Showing papers on "Lattice constant published in 1977"

Gap junction structures: Analysis of the x-ray diffraction data

Abstract: Models for the spatial distribution of protein, lipid and water in gap junction structures have been constructed from the results of the analysis of X-ray diffraction data described here and the electron microscope and chemical data presented in the preceding paper (Caspar, D. L. D., D. A. Goodenough, L. Makowski, and W.C. Phillips. 1977. 74:605-628). The continuous intensity distribution on the meridian of the X-ray diffraction pattern was measured, and corrected for the effects of the partially ordered stacking and partial orientation of the junctions in the X-ray specimens. The electron density distribution in the direction perpendicular to the plane of the junction was calculated from the meridional intensity data. Determination of the interference function for the stacking of the junctions improved the accuracy of the electron density profile. The pair-correlation function, which provides information about the packing of junctions in the specimen, was calculated from the interference function. The intensities of the hexagonal lattice reflections on the equator of the X-ray pattern were used in coordination with the electron microscope data to calculate to the two-dimensional electron density projection onto the plane of the membrane. Differences in the structure of the connexons as seen in the meridional profile and equatorial projections were shown to be correlated to changes in lattice constant. The parts of the junction structure which are variable have been distinguished from the invariant parts by comparison of the X-ray data from different specimens. The combination of these results with electron microscope and chemical data provides low resolution three- dimensional representations of the structures of gap junctions.

Infrared and Raman spectra of the IV-VI compounds SnS and SnSe

Abstract: The results of Raman scattering and infrared reflectivity measurements on the IV-VI layer-type semiconductors SnS and SnSe are presented. The infrared-active TO, the associated LO-phonon frequencies, and the dielectric constants for all three principal polarizations have been determined from a Kramers-Kronig analysis of the reflectivity data. The symmetries of the zone-center phonons observed in the different polarization configurations are in agreement with the group-theoretical analysis of the ${D}_{2h}^{16}$ space group of these compounds. Despite the center of inversion symmetry in this structure, some infrared- and Raman-active modes are found to be nearly degenerate, suggesting the importance of the layerlike character in these compounds as in the isomorphic GeS and GeSe. A comparison of the phonon frequencies of the corresponding modes in the spectra of SnS and SnSe, or GeS and GeSe, indicates that the frequencies vary as a power (-2.2) of the lattice constant.

Gap junction structures. I. Correlated electron microscopy and x-ray diffraction

Abstract: X-ray crystallographic methods and electron microscope image analysis have been used to correlate the structure and the chemical composition of gap junction plaques isolated intact from mouse liver. The requirement that the interpretations of X-ray, electron microscope, and chemical measurements be consistent reduces the uncertainties inherent in the separate observations and leads to a unified picture of the gap junction structures. Gap junctions are built up of units called connexons that are hexagonally arrayed in the pair of connected cell membranes. X-ray diffraction and electron microscope measurements show that the lattice constant of this array varies from about 80 to 90 A. Analysis of electron micrographs of negatively stained gap junctions shows that there is significant short range disorder in the junction lattice. even though the long range order of the array is remarkably regular. Analysis of the disorder provides information about the nature of the intermolecular forces that hold the array together.

Orientational epitaxy—the orientational ordering of incommensurate structures

Abstract: A new class of structures is predicted to exist for monolayer films on solid surfaces. These structures involve two incommensurate lattices---the monolayer lattice and the surface lattice--- which have a preferred relative orientation. The precise orientation depends upon the lattice constant and symmetry of each lattice. We believe this orientationally ordered incommensurate phase to be present in many physisorbed films. In particular, the existence of this phase appears to explain recent low-energy electron diffraction data for rare gases adsorbed homogeneous substrates.

Phase transition on Mo(100) and W(100) surfaces

Abstract: Low-energy-electron-diffraction studies of carefully cleaned and annealed surfaces of molybdenum (100) and tungsten (100) show that a phase transition can be induced by lowering the temperature below 300 K. The periodicity of the "reconstructed" surface is believed to be due to the formation of a displacement wave with a wavelength which is $2a$ ($a$ is the lattice parameter) for W(100) and $\ensuremath{\sim}2.2a$ for Mo(100). The phase transition is reversible and seemingly second order. It appears possible that displacements of this type also occur in chemisorption on these surfaces.

A correlation between the interstitial hole sizes in intermetallic compounds and the thermodynamic properties of the hydrides formed from those compounds

Abstract: A correlation has been established between the stabilities of metal hydrides (measured in terms of the free energies of formation of the hydride phase per mole H 2 ) and the radii of tetrahedral holes in both hexagonal AB 5 (D2 d ) and cubic AB (B 2 ) intermetallic compounds. The correlation demonstrates that as the tetrahedral hole size increases, the stability increases. The results of this correlation show conclusively that hole size can be employed effectively in determining the stabilities of intermetallic compound-hydrogen phases. A model, which depends solely upon lattice parameters, was developed to compute the radii of tetrahedral holes in hexagonal AB 5 intermetallic compounds. A similar model, which requires a ratio of metallic radii in addition to the lattice parameter, has been employed to compute the radii of tetrahedral holes in the cubic AB intermetallic compounds. The thermodynamic and structural properties of hexagonal AB 5 -hydrogen systems and cubic AB-hydrogen systems have been compiled and are presented. The quantitative correlations are excellent. A change in valence of the A atom in the hexagonal AB 5 intermetallic compounds may have a significant effect on the stabilities of the hydride phases formed. In those cases where the B atoms were partially substituted in the hexagonal AB 6 and the cubic AB intermetallic compounds, a good correlation of stability with hole size was found. Gross deviations of the Ce-base AB 5 hydride data from the correlation line established by all the other AB 5 hydrides were observed. These were rationalized on the basis of well-documented stress-induced lattice contractions of Ce intermetallic compounds. The resulting contracted hole sizes of the CeNi 5 and CeCo 5 compounds modified the stability of their hydrides. These compound hydrides demonstrate a displaced but similar correlation to the other AB 5 hydrides, i.e . the smaller the hole size, the less stable is the system.

Quarks and Strings on a Lattice

Abstract: Three lectures describe the lattice version of the color gauge theory of quarks. The string interpretation of the theory is emphasized. The strong coupling expansion is defined by a set of Feynman rules. The dominant diagrams are identified. The result is that for strong quark-gluon coupling, the lattice spacing is about 1/5 x 10−13cm, the nucleon has a mass of 1720 MeV/c2 while the N* mass is 1750 MeV/c. The π and ρ masses are fitted to experiment. The relativistic limit is explained for free field theories on a lattice. For the colored quark theory only a few aspects of the relativistic continuum limit are discussed. It is shown how short wavelength string fluctuations are suppressed. It is shown that the classical limit of the lattice theory is the relativistic continuum color gauge theory.

In1−xGaxAs‐GaSb1−yAsy heterojunctions by molecular beam epitaxy

Abstract: Smooth films of n‐In1−xGaxAs and p‐GaSb1−yAsy were grown by molecular beam epitaxy. As a function of the compositions, x and y, the lattice constants vary linearly while the energy gaps show a downward bowing. Abrupt heterojunctions made of these alloys with close lattice matching exhibit a series of current‐voltage characteristics which change from rectifying to Ohmic as x and y are reduced. The relative location of the band‐edge energies of the two semiconductors at the interface is shown to account for the unusual characteristics observed experimentally.

Effect of pressure on the atom positions in Se and Te

Abstract: The effect of pressure on atomic positions and lattice parameters is determined for trigonal Se under pressures from 0 to 86 kbar and for trigonal Te from 0 to 40 kbar by single-crystal x-ray diffraction using a diamond anvil high-pressure cell in a standard precession camera. The structural data confirm the lattice-dynamical homology that had been observed in the variation of the Raman frequencies at low pressures. However, the strongly nonlinear variations in the interatomic distances and the bond angles show deviations from a structural homology as the high-pressure phase transitions are approached.

Higher Order Laue Zone Effects in Electron Diffraction and their Use in Lattice Parameter Determination

Abstract: By fitting small probe-forming lenses into a conventional electron microscope, we have been able to observe higher order Lane zone (h.o.l.z.) diffraction effects from high symmetry zone axes of a wide variety of materials. Cooling the specimen with liquid nitrogen both greatly reduces the contamination rate and increases the visibility of the h.o.l.z. lines. An interpretation of these lines is given in terms of the dispersion surface construction and conditions for the visibility of h.o.l.z. effects are deduced. A theory from which numerical solutions have been obtained is outlined. Using h.o.l.z. lines, we can deduce the microscope operating voltage or the lattice parameter of the specimen to approximately one part in a thousand; relative changes can be measured about five times more precisely. The spatial resolution of the technique is approximately 10 nm. Strain gradients within the illuminated area can produce fringe patterns.

Preparation, Characterization, and Properties of Dy‐Doped Small‐Grained BaTiO3 Ceramics

Abstract: The effects of Dy doping and sintering parameters on the properties of BaTiO3 ceramics were studied. The average grain size decreases with increasing Dy content and is controlled at ∼1.5 μ m by 0.8 at.% Dy. The Curie temperature change, associated with ≤1.2 at.% Dy, is <3°C. The dielectric constant is ∼2600 for specimens doped with 0.8 at.% Dy, calcined at 1200°C, and sintered at 1450°C. The dielectric constant variation with ambient temperature is much less than that of conventional BaTiO3 ceramics. Lattice constant c decreases with increasing Dy concentration whereas a increases slightly. The effects of grain size on dielectric constant, lattice parameters, and linear thermal expansion coefficient are more pronounced than the chemical effects of Dy doping in the ferroelectric state, whereas in the paraelectric state, these characteristics are almost independent of grain size as well as Dy concentration. The decrease in the frequency of occurrence of 90° twins with decreasing grain size implies that internal stress, which develops when BaTiO3 ceramics are cooled below Tc, strongly influences the effects of grain size.

Phase Equilibria and Ordering in the System ZrO2-CaO

Abstract: The phase diagram of the system ZrO2-CaO for the region ZrO2-CaZrO3 was redetermined. The extent of the cubic solid solution field was ascertained by using a high-temperature X-ray furnace, precise lattice parameter measurements, and a hydrothermal technique. At 850 ± 150°C, the cubic solid solutions decompose by a eutectoid reaction. A reasonable agreement for the position of the eutectoid in this system was obtained by comparing the extrapolated data from high temperatures with the data obtained by the hydrothermal technique. Only one ordered compound, CaZr4O9, with monoclinic symmetry, was found; this compound is unstable above 1310 ± 40°C.

Distance between magnetic ions and fundamental properties in ferrites

Abstract: In the basic spinel NiFe2O4, ions of larger and larger ionic radius, Zn2+ and Cd2+, have been introduced with higher and higher concentrations. The corresponding materials of composition Ni1-xZnxFe2O4 and Ni1-xCdxFe2O4 have been prepared by using a special technologic process. The lattice constant increases linearly with the mean ionic radius in tetrahedral site. The variation of the Curie temperature due to a variation of the distance between magnetic ions is evaluated. The contribution to the Curie temperature due to the magnetic carriers distribution is shown by plotting a single intercomposition hypothetic curve. In the same way the influence upon the magnetization value of the variation of the distance between magnetic ions has been evaluated. Results obtained on spinels have been compared with those deduced from literature data in the case of garnets.

Ground-state electronic properties of diamond in the local-density formalism

Abstract: We use our previously reported method for solving self-consistently the local-density one-particle equations in a numerical-basis-set linear combination of atomic orbitals expansion to study the ground-state charge density, x-ray structure factors, directional Compton profile, total energy, cohesive energy, equilibrium lattice constant, and behavior of one-electron properties under pressure of diamond. Good agreement is obtained with available experiment data. The results are compared with those obtained by the restricted Hartree-Fock model: the role of electron exchange and correlation on the binding mechanism, the charge density, and the momentum density is discussed. I. INTRODU(.'TION The local density functional (LDF) formalism of Hohenberg, Kohn, and Sham, " and its recent extension as a local spin-density functional formalism, ' form the basis of a new approach to the study of electronic structure in that the effects of exchange and correlation are incorporated directly into a charge- density- dependent potential term that is determined self -consistently from the solution of an effective one-particle equation. Applications of the LDF formalism to atoms+' and molecules' have yielded encouraging results. Similar applications for solids are complicated by (i) the need to con sider both the short-range and the long- range multicenter crystal potential having nonspherical components, (ii) the difficulties in obtaining full self-consistency in a periodic system, and (iii) the need to provide a basis set with sufficient variational flexibility. Hence, theoretical. studies of ground- state electronic properties of solids in the LDF formalism have been mainly l.imited to muffin-tin models for the potential, " non-selfconsistent schemes, ' treatments of simplified jellium models'0 or spherical cellular schemes We have recently proposed"" a general selfconsistent method for solving the LDF formalism one-particle equation for realistic solids using a numerical-basis-set LCAO (linear combination of atomic orbitals) expansi. on and retaining all nonspherical parts of the crystal potential. We have demonstrated a rapid convergence of the selfconsistent (SC) cycle when the treatment of the full crystal charge density is suitably apportioned between real- space and Fourier- transformed reciprocal-space parts and have indicated the large degree of variational flexibility offered by a nonlinearly optimized (exact) numerical atomiclike basis set. We have shown that all multicenter interactions as well as the nonconstant parts of the crystal potential are efficiently treated by a three- dimensional Diophantine integration scheme.

Atomic radii and lattice parameters of the A15 crystal structure

Abstract: Some properties of the lattice parameters a of the A15 (A 3 B) crystal structure are reinvestigated on the basis of the previously reported experimental data for about seventy compounds. The relation between these parameters and the atomic radii of A and B atoms ( r A and r B ) in the A15 structure is discussed. In f.c.c. transition elements, r B is equivalent to the atomic radius of the element. The value of r B for non-transition elements varies according to whether the A site element is in Group IVA, Group VA or Group VIA of the periodic table. There is a linear relationship between a and r B . Taking account of such relationships, a unique set of A15 atomic radii is determined. Lattice parameters of the A15 compounds are calculated using these atomic radii.

Theory of Anharmonic Lattice Vibration in Metallic Fine Particles. I

Abstract: \Ve apply the self-consistent Einstein moclel to the theory of anharmonic lattice vibration in metallic fine particles, and discuss the size dependence of the melting and superconducting transition temperatures in the connection to the softening of the surface lattice vibrations. Assuming a simple interatomic potential and certain distribution of the particle size, we express both transition temperatures as functions of the average radius of fine particles and show that the numerical results calculatecl from the theoretical expressions arc in fairly good accord with the experiments. § I. Introduction In a previous paper, one of the present authors has discussed, on the basis of a self-consistent Einstein model, that the atoms on the surface of metal crystal perform oscillations with much larger amplitudes compared with the interior at­ oms.]) The large surface lattice vibration is related to the softening of the fre­ quencies of the surface atoms and also closely related to the so-called surface relaxation of the lattice constant. Since the surface to volume ratio of metallic fine particles is increased with decreasing size, the surface softening should give appreciable effects in the various thermal properties of metallic fine particles vvith sufficiently small radii. Up to the present time, there are many accumulated ex­ perimental facts to sho1v that this is indeed the case. It has long been known for instance that the metallic fine particles have melting points much lower than those of the corresponding bulk metals. The first observation of this depression of the melting point was made by Takagi2l on Pb, Sn and I3i thin films by the use of the electron diffraction method. Since then similar observations have been reported, for example, on Sn by vVronski, 31 on Pb and In by Coombes, 41 on Au by Buffat and BorePJ and so on. This phenomena are undoubtedly due to the surface effects, and phenomenological theories based on the thermodynamic arguments have been presented. 61 A simple microscopic theory 1vas first proposed by one of the present authorsn with a pretty success in explaining the main experimental facts. This paper contains a sophistication of the previous theory. Another example of the phenomena 1vhich seem to be related with the surface

Paramagnetic Gd(IO3)3. Crystal structure of the transition metal iodates. IV

Abstract: Gd(IO3)3, type I, crystallizes in the monoclinic system with space group P21/a and four formulas in the unit cell. The lattice constants, at 297 °K, are a=13.4365(9), b=8.5226(5), c=7.1356(5) A and β=99.717(7) ° for λCuKα1=1.540598 A. A total of 5012 independent reflections were measured on a CAD‐4 diffractometer, using Nb‐filtered MoKα radiation. The crystal structure was solved using a combination of Patterson and Fourier series, and was refined by the method of least squares. The final agreement factor R is 0.033. The iodate ions form a three‐dimensional network based on shared oxygen atoms, with the Gd3+ ion located within a distorted dodecahedron of oxygen atoms. The three independent IO−3 ions form triangular pyramids, with three short I–O bonds of average length 1.803 A and average O–I–O angle of 98.7°. Each I atom has three additional oxygen neighbors at distances in the range 2.741–3.194 A that complete its distorted octahedron. Gd(IO3)3, type I is the archetype for an isostructural family of of ...

Anomalous frequency and temperature dependence of the optical absorption of small gold particles

Abstract: Size effects have been studied in Au particles of various sizes (102 to 105 atoms/particle), which were prepared in a glass matrix. Absorption measurements at 300 K and 1.5 K in the spectral region from 0.5 to 4.2 eV revealed three effects, when the particle size was reduced : (i) The spherical surface plasmon band is broadened ; the imaginary part of the dielectric constant of the particle material increases. (ii) The temperature dependence of the plasmon band goes to zero. (iii) The interband transition threshold is shifted to lower energies and the slope of the edge is diminished. Effects (i) and (ii) can be explained by assuming discrete electron energy levels, effect (iii) points to lattice parameter changes and/or an increase of indirect transitions.

Measurement of surface tension by lattice parameter changes: theory for faceted microcrystals

Abstract: A number of workers have estimated surface tensions of solids from measurements of the differences in the lattice parameters of bulk crystals and microcrystals. The data are then analysed by an expression valid only for spherical, isotropic microcrystals. The author discusses problems arising from the fact that real microcrystals are generally faceted. A general expression is given for the change in volume of a microcrystal for an arbitrarily anisotropic surface tension and arbitrary crystal habit; common special cases are also given. The discussion of the relation between the volume change and the change in X-ray lattice parameter includes the effects of the dispersions in crystalline sizes and shapes, and the possible non-uniformity in internal strain produced. It is concluded that any errors will be small.