Young's modulus surface and Poisson's ratio curve for cubic metals

The general expressions for the compliance , Young's modulus E(h k l) and Poisson's ratio υ(h k l, θ) along arbitrary loading direction [h k l] are given for cubic crystals. The representation surface for which the length of the radius vector in the [h k l] direction equals to E(h k l) and representation curve for which the length of the radius vector with angle θ deviated from the reference directions , and equals to υ(100, θ), υ(110, θ) and υ(111, θ) for example, are constructed for six FCC metals Ag, Al, Au, Cu, Ni, Pb and seven BCC metals Cr, Fe, Mo, Nb, Ta, V, W.     

Generalized pressure-volume equations mimicking the Stacey reciprocal K-primed equation of state

Two generalized polynomial expressions, one based on a logarithmic form and the other on an exponential form have been set up that give pressure-volume (P-V) relationship and higher derivative properties mimicking the Stacey reciprocal K-primed equation of state. The results have been obtained for pressure P, bulk modulus K and its pressure derivative K′ for six metals viz. Ag, Al, Au, Cu, Mo and W at different values of compression down to V/V₀=0.5. The zero-pressure values of input parameters K₀ and have been taken from the literature, whereas and have been fixed to match the Stacey reciprocal K-primed equation. The polynomial equations thus formulated can be used as a substitute for the Stacey equations of state (EOS) for determining P-V relationship and higher derivative properties such as K and K′.     

Calculation of the surface energy of hcp metals by using the modified embedded atom method

With MEAM, the surface energies of three kinds of representative surfaces, (h 0 l), (h h l) and (h k 0) belong to [0 1 0], [] and [0 0 1] crystal band, respectively, have been calculated for 13 closed-packed hexagonal (hcp) metals Co, Dy, Er, Gd, Ho, Mg, Nd, Pr, Re, Sc, Tb, Tl and Zr. For all 13 hcp metals, the basal plane (0 0 1) has the minimum surface energy. So from surface energy minimization, the (0 0 1) texture should be favored in the hcp films, this is consistent with the experimental results. The fact that the short termination corresponds to much lower surface energy than long one implies the former is more stable for those surfaces having two possible terminations. Such as the prism plane (1 0 0), only the short termination was observed in experiment.     

Third and fourth order phase transitions: Exact solution for the Ising model on the Cayley tree

In this work we present the first exact solution of a system of interacting particles with phase transitions of order higher than two. The presented analytical derivation shows that the Ising model on the Cayley tree exhibits a line of third order phase transition points, between temperatures and , and a line of fourth order phase transitions between T_BP and ∞, where k_B is the Boltzmann constant, and J is the nearest-neighbor interaction parameter.     

Density and well width dependences of the effective mass of two-dimensional holes in (100) GaAs quantum wells measured using cyclotron resonance at microwave frequencies

Cyclotron resonance at microwave frequencies is used to measure the band mass (m_b) of the two-dimensional holes (2DHs) in carbon-doped (100) GaAs/ Al_xGa_1−xAs heterostructures. The measured m_b shows strong dependences on both the 2DH density (p) and the GaAs quantum well width (W). For a fixed W, in the density range (0.4×10¹¹ to 1.1×10¹¹ cm⁻²) studied here, m_b increases with p, consistently with previous studies of the 2DHs on the (311)A surface. For a fixed , m_b increases from 0.22m_e at to 0.50m_e at , and saturates around 0.51m_e for .     

Ground state electronic and magnetic properties of RCrSb3 (R=La, Ce, Nd, Gd and Dy): A first principles study

The electronic density of states (DOS) and magnetic moments of rare-earth antimonides (RCrSb₃) have been studied by the first principles full-potential linearized augmented plane wave (FP-LAPW) method based on density functional theory (DFT). For the exchange-correlation potential, the LSDA+U method is used. The effective moments of LaCrSb₃, CeCrSb₃, NdCrSb₃, GdCrSb₃, and DyCrSb₃ were found to be , , , and respectively. The exchange-splittings of Cr-3d state electrons and 4f-states of rare earth elements were analyzed to explain the magnetic nature of these systems. The Cr atom plays a significant role on the magnetic properties due to the hybridization between Cr-3d and Sb-5p state orbitals. The results obtained are compared and found to be in close agreement with the available data.     

Measurements of insulator band parameters using combination of single-electron and two-electron spectroscopy

We describe the application of low energy time-of-flight coincidence (e,2e) spectroscopy for measurements of the energy band parameters of a dielectric. The (e,2e) spectrometer can operate also in a single-electron mode by switching off coincidence conditions, and can be used for recording electron energy loss spectra (EELS). Thus, the combination of (e,2e) and EELS allows the measurement of energy gap E_g, valence bandwidth ΔE_val, electron affinity χ and excitonic levels position E_ex of a dielectric. The energy band parameters of LiF film deposited on Si(001) surface are measured: ΔE_val=      

The 2ν4 overtone bands of FClO3

The high resolution infrared spectrum of the mono-isotopic species F³⁵Cl¹⁶O₃ has been studied in the region of the 2ν₄ overtone, from 2560 to 2680 cm⁻¹. The perpendicular component is strong and clearly observed while the parallel component is very weak and almost completely hidden by the perpendicular one. Their origins differ by 12.6 cm⁻¹, the being located at higher wavenumbers. The band is perturbed by the anharmonic interaction between the v₄ = 2, l₄ = ?2 and v₂ = v₄ = v₅ = 1, l₄ = l₅ = ±1 excited states, both of E symmetry. In total 3157 transitions have been assigned, 83% of these to , 12% to , and 5% to . The three bands have been analyzed simultaneously, taking into account the Fermi resonance effective between the excited states of E symmetry. The ro-vibration parameters of the excited states have been obtained, including the deperturbed band origins of and , at 2628.5890(4) and 2619.3342(5) cm⁻¹, respectively. The W₂₄₅ anharmonic constant is equal to 4.0161(4) cm⁻¹. The x₄₄+g₄₄ and x₂₄+x₄₅+g₄₅ anharmonicity constants have been derived from the obtained band origins and those of ν₄ and ν₂ + ν₅.     

New chalcogenide glasses in the Ag2Te-As2Se3-CdTe system

Chalcogenide glasses from the Ag₂Te-As₂Se₃-CdTe system were synthesized. The basic physicochemical parameters such as density (d), microhardness (HV) and the temperatures of phase transformations (the glass transition T_g, crystallization T_cr and melting T_m) were measured. Compactness and some thermomechanical characteristics such as volume (V_h) and formation energy (E_h) of micro-voids in the glassy network, as well as the module of elasticity E were calculated. The overall mean bond energy 〈E〉, the mean coordination number Z, the mean bond energy of the average cross-linking/atom and the average bond energy per atom of the “remaining matrix”— and , as well as the average heteropolar bond energy E_hb, the degree of “cross-linking/atom” P_p and the radial bond strength were determined.The correlation between the composition and properties of the Ag₂Te-As₂Se₃-CdTe glasses was established and comprehensively discussed.     

Second harmonic generation in generalized Thue-Morse ferroelectric superlattices

In this paper the second harmonic generation (SHG) in generalized Thue-Morse (GTM(m, n)) ferroelectric superlattices is studied. Under the small-signal approximation, the SHG spectra in both real and reciprocal spaces are investigated. It is found that: (1) only when the structure parameters l, l_A, and l_B are all chosen to be proper, can SHG in GTM(m, n) ferroelectric superlattices be generated; (2) for Family A of generalized Thue-Morse, GTM(m, 1) ferroelectric systems, with the increase of parameter m, the intense peaks of SHG concentrate on the long wavelength (the fundamental beam (FB) wavelength is within ), but for Family B of generalized Thue-Morse, GTM(1, n) ferroelectric superlattices, with the increase of parameter n, the intense peaks of SHG concentrate on the middle wavelength ; and (3) for GTM(m, 1) ferroelectric superlattices, the bigger the m, the stronger the relative integral intensity (RII) of SHG would be, but for GTM(1, n) ferroelectric systems, the bigger the n, the weaker the RII of SHG would be.     

de Broglie’s wave hypothesis from Fisher information

Seeking the unknown dynamics obeyed by a particle gives rise to the de Broglie wave representation, without the need for physical assumptions specific to quantum mechanics. The only required physical assumption is conservation of momentum μ. The particle, of mass m, moves through free space from an unknown source-plane position a to an unknown coordinate x in an aperture plane of unknown probability density p_X(x), and then to an output plane of observed position y=a+z. There is no prior knowledge of the probability laws or , with the particle momentum at the source. It is desired to (i) optimally estimate a, in the sense of a maximum likelihood (ML) estimate. The estimate is further optimized, by minimizing its error through (ii) maximizing the Fisher information about a that is received at y. Forming the ML estimate requires (iii) estimation of the likelihood law p_Z(z), which (iv) must obey positivity. The relation p_Z(z)≡|u(z)|²≥0 satisfies this. The same u(z) conveniently defines the Fisher channel capacity, a concept central to the principle of Extreme physical information (EPI). Its output u(z) achieves aims (i)-(iv). The output is parametrized by a free parameter K. For a choice K=0, the result is u(z)=δ(z), indicating classical motion. Or, for a finite, empirical choice K=? (Planck’s constant), u(z) obeys the familiar de Broglie representation as the Fourier transform of the particle’s probability amplitude function P(μ) on momentum μ. For a definite momentum μ,u(z) becomes a sinusoid of wavelength λ=h/μ, the de Broglie result.     

Quantum tomograms from intermediate entangled states

We show that for quantum tomography there exist two mutually conjugating intermediate coordinate-momentum entangled states |η₁,η_2〉λ,ν and |?₁,?_2〉σ,τ. The Radon transforms of the Wigner operators are just the pure-state density matrices and , respectively. As a result, the tomogram of quantum states is the module-square of their wave function in these representations. A new convenient formalism of quantum tomogram is thus established.     

Optical phonon modes and structure of ZnGa2Se4 and ZnGa2S4

We present the infrared and Raman study of the optical phonon modes of the defective compounds ZnGa₂Se₄ and ZnGa₂S₄. Most of the compounds have been found to crystallize in the thiogallate structure (defect chalcopyrite) with space group where all cations and vacancies are ordered. For some Zinc compounds a partially disordered cationic sublattice with various degrees of cation and vacancy statistical distribution, which lead to the higher symmetry (defect stannite), has been reported. For ZnGa₂Se₄ we have found three modes of A symmetry, showing Raman activity only. In addition, we have observed each five modes of B and E symmetry, showing infrared as well as Raman activity. The number of modes and their symmetry assignment, based on polarized measurements, clearly indicate space group for the investigated crystals of ZnGa₂Se₄.Regarding ZnGa₂S₄ we have found three modes exclusively showing Raman activity (2A⊕1B₁), and only eight modes showing infrared as well as Raman activity (3B₂⊕5E). The assignment of the modes has been derived by analyzing the spectral positions of the vibrational modes in comparison to a number of compounds. From the number and symmetry assignment of the optical phonon modes we confirm that ZnGa₂S₄ most likely crystallizes in space group .     

Ordered zinc-vacancy induced Zn0.75Ox nanophase structure

Using transmission electron microscopy, a new nano-phase structure of Zn_0.75O_x induced by Zn-vacancy has been discovered to grow on wurtzite ZnO nanobelts. The superstructure grows epitaxial from the surface of the wurtzite ZnO nanobelts and can be fitted as an orthorhombic structure, with lattice parameters a′=2a, and c′=c, where a and c are the lattice parameters of ZnO. The superstructured phase is resulted from high-density Zn vacancies orderly distributed in the ZnO matrix. This study provides direct observation about the existence of Zn-vacancies in ZnO.     

Stretch-bend combination polyads in the ÃAu state of acetylene, C2H2

Rotational analyses are reported for a number of newly-discovered vibrational levels of the S₁-trans (ùA_u) state of C₂H₂. These levels are combinations where the Franck-Condon active and vibrational modes are excited together with the low-lying bending vibrations, and . The structures of the bands are complicated by strong a- and b-axis Coriolis coupling, as well as Darling-Dennison resonance for those bands that involve overtones of the bending vibrations. The most interesting result is the strong anharmonicity in the combinations of (trans bend, a_g) and (in-plane cis bend, b_u). This anharmonicity presumably represents the approach of the molecule to the trans-cis isomerization barrier, where ab initio results have predicted the transition state to be half-linear, corresponding to simultaneous excitation of and . The anharmonicity also causes difficulty in the least squares fitting of some of the polyads, because the simple model of Coriolis coupling and Darling-Dennison resonance starts to break down. The effective Darling-Dennison parameter, K₄₄₆₆, is found to increase rapidly with excitation of , while many small centrifugal distortion terms have had to be included in the least squares fits in order to reproduce the rotational structure correctly. Fermi resonances become important where the K-structures of different polyads overlap, as happens with the 2¹3¹B¹ and 3¹B³ polyads (B = 4 or 6). The aim of this work is to establish the detailed vibrational level structure of the S₁-trans state in order to search for possible S₁-cis (¹A₂) levels. This work, along with results from other workers, identifies at least one K sub-level of every single vibrational level expected up to a vibrational energy of 3500 cm⁻¹.     

First-principles study on the formation energies of intrinsic defects in LiNbO3

First-principles plane-wave ultrasoft pseudopotential method within local density approach (LDA) has been used to study three possible vacancy-defect models for non-stoichiometric lithium niobate (LiNbO₃): (1) the oxygen-vacancy model , (2) the niobium-vacancy model , and (3) the lithium-vacancy model . The corresponding formation energies are obtained via energy minimization of a supercell. In Nb-rich environment, the calculated defect formation energies, both under oxidation and reduction conditions, show little effect on the intrinsic defect structures. We find that the lithium vacancy model has the most stable configuration in the non-stoichiometric lithium niobate crystals. Our calculations also show that the formation of any type of neutral defects and Frenkel pairs in a Nb-rich environment is difficult.