Showing papers on "Lattice constant published in 1994"
TL;DR: In this article, X-ray diffraction and Raman scattering are used to analyze the Raman spectrum of CeO2 and find that the single allowed Raman mode shifts to lower frequency with increasing doping level for all the rare earths.
Abstract: Powdered samples of the type Ce1−xRExO2−y, where RE=La, Pr, Nd, Eu, Gd, and Tb, are synthesized over the range 0≤x≤0.5 starting from nitrate solutions of the rare earths. X‐ray diffraction and Raman scattering are used to analyze the samples. These compounds, at least in the low doping regime and for strictly trivalent dopants, form solid solutions that maintain the fluorite structure of CeO2 with a change in lattice constant that is approximately proportional to the dopant ionic radius. The single allowed Raman mode, which occurs at 465 cm−1 in pure CeO2, is observed to shift to lower frequency with increasing doping level for all the rare earths. However, after correcting for the Gruneisen shift from the lattice expansion, the frequency shift is actually positive for all the strictly trivalent ions. In addition, the Raman line broadens and becomes asymmetric with a low frequency tail, and a new broad feature appears in the spectrum at ∼570 cm−1. These changes in the Raman spectrum are attributed to O va...
1,034 citations
TL;DR: Infrared, Raman, and nuclear magnetic resonance studies show a drastic reduction of icosahedral symmetry, as might occur if the C60 molecules are linked, in accord with the reduced solubility of the pressure-induced phases.
Abstract: The fullerene C60 can be converted into two different structures by high pressure and temperature. They are metastable and revert to pristine C60 on reheating to 300°C at ambient pressure. For synthesis temperatures between 300° and 400°C and pressures of 5 gigapascals, a nominal face-centered-cubic structure is produced with a lattice parameter ao = 13.6 angstroms. When treated at 500° to 800°C at the same pressure, C60 transforms into a rhombohedral structure with hexagonal lattice parameters of ao = 9.22 angstroms and co = 24.6 angstroms. The intermolecular distance is small enough that a chemical bond can form, in accord with the reduced solubility of the pressure-induced phases. Infrared, Raman, and nuclear magnetic resonance studies show a drastic reduction of icosahedral symmetry, as might occur if the C60 molecules are linked.
572 citations
TL;DR: In this paper, the authors developed temperature dependent stability maps that predict the stable domain structure that forms during the paraelectric to ferroelectric transition (PE→FE) and discussed the role of dislocation stabilization of domain patterns.
Abstract: Possible mechanisms for strain relaxation in ferroelectric thin films are developed. The models are applicable to tetragonal thin film ferroelectrics grown epitaxially on (001) cubic single crystal substrates. We assume growth at temperatures in excess of the Curie temperature (Tc). The extent of strain accommodation by misfit dislocations is considered at the growth temperature (Tg). On cooling to Tc, further misfit dislocation generation is possible due to differences in thermal expansion behavior of the film and substrate. During the paraelectric to ferroelectric transition (PE→FE) additional strains develop in the film. The total strain for the FE phase may be relieved either by further misfit generation or by domain formation. We have developed temperature dependent stability maps that predict the stable domain structure that forms during the PE→FE transition. The stability maps incorporate the role of the following parameters: (i) substrate lattice parameter, (ii) differential thermal expansion characteristics between the film and substrate, (iii) cooling rate, and (iv) depolarizing fields and electrode geometry. Further, the role of dislocation stabilization of domain patterns is discussed.
473 citations
TL;DR: The modified embedded atom method (MEAM) is an empirical extension of EAM that includes angular forces as mentioned in this paper, which has previously been applied to the atoms in the FCC, BCC, and diamond cubic crystal systems, has been extended to the HCP crystal structure.
Abstract: The modified embedded atom method (MEAM) is an empirical extension of embedded atom method (EAM) that includes angular forces. The MEAM, which has previously been applied to the atoms in the FCC, BCC, and diamond cubic crystal systems, has been extended to the HCP crystal structure. Parameters have been determined for HCP metals that have c/a ratios less than ideal. The model is fitted to the lattice constants, elastic constants, cohesive energy, vacancy formation energy, and the BCC-HCP structural energy difference of these metals and is able to reproduce this extensive data base quite well. Structural energies and lattice constants of the HCP metals in a number of cubic structures are predicted. The divacancy is found to be unbound in all of the metals considered except for Be. Stacking fault and surface energies are found to be in reasonable agreement with experiment.
350 citations
TL;DR: In this paper, the authors report the development of a method for creating submicron periodic materials, which are composed of a body-centered cubic (BCC), face centered cubic (FCC), or random hexagonal stacked array of spherical particles in which the periodicity is locked into a hydrogel polyacrylamide network.
Abstract: We report the development of a method for creating new submicron periodic materials. These materials will have numerous applications in various areas of technology. This periodic material is composed of a body-centered cubic (BCC), face-centered cubic (FCC), or random hexagonal stacked array of spherical particles in which the periodicity is locked into a hydrogel polyacrylamide network.’ The lattice constant of this array can be varied between
321 citations
TL;DR: In this paper, the effect of rare-earth ion substitutions on magnetic and electrical properties of Ni-Zn ferrite was investigated. But the authors focused on the magnetic properties and not the electrical properties.
Abstract: The effect of Fe substitutions by rare-earth ions on magnetic and electrical properties of a Ni-Zn ferrite prepared by the classical method is investigated. A set of seven compounds with formula Ni0.7Zn0.3Fe1.98R0.02O4, where R identical to Yb, Er, Dy, Tb, Gd, Sm or Ce, was prepared. Emphasis is placed on current experimental results of bulk magnetic measurements and transport phenomena. The results obtained reveal that, by introducing a relatively small amount of R2O3 instead of Fe2O3, an important modification of both the structure and the magnetic and electrical properties can be obtained. We explain the influence of the rare-earth ions as an effect of the ionic radius. This assumption is supported by the lattice constant measurements. The best results from the viewpoint of magnetic and electrical characteristic acceptable for high frequencies were obtained for R ions with a large radius and with a stable valence of 3+ such as Gd in our work.
304 citations
TL;DR: The asymmetric charge distribution for a Si-C bond to be on the boundary separating the zinc-blende and wurtzite phases, which should be related to the polytypism of SiC.
Abstract: We study the structural and electronic properties of various polytypes of SiC through self-consistent ab initio pseudopotential calculations. For the wurtzite (2H), 4H, and 6H structures, the equilibrium lattice constants and bulk moduli are very similar to those for the cubic structure. The energies calculated for the polytypes considered here are very close to within 4.3 meV/atom, which may explain the polytypism of SiC. The 4H structure is found to be lowest in energy because of the attractive interactions between the alternating cubic and hexagonal stacking layers, while the wurtzite structure is most unstable among the polytypes. We find the asymmetric charge distribution for a Si-C bond to be on the boundary separating the zinc-blende and wurtzite phases, which should be related to the polytypism of SiC. In the hexagonal polytypes, the M conduction-band energy increases, while that of the K point decreases as the hexagonal close packing becomes more prominent. Thus, the conduction-band minimum state located at the X point for cubic SiC changes to the M point, and then to the K point for the 2H structure. For the cubic structure, the density of states near the conduction-band edge increases slowly with energy, while it shows very rapidly increasing behavior for the 6H polytype because its conduction-band edge states are flattened due to the band folding and the energy-increasing behavior of the M state when the hexagonal-close-packing nature is enhanced.
284 citations
TL;DR: The phase relationship between LiNiO2 and its related compounds was examined by X-ray diffraction, neutron diffraction and DTA-TG, and electrical, magnetic, and electrochemical measurements.
223 citations
TL;DR: In this article, the lattice constants of gallium nitride (wurzite structure) have been measured at temperatures 294-753 K. The measurements were performed by using x-ray diffractometry.
Abstract: Lattice constants of gallium nitride (wurzite structure) have been measured at temperatures 294–753 K. The measurements were performed by using x‐ray diffractometry. Two kinds of samples were used: (1) bulk monocrystal grown at pressure of 15 kbar, (2) epitaxial layer grown on a sapphire substrate. The latter had a smaller lattice constant in a direction parallel to the interface plane by about 0.03%. This difference was induced by a higher thermal expansion of the sapphire with respect to the GaN layer. However, this thermal strain was created mainly at temperatures below 500–600 K. Above these temperatures the lattice mismatch in parallel direction diminished to zero at a temperature of about 800 K.
210 citations
TL;DR: In this paper, a series of MCM-41 models with various lattice constants and wall thicknesses have been generated and analyzed, and the density of T-sites, concentration of silanols, distribution of ring sizes and the X-ray diffraction patterns were calculated for each structure with the latter compared to the experimental results.
Abstract: Model structures for MCM-41 materials have been obtained using the classical molecular dynamics simulation technique with effective interaction potentials. A series of MCM-41 models with various lattice constants and wall thicknesses have been generated and analyzed. The density of T-sites, concentration of silanols, distribution of ring sizes, and the X-ray diffraction patterns were calculated for each structure with the latter compared to the experimental results
194 citations
TL;DR: In this article, the phase changes among the cubic phase (Fm3m, Z=4), the t″ form and the t' form were investigated by neutron and X-ray powder diffraction.
Abstract: In the ZrO 2 -YO 1.5 solid solutions, the phase changes among the cubic phase (Fm3m, Z=4), the t″ form and the t' form were investigated by neutron and X-ray powder diffraction, where the t″ and t' forms are defined as tetragonal phases (P4 2 /nmc, Z=2) with axial ratios of c/a f =1 and c/a f >1, respectively, which were prepared by a diffusionless transition from the high-temperature cubic phase during quenching. a f is the lattice parameter of the pseudo-fluorite cell
TL;DR: The lattice parameter of titanium nitride is also a linear function of the nitrogen/metal ratio in the temperature range investigated in this article, where the lattice parameters were obtained from high-temperature X-ray diffraction (HTXRD) measurements made with high-dimensional (X-ray) in the range of 298-1473 K.
TL;DR: This paper provides the coefficients of a polynomial fit to the previously published a and c lattice constants of normal and deuterated ice Ih for the same temperature range and provides a table with more significant digits.
Abstract: In a previous paper we reported the lattice constants and thermal expansion of normal and deuterated ice Ih [Rottger et al. (1994). Acta Cryst. B50, 644–648]. Synchrotron X-ray powder diffraction data were used to obtain the lattice constants and unit-cell volumes of H2O and D2O ice Ih in the temperature range 15–265 K. A polynomial expression was given for the unit-cell volumes. It turns out that the coefficients quoted have an insufficient number of digits to faithfully reproduce the volume cell data. Here we provide a table with more significant digits. Moreover, we also provide the coefficients of a polynomial fit to the previously published a and c lattice constants of normal and deuterated ice Ih for the same temperature range.
TL;DR: In this article, the relative orientation of the organic monolayer and the Au(111) substrate has been determined unambiguously both with GIXD, and by AFM, taking advantage of an earlier finding that AFM tips can reversibly displace the thiol molecules under high loads.
Abstract: Atomic force microscopy (AFM) and grazing incidence x‐ray diffraction (GIXD) have been used to study the structure of self‐assembled monolayers of CF3(CF2)n(CH2)2SH (n=11, 7, and 5) on the Au(111) surface. Surprisingly, although the nearest‐neighbor fluorinated alkane thiol distance is very close to the lattice constant of a commensurate p(2×2) structure, the close‐packed rows of molecules are rotated ∼30° with respect to the underlying gold lattice. That packing is incommensurate or at most only close to the high‐order commensurate c(7×7) structure. The relative orientation of the organic monolayer and the Au(111) substrate has been determined unambiguously both with GIXD, and by AFM, taking advantage of an earlier finding (Ref. ) that AFM tips can reversibly displace the thiol molecules under high loads. In addition, we demonstrate that the two techniques provide complementary information on the order and the domain structures of these monolayers.
TL;DR: In this paper, the authors demonstrate that a two-dimensional lattice of metal cylinders can form a complete photonic band-gap (PBG) structure, which exhibits a single broad PBG extending from zero frequency to a threshold frequency, above which all modes may propagate in some direction.
Abstract: We demonstrate, by both microwave experiments and numerical simulation, that a two‐dimensional lattice of metal cylinders can form a complete photonic band‐gap (PBG) structure. The band structure exhibits a single broad PBG extending from zero frequency to a threshold frequency, above which all modes may propagate in some direction. A single cylinder removed from the lattice produces a defect mode localized about the defect site, with an energy density attenuation rate of 30 dB per lattice constant. The frequency dependence of the transmission through a finite thickness of this structure is also calculated in good agreement with the measurements. We suggest that the defect mode resonant cavity when formed by appropriate low loss metals may be advantageous for use in PBG high energy accelerator structures that we are evaluating.
TL;DR: In this article, the authors investigated the domain epitaxial growth in metal-semiconductor systems with a large lattice mismatch and showed that the residual mismatch is responsible for a coherent strain energy.
Abstract: Epitaxial growth in the TiN/Si and TiN/GaAs metal‐semiconductor systems with a large lattice mismatch was investigated. The orientation relationships have been found to be 〈001〉TiN∥〈001〉Si for TiN growth on Si(001) and [001]TiN∥[110]GaAs and [110]TiN∥[110]GaAs for TiN growth on GaAs(001). The epitaxial growth is characterized by domain epitaxial orientation relationships with m lattice constants of epilayer matching with n of the substrate and with a small residual domain mismatch present in the epilayer. This residual mismatch is responsible for a coherent strain energy. The magnitude of compression of Ti—N bond in the first atomic layer, contributing to the chemical free energy during the initial stages of growth, is found to be a very important factor in determining the orientation relationship. This result was used to explain the differences in the orientation relationships between TiN/Si and TiN/GaAs systems. The various energy terms associated with the domain epitaxial growth are evaluated to illu...
TL;DR: This study demonstrates that it is both possible and practical to treat gallium 3[ital d] electrons explicitly using the PWPP method and yields larger lattice constants and smaller energy gaps as compared with previous PWPP results.
Abstract: The plane-wave pseudopotential (PWPP) method has been used to calculate structural and electronic properties of wurtzite and zinc-blende GaN. In contrast to previous studies using the PWPP method, the gallium 3[ital d] electrons were treated as valence electrons. This yields larger lattice constants and smaller energy gaps as compared with previous PWPP results. For wurtzite, the three structural parameters were found to be [ital a]=3.162 A, [ital c]=5.142 A, and [ital u]=0.377. For zinc blende, the cubic lattice constant was found to be [ital a][sub 0]=4.460 A. The lattice constants are about 1% smaller than measured values and the cubic lattice constant is within about 0.2% of results from full-potential all-electron calculations. This study demonstrates that it is both possible and practical to treat gallium 3[ital d] electrons explicitly using the PWPP method.
TL;DR: In this paper, an x-ray diffraction study of the substitution of gallium in Tb2Fe17 to form the Tb 2Fe17−xGax solid solutions indicates that the compounds adopt the rhombohedral Th2Zn17 structure.
Abstract: An x‐ray diffraction study of the substitution of gallium in Tb2Fe17 to form the Tb2Fe17−xGax solid solutions indicates that the compounds adopt the rhombohedral Th2Zn17 structure. The unit cell volume and the a‐axis lattice parameter increase linearly with increasing gallium content. The c‐axis lattice parameter increases linearly from x=0 to 6 and then decreases between x=7 and 8. Magnetic studies show the Curie temperature increases by ∼150° above that of Tb2Fe17 to reach a maximum between x=3 and 4, and then decreases with further increases in x. Neutron diffraction studies of Nd2Fe15Ga2 and Tb2Fe17−xGax, with x equal to 5, 6, and 8, indicate that the gallium completely avoids the 9d site, occupies the 6c ‘‘dumbell’’ site only at high values of x and strongly prefers the 18f site at high values of x. The magnetic neutron scattering indicates both that the terbium sublattice magnetization couples antiferromagnetically with the iron sublattice and that there is a change in easy magnetization direction f...
TL;DR: In this article, the mechanical properties of compositionally modulated Au-Ni films were investigated by submicrometer depth-sensing indentation and by deflection of micrometer-scale cantilever beams.
Abstract: The mechanical properties of compositionally modulated Au-Ni films were investigated by submicrometer depth-sensing indentation and by deflection of micrometer-scale cantilever beams. Films prepared by sputter deposition with composition wavelengths between 0.9 and 4.0 nm were investigated. Strength was found to be high and invariant with composition wavelength. Experimental and data analysis methods were developed to provide more accurate and precise measurements of elastic stiffness. Large enhancements in stiffness (the “supermodulus effect”) were not observed. Rather, relatively small but significant minima were observed at a composition wavelength of about 1.6 nm by both techniques. These variations were found to be strongly correlated with variations in the average lattice parameter normal to the plane of the film. Both structural and mechanical property variations are consistent with a simple model in which the film consists of bulk-like Au and Ni layers with interfaces of constant thickness.
TL;DR: By adding quasiparticle corrections to the DFT-LDA band structures, the ordering of the conduction-band minima is state more precisely and the empirical Choyke-Hamilton-Patrick relation is given.
Abstract: Ab initio total-energy studies are used to determine the lattice constants and the atomic positions within the unit cells for 3C-, 6H-, 4H-, and 2H-SiC. The electronic structures are calculated for the atomic geometries obtained theoretically within the density-functional theory (DFT) and the local-density approximation (LDA). We state more precisely the ordering of the conduction-band minima and derive effective masses. By adding quasiparticle corrections to the DFT-LDA band structures we find indirect fundamental energy gaps in agreement with the experiment. A physical explanation of the empirical Choyke-Hamilton-Patrick relation is given. Band discontinuities, bandwidths, crystal-field splittings, and ionic gaps are discussed versus hexagonality.
TL;DR: In this paper, a linear extrapolation between the different lattice constants opens the possibility to predict the SiGeC structure in dependence on the carbon content, and it is possible to grown epitaxial SiGeCs with up to 2% carbon.
Abstract: Si1−x−yGexCy layers have been grown on Si(001) substrates with molecular beam epitaxy and investigated with transmission electron microscopy and x‐ray diffraction. We show that it is possible to adjust the strain in pseudomorphic SiGe layers by adding small amounts of carbon. A simple linear extrapolation between the different lattice constants opens the possibility to predict the SiGeC structure in dependence on the carbon content. It is possible to grown epitaxial SiGeC layers with up to 2% carbon. Larger carbon concentrations lead to a crystallographic degradation of the layers. We were able to grow the first pseudomorphic SiGeC layer on Si(001) that is under tensile stress. These layers exhibit a lattice plane spacing in growth direction smaller than that of silicon.
TL;DR: For the spin-1/2 Heisenberg antiferromagnet on the kagom\'e lattice the high-temperature series for the specific heat and the structure factor is calculated and the uniform susceptibility has a maximum at T\ensuremath{\approxeq}1/6 and vanishes exponentially for lower temperatures.
Abstract: For the spin-1/2 Heisenberg antiferromagnet on the kagom\'e lattice we calculate the high-temperature series for the specific heat and the structure factor. A comparison of the series with exact-diagonalization studies shows that the specific heat has further structure at lower temperature in addition to a high-temperature peak at T\ensuremath{\approxeq}2/3. At T=0.25 the structure factor agrees quite well with results for the ground state of a finite cluster with 36 sites. At this temperature the structure factor is less than two times its T=\ensuremath{\infty} value and depends only weakly on the wave vector q, indicating the absence of magnetic order and a correlation length of less than one lattice spacing. The uniform susceptibility has a maximum at T\ensuremath{\approxeq}1/6 and vanishes exponentially for lower temperatures.
TL;DR: In this article, a new high-temperature and nontoxic superconductor family of Cu1-xBa2Can-1CunO2n+4-δ with critical temperature (Tc)>116 K was discovered.
Abstract: A new high-temperature and nontoxic superconductor family of Cu1-xBa2Can-1CunO2n+4-δ with critical temperature (Tc)>116 K was discovered. These materials were prepared by the high-pressure technique. A superconductor sample with the highest T c contains mainly a Cu1-x Ba2Ca3Cu4O12-δ phase. The T c value of the Cu1-x Ba2Ca3Cu4O12-δ phase is 116.4 K. The phase has two kinds of tetragonal structures: body-centered tetragonal (bct) and simple tetragonal. The lattice parameters of bct are a=7.7114 A and c=35.986 A. The disordering or full occupation of Cu-vacancy sites leads to the simple tetragonal phase with the space group of P4/mmm and the half values of the lattice constants (a=3.8557 A and c=17.993 A) of the bct phase. The relationship between the lattice constant c and the number of CuO2 layers n is c/2=8.4+3.2(n-1) ( A). The small CuO2-block spacing (8.4 A) of this family suggests a lower anisotropy and higher J c than in Hg- and Tl-based superconductor families.
TL;DR: In this paper, the structure of the Pt(100)-hex-R0.7° reconstructed phase has been studied by scanning tunneling microscopy (STM) and the hexagonal first layer superstructure of this surface, written in matrix notation as N 1 −1 5, N = 12−14, was imaged with atomic resolution.
TL;DR: In this paper, the authors show that planar deformation features (PDFs) occur predominantly parallel to (1010) or (0001), where minimum strain is present, supporting the assumption that these PDFs consist, under compression, of superheated melt.
TL;DR: In this paper, the in situ growth of three distinct phases of LiCoO2 by laser ablation deposition on heated substrates in an oxygen background was reported, which was characterized by x-ray diffraction from which crystal structure, crystal orientation, lattice constants, and phase information were obtained.
Abstract: A study is reported of the in situ growth of three distinct phases of LiCoO2 by laser ablation deposition on heated substrates in an oxygen background. Films were characterized by x‐ray diffraction from which crystal structure, crystal orientation, lattice constants, and phase information were obtained. Electron microscopy was used to investigate crystal grain size and overall film morphology. For deposition under 2000 mTorr O2, substrate temperatures of 22–250 °C resulted in a rock‐salt structure, 300–450 °C produced a modified spinel structure (low‐temperature LiCoO2), and 680 °C gave a hexagonal layered structure (high‐temperature LiCoO2). Growth at 500 and 550 °C produced mixed‐phase spinel and layered LiCoO2; however, at 550 °C, reducing the O2 pressure to 100 mTorr resulted in single‐phase high‐temperature LiCoO2. In the case of the rock‐salt phase, modified film stoichiometries of composition Li0.5Co1.5O2 and Li0.75Co1.25O2 were also produced by using ablation targets of the same composition and gr...
TL;DR: In this article, the authors reported the preparation of pure crystalline Sc_2@C_(84) and analyses of its structure by electron diffraction and high-resolution transmission electron microscopy.
Abstract: IT was first proposed in 1985 that fullerenes can confine atoms in their interior because of their closed-cage structure. Attempts to verify this conjecture following the mass production of fullerenes have yielded metallofullerenes in bulk, and there is now good evidence that these compounds are endohedral—that is, that the metal atoms are inside. But direct confirmation in the form of structural data has been lacking, in part because of the difficulty of separating different metallofullerenes and obtaining pure crystals. Here we report the preparation of pure crystalline Sc_2@C_(84) and analyses of its structure by electron diffraction and high-resolution transmission electron microscopy. At room temperature the Sc_2@C_(84) molecules pack in a hexagonal-close-packed structure with a ratio of lattice constants c/ɑ = 1.63, the value expected for ideal-sphere packing. The molecular spacing of 11.2 A is the same as that found earlier in crystalline C_(84) (refs 5, 6). The match between our microscopic images and simulations is markedly better for endohedral models than for those in which the metal atoms reside in the lattice outside the C_(84) cages. We believe that this combination of observations points inevitably to the conclusion that the metal atoms are inside the fullerenes.
TL;DR: Ab initio periodic Hartree-Fock (HF) theory was used to determine the elastic constants and selected phonon frequencies of bulk MgO and these data will be used to parametrize electrostatic shell models of M gO.
Abstract: Ab initio periodic Hartree-Fock (HF) theory was used to determine the elastic constants and selected phonon frequencies of bulk MgO; the accuracy of a posteriori correlation corrections to the periodic Hartree-Fock calculations is also discussed. Inclusion of diffuse atomic orbitals in the MgO basis was necessary to accurately describe elastic distortions and phonon vibrations of the solid. The computed HF lattice constant (4.195 \AA{}) agrees with experiment (4.19 \AA{}) and the elastic constants are within +15% of the observed values. Correlation corrections to these energetics shorten the lattice parameter to 4.09 \AA{} and further stiffen the elastic constants. The HF phonon frequencies at the (\ensuremath{\Gamma}, X, and L) points in the Brillouin zone were within 15% of experiment and the correlation corrections softened the modes improving agreement with experiment. These data will be used to parametrize electrostatic shell models of MgO.
TL;DR: In this paper, a small angle neutron scattering study of the vortex lattice in magnetic fields of 0.5 T applied along and close to the $c$ axis was performed, where the vortices formed an oblique lattice with two nearly equal lattice constants and an angle of 73 degrees between primitive vectors.
Abstract: We report a small angle neutron scattering study of the vortex lattice in Y${\mathrm{Ba}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7}$ in magnetic fields of $0.5\ensuremath{\le}H\ensuremath{\le}5$ T applied along and close to the $c$ axis. Over the entire field range, the vortices form an oblique lattice with two nearly equal lattice constants and an angle of 73\ifmmode^\circ\else\textdegree\fi{} between primitive vectors. Numerical calculations suggest that variations of the superconducting order parameter near the vortex core are important in stabilizing this structure. An analysis that accounts for the fourfold symmetry of the vortex core qualitatively explains both the symmetry and the orientation of the observed vortex lattice. A quantitative explanation of our data will require calculations based on a realistic gap equation.
TL;DR: In this article, the lattice constant of the films varies linearly with alloy composition x (Vegard's law is obeyed) and homogeneous and inhomogeneous strain and alloy clustering are minimized in these self-nucleated AlxGa1−xN films.
Abstract: High quality AlxGa1−xN alloy films with x<04 have been prepared on self‐nucleated (001) sapphire substrates by low‐pressure metalorganic chemical vapor deposition It has been shown that the lattice constant of the films varies linearly with alloy composition x (Vegard’s law is obeyed) and that homogeneous and inhomogeneous strain and alloy clustering are minimized in these self‐nucleated AlxGa1−xN films Consistent with their reduced strain and chemical uniformity, the derived optical band gaps of these AlxGa1−xN films also show a linear dependence on alloy composition x, yielding a bowing parameter b≊0 eV