Showing papers on "Lattice constant published in 1978"

Band gap versus composition and demonstration of Vegard’s law for In1−xGaxAsyP1−y lattice matched to InP

Abstract: Measurements of lattice parameters and compositions for In1−xGaxAsyP1−y lattice matched to InP demonstrate the validity of Vegard’s law for this quaternary. The measured compositional dependence of the band gap shows a bowing parameter smaller than predicted from the previously measured band gaps of the four constituent ternaries.

Interionic potentials for alkali halides. II. Completely crystal independent specification of Born-Mayer potentials

Abstract: For pt.I see ibid., vol.11, p.1523 (1978). A set of interionic potentials of the Born-Mayer form is derived for the alkali halides. The specification is completely in terms of parameters of two types, (a) parameters which relate to the constituent ions and (b) parameters which apply to all crystals. Thus the parametrisation scheme contains no crystal dependent terms and is of a form which may readily be applied to systems of mixed alkali halides. Each of the nine ions is described by five parameters, its polarisability, its shell charge and three parameters which relate to the ion size. The van der Waals coefficients are calculated consistently from the ion polarisabilities. The model system, which has 47 free parameters, reproduces the lattice constants, high and low frequency dielectric constants and transverse optic frequencies for the 20 crystals to high accuracy. Of crystal properties which are not included in the fitting procedure, the cohesive energies are given in most cases to better than 1%, the NaCl/CsCl structural relative stability is correctly described in all cases except CsF, and reasonable phonon dispersion relations and elastic constants are obtained.

Crystal structure and compression of ruby to 46 kbar

Abstract: Crystal structures and lattice constants have been determined for ruby at hydrostatic pressures up to 46 kbar using a gasketed opposed‐anvil diamond cell on a four‐circle diffractometer. The measured compressibility is slightly anisotropic, having a value of 1.36±0.03×10−4 kbar−1 parallel to c and 1.22±0.03×10−4 kbar−1 perpendicular to c. If a Birch‐Murnaghan equation of state is used and K′0 is assumed to be 4, the isothermal bulk modulus is 2.57±0.06 Mbar. Refined atomic coordinates do not change with pressure; therefore, the structure compresses in a uniform manner. This study demonstrates that crystal structures may be determined at high pressure on single crystals with a precision approaching that of room‐pressure results.

Energy bandgap and lattice constant contours of iii–v quaternary alloys

Abstract: Energy band gap and lattice constant contours are presented for the nine quaternary alloys formed from Al, Ga, In and P, As, Sb. The quaternary bandgaps were obtained using an interpolation formula proposed by Moonet al. The quater nary lattice constants were obtained by use of a linear interpolation technique using the binary lattice constants as boundary values.

Growth morphology of the tetragonal phase in partially stabilized zirconia

Abstract: The zirconia-rich, metastable tetragonal phase in partially stabilized zirconia—magnesia, zirconia—calcia and zirconia—yttria is examined using electron microscopy and electron and X-ray diffraction. The tetragonal phase precipitate distribution is that normally associated with homogeneously nucleated coherent precipitation. An attempt is made to explain the growth morphology of the tetragonal phase in terms of the cubic—tetragonal lattice parameter mismatch. It is found that the tetragonal phase is retained at room temperature provided coherency with the cubic matrix is retained. Once coherency is lost, due to growth strains or mechanical influences, the precipitate reverts to the room temperature stable monoclinic form.

A Fluorite Isotype of SnO2 and a New Modification of TiO2: Implications for the Earth's Lower Mantle

Abstract: The existence of a cubic fluorite-type SnO_2 and a hexagonal TiO_2 (which may be related to the fluorite structure) have been demonstrated by an in situ x-ray diffraction study in which a diamond-anvil pressure cell was used after the samples had been heated by a continuous yttrium-aluminum-garnet laser. At room temperature, the lattice parameter for SnO_2 (fluorite) is a = 4.925 ± 0.005 angstroms and those for Ti_2 (fluorite-related) are a = 9.22 ± 0.01 angstroms and c = 5.685 ± 0.006 angstroms at about 250 kilobars. The volume change associated with the transition from rutile to fluorite (or related structure) is about –8 percent for SnO_2 and –10.5 percent for TiO_2 at transition. Upon release of pressure, both the fluorite-type SnO_2 and the TiO_2 reverted to the α-PbO_2 structure at room temperature. The hypothesis that the earth's lower mantle is composed of oxide phases might be feasible if it were possible for SiO_2 to possess the fluorite structure or its related forms at high pressure, as shown for SnO_2 and TiO_2 in this study. The oxide hypothesis proposed here differs from that postulated by Birch in that the primary coordination of silicon is 6 for Birch's hypothesis and 8 for the hypothesis presented here.

The effect of elastic strain on energy band gap and lattice parameter in III‐V compounds

Abstract: The elastic and misfit strain in vapor‐grown InGaP/GaAs crystals was determined by measuring the lattice parameter of the InGaP before and after removal of the GaAs substrate. The energy‐band‐gap shift as a function of strain was measured in a similar manner using photoluminescence. Up to 70% of the misfit strain was found to be accommodated elastically. The critical resolved shear stress for dislocation motion was found to be ∼2×109 dyn/cm2. The rather low band‐gap shift with applied stress of ∼3×10−9 meV/dyn cm−2 was attributed to the Poisson effect. Photoluminescence was found to be a very accurate means to measure composition (and therefore lattice parameter), and empirical expressions were determined for the variation of photoluminescence wavelength with composition, lattice parameter, and energy band gap.

Composition dependence of the band gaps of In1−xGaxAs1−yPy quaternary solids lattice matched on InP substrates

Abstract: The In‐Ga‐As‐P quaternary phase diagram required for the growth of lattice‐matched In1−xGaxAs1−yPy layers on InP substrates has been determined experimentally at 650 °C. The liquidus isotherms were obtained by the seed‐dissolution technique. The solidus iostherms were determined by electron‐microprobe analysis performed on surfaces of quaternary epitaxial layers grown on Sn‐doped InP (111) B substrates from quaternary saturated melts. Lattice constants of layers were measured by an x‐ray‐diffraction technique. The liquid‐phase‐epitaxy growth conditions of lattice‐matched In1−xGaxAs1−yPy (0⩽x⩽0.47, 0⩽y⩽1.0) layers on InP were found from the results of the phase diagram and lattice constant measurements. Lattice‐matched layers with various band gaps (from 1.34 to 0.74 eV at room temperature) were grown by using these conditions. Band gaps of the layers were determined by photoluminescence measurements at 300 and 77 K. The band gap at each temperature was found to be linearly dependent on alloy‐composition p...

Energy bandgap and lattice constant contours of iii-v quaternary alloys of the form A x B y C z D or AB x C y D z

Abstract: Energy bandgap and lattice constant contours are presented for the six quaternary alloys formed from Al, Ga, In and P, As, Sb, with compositions of the form Ax By C(1−y). D or ABx Cy D1−x−y . The quaternary bandgaps and lattice constants were obtained using an interpolation formula proposed by the present authors.

Solid‐Liquid Equilibria in the System Si3N4‐AlN‐Si02‐A12O3

Abstract: Solid-liquid equilibria at 1750°C and subsolidus phase relations in the system Si3N4−AlN-SiO2−Al2O3 were determined for the composition region bounded by the β-Si3N4 solid solution line and silica-alumina join X-ray diffraction and optical microscopy were used to determine the phases present in specimens cooled rapidly after equilibration. The extent of a single liquid-phase region and the tie lines for the βsolid solution + liquid field at 1750°C were established from quantitative X-ray diffractometry and lattice parameter measurements of βsolid solutions in equilibrium with liquid. The results were corroborated by optical microscopy and melting behavior observations. A new composition, Si12Al18O39N8, is suggested for the x1 phase. The lowest melting temperature in the system is ≅ 1480°C and the corresponding composition is 10 eq% Al-90 eq%O.

Magnetic properties, electrical resistivity and thermal expansion of (Ho,Y)Co2

Abstract: The influence of the Ho substitution on the Co moments in (HoxY1-x)Co2 has been investigated by means of magnetic, resistivity and lattice parameter measurements. A first-order phase transition and a field-induced metamagnetism can be detected for x>or=0.7. At the magnetic transition temperature anomalies of the lattice parameters were measured for x>or=0.3. In connection with the first-order transition a discontinuity in the rho (T) curves appears for x>or=0.7. For 0.3 150K) the rho (T) curves show a tendency to saturation, which is the same for all x values. Considering the substitution of Ho into YCo2 the existence of a critical RE concentration (x>0.1) for the appearance of a long-range magnetic order is evidenced. The Co moments mu Co are compared with neutron diffraction results. The overall agreement is very good and supports the assumption of induced Co moments. For the whole pseudobinary system, a Fermi energy situated in a steep flank of the density of states function was assumed.

Phase Diagram of the In‐Ga‐As‐P Quaternary System and LPE Growth Conditions for Lattice Matching on InP Substrates

Abstract: The phase diagram of the In‐Ga‐As‐P quaternary system has been determined experimentally for several As isoconcentration sections at 600° and 650°C. The liquidus data were obtained by the seed dissolution technique, and the solidus data were determined from liquid phase epitaxial layers grown on substrates by using EPMA. Lattice constants of the quaternary solid solutions were measured by an x‐ray diffraction technique. The LPE growth conditions of exactly lattice‐matched layers on substrates were found from the results of the phase diagram and lattice constant measurements. The phase diagram was also calculated by using a simple solution model and was compared with experimental results.

A low-temperature X-ray diffraction study of Pd and some Pd-H alloys

Abstract: The lattice parameter of Pd has been measured between room temperature and 6K and has been found to be a smooth function of temperature over this range. An investigation of the X-ray diffraction patterns of some beta phase Pd-H alloys and a mixed ( alpha + beta ) phase alloy and of their dependence on cooling through the 50K region, where anomalies in a number of physical properties of beta -phase Pd-H are known to occur, showed no discernible effect on the state of strain of the Pd lattice, i.e., no indication of homogeneous lattice strain in excess of 2.5*10-5, nor evidence of line broadening indicative of inhomogeneous strains. Some consequences of this result for mechanisms which have been suggested to account for these anomalies are considered.

Magnetic properties of rare‐earth magnesium compounds of the type RMg2

Abstract: The magnetic and crystallographic properties of rare earth compounds of the type RMg2 were studied. The compounds in which R represents La, Ce, Pr, Nd, Sm and Gd were found to be of the cubic Laves phase structure. The remainder of compounds of this series crystallize in the hexagonal Laves phase structure. For all compounds the lattice constants were determined. Most of these compounds order ferromagnetically at temperatures well below 100 K. Exceptions are LaMg2, YbMg2 and YMg2 which exhibit Pauli paramagnetism, whereas SmMg2 and EuMg2 order antiferromagnetically. From the magnetic properties and from the lattice constants it is concluded that Eu and Yb are both divalent in these compounds. A peculiar temperature dependence of the magnetization was observed in SmMg2. A sharp peak‐like rise in the magnetization occurs within a temperature range of 10 K only, the magnetization being nearly temperature‐independent otherwise. Details regarding the nature of the crystal fields in the cubic RMg2 compounds were derived from specific heat measurement performed on LaMg2, CeMg2 in the temperature range 1.5–40 K.

Elastic neutron scattering of the "phase ordering" phase transition in Hg 3 − δ As F 6

Abstract: Elastic-neutron-scattering experiments performed on the linear-chain mercury compound ${\mathrm{Hg}}_{3\ensuremath{-}\ensuremath{\delta}}\mathrm{As}{\mathrm{F}}_{6}$ are presented. On cooling, a progressive phase ordering between the Hg chains, randomly phased at room temperature, has been found and characterized. Short-range order gradually builds up, with transverse coherence lengths of a few lattice constants, as a result of parallel chain-chain interactions. At 120 K, the competing orthogonal chain-chain interaction leads to three-dimensional order and a phase-ordering phase transition. The three-dimensional low-temperature phase is accompanied by an incommensurate modulation of the Hg chains indicating an interaction with the host lattice.

Effect of local environment on formation of local moments in BCC Fe-V alloys: Mossbauer study

Abstract: The Mossbauer spectra of BCC Fe-V alloys in the concentration range 40-80 at.% V have been obtained for both the ordered and disordered states. No broadening of the absorption line has been detected in an 80 at.% V alloy even at liquid He temperature indicating that the alloy is nonmagnetic. Broadening of absorption lines due to the magnetic hyperfine field has been observed for the alloys containing less than 70 at.% V. The spectra obtained at 5K were analysed to yield the hyperfine field distribution curves. It was found that the hyperfine field is notably reduced by atomic ordering. This change in hyperfine field is explained as the result of the change in Fe atomic moment which increases with increasing the number of Fe nearest neighbours. Profiles of the hyperfine field distribution curves are explained on the same basis. The dependence of the Fe atomic moment on the near-neighbour Fe composition is compared with the result of CPA calculations. Correlation between the lattice constant and the magnetic moment is discussed.

Reconstitution of an ordered structure from major outer membrane constituents and the lipoprotein-bearing peptidoglycan sacculus of Escherichia coli.

Abstract: An ordered hexagonal lattice structure with a lattice constant of about 7 nm was reconstituted on the entire surface of the lipoprotein-bearing peptidoglycan from outer membrane protein O-8 and lipopolysaccharide. The lattice structure resembled that observed in the cell envelope which had been treated with sodium dodecyl sulfate (Steven et al., J. Cell Biol. 72:292-301, 1977). The omission of either O-8 or lipopolysaccharide resulted in the failure of formation of the lattice structure. No ordered lattice was formed on the peptidoglycan lacking the bound form of the lipoprotein. In the absence of the lipoprotein-bearing peptidoglycan, O-8 and lipopolysaccharide assembled into vesicles with an ordered hexagonal lattice, the lattice constant of which was also about 7 nm. A preliminary experiment indicated that protein O-9 gave the same result as did O-8. These results strongly indicate that O-8 and/or O-9 and lipopolysaccharide provide the ordered framework of the outer membrane and that the bound form of the lipoprotein plays a role in the holding of the framework on the peptidoglycan layer.

Piezoelectric langbeinite‐type K2Cd2(SO4)3 structure at four temperatures below and one above the 432°K ferroelastic–paraelastic transition

Abstract: K2Cd2(SO4)3 is orthorhombic below 432°K, with space group P212121, and cubic above with space group P213. A structural study has been completed at 298, 351, 390.5, 417.5, and 443.5°K based, respectively, on 3383, 1377, 1803, 1724, and 1022 symmetry‐independent structure factors. Measurement of integrated intensities was made using a CAD‐4 diffractometer with Nb‐filtered MoKα radiation. An air‐flow microfurnace with temperature controller provided a thermal stability better than ±1°. The a, b, c lattice constants in the orthorhombic phase are 10.2084(8), 10.2813(8), 10.1684(8) A at 298°K; 10.2239(8), 10.2897(8), 10.1821(8) A at 351°K; 10.2386(8), 10.2951(8), 10.1981(8) A at 390.5°K; and 10.2501(10), 10.2972(8),10.2132(9) A at 417.5°K. In the cubic phase, a=10.2704(10) A at 443.5°K. The model previously obtained at room temperature [J. Chem. Phys. 67, 2146(1977)] was refined by the method of least squares using the new sets of measurements. The final agreement factors are R=0.028 (298°K), 0.032(351°K), 0.02...

Phase studies, crystal growth, and optical properties of CdGe(As1−xPx)2 and AgGa(Se1−xSx)2 solid solutions

Abstract: We report lattice constants, pseudobinary phase diagrams, crystal growth, and optical properties of the chalcopyrite CdGe(As1−xPx)2 and AgGa(Se1−xSx)2 solid solutions. The type‐II phase‐matching angle for frequency doubling of 10.6‐μm radiation has been measured for CdGe(As1−xPx)2 crystals with x=0, 0.13, and 0.19. On the basis of the results, it is estimated that 90° phase matching would be obtained for x∼0.3.

Local-density self-consistent energy-band structure of cubic CdS

Abstract: Self-consistent ab initio studies of the electronic-energy-band structure of cubic CdS are reported within the local-density-functional (LDF) formalism. All electrons are included using our previously reported linear-combination-of-atomic-orbitals method in a numerical basis representation. In the first set of calculations we employ the same lattice constant, exchange (only) potential, and computational parameters as were used by Stukel et al. in their early self-consistent orthogonalized-plane-wave (SCOPW) investigation so that a direct comparison of results can be made and the validity of the SCOPW approach for covalently bonded $4d$ systems can be assessed. In the second set of calculations, the Stukel et al. computational restrictions are relaxed, a more accurate lattice parameter is employed, and the Kohn-Sham exchange and the Singwi et al. correlation potential are used to obtain the local-density formalism solutions to the band problem, including variation of the band structure and related properties with pressure (change of lattice constant). Comparison with optical and x-ray and uv photoemission experiments for excitations of both the $s\ensuremath{-}p$ and metal $d$ bands in the 5-19 eV region indicate very good agreement. The direct gap at $\ensuremath{\Gamma}$ is, however, found to be 0.5 eV (25%) too small, a discrepancy similar to that previously found in nonempirical studies for other heteropolar insulators (e.g., Ne and LiF). This is traced to the neglect of the different orbital relaxation at the ${\ensuremath{\Gamma}}_{25}$ and ${\ensuremath{\Gamma}}_{1}$ band edges and to the noncancellation of the self-interaction terms characteristic of the local-density potential. Simple atomic total-energy models for these effects are shown to bring this gap into good agreement with experiment. It is concluded that a first-principles (parameter-free) exchange and correlation LDF model describes very well the main electronic-structure features of the system.