Lattice mechanical properties of alkaline earth metals in bcc and fcc phases

A model pseudopotential depending on an effective core radius treated as a parameter is used for alkaline earth metals in bcc and fcc phases to study the Binding energy, Interatomic interactions, phonon dispersion curves, Phonon density of states, Debye-Waller factor, mean square displacement, Debye-Waller temperature parameters, dynamical elastic constants (C₁₁, C₁₂ and C₄₄), bulk modulus (B), shear modulus (C′), deviation from Cauchy relation (C₁₂−C₄₄), Poisson's ratio (σ), Young's modulus (Y), behavior of phonon frequencies in the elastic limit independent of the direction (Y₁), limiting value in the [1 1 0] direction (Y₂), degree of elastic anisotropy (A) and propagation velocities of the elastic waves. The contribution of s-like electrons is incorporated through the second-order perturbation theory due to model potential. The theoretical results are compared with the existing experimental data. A good agreement between theoretical investigations and experimental findings has confirmed the ability of our potential to yield large numbers of lattice mechanical properties of certain alkaline earth metals.     

A simple analytical EAM model for bcc metals including Cr and its application

An analytical embedded atom method (EAM) model, which can treat bcc transition metal Chromium, has been developed. In this model, a new potential was presented, and a modified term has been introduced to fit the negative Cauchy pressure P _c=(C₁₂-C₄₄)/2 for element Cr. The new model was applied to calculating the thermodynamic properties of binary alloys of all bcc transition metals V, Nb, Ta, Cr, Mo, W and Fe. The calculated dilute-solution enthalpies and formation enthalpies of random alloys are in good agreement with the experimental data available, the results from the first-principles calculations, and the results of thermodynamic calculations.     

Structural and magnetic phase formation in nanophase brass—iron electron compounds

Starting with Cu0.65Zn0.35 with an e/a ratio of 1.35 we studied the phase formation in nanophase (Cu_0.65Zn_0.35)_1?x Fe _x alloys in the concentration range 0.1 ≤x ≤0.7 to see the effect of altering the electron concentration. The evolution of bcc phase from the fcc phase as a function of Fe concentration was investigated by Mössbauer spectroscopy and X-ray diffraction. The grain size, lattice parameters, and average hyperfine magnetic field distributions were estimated for the nanophase alloys. The fcc phase was observed to persist up to 40 atomic per cent Fe substitutions, a mixed (fcc + bcc) phase region up to 70 atomic per cent Fe and bcc phase beyond 70 atomic per cent Fe. The magnetic state of the alloys changed from nonmagnetic forx ≤0.3 to magnetically ordered state at room temperature forx ≤0.33, which lies in the fcc phase region. The fcc phase alloys of Fe with non-magnetic metals have very low magnetic transition temperatures. However, in this system the room temperature state is unusually magnetic     

The first principles study on the Boron antimony compound

We present the results of our calculations on Boron antimony (BSb) compound in zinc-blende (ZB) and rock-salt (RS) structures by performing ab initio calculations within the local density approximation (LDA). Some basic physical properties, such as lattice constant, bulk modulus, cohesive energy, phase transition pressure, second-order elastic constants (C_ij), phonon frequencies, and some band structural parameters are calculated and compared with those obtained with other recent theoretical works. In order to further understand the behaviour of BSb compound, we have also predicted, the pressure-dependent behaviours of the band gap, second-order elastic constants (C_ij), Young's modulus, poison ratios (ν), Anizotropy factor (A), sound velocities, and Debye temperature for this hypothetical compound.     

Mechanical properties of bcc Fe-Cr alloys by first-principles simulations

The effect of chromium content on the fundamental mechanical properties of Fe-Cr alloys has been studied by first-principles calculations. Within a random solid solution model, the lattice constants and the elastic constants of ferromagnetic bcc Fe_1?x Cr _x (0? · ?0.156) alloys were calculated for different compositions. With addition of Cr content, the lattice parameters of Fe-Cr alloys are larger than that of pure Fe solid, and the corresponding Young??s modulus and shear modulus rise nonmonotonically with the increasing Cr content. All alloys (except 9.4 at% Cr) exhibit less ductile behavior compared with pure bcc Fe. For the Fe_1?x Cr _x (0? · ?0.156) alloys, the average magnetic moment per atom decreases linearly with the increasing Cr concentration.     

Electronic structure and elastic constants of TiCxN1−x, ZrxNb1−xC and HfCxN1−x alloys: A first-principles study

The structural, electronic and elastic properties of TiC_xN_1−x, Zr_xNb_1−xC and HfC_xN_1−x alloys have been investigated by using the plane-wave pseudopotential method within the density-functional theory. The calculations indicate that the variations of the equilibrium lattice constants and bulk modulus with the composition are found to be linear. The calculated elastic constants C₄₄ and shear constants as a function of alloy concentration reveal the anisotropic hardness of these compounds. The partial and total density of states (DOS) for the binary and ternary compounds had been obtained, and the metallic behavior of these alloys had been confirmed by the analysis of DOS.     

Theoretical investigation of new type of ternary magnesium alloys AMgNi4 (A=Y,La, Ce,Pr and Nd)

New ternary magnesium alloys AMgNi₄ (A=Y, La, Ce, Pr and Nd) have been studied by First-Principles calculations within the generalized gradient approximation. The optimized structural parameters were in good agreement with the available experimental data. The calculated cohesive energies and formation enthalpies showed that these alloys had strong structural stability. Then the elastic constants C_ij of these AMgNi₄ alloys were calculated, and the bulk modulus B, shear modulus G, Young's modulus E, Poisson's ratio ν and anisotropy value A of polycrystalline materials were derived from the elastic constants, the related mechanical properties were further discussed. The electronic structures were also calculated to reveal the underlying mechanism for the structural stability and the elastic property.     

The origin of an elastic line in the L 3 x-ray emission spectrum of metallic manganese

A strong elastic line has been found in the L ₃ x-ray emission spectrum of metallic Mn. To unravel its physical nature, the ground-state properties of α-Mn were studied in comparison with those of 3d metals (Cr and Fe in bcc structure), as well as the properties of the L ₃ absorption final states of these three transition metals. To model the electronic structure, LSDA band-structure calculations of Cr, Mn, and Fe were carried out, and L ₃ absorption spectra of these metals were computed in the atomic approximation. A joint analysis of the properties of the ground state and of the final absorption state excited by an x-ray-produced core hole suggests that the elastic line in the α-Mn spectra should be assigned to the specific character of the absorption final-state multiplet.     

Structural,mechanical and thermal properties of some Holmium Pnictides under pressure: A theoretical approach

The high pressure structural, elastic and thermal properties of holmium pnictides HoX (X=N, P, As and Bi) were investigated theoretically by using an inter-ionic potential theory with modified ionic charge parameter. We have predicted a structural phase transition from NaCl (B₁) to CsCl (B₂)-type structure at pressure of 139 GPa for HoN, 52 GPa for HoP, 44 GPa for HoAs and 26 GPa for HoBi. Other properties, such as lattice constant, bulk modulus, cohesive energy, second and third-order elastic constants were calculated and compared with the available experimental and theoretical data. In order to gain further information the brittle behaviour of these compounds was observed. Some other properties like Shear modulus (G), Young's modulus (E), Poisson's ratio (ν), anisotropy factor (A), sound velocities, Debye temperature (θ_D) were calculated. The variation of elastic constants (C₁₁ and C₄₄) and Debye temperature (θ_D) with pressure was also presented.     

Electronic structure of solid C48N12 aza-fullerene

I report electronic structures and the cohesive energy for face-centered-cubic (fcc) solid C₄₈N₁₂ using generalized-gradient density-functional theory. The full vibrational spectrum of the C₄₈N₁₂ cluster is calculated within the harmonic approximation at the B3LYP/6-31G* level of theory. The results show that fcc is energetically preferred and a more stable crystal form than body-centered-cubic (bcc). C₄₈N₁₂ clusters are found to condense by a weak (0.29 eV) van der Waals force. The band gap of fcc C₄₈N₁₂ is calculated to be 1.3 eV at the GGA-PW91 level, whereas the HOMO-LUMO gap is calculated to be 2.74 eV using B3LYP/6-31G*.     

New phases and chemical short range order in co-deposited CoFe thin films with bcc structure: an NMR study

A ⁵⁹Co NMR study has been carried out on several series of co-evaporated Co₁-_xFe_x thin-film alloys prepared on MgO (001), GaAs (100), and GaAs (110) substrates at deposition temperatures between 175°C and 500°C. The sample thicknesses varied between 100 Å and 1000 Å and the alloy concentrations were in the range 0:1 < x < 0:3. X-ray diffraction and NMR show that the stability limits of the bcc phase in CoFe alloys is shifted from the x = 0:25 observed in the bulk alloys down to about x = 0:11 in thin films. For x = 0:27 and at the deposition temperature of 500°C, a new ordered phase has been stabilised where Co has two Fe atoms only in its first coordination shell. Other samples, grown at lower temperatures, also exhibit an exotic chemical short range order (CSRO) where Co coordinations with zero and two Fe neighbours dominate. A mixture of bcc Co (and not fcc Co as in the bulk alloys) and unknown ordered bcc intermetallics can account for the observed CSRO. Theoretical ground-state phases for the bcc lattice are considered in order to explain the observations.     

Effect of hydrogen-doping on bonding properties of Ti3SiC2

Using the first principles method based on the density functional theory, we investigated the effect of hydrogen-doping on bonding properties of Ti₃SiC₂. The formation energies of hydrogen interstitials in three possible positions were calculated. The results show that hydrogen favors residing near the (0 0 1) Si plane. In these positions, hydrogen is hybridized most with 1s states of lattice atoms (Si and C), instead of Ti. The presence of hydrogen does not substantially influence the bonding nature of Ti₃SiC₂; chemical bonding is characterized by the hybridizations of Ti d-Si p and Ti d-C p states, and yields high strength. This is contrary to hydrogen-doping in transition metals, where the electron of hydrogen fills in the d bands of the metals and, as a consequence, decreases the cohesive strength of the lattice.     

The volume dependent total energy of metals and the ionic radii

The cohesive energies, lattice constants and compressibilities for a number of metals are correlated with the ionic radii through second order pseudo-potential theory. The model yields reasonable results not only for simple metals of arbitrary valency, but for transition elements with no more than 5 d-electrons.     

Theory for superconductivity in amorphous transition metals

A theory is presented for superconductivity in amorphous transition metals. It is shown that in contrast to simple metals for transition metals the changes in the phonon spectrum, in the electronic density of states and in the electronic matrix elements which result from strong lattice disorder can enhance as well as decreaseT _c. The numerical results for the superconducting transition temperatureT _c of amorphous 4d-and 5d-transition metals agree well with the experimental results.     

Calculation of the surface energy of bcc transition metals by using the second nearest-neighbor modified embedded atom method

The surface energies for 24 surfaces of all bcc transition metals Fe, Cr, Mo, W, V, Nb and Ta have been calculated by using the second nearest-neighbor modified embedded atom method. The results show that, for all bcc transition metals, the order among three low-index surface energies E_(1 1 0) < E_(1 0 0) < E_(1 1 1) is in agreement with experimental results and E_(1 1 0) is also the lowest surface energy for various surfaces. So that from surface energy minimization, the (1 1 0) texture should be favorable in the bcc films. This is also consistent with experimental results. The surface energy for the other surfaces increases linearly with increasing angle between the surfaces (h k l) and (1 1 0). Therefore, a deviation of a surface orientation from (1 1 0) can be used to estimate the relative values of the surface energy.     

First-principles study on electronic structure and elastic properties of Fe16N2

We have performed first-principles study on structural stability, elastic properties and electronic structure of Fe₁₆N₂ by applying LSDA+U method. The calculated values of formation energy and reaction enthalpy for decomposition reaction indicate that Fe₁₆N₂ is a thermodynamically stable phase at the ground state. The six independent elastic constants are derived and the bulk modulus, Young's modulus, shear modulus, and Poisson's ratio are determined as 180 GPa, 199 GPa, 76 GPa and 0.32, respectively. The elastic constants meet all the mechanical stability criteria. The ductility of Fe₁₆N₂ is predicted by Pugh's criterion. The strong bonding between Fe and N atoms results in high values of elastic constants C₁₁ and C₃₃, and contributes to the strengthening of the Fe₁₆N₂ structural stability. The total and partial densities of states (DOS) suggest the existence of hybridization between N-p and Fe-d bands. The position of the Fermi level in DOS curve implies that Fe₁₆N₂ is a metastable phase.     

A model analysis of the elastic constants of metals and alloy phases

A lattice energy function using a Mie inverse power interatomic potential and a quadrupole distortion term was fitted to the cohesive energy, lattice parameter, bulk modulus and C₄₄ of pure metals. Using this function and the fitted parameters, values were then predicted for C₄₄ and other elastic constants of alloy phases. It was found that the maximum discrepancy in C₄₄ for B2, C15, and L1₂ type phases was 40%, with the RMS value equal to 25%.It was found that the predicted nearest-neighbor bond angle dependent elastic constants were always smaller than the observed values. It is believed that this result is due to the formation of eovalent bonds in the alloy phases, a phenomenon that is not included in the model. An empirical procedure for correcting the elastic constants to account for eovalent bonding reduces the maximum discrepancy in both shear constants to less than 20%. Evidence is presented in support of this hypothesis. One of the consequences of this work is that ground state superstructures, of heteroelectronic type alloy components that are deduced on the basis of constancy of pair or many body interactions, need not necessarily correspond to the most stable superstructures.     

The elastic behaviour of In-Tl alloys in the vicinity of the martensitic transition

To test further the prediction of collapse of the [110], q|| [11&#x0304;0] acoustic mode at the martensitic phase transition, pulse superposition measurements of ultrasonic wave velocities have been made in indium-thallium alloys containing 25 and 27 at. % thallium. These alloys are f.c.c. at room temperature and transform on cooling to the f.c.t. phase at 196 ± 2°K and 127 ± 2°K, respectively. Results show that $\text{1}\text{2}$(C₁₁ ? C₁₂) goes to zero within experimental error at the transition temperature. The room temperature elastic constants of the tetragonal 11.5 and 15 at. % thallium alloys are also reported.     

The second-order elastic constants of AgBr from 77 to 300 K

The three independent second-order elastic constants of AgBr have been measured from room temperature down to liquid nitrogen temperature A single crystal with a (110) axis was used for the measurements The measured longitudinal elastic constant C'₁₁ = (C₁₁ + C₁₂ + 2C₄₄)/2 increases by 16% over this temperature range The elastic shear constant C₄₄) increases by almost 11%, while the elastic shear constant C' = (C₁₁ ? C₁₂)/2 increases by 50% over this range The measured bulk modulus B = (C₁₁) + 2C₁₂)/3 increases by almost 15% as the lattice becomes stiffer The initial temperature derivatives of the elastic constants are similar to those previously measured The changes in the elastic constants are basically linear down to approximately 150 K, where the temperature derivatives begin to decrease in magnitude These results are similar to those previously obtained for AgCl     

Dynamics of the first-order magnetostructural transition in Gd<Subscript>5</Subscript>(Si<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>Ge<Subscript>1-<Emphasis Type="Italic">x</Emphasis></Subscript>)<Subscript>4</Subscript>

For a given crystal structure, say body-centred-cubic, the many-body Hamiltonian H in which nuclear and electron motions are to be treated from the outset on the same footing, has parameters, for the elements, which can be classified as (i) atomic mass M, (ii) atomic number Z, characterizing the external potential in which electrons move, and (iii) bcc lattice spacing, or equivalently one can utilize atomic volume, . Since the thermodynamic quantities can be determined from H, we conclude that T _c , the superconducting transition temperature, when it is non-zero, may be formally expressed as T _c = . One piece of evidence in support is that, in an atomic number vs. atomic volume graph, the superconducting elements lie in a well defined region. Two other relevant points are that (a) T _c is related by BCS theory, though not simply, to the Debye temperature, which in turn is calculable from the elastic constants C ₁₁, C ₁₂, and C ₄₄, the atomic weight and the atomic volume, and (b) T _c for five bcc transition metals is linear in the Cauchy deviation C ^* = (C ₁₂ - C ₄₄ )/(C ₁₂ + C ₄₄ ). Finally, via elastic constants, mass density and atomic volume, a correlation between C ^* and the Debye temperature is established for the five bcc transition elements.Received: 13 May 2004, Published online: 23 July 2004PACS: 74.62.-c Transition temperature variations - 74.70.Ad Metals; alloys and binary compounds