Showing papers on "Lattice constant published in 1969"
TL;DR: In this paper, the lattice parameter of pure pure Cu is 3.61491 A (corrected for refraction), and thermal expansion coefficient α = 14.87 × 10−6°C−1 between 15 and 55°C.
Abstract: Spectroscopically pure Cu has a lattice parameter a25 = 3.61491 A (corrected for refraction), and a thermal expansion coefficient α = 14.87 × 10−6°C−1 between 15 and 55°C. The measured density d25 is 8.9314 ± 0.0002 g.cm−3 in agreement with the calculated value dx = 8.9316. In the α solid solution region additions of In increase the lattice parameter of Cu according to ax = 3.6149 + 0.0091x up to x = 10.4 (x = atomic % In, balance Cu). The thermal expansion coefficients between 15 and 65°C of the homogeneous alloys increase from 14.87 (pure Cu) to 17.2 × 10−6°C−1 at the solid solubility limit (10.4 atomic % In, quenched from 650°C). With the increase of In content the experimental densities become increasingly lower than the calculated ones because of void formation. Upon cold rolling the voids close and the differences disappear. The α phase represents a substitutional solid solution without structural defects. Alloys quenched from the liquid state do not show any microporosity; the voids appear after homogenization at 800°C. Micropore formation is explained by differential shrinkage of the various crystalline fractions formed during solidification, giving rise to internal stresses in the solid alloy. Relief of stresses results in vacancies or micropores, which coalesce into voids upon heat treatment.
258 citations
TL;DR: Ferroelectric Ba(4+x)Na(2 − 2x)Nb10O30, with a Curie temperature of 833°K, has a tungsten bronze-type structure and crystallizes in the orthorhombic system as mentioned in this paper.
Abstract: Ferroelectric Ba(4+x)Na(2 − 2x)Nb10O30, with a Curie temperature of 833°K, has a tungsten bronze‐type structure and crystallizes in the orthorhombic system, with subcell lattice constants a = 17.59182 ± 0.00001, b = 17.62560 ± 0.00005, and c = 3.994915 ± 0.000004 A at 298°K. The space group is Cmm2, and there are two formulas in the subcell. The c axis of the true cell is double that of the subcell. The integrated intensities of 6911 reflections within a reciprocal hemisphere of radius (sinθ)/λ = 1.02 A−1 were measured with PEXRAD, 1873 symmetry‐independent structure factors being significantly above background. The metal atom positions were determined from the three‐dimensional Patterson function and the oxygen atoms from metal‐phased Fourier series. The final agreement index between measured and calculated structure factors is 0.0579. The structure differs only in detail from previously determined tetragonal tungsten bronze structures. In the general formula (A1)2(A2)4C4(B1)2(B2)8O30, the B1 and B2 sites are fully occupied by Nb, the A2 sites by Ba and the A1 site by 87.0% Na and 6.5% Ba. Evidence from chemical analysis, x‐ray density calculations and the present determination suggests that the best approximation to the formula of the crystal studied is Ba4.13Na1.74Nb10O30. The Ba and O atoms at z ≃ 12 are disordered in a manner similar to the O atoms in the Ba layer in barium strontium niobate. The four crystallographically independent Nb atoms, each in octahedral coordination, are linked to O atoms by distances ranging from 1.765 ± 0.021 to 2.270 ± 0.021 A, with a mean value of 1.989 A. Ba is 10 coordinated, with Ba–O distances ranging upward from 2.671 ± 0.013 A. Na is 12 coordinated, with Na–O distances ranging from 2.660 ± 0.014 to 2.990 ± 0.015 A, with a mean of 2.788 A. The Nb‐atom displacements from the mean oxygen planes lie in the range 0.171–0.205 A; the parabolic relation with Curie temperature predicts a displacement of 0.204 A. The measured value of Ps at room temperature is 40 μC cm−2: the linear relation between displacement and polarization predicts a saturation value of 44–53 μC cm−2. All metal atoms are displaced from the oxygen planes in the sense given by the macroscopic positive polarity.
228 citations
TL;DR: In this article, solid solutions between two hexagonal end members, such as Fe2P or Ni2P with Mn2P, may exhibit orthorhombic structures at intermediate compositions.
Abstract: Several phosphides with the chemical formula M2P crystallize in a hexagonal structure: Mn2P, Fe2P, and Ni2P. The structure of Co2P is orthorhombic. These two structures are related via an identical elementary subcell consisting of a tetrahedral‐site and a pyramidal‐site M‐atom pair. This investigation shows that solid solutions between two hexagonal end members, such as Fe2P or Ni2P with Mn2P, may exhibit orthorhombic structures at intermediate compositions. Fe2P shows complete solid solubility with Ni2P. Curiously, hexagonal and orthorhombic symmetries alternate with decreasing number of 3d electrons, Ni2P(hex) ‐Co2P(ortho) ‐Fe2P(hex) ‐FeMnP(ortho) ‐Mn2P(hex). Lattice parameter variations with composition and Mossbauer studies reveal atomic ordering in the mixed systems, Mn and Cr substituting for pyramidal‐site iron in FeMnP and FeCrP while Ni and Co substitute preferentially for tetrahedralsite iron in FeCoP and FeNiP. While neither Co2P nor Mn2P are ferromagnetic, intermediate phases are, the Curie te...
214 citations
TL;DR: In this paper, the lattice constants and the atomic position parameter, z, of a high purity, low strain, single-crystal of arsenic have been determined using low extinction reflections of filtered Mo Kα and Ag Kα radiation.
Abstract: The lattice constants and the atomic position parameter, z, of a high purity, low strain, single-crystal of arsenic have been determined. Low extinction reflections of filtered Mo Kα and Ag Kα radiation were used for the determination of z. The Bond precision technique with Mo Kα radiation was used for the determination of the unit-cell dimensions a and c. Average values for a and c in A, and for z are: 4.2°K z = 0.22764 a = 3.7597 c = 10.4412; 78°K z = 0.22754 a = 3.7595 c = 10.4573; 299±3°K z = 0.22707 a = 3.7598 c = 10.5475. The estimated standard deviation of z is ±0.00004 at 4.2°K, ±0.00002 at 78°K and ±0.00005 at 299°K. The precision of a is estimated to be ±0–0001 A and that for c to be ±0.0002 A. The results for As are compared with those reported earlier for Sb and Bi.
208 citations
190 citations
TL;DR: BaMnF4, pyroelectric at room temperature and paramagnetic above 30°K, crystallizes in the orthorhombic system with space group A21am and lattice constants a
Abstract: BaMnF4, pyroelectric at room temperature and paramagnetic above 30°K, crystallizes in the orthorhombic system with space group A21am and lattice constants a = 5.9845 ± 0.0003, b = 15.098 ± 0.002, and c = 4.2216 ± 0.0003 A at 298°K. The integrated intensities of 5085 reflections within a reciprocal lattice hemisphere of radius (sinθ) / λ = 1.02 A−1 were measured using pexrad. The crystal structure has been solved and refined by a combination of Patterson and Fourier series and the method of least squares, using 455 independent and significantly nonzero F(meas). The final agreement factor R, for atoms with anisotropic temperature coefficients, is 0.0466. The structure consists of MnF6 octahedra sharing corners to form puckered sheets parallel to (010). These sheets are linked by Ba2+ ions only, giving rise to excellent (010) cleavage. Within the sheets there are nearly linear –Mn–F–Mn–F– chains parallel to c. Parallel to a there is a second set of planar zigzag –Mn–F–Mn–F– chains, formed by adjacent shared ...
166 citations
TL;DR: In this paper, the lattice constants of yttrium and gadolinium iron and gallium garnets were measured in the temperature range 296-1400°K and the results showed that among these, GdGaG gave the closest match of Δa/a0 vs. T to YIG and to GdIG.
Abstract: Lattice constants of yttrium and gadolinium iron and gallium garnets and of yttrium aluminium garnet have been measured in the temperature range 296–1400°K. The results show that among these, GdGaG gives the closest match of Δa/a0 vs. T to YIG and to GdIG.
118 citations
TL;DR: In this article, the magnetic moment decreases very sharply from 1.3µ B in 30 at% Ni to 0.2 µ B in 20 at%Ni and the Mossbauer absorption spectra observed at liq. He temperature show the appearance of antiferromagnetism in the low nickel concentration range.
Abstract: Magnetization, Mossbauer absorption spectra and lattice constants have been measured on the γ phase (f.c.c.) Fe-Ni alloys of 20∼30 at% Ni using finely grained samples in which the γ→α martensitic transformation can be suppressed even at liq. He temperature. The magnetic moment decreases very sharply from 1.3µ B in 30 at% Ni to 0.2µ B in 20 at% Ni. The Mossbauer absorption spectra observed at liq. He temperature show the appearance of antiferromagnetism in the low nickel concentration range. These experimental facts indicate that in these composition range the alloys consist magnetically of two phases, namely ferromagnetic and antiferromagnetic ones. This magnetic heterogeneity is caused by the statistical concentration fluctuation and is discussed quantitatively by considering a Gaussian type concentration distribution. The temperature and composition variations of the lattice constant and the thermal expansion coefficient can also be interpreted quantitatively on the basis of the same Gaussian type conce...
112 citations
TL;DR: The relative heat of formation and the reduced melting temperatures of the lanthanide compounds are correlated with the magnitude of the contraction in these compounds relative to the contraction of the pure metals.
Abstract: The relative heats of formation and the reduced melting temperatures (the melting point of the compound divided by the melting point of the metal) of the lanthanide compounds are correlated with the magnitude of the lanthanide contraction in these compounds relative to the lanthanide contraction in the pure metals If the lanthanide contraction (as determined from the lattice constants) in the compounds is greater than that observed for the metals, the heat of formation is expected to increase as one proceeds from lanthanum to lutetium The opposite is expected if the lanthanide contraction is less in the compounds than in the metals This has been substantiated for the five series for which sufficient thermodynamic data exist, specifically, RCd, RCl 3 , RH 2 , RMg and R 2 O 3 For the melting points, 15 of 17 lanthanide compound series show agreement between the observed reduced melting points and that expected from the relative lanthanide contraction Discrepancies are more likely to occur when correlating the melting points, since only part of the various bonds, RM, MM and RR, are broken upon melting, than for the heats of formation since this quantity is a measure of forming all of the bonds in the crystal
108 citations
TL;DR: The structure of vaterite can be considered as a disordered stacking sequence of single layers of trigonal symmetry which are mostly related by glide reflections and sometimes by a screw operation as mentioned in this paper.
Abstract: Single-crystal photographs of vaterite (/1 CaC03) show numerous diffuse streaks II e* with maxima which require an increase in the previous lattice parameter a by a factor -y3 to 7.15 A, and doubling (sometimes trebling) of e to 16.94 A; moreover satellite reflections were observed. The structure of vaterite can be considered as a disordered stacking sequence of single layers of trigonal symmetry which are mostly related by glide reflections and sometimes by a screw operation lie. Sequences of two layers AA' and of four layers AA'BB' may be considered as states of order which are approached; the partial sequences ABAB and A'B'A'B' correspond to the principle of the hexagonal closest packing. For a more exact treatment one has to consider the deformations of the primitive hexagonal partial lattice array of the calcium atoms also. The average structure agrees in general with KAMHI'S proposal; but the C03 group has to be centered around (i) of space group P 63/mme with an occupancy of one sixth only. The least-squares refinement reduced R to 0.115. The oxygen atoms form distorted cubes around the calcium atoms. Conclusions are drawn concerning the structures of rare-earth borates and of the bastnaesite-vaterite series.
98 citations
TL;DR: In this article, a strong correlation exists between both A0 and E in the Arrhenius expression for the exchange reaction and corresponding functions for N2O decomposition, since these functions vary in a regular manner with lattice parameter.
TL;DR: In this paper, the effect of a mixed crystal transition zone (grading) on the perfection of crystals grown by epitaxial deposition onto substrates of differing lattice parameter and expansion coefficient is considered.
Abstract: The effect of a mixed crystal transition zone (grading) on the perfection of crystals grown by epitaxial deposition onto substrates of differing lattice parameter and expansion coefficient is considered. The number of misfit dislocations required to compensate lattice mismatch at the growth temperature and magnitude of bending stresses which develop during subsequent cooling have been computed as a function of the width of the transition zone δ. These results have been applied to the case of GaP grown onto GaAs seeds. Using a simple model for lattice displacements, it is predicted that grading does not reduce the number of misfit dislocations but merely distributes them over the width δ so that the density is reduced in proportion to δ−1. The bending stresses in the grown layer are shown to be highly dependent on the width of the transition zone and thickness of the grown layer. Moreover, for a given seed thickness and zone width there is an optimum thickness for the growth layer for which the bending stress is smallest.
TL;DR: In this paper, the anisotropic lattice is reduced to an isotropic one, in which each lattice point represents N* units (segment) along the chain axis of the reduced lattice [N = 2(f/g)1/2], where Vibrational modes correspond to interchain modes of the original lattice, i.e., modes whose frequencies are governed by interchain potential.
Abstract: Polymer crystals are characterized by strong anisotropy of binding forces among units, i.e., the intrachain force constant f is much larger than the interchain force constant g. The anisotropic lattice is reduced to an isotropic one, in which each lattice point represents N* units (segment) along the chain axis of the anisotropic lattice [N = 2(f/g)1/2]. Vibrational modes of the reduced lattice correspond to interchain modes of the original lattice, i.e., modes whose frequencies are governed by interchain potential. Anharmonicity of crystalline force field is assumed to be related predominantly with interchain force alone. Thermodynamic and transport equations for a simple lattice are applied to the reduced, isotropic lattice, and numerical results are obtained for high-density polyethylene. The Gruneisen constant γ was obtained from the pressure dependence of sound velocity. The heat capacity of the reduced lattice, Cinter (interchain specific heat), was calculated from Gruneisen's equation, α = γβCinter (where α = thermal expansion coefficient, β = compressibility), and the mass of a segment m* was estimated from Dulong-Petit's equation, Cinter = 3ρk/m* (where ρ = density, k = Boltzmann constant). The value of m* is consistent with N* from force constants, m* = N*m (where m = mass of a unit in the original lattice). m*θ3 (where θ denotes the Debye temperature of the reduced lattice) is calculated from low temperature specific heat. The value of m* calculated from m*θ3 and θ from other sources agrees with that from the estimate by Dulong-Petit's equation. The high-temperature thermal conductivity K was calculated through Leibfried-Schloemann's equation by employing γ and m*θ3 as estimated as described above; satisfactory agreement was obtained with experiment. Poly(methyl methacrylate) and polystyrene were also studied by similar methods.
TL;DR: In this article, the optical constants n and? of crystalline C6, n-type SnSe2, at 290 and 77?K, have been measured over the photon energy range 0?05-3?7 ev.
Abstract: The optical constants n and ? of crystalline C6, n-type SnSe2, at 290 and 77 ?K, have been measured over the photon energy range 0?05-3?7 ev. An analysis of the absorption measurements indicates that the intrinsic SnSe2 absorption edge (at 77 ?K) arises from forbidden indirect transitions across energy gaps of less than or equal to 1?03 and 1?30 ev, and allowed direct transitions across an energy gap of 1?97 ev; the direct transitions give rise to an inflexion in the spectral distribution of 2, the imaginary part of the dielectric constant. The crystal birefringence ? (at a wavelength of 1 ?m) has been determined, and the electrical conductivity Eperpendicularc and lattice parameter a0 measured over the temperature range 77-290 ?K. The properties of SnSe2 are compared with those of other isostructural IV-VI compounds.
TL;DR: The body-centered cubic Pu 2 C 3 -type structure of yttrium sesquicarbide has been prepared in high yield by high pressure-high temperature techniques as discussed by the authors.
Abstract: The body-centered cubic Pu 2 C 3 -type structure of yttrium sesquicarbide, Y 2 C 3 , has been prepared in high yield by high pressure-high temperature techniques Lattice parameter measurements indicate a homogeneity range for the compound Magnetic susceptibility measurements show the material is superconducting over the entire homogeneity range with the superconducting transition temperature varying from a low of 60 °K to a high of 115 °K High temperature-ambient pressure annealing of samples prepared by the high pressure-high temperature techniques destroyed the Pu 2 C 3 -type structure No superconducting transition was observed on the annealed samples for measurements down to 20 °K
TL;DR: In this article, two types of dislocations are grown into GaAs1−xPx epitaxial crystals and their effects on photoluminescence efficiency are studied.
Abstract: Dislocations, their origins, and their effects on photoluminescence efficiency have been studied in GaAs1−xPx single crystals grown by vapor phase epitaxy. Dislocations were observed using etch pit, optical‐transmission microscopy, and x‐ray topography techniques. Two types of dislocations are grown into GaAs1−xPx epitaxial crystals. Near the GaAs (substrate)‐GaAs1−xPx interface a high density (>108 cm−2) of pure edge dislocations with axes and Burgers vectors lying in the growth plane was observed. These originate from the lattice parameter mismatch between substrate and epitaxial layer. In the bulk GaAs1−xPx, a high density (∼106 cm−2) of dislocations was observed with 〈211〉 and 〈100〉 directions and Burgers vectors parallel to those of the mismatch dislocations. These dislocations originate from the mismatch dislocations at the substrate‐epitaxial layer interface. The effect of dislocations on photoluminescence efficiency was studied by a novel technique. The photoluminescence was excited by focusing a ...
TL;DR: The lattice parameters of the martensite and the face-centered cubic phase (austenite) were determined for a series of Fe-Ni alloys in this article, with compositions ranging from pure Fe to Fe-35 at.% Ni.
Abstract: The lattice parameters of the body‐centered cubic phase (martensite) and the face‐centered cubic phase (austenite) were determined for a series of Fe–Ni alloys. Compositions ranged from pure Fe to Fe‐35 at.% Ni. Careful film and diffractometer Debye‐Scherrer techniques on powder and bulk samples and computerized calculations and error analyses were employed. Results indicate that the martensite lattice parameter reaches a maximum between 10 and 20 at.% Ni and the room‐temperature lattice parameter of the face‐centered cubic phase has a maximum in alloys having greater than 35 at.% Ni.
IBM1
TL;DR: In this article, two series of self-consistent energy-band calculations in lithium by the augmented plane-wave (APW) method are reported, and a virial theorem is derived which is valid for Hartree-Fock-Slater calculations in solids, and the numerical results in fact satisfy the virial expression.
Abstract: Two series of self-consistent energy-band calculations in lithium by the augmented-plane-wave (APW) method are reported. The first used the exchange approximation proposed by Slater; the second used two-thirds of this quantity, as proposed by Gaspar, Kohn, and Sham. In each series, the lattice constant was varied, and the total energy was found as a function of this parameter. From this, the equilibrium lattice constant, the cohesive energy, and the compressibility were found. These quantities differ markedly for the two exchange approximations used, and roughly bracket the experimental values. A virial theorem is derived which is valid for Hartree-Fock-Slater calculations in solids, and it is shown that the numerical results in fact satisfy the virial expression.
TL;DR: In this paper, structural phase changes in K 2 SeO 4 have been found at 129.5°K and 93°K by introducing free radical SeO4 -as a probe.
Abstract: Structural phase changes in K 2 SeO 4 have been found at 129.5°K and 93°K by introducing free radical SeO 4 - as a probe. The structure in the temperature range between 129.5°K and 93°K is expected to be orthorhombic with the crystallographic axes coincident with those of room temperature. The unit cell may contain twelve molecules located at three different sites. A superstructure, a tripled lattice parameter along the a axis, has been found by X-ray diffraction method and an expected space group is Pnam . It is ferroelectric along the c axis below 93°K. A possible unit cell contains twelve molecules located at six different sites and is monoclinic in the space group P 2 1 , in which the superstructure is maintained. The crystal probably consists of fine twins with the common c axis and they are related with each other by mirror planes. The higher transition is of second order and the lower of first order. Conformations of radicals SeO 2 - and SeO 3 - in the crystal lattice are illustrated.
TL;DR: In this paper, the phase relation and electric and magnetic properties of Li x V 2−x O 2 were studied in the temperature range from liquid helium to 400°C, and the one phase region was determined to be in the range of 0.8≤x≤1.2 in Li xV 2−X O 2.
TL;DR: In this article, the gadolinium-cobalt system has been investigated over the whole concentration range by means of X-ray diffraction, thermoanalysis, and metallography.
Abstract: The gadolinium-cobalt system has been investigated over the whole concentration range by means of X-ray diffraction, thermoanalysis, and metallography. Eight intermetallic compounds have been observed: Gd3Co, GdxCo (with x≈ 7 4 ), Gd4Co3, GdCo2, GdCo3, Gd2Co7, GdCo5 and Gd2Co17. The compounds Gd2Co7 and Gd2Co17 show a structure transformation. For all compounds except GdxCo the lattice constants and the structure type are given. The compounds GdCo5 and Gd2Co17 possess large homogeneity regions at elevated temperatures. For GdCo5, the variation of the saturation moment and the coercive force within the homogeneity region have been studied. High values for the coercive force (up to 43,000 Oe) have been observed for some of the other gadolinium-cobalt compounds.
TL;DR: In this paper, the detailed kinetics of the film growth as revealed by the moire fringes are discussed in the light of growth mechanisms, and the lattice spacing anomalies in pseudomorphic overgrowth have been examined by means of high-resolution still-electron m...
Abstract: Growth processes of metallic vacuum deposits, Ag and Au, and nonmetallic deposits, PbS and PbSe, on MgO and MoS2 substrates have been studied by means of direct cine recording of electron micrographs resolvable down to 17 A moire spacing. The detailed kinetics of the film growth as revealed by the moire fringes are discussed in the light of growth mechanisms. The main differences between the metallic and nonmetallic film growths are the absence, in the cases of nonmetallic film growth, of “liquid-like” behavior during coalescence, and lack of the secondary nucleation, which are known to be very important in metallic film growth. Growth processes of so-called multiply-twinned particles and twin formation and release in the metallic film growth have also been studied. The direct observation of formation of pseudomorphic interfacial dislocations was carried out in the case of PbSe on PbS. The lattice spacing anomalies in pseudomorphic overgrowth have been examined by means of high-resolution still-electron m...
TL;DR: An extensive study has been made on the growth and characterization of singlecrystal magnesium aluminate spinel as mentioned in this paper, which has received attention as a superior substrate for epitaxial silicon-integrated electronic devices.
Abstract: An extensive study has been made on the growth and characterization of single‐crystal magnesium aluminate spinel. This material has received attention as a superior substrate for epitaxial silicon‐integrated electronic devices. Large spinel single crystals within the compositional range MgO:Al2O3–MgO:3Al2O3, have been successfully grown by flame fusion using a modern three‐tube post‐mix‐type Verneuil burner. Substrate wafers of (111), (100), and (110) orientations were prepared for silicon epitaxy. Surface preparation of the substrates was studied, including mechanical polishing, hydrogen annealing, and chemical etching. The composition, lattice parameter, crystalline perfection, mechanical hardness, thermal stability, and dielectric properties of the spinel single crystals have been characterized by various techniques in an effort to obtain a basic understanding for substrate use of this material system. Some trends in the dependence of these properties on composition were observed. In particular, the th...
TL;DR: In this article, it was shown that at a critical thickness (∼200-300 A), there is a transformation from the fcc phase to the normal hcp phase in deposits on the (001) and (111) substrate surfaces.
Abstract: Single crystal thin films of titanium have been epitaxially grown on NaCl substrates of three different orientations [(001), (110), (111)]. At thicknesses above 500 A, the normal hexagonal close-packed structure is obtained. Below approximately 350 A, the metal is seen to grow in a previously unreported face-centered cubic structure with the lattice parameter, ao = 4.33 A. This structure is thought to result from pseudomorphic type growth on the NaCl substrate in keeping with proposed misfit theories. At a critical thickness (∼200–300 A), there is a transformation from the fcc phase to the normal hcp phase in deposits on the (001) and (111) substrate surfaces. The deposit on the (110) NaCl surface demonstrated a coexistence of fcc and hcp material at all thicknesses.
TL;DR: In this paper, the argon-krypton mixture crystallized into a single face-centred cubic phase whose lattice parameter depended in a non-linear manner on the atomic concentration of argon in the mixture and was intermediate between the lattice parameters of the two pure components.
Abstract: Gaseous mixtures of argon with krypton, and of argon with neon, were condensed on to substrates held at 7°K inside an electron diffraction camera. Diffraction studies of the deposits so formed were subsequently carried out with 50 kv electrons. The argon-krypton mixture crystallized into a single face-centred cubic phase whose lattice parameter depended in a non-linear manner on the atomic concentration of argon in the mixture and was intermediate between the lattice parameters of the two pure components. The argon-neon mixture crystallized into two separate phases, one consisting of crystals of pure neon, the other being very disordered and probably consisting principally of argon. These results are discussed with reference to a theoretical model of binary mixtures proposed by Prigogine and by Scott.
TL;DR: In this paper, the crystal structure of the interstitial solid solution of alpha titanium-oxygen system has been investigated by a combined method of electron, neutron and X-ray diffraction as functions of composition and annealing temperature.
Abstract: The crystal structure of the interstitial solid solution of alpha titanium-oxygen system has been investigated by a combined method of electron, neutron and X-ray diffraction as functions of composition and annealing temperature. The existence of two-types of interstitial superstructure has been established over nearly the whole composition range below the critical temperature. One of them designated as α' has a layer-ordered structure of the anti-Cd(OH) 2 type (space group P \bar3 m 1) involving out-of-steps with regard to oxygen distribution. The other is a low-temperature form α'' which has a trigonal symmetry (space group P \bar31 c ) with the cell dimension of \(a{=}\sqrt{3}a_{0}\) and c =2 c 0 ( a 0 and c 0 are the lattice constants of the original h.c.p. cell). The oxygen distribution in this phase is generally specified in terms of composition dependent parameters of occupation probabilities for the three octahedral interstitial sites 2(a), 2(c) and 2(d). The structure of α'' at a special composit...
TL;DR: In this article, the spontaneous volume magnetostriction of metallic ferromagnets is discussed based on the band theory and the dependence on lattice parameters of the band width and of the molecular field coefficient are taken into account.
Abstract: The spontaneous volume magnetostriction of metallic ferromagnets is discussed based on the band theory. Dependences on lattice parameter of the band width and of the molecular field coefficient are taken into account. The difference between the lattice parameters in the ferromagnetic and paramagnetic states at 0°K is expressed in terms of the difference between the energies in the ferromagnetic and paramagnetic states. It is understood qualitatively why the absolute value of negative spontaneous volume magnetostriction ( e.g. in Ni) is generally small while that of positive one ( e.g. in Invar) is sometimes large. By assuming a simple but reasonable density of states curve for fcc Fe–Ni alloys the spontaneous volume magnetostriction of the alloys is calculated. The calculated value for Invar alloy is seven times larger than that for Ni metal in absolute value; the agreement with experimental results is satisfying.
TL;DR: In this article, a paramagnetic α−Nd2(MoO4)3, prepared below the transition temperature of 960°C, crystallizes in a subtle variant of the scheelite structure.
Abstract: Paramagnetic α‐Nd2(MoO4)3, prepared below the transition temperature of 960°C, crystallizes in a subtle variant of the scheelite structure. The lattice constants of the basic tetragonal unit cell are a = 5.298 ± 0.007 and c = 11.705 ± 0.023 A, with space group I41/a and 43 of a Nd2(MoO4)3 formula per unit cell. The ordered distribution of two Nd atoms over every three available sites results in additional weak scattering corresponding to a monoclinic unit cell with a = 27.02, b = 11.705, and c = 11.85 A, with β = 105.3°, space group C2. The integrated intensities of 2490 scheelitelike reflections within a reciprocal hemisphere of radius (sinθ) / λ = 1.02 A−1 were measured with PEXRAD, of which 198 were independent and above background. Refinement of the atomic positions, assuming a statistical distribution of 23 Nd on each scheelite 4b site, resulted in an agreement factor between measured and calculated structure factors of 0.0375. Each Nd atom is dodecahedrally coordinated to eight oxygen atoms, with four Nd–O distances of 2.492 ± 0.010 A and four others of 2.509 ± 0.011 A. Each Mo atom occupies a tetrahedron of oxygen atoms, with four identical Mo−O distances of 1.800 ± 0.011 A. An arrangement of Nd atoms and vacancies in the monoclinic cell giving a predicted scattering pattern in satisfactory agreement with observation is presented.
TL;DR: In this paper, the precision of relative lattice parameter determinations by X-ray Bragg reflexion is reduced to a few parts in 10$^7$ by the dispersed profiles of single spectral lines.
Abstract: The precision of relative lattice parameter determinations by X-ray Bragg reflexion is usually limited to a few parts in 10$^7$ by the dispersed profiles of single spectral lines. In a new technique described herein this primary limitation is removed because changes of Bragg angle are measured in a non-dispersive double crystal arrangement. As a result it is shown that lattice parameter changes of one part in 10$^9$ can be detected. Preliminary measurements of the lattice parameter difference between a highly doped silicon sample and an undoped silicon crystal are in good agreement with measurements obtained on the same material by conventional techniques. The influence of experimental parameters on the sensitivity of the technique are considered in detail and some convenient developments of the basic method are suggested.
TL;DR: In this article, thermal expansion and magnetostriction measurements on single-Q, single-crystal chromium give the lattice parameter ratios in the transverse spin-density wave phase, through the spin-flip transition, and in the longitudinal spin density wave phase.
Abstract: Thermal‐expansion and magnetostriction measurements on single‐Q, single‐crystal chromium give the lattice parameter ratios in the transverse spin‐density‐wave phase, through the spin‐flip transition, and in the longitudinal spin‐density‐wave phase. The spin‐flip transition is found to be accompanied by anisotropic discontinuities in length, resulting in a net volume dilatation of 1.4×10−6 with decreasing temperature. The Q direction is found to be the longest axis at 300°K and to bcome the shortest axis below about 220°K.