Method Of Inverse Pole Figures Research Articles

TEXTURAL AND STRUCTURAL REGULARITIES OF DEFORMATION BY ROLLING OF Zr-2.5%Nb ALLOY

A review of studies of regularities of changes in the crystallographic texture of the longitudinal and cross rolling of the Zr-2.5%Nb alloy is given. Accordingly with this, plates were made from longitudinal fragments and rings of a tube 15.01.5 mm from the fuel assemblies of Russian RBMK reactors. The plates were annealed at 580 °C for 3 h. X-ray studies of texture changes with the degree of deformation of the plates by rolling were carried out. The principle of method of inverse pole figures was used with the calculation of the Kearns texture coefficients, as well as measurements of tilt curves (0002) was. Non-uniformiity of deformation during straightening of the tube blanks was taken into account. It is found that the main rotations of crystallographic c-axes in the plates at any rolling direction are carried out in the plane corresponding to the cross-section of the original tube. Existence of an initial stage of increased textural changes during deformation of the plates is found, what is qualitatively and quantitatively related to activity of tensile twins of the {1012}[1011] system. Regularities in texture changes at the subsequent moderate stage of deformation with the participation of compression twins are considered. The purely twinning nature of the textural doublet, which latter is characteristic of the rolling texture of metals of the titanium subgroup, is explained. It is noted and explained a fact that during cross rolling of plates (made from tube rings), textural changes occur at a rate twice as high as during longitudinal rolling. As considered, all similar regularities can be carried out for the metals of the titanium subgroup.

Sputtering by inverted magnetrons: influence on the texture and residual stresses in four layer Ta/W/Ta/W coatings

The aim of the study is to examine the possibilities of sputtering of multilayer coatings at a high rate of deposition on products of complex shape using inverted magnetrons. The formation of texture and residual stresses in magnetron four-layer Ta/W/Ta/W coatings deposited at voltages from 0 to –200 V on cylindrical and flat copper substrates imitating elements of the surface of complex shape products was evaluated using the X-ray method of inverse pole figures and the sin2Ψ method. The patterns of texture formation in coatings depend mainly on the bias voltage on the substrate (Us), while at Us = –200 V they differ for W and Ta layers. At Us = –100 V, the epitaxial mechanism of texture formation is realized. In the case of a cylindrical substrate, this leads to intense texture (111) of all four layers. In the case of a flat substrate, this can lead to the formation of a single-crystal texture (111) in all layers with a texture maximum width of 12°–14°. The presence of a single-crystal (111) tantalum texture corresponds to the maximum Young moduli and, accordingly, the interatomic bonding forces normal to the coating plane. This suggests that multilayer coatings with an external Ta layer have high tribological characteristics. Increasing the voltage on a flat substrate from 0 to –200 V leads to an increase in residual compressive stresses from 0.5 to 2.7 GPa for the four-layer coating under study.

Surface Purity Effect on Irregularities of Changes in Deformation Texture of Zr-2.5% Nb Alloy

This work is a continuation of a series of works on the study of regularities and structural mechanisms of changes in characteristics of crystallographic texture during cold deformation of plates made of Zr2.5%Nb alloy. Effects of influence of surface cleanliness of the plates on the textural regularities during their rolling were investigated. For this, longitudinal fragments of the tube Æ15.0´1.5 mm² were used, flattened, annealed at 580°C in a vacuum of 1.5...3.0 Pa and rolled along the axis of the original tube with various degrees deformation up to 56%, which is likened to longitudinal rolling of plates. Techniques of maximally uniform straightening of tube fragments were used. An analysis of the results of studies of textural changes during cross rolling of plates, straightened from rings of the same tube and pretreated under similar conditions, is also carried out. To analyze the results, the method of inverse pole figures was used, which, in these studies, is distinguished by the possibility of achieving satisfactory accuracy in calculating the integral characteristics of texture. On this basis, the Kearns textural coefficient was calculated along the normal to the plates’ plane. Corrections were introduced for texture dissimilarity along the thickness of the plates, which is caused by the unbending of the preliminary blanks. Additionally, the analysis of texture distributions was carried out using original techniques. According to the results obtained – as a result of X-ray measuring from the plates’ surface – oscillations of the course of changes in the texture coefficient were revealed. This is associated with an alternating process of relaxation of residual stresses during deformation. It has been established that this effect is initiated from the near-surface regions, is associated with a near-surface impurity, and in some cases can penetrate to a considerable depth of the plates. The twinning nature of such regularities is confirmed and active systems of twins are noted.

Changer in the texture orientation of electrolytic nickel by cold air plasma

The effects of cold air plasma influence on the change in the microstructure, stress state and texture of the cathode nickel brand H-1 were studied. By the method of target metallography it has been established that the microstructure does not change under exposure to the cold air plasma. A decrease in the level of micro- and macrostress is shown. By the method of inverse pole figures it has been established that the pole density of the orientations (111), (200) and (311) decreases when exposed to plasma; orientation (311) changes the least intensively. The pole density of the orientation (220) increases from 4.42 in the initial state to 13.3 after plasma treatment, which means an increase in the electrolytic deposition texture. The causes of the observed effects are being discussed. It is assumed that the changes introduced by the plasma occur at a scale level that is much smaller than the size of the coherent scatter blocks.

Study of the anisotropy of the polycrystal properties based on texture data

The results of studying correlation between the crystallographic texture of polycrystalline materials and anisotropy of their physical and mechanical properties are considered. The methods for calculating the anisotropic properties of polycrystals based on the data obtained by X-ray methods of direct and inverse pole figures are reviewed. Calculation methods based on the use of the distribution function of crystallite orientations require the use of a large amount of experimental data and, hence, they are not suitable for express estimation of the anisotropy level of the physical properties of samples upon their thermomechanical processing. A method for rapid estimation of the anisotropic properties of the sample based on the use of Д; ("orientation factors") in the calculations, is proposed. Experimental data of X-ray analysis (method of inverse pole figures) are used to calculate the absolute and relative deviations of the physical parameter of textured polycrystal from the same value in the isotropic sample. The contributions of individual crystallographic orientations to the formation of the anisotropy of the properties of the sample are estimated. The dynamics of quantitative changes in the anisotropic properties of a polycrystal in the process of texture formation is studied. To analyze the source of the most rapid changes in the anisotropy of properties, we used the coefficients of the "response" matrix, the calculation of which does not depend on the results of specific diffractometric measurements, but is common for all metals with a hexagonal close-packed (hep) lattice. The anisotropy of the coefficient of thermal conductivity, electrical conductivity, and thermal diffusivity was calculated for the samples of deformed yttrium which underwent cold rolling with a reduction ratio of e = 25%. It is shown that the final physical properties_of the hep polycrystal are largely determined by the pyramidal crystallographic orientations {1015}, {1124}. The results of the study form a basis for analysis of the anisotropy of the physical properties of hep-metal samples upon thermomechanical processing.

On Structural Aspects of Texture Changes During Rolling of Zr-2.5%Nb Alloy

Using X-ray structural analysis, features of changes in characteristics of crystallographic texture during cold working of Zr-2.5%Nb alloy plates by longitudinal and cross rolling has been investigated. To make original plates, longitudinal fragments and rings of Æ15.0´1.5 mm² tube annealed at 580 °C were used. The plates were rolled at room temperature to the degrees in the range from 6 to 56% with 5…7% per pass and the rate of 5...10s-1. Using the method of inverse pole figures with measuring by the Bragg-Brentano optical scheme, densities of reflections along normal to plane of the plates (pole densities) was determined. Based on this, distributions of orientations of c-axes of hcp lattice of the material have been analyzed. Local features of the distributions, which were attributed to signs of twinning effects in texture changes in the alloy, are revealed. At subsequent analysis, an effect of strain non-uniformity associated with prehistory of the plates was taken into account. It is established that the second stage of (moderate) changes in Kearns textural coefficient of the plates with the deformation degrees differs from the initial stage of accelerated changes by activation of compression twins. By the method of tilt scanning (of rocking curves) around the Bragg-Brentano position at registration of (0004) reflection intensities, changes in orientation distributions of c-axes in longitudinal and cross section of the plates for both parties were investigated. It is noted that the main textural changes in process of deformation of the plates occur in the cross-sectional plane of the original tube and are most expressed on the cross-rolling plates. The doublet in the distributions of c‑axes, characteristic for rolling texture of hcp metals of titanium subgroup, was noted just at the second stage of the texture changes in the material. Its directionality is mainly associated with the plane of cross-section of the original tube. A connection is revealed between features of the pole density distributions and expression degree of the textural doublet on the rocking curves. According to the results obtained and analysis of other publications, twinning nature of the textural doublet was confirmed and a schematic sequence of its formation was proposed with participation of compression twins of{112-2}{1-1-23} system and tensile twins of {101-2}{1-011} and{112-1}{1-1-26} systems.

Regularities of Changes in Kearns Texture Coefficient at Cold Rolling of Zr-2.5%Nb Alloy

-ray studies of the changes in characteristics of crystallographic texture with cold deformation of Zr‑2.5%Nb alloy plates by longitudinal and cross rolling up to 56% at the speed of 5…10 sec-1 were carried out. The original plates were made from longitudinal fragments and rings cut from Æ15.0´1.5 mm² tube, and were then annealed at 580 °C. Texture of the plates was studied by the method of inverse pole figures with calculation of the Kearns texture coefficient along the normal to the plate plane. Dependences of the texture coefficient on degrees of deformation of the plates are built. A discrepancy was found between texture coefficient values measured on different sides of the plates, which is associated with the straightening of the original tube fragments and invariance of “c”-axes distribution after subsequent annealing of the initial plates. By introducing corrections to the degree of deformation calculated from the parameters of the cross section of the original tube, such discrepancies were eliminated for the data on cross-rolling of the material. As a result, for both deformation schemes, two stages of changes in the texture coefficient with alloy deformation were revealed: the initial stage of its growth and the subsequent stage of minor changes. Both stages are mainly linear and have the boundary value of the texture coefficient equal to 0.65...0.68. To study the structural mechanisms of changes in the texture of the alloy, an original technique of comparative analysis of changes in the texture coefficient of the material and in the distribution of crystallographic orientations is applied. It is established that at the initial stage of changes in the texture coefficient with deformation in both schemes, the rotation of the crystallographic “c” axes of the material occurs abruptly, and it does at angles of more than 60°. This confirms the essential role of twinning in the texture changes of the alloy. In particular, we have shown that the initial stage is significantly dominated by the {102}á011ñ system of tensile twins. Connection of twinning with differences in texture changes at the longitudinal and cross rolling of the alloy is discussed.

Phase composition, microstructure and microhardness of alloy In–Sn, obtained by rapid crystallization

The results of studying of the structure and properties of the In – 42 at.% Sn alloy in the form of foil obtained by the method of rapid solidification with a cooling rate of the melt of at least 105K/s are presented. X-ray diffraction analysis showed that the phase composition of the alloy corresponds to the equilibrium state diagram. Foils consist of an InSn4compound (γ-phase) and an In3Sn compound (β-phase). The grain structure of foil was studied by electron backscatter diffraction technique. It is established that the foil have a microcrystalline structure. The parameters of the microstructure are determined by the method of random linear secants: the volume fraction of the phases, average chord length of the random linear secant on the inclusions of each phase, the specific surface of the interface. Microstructure and distribution of components was also studied for both foil surfaces. The texture of both phases of the polycrystalline foils was studied by the method of inverse pole figures. It is established that the initial foils of the investigated alloy are in an unstable state. It is shown that an increase in the microhardness of the alloy during aging and annealing caused by change in the parameters of the grain structure.

Methodological aspects of the quantitative texture analysis of HCP Alloy (Ti, Zr) sheet semiproducts

The specific features of the existing methods of quantitative texture analysis of semiproducts and products made of titanium and zirconium alloys are analyzed. A technique is proposed to determine the Kearns coefficients (f parameters) for sheets made of hcp-metal-based alloys with allowance for the weighting factor of each reflection in the standard stereographic triangle. The f parameters calculated for sheets made of a zirconium alloy and various titanium alloys using different techniques are compared. The accuracy of measuring the Kearns coefficients by the inverse pole figure method is estimated.

INFLUENCE OF COLD ROLLING TO THE TEXTURE PARAMETER OF PURE HAFNIUM AND ZIRCONIUM

Results of X-ray investigations of dependence of the crystallographic texture of hafnium and zirconium on degrees of cold rolling are presented. To obtain numerical principles, the method of inverse pole figures (IPF) with calculation of the texture parameters of Kearns (TP) for a chosen direction has been used. Measuring was carried out in the plane of the plates, as well as in the other two directions relating to rolling. The trigonal diagram of TP changes with degrees of deformation was built. Two stages of TP changes with deformation degrees are revealed: rate of the TP changes at the initial stage and, in part, characteristics of the subsequent stage depend on the initial texture of the materials. The second stage is characterized either by achievement of a minimum of TP in the rolling direction of the plates, or by moderate and even slight changes of them. In an example of hafnium, it has established that the increased rate of initial changes in TP is exclusively associated with intensive twinning predominantly by the {10‾12} system. Arguments for dominance of twinning in the texture formation in hafnium and zirconium on the subsequent stage of rolling deformation are given

A generalized inverse-pole-figure method to analyze domain switching in polycrystalline ferroelectrics

In this study, a generalized inverse-pole-figure (IPF) method has been suggested to analyze domain switching in polycrystalline ferroelectrics including composition of morphotropic phase boundary (MPB). Using the generalized IPF method, saturated domain orientation textures of single-phase polycrystalline ferroelectrics with tetragonal and rhombohedral symmetry have been analytically calculated and the results have been confirmed by comparison with the results from preceding studies. In addition, saturated domain orientation textures near MPBs of different multiple-phase polycrystalline ferroelectrics have been also analytically calculated. The results show that the generalized IPF method is an efficient method to analyze not only domain switching of single-phase polycrystalline ferroelectrics but also MPB of multiple-phase polycrystalline ferroelectrics.

Estimation of Intrinsic Contribution of Piezoelectric Properties in Ferroelectric Ceramics

A domain switching model is proposed to estimate the intrinsic contribution of piezoelectric properties in pseudocubic (rhombohedral) ferroelectric ceramics. Two-dimensional orientation distribution function (ODF) is used to describe domain patterns. The estimation of intrinsic contribution of piezoelectric properties is then achieved through tensor calculation and integration via the ODF. Our approach treats saturated and unsaturated domain texture in a unified scheme, while the inverse pole figure method reported in literature could not deal with unsaturated domain texture. The numerical method is useful in separation of intrinsic and extrinsic contribution of piezoelectric effect and in tailoring piezoelectric properties of ferroelectric ceramics.

Modeling on domain switching in ferroelectric ceramics near the morphotropic phase boundary

In this paper, domain switching in ferroelectric ceramics near the morphotropic phase boundary (MPB), where tetragonal phase and rhombohedral phase coexist, is analyzed by a micromechanical model using an inverse-pole-figure (IPF) method. Charge screening effect in ferroelectric ceramics is taken into account, thus the depolarization field by polarization switching vanishes. The mechanical constraint caused by non-180° switching, however, cannot be neglected and is assumed to be proportional to the switching strain caused by non-180° domain switching with a factor β as the measure of the constrained level. Using the IPF method, the domain switching induced polarization and strain can be explicitly obtained via integrations over the unit spherical surface. Two limiting cases are studied in this paper, i.e., the energy barrier for the interphase non-180° domain switching is equal to or much larger than that for the in-phase non-180° switching. In the former case, it is found that domains always tend to switch to the rhombohedral phase especially when the constrained level is high, i.e., at a large value of β. If the mechanical constraint is neglected, i.e., β=0, the maximum achievable polarization and strain can be analytically obtained in this case. While in the latter case, interphase domain switching is suppressed, thus domain switching in MPB ceramics is only a superposition of independent in-phase domain switching in tetragonal ceramics and rhombohedral ceramics.

An inverse-pole-figure method for the analysis of domain switching in polycrystalline ferroelectrics/ferroelastics

An inverse-pole-figure (IPF) method is proposed to analyze domain switching in polycrystalline ferroelectrics/ferroelastics subjected to electric/mechanical loading. The IPF method fixes the crystallite coordinates and makes electric/mechanical loading directions vary. Both the accuracy and efficiency of the IPF method are examined and proved superior to the conventional random statistic (RS) method. Furthermore, using the IPF method, it is very convenient to account for the depolarization field/stress caused by domain switching, thus predicting the observed incomplete switching in real ceramics.

Texture Evaluation in Zr-2.5 % Nb Pressure Tubes Using Kearn’s f Parameter

Abstract The anisotropic properties of Zr-2.5 wt % Nb pressure tube material, used in pressurized heavy water reactors (PHWR) depend primarily on the texture associated with the material. Particularly properties such as coefficient of thermal expansion, mechanical anisotropy, irradiation growth, stress corrosion cracking, and delayed hydrogen cracking, are directly correlated. Thus, the knowledge of preferred orientation becomes an essential prerequisite for property evaluation. In the present paper the correlation between the preferred orientation factor, namely Kearn’s f′ parameter, and some of the important properties of the material is summarized. The f parameters were deduced from the X-ray diffraction data, using the inverse pole figure method, and then subsequently the values were verified experimentally using the direct pole figure method.

The Random Orientation Probability in Consecutive Inverse Pole Figure Method for Texture Determination

The Random Orientation Probability in Consecutive Inverse Pole Figure Method for Texture Determination

A method to estimate magnetic induction from texture in non-oriented electrical steels

A model to estimate magnetic induction in electrical steel sheets is presented. Considering only M s (magnetization of saturation) and K 1 (first-order magnetocrystalline anisotropy constant), it is possible to estimate the magnetic induction for a applied field H, depending on the texture of the sheet. Data from the model and experimental texture analysis by inverse pole figure method are compared with magnetic induction B 25 and B 50 measurements obtained from Epstein test.

Texture strengthening of copper electrical conductors

Summary Commercial tough-pitch copper of high grade has been used to correlate the texture of wires to their tensile strength. Twentyfour samples were prepared by cold drawing of copper wires in one direction for four different reductions in area and subjecting them to different temperatures of preliminary and final annealings. The texture of these samples was calculated by the method of inverse pole figures. The final annealing temperature was found to be the factor affecting the texture of the wire irrespective of the pre-annealing temperature. It was found that Young's modulus depends mainly on the texture of the wire, while the other mechanical properties depend more on the grain size and the annealing state. The values of electrical resistivities of all wires are isotropic with respect to texture.

インバース・ポール・フィギュアーによる燃料ウランロッドの解析, (I)

To develop the fuel element for Japan Research Reactor-3, the properties of uranium fuel rod fabricated into 10m/m in diameter, are studied, and a part of the results has. already been reported in this journal. The effect of β-treatment on uranium fuel rod were studied from the points of thermal cycling growth coefficient, thermal expansion coefficient, hardness and microstructure, which has been reported in the reference. The effect of β-treatment on the texture of the same uranium fuel rod, as was used in the previous study is reported this time. As the preparation of the pole figure of a uranium fuel rod is very troublesome, inverse pole figure method has been prefered, to describe the texture of the specimen. (001) projection of α uranium is used in this inverse pole figure. Intensities of the diffractions from 22 planes of a specimen have been measured by G.E. diffractometer and they are used for calculation. Inverse pole figures of β-treated uranium rods rolled at 300° and 600°C respectively have also been made. From the results, β-treatment at 720°C has been found to have better effect on the texture of uranium rod than that at 680°C; more homogenous distribution of crystallographic planes could be obtained, which is, therefore, the reason why β-treatment at 720°C will give smaller thermal cycling coefficient. The more homogenous is the distribution of the planes in the β-treated specimen, the smaller thermal cycling coefficient can be obtained.