs only weakly from the corresponding LBMO parameter, whereas in the bulk of manganite films grown on LaAlO₃ substrates, stresses relax partially. Stresses do not relax in the LBMO interface about 4 nm thick adjoining LaAlO₃. The electro- and magneto-transport parameters of partially relaxed LBMO films have been compared with those obtained for coherently grown manganite films with approximately the same tetragonal distortion of the lattice cell (a _⊥/a _‖ = 1.024–1.030; a _‖ and a _⊥ are the unit cell parameters in the substrate plane and normal to it, respectively). At temperatures substantially lower than the Curie temperature, the electrical resistivity ρ of LBMO films fits the relation ρ = ρ₀ + ρ₁ T ² + ρ₂(H)T ^4.5; the coefficients ρ₀ and ρ₁ do not depend on temperature T and magnetic field, and ρ₂ does not depend on temperature but almost linearly decreases with increasing magnetic field strength H. The coefficient ρ₂ for partially relaxed LBMO films is substantially larger than that for coherently grown manganite layers.     

Critical behaviour in baryonic matter

First we consider the phenomenology of deconfinement and chiral symmetry restoration for strongly interacting matter at non-vanishing baryon number density. Subsequently, we present numerical results obtained by a Monte Carlo evaluation of statistical QCD on an 8³×3 lattice, using Wilson fermions withN _f =2, in fourth order hopping parameter expansion, and suppressing the imaginary part of the fermion action. We consider baryonic chemical potentials up to μa=0.6μa=0.6 (μ/Λ _L ?200); in this range, the critical parameters for deconfinement and chiral symmetry restoration are found to coincide.     

Evidence for a relation between interstitial long-range migration in h.c.p. metals and their c/a-ratio

The temperature for the long-range migration of an interstitial atom in h.c.p. metals is - when normalized to the melting temperature - observed to be a linear function of the c/a-ratio. This can be understood in terms of the relative size of open atomic lenses in the lattice. The special cases of Zn and Cd (extremal c/a-values) are tentatively explained by a crowdion mechanism for the creation and annealing of Frenkel defects.     

Coercivity mechanism of Sm(Co, Cu)5

The mechanism of the high intrinsic coercivity of the Sm(Co_1−xCu_x)₅ (0≦x<1) system was studied by relating the coherency between the lattice constants of hexagonal Sm(Co, Cu)₅ and hcp Co to the coercive force. It was found analytically that the intrinsic coercive force reaches a maximum in the composition range from x=0.6 to 0.8, where the lattice mismatch approaches zero, so that there is a strong correlation between lattice matching and coercive force. When a Sm ion was located within a Sm(Co, Cu)₅ grain and in the outmost edge of the a and c planes of its grain surrounded or not surrounded by the coherent Co phase, the crystal field parameter at each Sm³⁺ site was calculated using a point charge model under the assumption that the Co and Cu atoms located in a grain and the hcp Co atoms situated at the interface uniformly have a charge of 3/5−. The results indicated that the Co phase precipitated coherently along the grain boundaries effectively enhances the magnetocrystalline anisotropy of Sm ions located in the outmost edges of the a and c planes of a Sm(Co, Cu)₅ grain.     

Two-dimensional and layered structures in the discrete φ4 model

The properties of phase transitions in two-dimensional and layered systems are investigated on the basis of a discrete φ⁴ model by numerical and analytical methods. The only parameter a of the discrete φ⁴ model determines the behavior of the system and makes it possible to investigate phase transitions ranging from transitions of the displacement type (a → +0) to order-disorder type (a → +∞). The behavior of a two-dimensional system is investigated in a wide range of values of the parameter a. The temperature dependences of the squared order parameter η²(T) and the phase transition temperature T _c as a function of the thickness N of the system are obtained for three characteristic values of the parameter a using the Monte Carlo method. The properties of phase transitions in the discrete φ⁴ model are investigated on the basis of the mean-field approximation and the independent-mode approximation. The results obtained in the numerical experiments are compared with the analytical approximations. It is shown that the mean-field approximation qualitatively describes the behavior of the phase-transition temperature T _c as a function of the thickness N of the system for a wide range of values of the parameter a, and the independent-mode approximation describes quantitatively, to within 5%, the results of the numerical simulation for small values of a.     

Atomic Arrangement in B2 FeAl Prepared by Self-Propagated High-Temperature Synthesis at Varying Al Content and Annealing

Atomic arrangement in B2 FeAl prepared by self-propagated high temperature synthesis (SHS) as a function of Al concentration and annealing temperature has been studied by ⁵⁷Fe Mössbauer spectroscopy (MS) and X-ray diffraction (XRD). The increase of B2 FeAl isomer shift (IS) and lattice parameter (a) with Al concentration in the whole concentration range has been detected. This may originate from the formation of Al antisite atoms. Calculation of s-electron populations against number of Al antisites using a cluster approach and MO LCAO method supported this assumption. Annealing resulted in atomic rearrangements both in near-stoichiometric and Al-rich B2 FeAl.     

Structural and physical–chemical properties of the CuGa5Se8, CuGa3Se5 and CuIn3Se5 compounds

Large-block (8×4×3 mm³) CuGa₅Se₈ crystals were obtained by the horizontal Bridgman method. Homogeneous CuGa₃Se₅ and CuIn₃Se₅ single crystals 12 mm in diameter and up to 40 mm in length were grown by directed crystallization of the melt. All three compounds were found to have the chalcopyrite-related structure. The melting points of these compounds were defined by means of the differential thermal analysis. The lattice parameters a and c as well as the axial thermal expansion coefficients α_a and α_c were determined as a function of temperature in the range from 90 to 650 K by the X-ray diffraction method. It is revealed that for all three compounds the coefficients of expansion along the a-axis are larger than those along the c-axis over the entire temperature range studied.     

Amplitudes of thermal vibrations in molecular solids

The mean-square nuclear displacements 〈U²〉 _T have been evaluated for the molecular (rare-gas) solids by a lattice dynamical rigid-atom Model. The model derives the inter-molecular interaction from a “two-piece four parameter” pair-potential, includes the contribution of zero-point vibration through potential parameters by a self-consistent method, and accounts for the cubic and quartic anharmonic potential terms as perturbations to the harmonic Hamiltonian. The effect of many body interactions has been included on the basis of Axilrod-Teller approximation. The effect of including three-body forces as well as anharmonicity is found to decrease the values of 〈U²〉_T at all temperatures for all the solids. However, the ratio of the root mean-square nuclear displacements at melting to the nearest-neighbour distance, i.e. the Lindemann parameter (δ) is approximately the same for all the solids under study, which shows that the Lindemann parameter is structure as well as interaction dependent. The results are consistent with the other conventional calculations.     

Comparative investigations of the P-V-T relationship of NaCl at high pressure and temperature

Two different potential models of molecular dynamics (MD) simulations have been applied to investigate the pressure-volume-temperature (P-V-T) relationship and lattice parameter of NaCl under high pressure and temperature. The first one is the shell model (SM) potentials in which due to the short-range interaction pairs of ions are moved together as is the case in polarization of a crystal due to the motion of the positive and negative ions, and the second one is the two-body rigid-ion Born-Mayer-Huggins-Fumi-Tosi (BMHFT) potentials with full treatment of long-range Coulomb forces. The P-V relationship at 300 K, T-V relationship at zero pressure, and lattice parameter a, have been obtained and compared with the available experimental data and other theoretical results. Compared with SM potentials, the MD simulation with BMHFT potentials is very successful in reproducing accurately the measured volumes of NaCl. At an extended pressure and temperature ranges, P-V relationship under different isotherms at selected temperatures, T-V relationship under different pressures, and lattice parameter a have also been predicted. The properties of NaCl are summarized in the pressure range 0-30 GPa and the temperature up to 2000 K.