XOY Plane Research Articles

Structure magnétique de Na 5FeO 4

The magnetic structure of the oxycompound Na5FeO4, showing discrete FeO5−4 anions, has been determined by neutron diffraction. Spectra have been recorded at 2.5, 15.8, and 100 K, the Neel temperature having been found earlier equal to 5.40 K by Mossbauer spectroscopy. A group theory analysis has been made, the magnetic group is Pb'ca, the moments (M = 3.75 ± 0.1 μB at 2.5 K) are parallel to the xoy plane, the angle with oy being equal to about 17°. The Fe3+ ions are coupled ferromagnetically parallel to oy and antiferromagnetically essentially in the xoz plane. The magnetic interactions have been analyzed, the exchange integrals are small −2 K ≤ Ji/k ≤ 0.5 K (i = x, y, z).

Computation of forces in pyramidal foundations

The need to determine forces in an arbitrary section t along the height of a pyramidal foundation due to forces N, M, and Q acting in the XOY plane (Fig. la) arises in calculating the body of the foundation in a tamped trench, a pyramidal pile, etc. Let us assume that the principle of the independence of forces is valid; the flexibility of the foundation can be neglected; the reactive pressure of the soil o N due to the action of N is distributed uniformly over the area of the foundation's horizontal projection; and, the stresses OM in the soil due to the action of M and Q in the XOY plane are distributed parabolically over the height (Fig. ib), i.e.,

A geometric method incorporated with a computer program for indexing crystal faces of microcrystallites

A way of indexing microcrystallites is described in which analytical geometry is used. Two micrographs obtained at different tilting angles of the object are considered as the two orthogonal projections of the object on the XOY plane of a Cartesian coordinate system. The abscissae and the ordinates of three noncollinear points of each indexable habit face are determined by direct measurement and the Z coordinates are calculated. The habit faces are regarded as planes in three-dimensional space and the angle between each pair of indexable faces is calculated: The indexing is performed by comparing the calculated angles between the habit faces and the angles between the already known equilibrium planes (predicted by the theory). A computer program for experimental data processing is briefly described.

Orientation of asbestos in asbestos cement

The orientation of asbestos fibers in abestos cement can be described by a directional distribution function characterized by two parameters: 1. σ 1 2 — the distribution dispersion in a plane normal to the direction of the external pressure applied in forming the product (XOY plane), and 2. σ 2 2 — the distribution dispersion in a plane containing the direction of the applied pressure. The two parameters are determined by X-ray diffractometry. The value of σ 2<15° for materials formed on Hatschek machines and accordingly 90–95% of fibers make an angle of less than 20° with the XOY plane. The number of fibres orientated approximately parallel to the direction of the felt movement is 1.5 to 2 times greater than the number orientated in the transverse direction.

Finite difference solution of a boundary value problem for an equation of mixed type

Let D be a simply connected finite region of the xoy plane, bounded by the Jordan line σ with ends at the points A(0, 0) and B(1, 0), located in the upper half-plane y > 0, and the characteristics AC: x + y = 0 and BC: y = x − 1, issuing from the points C( 1 2 , −1 2 ) . Let D 1 and D 2 respectively be the elliptic and hyperbolic parts of the mixed region D.