Equilibrium Crystal Structure Research Articles

Ab initio structural and energetic study of [formula omitted] ( [formula omitted], Ga) perovskites

The equilibrium crystal structure parameters and the total energies of the polymorphous LaMO 3 perovskites ( M = Al , Ga) and their constituent binary oxides A- La 2 O 3 , α - Al 2 O 3 and β - Ga 2 O 3 were calculated with ab initio method based on density function theory (DFT) and projector augmented wave method (PAW) using both local density approximation (LDA) and generalized gradient approximation (GGA). The relative lattice stabilities of the various configurations with respect to the ground state and the enthalpies of formation of the stable perovskites from the constituent binary oxides were obtained. The enthalpies of formation at 298.15 K calculated within LDA, - 67.19 and - 49.99 kJ mol - 1 for the stable configurations of LaAlO 3 and LaGaO 3 , respectively, agree well with the available experimental data, while the enthalpies calculated within GGA are much less negative. It was the first time that recurred the experimental enthalpies of formation at 298.15 K for the stable configurations of LaAlO 3 and LaGaO 3 from a fundamental ab initio calculation.

Vibrations in submonolayer structures of Na on Cu(111)

We present the results of a comparative study of the equilibrium crystal structure and vibrational properties of the $\mathrm{Na}∕\mathrm{Cu}(111)$ system at coverages up to monolayer saturation. The calculations are performed with interaction potentials from the embedded-atom method. The following ordered structures are considered: $p(3\ifmmode\times\else\texttimes\fi{}3)$, $p(2\ifmmode\times\else\texttimes\fi{}2)$, $(\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3})30\ifmmode^\circ\else\textdegree\fi{}$, and $(3∕2\ifmmode\times\else\texttimes\fi{}3∕2)$. The surface relaxation, phonon dispersion, and polarization of vibrational modes for the adsorbate and substrate atoms as well as the local density of states are discussed. It is found that the bond length between an adsorbate and the nearest-neighbor substrate atom slightly increases with increasing coverage. Adsorption of sodium also results in a small rumpling in two upper substrate layers. The mode associated with adatom-substrate stretch vibrations was obtained in our calculation at about $22\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$ for all the structures considered. The strength of this mode decreases with increasing coverage in accordance with the experiment. On the other hand, we find that the frustrated translation mode frequency of sodium on Cu(111) is strongly coverage dependent.

Faceted single crystals of mesoporous silica SBA-16 from a ternary surfactant system: surface roughening model

We have synthesized mesoporous silica SBA-16 at room temperature and low pH condition by using the surfactant system C 8TMAB/SDS/F127 as template. Faceted single crystals of rhombdodecahedron form can be obtained under well-controlled conditions. Synthetic factors in controlling the morphology, including stirring, water content, the ionic surfactants and acidity are explored. A schematic theory for the formation of the equilibrium crystal structure based on surface roughening transition is proposed to explain the formation of faceted single crystal.

Stacking faults in colloidal crystals grown by sedimentation

A real-space study is presented on the occurrence of stacking faults in crystals of silica colloids with diameters of about 1 and 1.4 μm formed through sedimentation. The softness of the interaction potential is varied from slightly repulsive to hard-sphere like, both intrinsically by variation of the diameter, as well as through the addition of salt, which screens the surface charges. Our results indicate that the equilibrium crystal structure for these colloids is an fcc-crystal, with the number of stacking faults determined by the interplay between sedimentation and crystallization kinetics, irrespective of the softness of the interaction potential. For spheres with a certain diameter the number of stacking faults decreases with decreasing initial volume fractions. These results provide a way to grow fcc-crystals of hard-sphere particles by slow sedimentation. The relative number of stacking faults in the first few layers above the bottom wall can be as much as a factor of 10 higher than deeper into the crystal. This effect is due to the crystallization kinetics on a plain wall in a gravitational field. A patterned bottom wall that favors a specific hexagonal orientation was found to drastically reduce the number of stacking faults in the crystal.

The Orthorhombic Phase of CaSiO3 Perovskite

AbstractAb initio total energy calculations, combined with the global parametrization method of perovskite structures, are used to investigate the stability of cubic CaSiO3 against octahedral rotations. We propose an equilibrium crystal structure of orthorhombic Pbnm symmetry. The larger compressibility of the SiO6 octahedra relative to the CaO12 polyhedra is reflected in gradual reduction of the orthorhombic distortion with hydrostatic pressure.

Structure of the First-Shell Active Site in Metallolactamase: Effect of Water Ligands

In this study we have examined the behavior of the first-shell active site of metallolactamases as a function of water both bound directly as a zinc ligand and hydrogen bonded to protein-residue ligands in the active site and as a function of metal−metal distance. The inherent effective interaction energy of the bimetallic metallolactamase active site is relatively flat between the metal cations. This leaves the metal−metal distance susceptible to both perturbations from environmental interactions and protonation of active-site residues. Although the crystal structure of the active site of the zinc lactamase from Bacteroides fragilis is the initial starting point for the structure optimizations, structures very different from the equilibrium crystal structure as well as details of the water hydrogen-bonding pattern in the active site are obtained. Structures with Zn−Zn distances >4 A, with each metal cation acting as the center of a separate complex, result when only the crystallographic water that is dir...

Observation of a hexagonal(4H)phase in nanocrystalline silver

We report the observation of an unusual hexagonal $(4H)$ phase in silver nanoparticles deposited by high-pressure dc magnetron sputtering. X-ray-diffraction and transmission electron microscopy studies clearly reveal the presence of a hexagonal $4H$ phase in the silver nanoparticles in addition to the cubic $3C$ phase---which is the equilibrium crystal structure for bulk silver. The smaller the average particle size, the larger was the volume fraction of the $4H$ phase. The hexagonal phase can be made to revert to the usual cubic structure by heating the nanocrystalline sample and allowing the grains to grow. This rare hexagonal phase had previously been observed only in certain mineral deposits. We show that there is a size-induced stabilization of this phase in nanocrystalline silver below \ensuremath{\approx}30 nm.

Local fluctuations in feldspar frameworks

AbstractAt any set of thermodynamic conditions a mineral will have some well defined equilibrium crystal structure. However, this structure can be locally disturbed by crystal defects, such as domain walls or solute atoms. This distorted structure will only affect a finite volume within the crystal, but the need to retain continuity within the crystal means that this volume must be non-zero. This means, for example, that the boundary between two domains will include a transition zone from one domain's crystal structure to that of the other domain. Thick twin domain walls can be studied quantitatively, by measuring the intensity of diffuse diffraction between pairs of twin-related Bragg peaks. In alkali feldspar (Or30) at room temperature, these walls are approximately 25 Å thick. Similarly, a single solute atom in a mineral will only affect a small region within a crystal. As a result, chemical mixing will only occur in a substitutional solid solution once there is significant overlap between the strain fields around individual solute atoms. This causes the ‘plateau effect’, where the properties of a phase transition are independent of composition. In alkali feldspar, this plateau extends from albite to 2% Or, which corresponds to a strain field radius of 10 Å.These phenomena can be modelled using Ginzburg-Landau theory, which predicts that the range of these strain fields will increase as the temperature is raised to Tc. This has been confirmed by measuring the thickness of twin walls as a function of temperature.

Temperature dependent elastic, piezoelectric and pyroelectric properties of β-poly(vinylidene fluoride) from molecular simulation

Detailed calculations of the elastic, piezoelectric and pyroelectric properties of the β phase of poly(vinylidene fluoride) are reported. The calculations are based on an empirical atomistic force field that uses the shell model of electronic polarization. Quasi-harmonic lattice dynamics is used to include the vibrational entropy in the calculation of the crystal free energy. The equilibrium crystal structure and polarization are determined as functions of temperature by minimization of the crystal free energy. The piezoelectric and pyroelectric responses are calculated by taking derivatives of the polarization with respect to strain and temperature, respectively. Changes in the unit cell volume dominate the piezoelectric and pyroelectric responses. Dipole oscillations make negligible contributions to the piezoelectric response. The primary pyroelectric response accounts for approximately 9% of the total pyroelectricity at 300 K. The temperature dependence of the piezoelectric stress coefficients is small. The temperature dependence of the piezoelectric strain coefficients is significant and correlates with the temperature dependence of the elastic compliance constants. Likewise, the temperature dependence of the pyroelectric response reflects that of the thermal expansion coefficients.

The structure of MD simulated cryolite melt

Molecular dynamics (MD) simulations have been performed for molten cryolite (Na3AlF6), employing Born-Mayer-type pair potential functions. The structure of the simulated liquid is characterized by the partial pair radial distribution functions and also by the distribution of Voronoi and direct polyhedra. The results obtained are compared with those obtained from the Monte Carlo (MC) calculations of Qiu and Xie and with X-ray crystal data. The MD results agree well with the equilibrium crystal structure, while significant differences between the MD and MC simulations are attributed to various sources. Both the MD and MC simulated melt structures do not confirm Gilbert's dissociation scheme for the hexafluoroaluminate anion.

Theoretical study of electronic, magnetic, and structural properties of alpha -Fe2O3 (hematite).

Antiferromagnetic rhombohedral \ensuremath{\alpha}-${\mathrm{Fe}}_{2}$${\mathrm{O}}_{3}$ has been studied by calculations of the ground-state spin-polarized wave function and total energy, using the ab initio periodic unrestricted Hartree-Fock approach. All-electron basis sets of contracted Gaussian-type functions are employed to represent the O and Fe atoms (18 and 27 orbitals, respectively); Fe is alternatively described by a large-core pseudopotential plus 18 valence-shell orbitals. Computations have been performed for both the antiferromagnetic (AF) and ferromagnetic (FM) structures; the correct relative stability is reproduced, with \ensuremath{\Delta}E(AF-FM)=-0.0027 hartree per formula unit (including a correction for correlation energy). The dependence of \ensuremath{\Delta}E(AF-FM) on variations of the Fe-O bond lengths and Fe-O-Fe' angles involved in superexchange is analyzed, finding that for some configurations the FM structure becomes more stable than the AF one. The athermal equation of state, equilibrium crystal structure, elastic bulk modulus, and binding energy have been computed and compared to experimental quantities. An analysis of the density of electronic states show that the band gap is of p-d rather than d-d type, confirming the charge-transfer-insulator nature of hematite as inferred from photoelectron spectra. The overall shape of the valence band is also fully consistent with spectroscopic results. Mulliken electron population data indicate a charge back transfer of 0.29\ensuremath{\Vert}e\ensuremath{\Vert} from ${\mathrm{O}}^{2\mathrm{\ensuremath{-}}}$ to the d shell of ${\mathrm{Fe}}^{3+}$, causing a partial spin pairing with a magnetic moment of 4.7${\mathrm{\ensuremath{\mu}}}_{\mathit{B}}$.

Computer simulation studies on β-quinol clathrates with various gases. Interdependence of host and guest molecules

The equilibrium crystal structure of a β-quinol clathrate occupied by various gases is determined through empirical force field calculations. The guests with van der Waals volume Vm≤27 cm3/mol affect the structure and rigidity of the lattice in a manner independent of their chemical nature: The guest-host attraction leads to a shrinking of the host cages. On the other hand, the inclusion of molecules of the volume 27 cm3/mol≤Vm≤46 cm3/mol expands the cages. Guest molecules render the host lattice more rigid, except for large spherical rotor type molecules, which soften the lattice, eventually destroying it. The inclusion of molecules with Vm≳46 cm3/mol is likely to be impossible. The energy of clathrate formation increases with increasing Vm, with the polar guests forming more stable clathrates than the nonpolar ones with the same Vm. Interestingly, the optimal guest-cage compatibility occurs when the volume of guest molecules differs by less than 50% from the volume of the empty cage. The orientation of a guest molecule in a cage is mainly determined by a competition of three types of interactions. (i) Van der Waals interactions tend to direct the long axis of the guests along the c-axis of the cage. (ii) The electrostatic guest-host interaction tends to place a positively charged guest atom into the center of the cage. (iii) Electrostatic guest–guest interactions tend to align the dipole moments of the included molecules along the c-axis. The different orientations are rationalized in terms of the complementary influences of the guest size, guest polarity and an ‘‘atomic size’’ factor. The calculated barriers hindering the reorientation movement of guest molecules in a cage are found to be in a qualitative agreement with experimental data except for the N2 and CO molecules, which are supposed to be considerably polarized by the cage. The C3-reorientation motion of ethane is predicted to be accompanied by its synchronous rotation around the C–C bond.

Characterization of group Ill-nitrides by high-resolution electron microscopy

The Group III-nitride semiconductors A1N, GaN, and InN are of interest for their potential applications in short wavelength optoelectronic devices. This interest stems from their direct wideband gapswhich range from 1.9 eV (InN), to 3.4 eV (GaN), to 6.2 eV (A1N). If high quality nitride films can besuccessfully grown, then optoelectronic devices with wavelengths ranging from the visible to the deepultraviolet region of the electromagnetic spectrum are theoretically possible. Recently, LED's basedon GaN and InGaN QW's were demonstrated. Also, their excellent thermal properties make them ideal candidates for high-temperature and high-power devices. Many problems plague nitride research, especiallythe lack of suitable substrate materials that are both lattice- and thermal-matched to the nitrides. The crystal structure of these materials is strongly influenced by the substrate and its orientation.For example, although the equilibrium crystal structure of these nitrides is wurtzite, zincblende phase can be nucleated under nonequilibrium growth conditions but only on cubic substrates. These zincblende nitrides represent new material systems with properties that differ from their wurtzite counterparts. Recently, good quality material has been produced employing metalorganic vapor phase epitaxy (MOVPE) and reactive molecular beam epitaxy (RMBE) techniques with incorporation of buffer layers.

Lattice dynamics of ortho-terphenyl

A lattice dynamical calculation for the known crystal structure of orthoterphenyl has been carried out under the rigid molecule approximation. The optimized parameters for the intermolecular potential reproduce adequately both the equilibrium crystal structure as well as the experimental heat capacity up to 35 K. The values for the mean-square-displacement as calculated from the computed vibrational density of states show that for temperatures well above 50 K most of the motions contributing to the atomic displacements as measured by neutron quasielastic scattering arise from the thermally excited internal molecular modes. The implications for the recent tests of kinetic theory predictions regarding the liquid-glass transitions using this material are briefly discussed.

Observation and modeling of quasiepitaxial growth of a crystalline organic thin film

We directly observe, using the scanning tunneling microscope, a two-dimensional crystal of the organic compound 3, 4, 9, 10-perylenetetracarboxylic dianhydride (PTCDA). The surface unit cell dimension is found to be 21.6±2.2 Å by 15.2±1.6 Å, or approximately 20% larger than the bulk unit cell. Furthermore, the organic lattice is oriented with respect to the graphite substrate even though the two lattices are incommensurate. These observations are consistent with reflection high energy electron diffraction measurements, and energy minimization calculations, assuming that the van der Waals bond is the predominant intermolecular force which determines the equilibrium crystal structure. The combination of measurement and theory provides the first step in developing tools for predicting the conditions which lead to quasiepitaxial growth of these technologically important van der Waals solids.

Potential energy maps and H + conduction mechanism in HTaWO 6· xH 2O pyrochlore

Least-energy paths of proton in the structures of HTaWO 6 and HTaWO 6 ·H 2 O have been calculated by the Born model of crystal energy. The atomic charge on O and the repulsive parameters are fitted to reproduce the equilibrium crystal structure of the pyrochlore KNbWO 6 , obtaining z o =−0.70 e . Maps of H + potential energy in the anhydrous compound show that proton hopping occurs between adjacent H sites along edges of (Ta, W)O 6 coordination octahedra, with a theoretical activation energy of 0.60 eV in good agreement with the experimental value (0.66 eV). In the hydrated compound the proton transfer occurs by a similar mechanism, excluding an active role of water molecules. The small experimental activation energy observed in the latter case is probably due to surface conduction induced by humidity at grain boundaries.

Ground state structures of intermetallic compounds: A first-principles Ising model

Predictions of the equilibrium crystal structure of simple compounds, e.g., within first-principles total energy methods are usually carried out by searching for the lowest energy among a small number, O(10), of intuitively selected candidate structures. We show how calculations of the total energies of O(10) structures can be used instead to define a first-principles, multi-spin Ising Hamiltonian, whose ground state structures on a fixed lattice can be systematically searched using lattice theory methods. This is illustrated for the intermetallic compounds CuAu, CuPd, CuPt, and CuRh, for which the correct ground states are identified out of more than 65,000 possible structures.

Shear induced order of hard sphere suspensions

Hard spheres serve as one of the basic models in classical equilibrium statistical mechanics, as well as, in fluid mechanics. Sterically stabilized polymethylmethacrylate (PMMA) spheres suspended in certain organic solvents have interparticle interactions which approximate the hard sphere interaction. Thus the equilibrium properties of PMMA particle suspensions should correlate with theoretical and computer simulation results of pure hard sphere systems. However, non-equilibrium properties must be compared with theories which include the hydrodynamic effects of the suspending medium. Experimental results are presented which suggest hard sphere behaviour: a solid-liquid phase transition, equilibrium crystal structure, liquid and crystal sedimentation velocities. Non-equilibrium microstructure in steady and oscillatory shear flows is then examined using light scattering from samples where the solvent index of refraction matches that of the particles. Oscillatory shear flows of the proper strain amplitude can shake crystal-like order into an equilibrium liquid-like sample. These results may be understood in terms of a simple hard sphere model.

Orbital magnetism in Fe, Co, and Ni.

The spin and orbital contributions to the magnetic moments of Fe, Co, and Ni are calculated from first principles, using the linear muffin-tin orbitals method with the spin-orbit coupling treated at each variational step. In these calculations the spin and orbital moments agree with previously reported results obtained from spin-polarized Dirac calculations. When Hund's second rule is accounted for in the band Hamiltonian by adding an additional term for orbital polarization, the orbital moments agree better with experiment and the trends in the experimental orbital moments across the series can be explained. Specifically, the maximum orbital moment for Co is shown to occur because of its hcp equilibrium crystal structure.

Rapid solidification of intermetallic compounds

This review surveys recent studies of rapid solidification at alloy compositions where the equilibrium phase is an intermetallic compound (or mixture of intermetallic compounds). Glass forming intermetallic compositions are considered and criteria for ‘easy’ glass formation are discussed. The limited data on synthesis of intermetallics from amorphous precursors are reviewed. This is a promising route to refine the microstructure of intermetallics with the potential for improved mechanical properties. It is an area that needs more study. The greatest effort has been devoted to studies of rapid solidification of the nickel-, iron-, or titanium-base aluminides. Rapid solidification of nickel base aluminides results in a refined microstructure (grain size and/or antiphase domain size) which can influence mechanical properties. The equilibrium crystal structure is maintained, however. Certain rapidly solidified Fe–Al–C base alloys can form a metastable fcc or L 12 structure (a point of continuing controversy) with good strength and ductility. The titanium base aluminides exhibit a marked tendency for formation of metastable structures on rapid quenching. The potential for improving the ductility of these compounds has made rapid solidification of Ti3Al and TiAl the subject of much recent activity.