Texture and Magnetic Properties

Expressions are derived for the dependence of the magnetic properties of cubic materials on texture. The theoretical development generally parallels that of Bunge, but employs Roe's formalism. The expressions, together with limited experimental data, enable one to express magnetic property variations in the plane of the sheet, to obtain property values for comparable texture-free specimens, and to separate magnetic properties into texture-dependent and texture-independent components. Core loss, magnetic permeability and torque or specimens of "nonoriented" nominal 3% silicon-iron are fitted to simple fourth-order equations.

A Note on the Rolling Texture of Nickel-Iron-Niobium Alloy

The nickel-iron-niobium alloy containing about 79% Ni, 8% Nb and 13% Fe in sheet form has been prepared and fabricated. The rolling texture of the alloy after cold reduction of 50 and 94% has been determined by using X-ray counter diffractometer and the results are presented in pole figures. In comparison with Ni-Fe-Mo, the results are discussed from a view of the difference of mechanical hardness between these two categories of alloys.

A New Library Program for Generating Augmented Jacobi Polynomials for Texture Calculations

A new library program for generating augmented Jacobi polynomials for texture analysis is presented. By using this program, the spatial orientation distribution maps for the three-dimensional texture analysis can be produced.

An Electronic "Angle Marker" for the Siemens Texture Diffractometer

An electronic circuit is described which produces output pulses in response to preselected increments in specimen rotation on a Siemens Texture Diffractometer. The output pulses give an accurate indication of the specimen position, and may be used to trigger X-ray scaler read-out and reset operations for automatic data logging. The accuracy with which specimen position is determined is unaffected by variations in line frequency of the goniometer motor electrical supply, or by goniometer motor inertia when it is first switched on.

Geometry of Texture Measurements for Dispersive Methods

The application of energy-dispersive neutron and X-ray methods in texture studies is briefly reviewed and discussed. New geometries of texture measurement using energy-dispersive methods with stationary counters and specimen are suggested. Depending on the number of counters the experimental data can be sufficient for the orientation distribution function (ODF) or the ideal orientations determination. Coarse-grained materials can be studied not only by neutron diffraction but also by using the energy-dispersive X-ray method. Studies of texture changes under the influence of temperature, time and external stresses can also be conducted conveniently. The energy-dispersive X-ray method may readily be adapted to industrial texture control.

A Method for Obtaining the Complete Pole Figure With a Single Sample Using the Schulz Technique

A theoretical expression, which alIows the diffracted intensities to be corrected for defocusing, is derived from the convolution over the geometrical defocusing width of a diffraction peak fitted by a Cauchy function. Alignment errors are taken into account, and a good agreement between theoretical curves and experimental points is established.

Correction of Integrated X-Ray Intensities for Preferred Orientation in Hexagonal Close-Packed Powders Using Edxrd

It is shown that energy-dispersive x-ray diffraction (EDXRD) method can be used for correction of integrated intensities for preferred orientation in hexagonal close-packed powders. The theory is based upon examination of the polar axis density distribution and upon the use of hexagonal harmonics in its representation. The reflexion method by Schulz added with defocusing correction was used. Measurements were carried out on three zinc samples with different degrees of orientation, the largest correction being 54 percent.

Elastic Properties of Cold-Rolled and Annealed Sheets of Phosphorus Steel Having High Normal Plastic anisotropy

The elastic properties of as-cold-rolled and of the subsequently annealed sheets of a phosphorus steel having high normal plastic anisotropy and low planar plastic anisotropy have been calculated according to the averaging procedures of Voigt, Reuss, and Hill incorporated with texture-weighting functions. The calculated values of Young's modulus in the various directtions lying in the plane of the sheet were compared with those determined experimentally by ultrasonic measurements. Results indicate that the Hill averages are very close to reality, whereas the Voigt and Reuss averages are somewhat too high and too low, respectively, in comparison with experimentally measured values. This paper has been prepared to help familiarize metallurgists, engineers, and students with the mathematical treatments that can be used for such studies. The procedures used for the calculations are described in detail, and examples of calculations are provided in the Appendix.

Calculation of Augmented Jacobi Polynomials by Means of a Recurrence Relation

A recurrence relation for Zℓmn(ξ) is deduced from the recurrence relations for Jacobi polynomials. Based on this relation an ALGOL-60 program has been written for efficiently calculating the Zℓmn(ξ) required in ODF analysis.

Lattice Curvatures Produced by the Heavy Deformation of Polycrystals

An outline nomenclature is given for some of the microstructural heterogeneities found in heavily deformed single phase cubic metals. The relationship of these features to the development of lattice curvatures is discussed and the importance of lattice curvatures in relating deformation and annealing textures is assessed.