Single-phase Polycrystalline Materials Research Articles

New Method of Modeling Infrared Spectra of Non-Cubic Single-Phase Polycrystalline Materials with Random Orientation

A new approach has been used to model optical properties of noncubic single-phase polycrystalline materials with random orientation and crystallites small compared to the resolution limit of light. This method has been applied to fresnoite (Ba2TiSi2O8) and proved to provide widely adequate results to effective medium approximation (EMA) and an excellent correspondence between simulated and measured spectra. In contrast to EMA, the new theory predicts that the deviation between damping constants of polycrystalline and single crystal fresnoite can be adjusted by one common factor for all damping constants. Based on EMA and the new model, much smaller damping constants have been determined for polycrystalline fresnoite compared to conventional dispersion analysis; the latter is able to provide a relevant dielectric function, but seems to be of little reliability concerning the determination of meaningful oscillator parameters due to the implicit assumption of an arithmetic average of the principal dielectric functions. This approximation, which can be derived in a similar form from EMA and is of widespread use, is shown to be inferior to an approximation based on the arithmetic average of the principal refractive indices.

Modelling IR spectra of single-phase polycrystalline materials with random orientation in the large crystallites limit$mdash$extension to arbitrary crystal symmetry

A formalism based on Yeh's 4 × 4 matrix algebra is developed to model reflectance and transmittance spectra of randomly oriented polycrystalline materials (sintered ceramics or glass ceramics) with arbitrary crystal symmetry provided that the crystallites are larger than the resolution limit of light. It may be applicable to powders, if the particle sizes are large compared to wavelength or show a broad distribution. The formalism is used to model the spectrum of polycrystalline fresnoite (Ba2TiSi2O8, optically uniaxial). The modelled and the measured spectra show a good correspondence, especially regarding peak position and form. Furthermore, approximations are derived for uniaxial crystal symmetry, which are superior to other approximations known from the literature such as the magic-angle arrangement. As a consequence of the formalism, randomly oriented polycrystalline materials consisting of ordered regions larger than the resolution limit should exhibit a non-zero cross polarization, despite being optically isotropic, which is proved experimentally. For an adequate interpretation of spectra of polycrystalline materials with non-cubic crystal symmetry, the particle size effect arising from the anisotropic crystal structure is demonstrated to be non-negligible.

Internal stress superplasticity in anisotropic polycrystalline materials

A theoretical model of internal stress superplasticity is developed in a single-phase polycrystalline material with an anisotropic thermal expansion. Quasi-steady-state creep equation during a thermal cycle is derived quantitatively based on continuum micromechanics. The model assumes that the generated mismatch strain is accommodated simultaneously by the plastic flow of the material. The linear creep deformation, which corresponds to internal stress superplasticity, is obtained at low applied stress region, and the creep rate depends on the crystallographic texture of the material. The validity of the model is experimentally verified using polycrystalline zinc which is a typical metal having large anisotropy in thermal expansion. The calculated strain rates using the texture information and the isothermal creep equation agree quantitatively well with the experimental results. The apparent activation energy of thermal cycling creep reveals 1/ n ( n: stress exponent of isothermal creep) of that of isothermal creep, which is one of the characteristics of internal stress superplasticity. Except for the factors attributable to the material geometry, the thermal cycling creep equation in the polycrystalline material is identical to that in a metal matrix composite.

Advanced Instrumentations for Interface Studies by Electron Energyloss Spectroscopy (EELS, ELNES and ESI)

Abstract Most materials used in technology are polycrystalline. Therefore, the properties of the internal interfaces often control the properties of the materials (interface-controlled materials). In single phase polycrystalline materials, grain boundaries are the internal interfaces (homophase boundaries) of interest, whereas in composites interfaces between different components (heterophase boundaries) play a crucial role. It is of great importance to investigate the structure, composition and bonding of the different interfaces. The atomistic structure of specific interfaces is obtained by high-resolution transmission electron microscopy studies, whereas analytical electron microscopy (AEM) investigations produce information on the composition of interfaces. AEM studies include energy-dispersive X-ray spectroscopy (EDX) as well as electron energy-loss spectroscopy (EELS). From the energy-loss near-edge structure (ELNES) of ionization edges measured by EELS, information on the local electronic structure at interfaces can be obtained. Information on bonding and its modifications by segregated atoms can be extracted from the ELNES studies.

Discontinuous grain growth in recrystallised vein quartz — implications for grain boundary structure, grain boundary mobility, crystallographic preferred orientation, and stress history

Grain growth is a process driven by the reduction of interfacial free energy, leading to an increase in grain size and a reduction of the number of grains in a given volume of a single phase polycrystalline material. Discontinuous grain growth (DCGG), as opposed to normal grain growth (NGG) involves just a few grains (blasts) growing at the expense of a matrix, that itself undergoes much slower modification in grain size, hence producing a bimodal grain size distribution as a transient state prior to impingement of the blasts. Such a transient state has been found in a quartz layer in metamorphic rocks of the Sesia Zone, Western Alps. There, large strain-free quartz grains occur that reveal concave outward grain boundaries against a matrix of small grains with a pronounced crystallographic and a weak dimensional preferred orientation. The misorientation of the blasts with respect to the matrix grains systematically exceeds 30°. This finding suggests that the mobility of high-angle grain boundaries in a natural quartzite depends on the degree of their misorientation (among other factors), as known for metals and alloys. The width of the grain boundaries must be sufficiently small to allow for this effect. DCGG is promoted by a pronounced crystallographic preferred orientation (CPO), that leaves only a few grain boundaries with sufficient misorientation to be mobile. In contrast to NGG, DCGG wipes out any pre-existing CPO and information on activated glide systems or kinematics during the preceding stage of flow is lost after DCGG has gone to completion. A complementary new CPO could even develop, that could be difficult to interpret. With respect to tectonic history, interfacial free energy driven grain growth reflects a period of low stress annealing and thus constitutes a first order signal.

A multiple-component order parameter phase field model for anisotropic grain growth

A phase field model for anisotropic grain growth is presented. The model uses multiple-component order parameters to describe the grain orientations. These order parameters are the structural amplitudes related to the star of the shortest reciprocal lattice vectors of the crystalline phase. The free energy of the system is formulated as a Landau expansion of the order parameters, which incorporates the symmetry of the crystalline phase. The spatial and temporal evolution of these order parameters is governed by the time-dependent Ginburg-Landau (TDGL) equations. In this model, the anisotropy is introduced naturally, since the effect of the underlying symmetry is taken into account in both the gradient and bulk terms in the free energy expansion. We consider a simple binary two-phase solid-liquid mixture in two dimensions with the solid having a square lattice. As an example, we studied the growth and morphology of a single solid particle in a liquid. Potential applications of the model to simulating the anisotropic grain growth in single-phase polycrystalline materials as well as in the presence of a liquid phase are discussed.

Superconducting YBa 2Cu 3O 7 − δ and YBa 2Cu 3O 7 − δ + Ag thick films by dip-coating on YBa 2HfO 5.5 ceramic substrate

YBa 2HfO 5.5 5 has been synthesised and sintered as a single phase polycrystalline material for use as a substrate for YBa 2Cu 3O 7 − δ films. Superconducting YBa 2Cu 3O 7 − δ and YBa 2Cu 3O 7 − δ + Ag thick films were fabricated by dip-coating the substrate at room temperature into a mixture of the 1–2–3 powder and n-butanol. Zero resistivity superconducting transitions, T c(0) = 92 K, were exhibited for both films after suitable heat treatments. The YBa 2Cu 3O 7 − δ and YBa 2Cu 3O 7 − δ + Ag films on YBa 2HfO 5.5 substrates gave critical current densities of 2 × 10 4 and 8 × 10 4 A/cm 2, respectively, at 77 K in zero magnetic field. The YBCO and YBCO-Ag films exhibited excellent adhesion to YBa 2HfO 5.5 substrates. Dip-coating was found to be one of the easiest methods for obtaining superconducting YBCO thick films of thickness as low as ≈2 μm.

Structural and physical properties of UFe 10Mo 2

UFe 10Mo 2 was obtained as single-phase polycrystalline material by annealing at 1450 K a polyphasic sample prepared by melting the elements. This compound was characterized by single-crystal X-ray diffraction, 57Fe Mössbauer spectroscopy and magnetization measurements. UFe 10Mo 2 was found to crystallize in the space group I4/ mmm with cell parameters a = 8.4859(3) A ̊ , c = 4.7508(2) A ̊ , V = 342.103(21) A ̊ 3, Z = 2 and a ThMn 12-type structure that was solved by single-crystal X-ray diffraction to a final R = 0.0345 ( wR = 0.0372). The Mo atoms are randomly distributed in the 8 i positions. Magnetization measurements show a ferromagnetic-like behaviour for T < 198 K and, in free powder, a saturation magnetization at low temperature of 8.8 μ B per formula unit. Comparison with fixed powder measurements indicates a basal plane type of anisotropy. 57Fe Mössbauer spectra below T c show a distribution of hyperfine fields from 0 to 20 T. This distribution was analysed considering the different local configurations around each Fe atom and assuming the Fe site distribution deduced from X-ray data.

Stabilization of superconducting LnPt 2B 2C by partial substitution of gold for platinum

The quaternary intermetallic compounds LnPt 2B 2C (Ln=La, Pr and Y) were recently shown to be superconducting at temperatures up to 10.5 K. Annealing conditions were not found, however, which yielded single-phase material. Here it is reported that the partial substitution of Au for Pt in LnPt 2B 2C yields essentially single-phase polycrystalline material under annealing conditions readily accessible by conventional techniques. This is accomplished through arcmelting LnPt 1.5Au 0.6B 2C, a composition slightly superstoichiometric in transition metal, and annealing at 1100°C in Ta foil: a small amount of melt phase formed in the anneal is wicked away from the sample leaving good-quality material behind.

Electrical and magnetic properties of oxygen deficient layered perovskite Sr 2VO 4−δ with δ=0.18, 0.29, 0.38

The effect of the oxygen deficiency δ on the electrical and magnetic properties of Sr 2VO 4−δ was investigated. Single phase polycrystalline materials of Sr 2VO 4−δ with δ=0.18, 0.29, 0.38 were synthesized with the solid state reaction. It was revealed by the Rietveld analyses of X-ray diffraction data that the tetragonal distortion of VO 6 octahedron increased with increasing δ. Electrical resistivity measurements showed that all the samples were semiconductive. In magnetic measurements, a spin glass-like behavior imposed by a large diamagnetism was observed at temperatures below about 33K. The diamagnetism became larger for larger δ. The spin glass-like behavior is considered due to the occurrence of the random magnetic field caused by the oxygen deficiency.

Entropy optimization in quantitative texture analysis. II. Application to pole-to-orientation density inversion

Anisotropic behavior of single-phase polycrystalline material is controlled by its constituent crystal grains and their spatial orientation within the specimen. More specifically, a macroscopic physical property in a given direction is the mean value of the corresponding property of the individual crystallites with respect to the statistical distribution of their orientations. Thus, the statistical orientation distribution is a mathematical approach of describing and quantifying anisotropy. Unfortunately, the orientation density function (ODF) can generally not be measured directly. Therefore, it is common practice to measure pole density functions (PDFs) of several distinct reflections in x-ray- or neutron-diffraction experiments with a texture goniometer. Recovering an ODF from its corresponding PDFs is then the crucial prerequisite of quantitative texture analysis. This mathematical problem of texture goniometry is essentially a projection problem because the measured PDFs represent integral properties of the specimen along given lines; it may also be addressed as a tomographic problem specified by the crystal and statistical specimen symmetries and the properties of the diffraction experiment itself. Mathematically, it reads as a Fredholm integral equation of the first kind and was conventionally tackled by transform methods. Because of the specifics of the problem, these are unable to recover the part of the ODF represented by the odd terms of the (infinite) series expansion. In this situation, more sophisticated iterative methods, especially finite-series-expansion methods were developed within which the required non-negativity of the ODF to be recovered plays the prominent role. An efficient way to guarantee non-negativity is to employ entropy optimization.

Directed reaction process producing single-phase superconducting compound YBa 2Cu 3O 6.5+σ

A directed reaction process (DRP) based on physico-chemical principles has been used for producing single-phase 90 K “zero- resistance” superconducting compound YBa 2Cu 3O 6.5+σ. The reliability of the DRP has been well proved by the stability and reproducibility of results in resistance and a.c. magnetic susceptibility measurements of samples taken randomly from five consecutive batches of products. The products were identified by X-ray diffraction as single-phase polycrystalline material of orthorhombic structure with lattice parameters a = 3.89A, b = 3.82A and c = 11.65A. The nonstoichiometric fraction, value, was determined to be + 0.27.

DIRECTED REACTION PROCESS AND STRUCTURAL STUDY OF SINGLE-PHASE SUPERCONDUCTING COMPOUND YBa2Cu3O6.5+δ

A directed reaction process based on physico-chemical principles has been designed for producing single-phase 90 K “zero-resistance” superconducting compound YBa2Cu3O6.5+δ. The reliability of the process has been well proved by the stability and reproducibility of results in resistance and AC magnetic susceptibility measurements of seven samples taken randomly from three batches of products. X-ray diffraction, SEM and TEM examinations have identified the product as single-phase polycrystalline material of orthorhombic structure with lattice parameters a=3.89 Å, b=3.82 Å and c=11.65 Å. Many micro-twinned defects were observed under TEM along [110] axes. The nonstoichiometric fraction, δ value, was determined using a physico-chemical method.

Structurization of single-phase polycrystalline materials based on cubic boron nitride

The authors study the crystallization of cubic boron nitrides by means of transmission electron microscopy and electron diffraction and the effects on crystal structure and microstructure of sintering, compacting, and heat treatment. Their results establish that the structurization of the nitrides is determined by structural phase transformations dependent on pressure and temperature and structural rearrangements through plastic deformation and relaxation in the initial and forming phases.

Synchrotron X-Ray Powder Diffraction

X-ray powder diffraction is one of the most widely used techniques by scientists engaged in the synthesis, analysis, and characterization of solids. It is estimated that there are now about 25,000 users throughout the world, of which about one third are in the United States. Any single-phase polycrystalline material gives an x-ray pattern which can be regarded as a unique “fingerprint,” and modern automated search-and-match techniques used in conjunction with the Powder Diffraction File (maintained by the International Center for Diffraction Data, Swarthmore, PA) allow routine analysis of samples in minutes. From an x-ray pattern of good quality it is possible to determine unit cell parameters with high accuracy and impurity concentrations of 1-5%, so that powder techniques are extremely valuable in phase equilibrium studies and residual stress measurements, for example. In addition, a detailed analysis of line shapes gives information about physical properties such as the size and shape of the individual crystallites, microscopic strain, and stacking disorder.In the early days of crystallography many simple (and some not-so-simple) structures were solved from x-ray powder diffraction patterns, but the obvious limitations to the number of individual reflection intensities which can be estimated and the increasing sophistication of single-crystal techniques resulted in a decline in the importance of this application in the 1950s and 1960s.

The Influence of Structure on the Corrosion of Glassy Copper-Zirconium Alloys

Abstract Differences in structure between crystalline and glassy copper-zirconium alloys lead to subtle increases in the corrosion rate of crystalline compared to glassy material. Glassy alloys of Cu60Zr40 were melt spun and subsequently devitrified, yielding single phase polycrystalline material. Comparing the potentiodynamic polarization response of these structural types revealed no significant difference in ϕcorr. ba, bc, icorr. and io. Other alloys, Cu58Zr42 and Cu55Zr45, compared in glassy and crystal-line forms revealed that inhomogeneity, caused by precipitation of a second phase, did not alter the corrosion behavior from that of single phase Cu60Zr40. Corroded glassy surfaces were generally smooth except for scattered hemispherical features, while crystalline surfaces were densely populated with these features. Corrosion of copper-zirconium alloy occurs by the selective dissolution of zirconium in the vicinity of ϕcorr, whereas, at potentials noble to −0.1 VSCE, copper contributes to the anodic current. Above approximately 0.0 VSCE the alloys passivate. Results of potentiodynamic polarization studies suggest that for these alloys, unlike transition metal-metalloid glasses, devitrification does not significantly affect the corrosion kinetics of copper-zirconium alloys.

Spinel-Type Ferrites Containing Florine

Charge compensation by substituting univalent fluorine for divalent oxygen in spinel type ferrites was studied by preparing and analyzing single-phase polycrystalline materials. Starting with a 1:1 molar ratio of divalent fluorides and Fe2O3, charge compensation was mainly achieved by metal vacancies, although some Fe2+ was also present. The preparative method, unit cell dimensions, chemical compositions, magnetic moments at 90°K and Curie points for these compounds are given. Their properties can be interpreted as those of solid solutions of mainly γ-Fe2O3 and a stoichiometric fluorine ferrite M22+Fe3+O32−F−, where M is Mg, Mn, Co, Ni, or Zn.

Explosion of carbonic acid in a coal mine

Stereological relations that can be routinely applied for the quantitative characterization of microstructures of heterogeneous single- and two-phase materials via global microstructural descriptors are reviewed. It is shown that in the case of dense, single-phase polycrystalline materials (e.g., transparent yttrium aluminum garnet ceramics) two quantities have to be determined, the interface density (or, equivalently, the mean chord length of the grains) and the mean curvature integral density (or, equivalently, the Jeffries grain size), while for two-phase materials (e.g., highly porous, cellular alumina ceramics), one additional quantity, the volume fraction (porosity), is required. The Delesse–Rosiwal law is recalled and size measures are discussed. It is shown that the Jeffries grain size is based on the triple junction line length density, while the mean chord length of grains is based on the interface density (grain boundary area density). In contrast to widespread belief, however, these two size measures are not alternative, but independent (and thus complementary), measures of grain size. Concomitant with this fact, a clear distinction between linear and planar grain size numbers is proposed. Finally, based on our concept of phase-specific quantities, it is shown that under certain conditions it is possible to define a Jeffries size also for two-phase materials and that the ratio of the mean chord length and the Jeffries size has to be considered as an invariant number for a certain type of microstructure, i.e., a characteristic value that is independent of the absolute size of the microstructural features (e.g., grains, inclusions or pores).