Physics /2. Physics of a firm body

d.f.-m. н. Urusova B. I, аss. Uzdenova F.A., аsp. Mamchueva F.M.

Karachaevo – Circassian state university, Russia

Calculation of the critical sizes the one - domain

Earlier by us in work [1] it has been shown that exchange energy which spot Curie temperature - and temperature dependence of spontaneous magnetization exceeds other kinds of energy.

It is known that in magnetized grain before saturation magnetostatic energy has the maximum value equal:

(1)

where = - a magnetic constant;

N - The degaussing factor.

And, gradual turn in grain volume leads to occurrence of domain walls, usually them name walls the Bloh [2]. Exchange energy, at a small turn spins from each other on a small corner is equal:

(2)

where - an exchange constant.

If at spatial change in the formula (2) to consider that _, then we will receive:

(3)

where - directing cosines of a vector .

From expression (2) follows that if turn on 1800 occurs on distance exchange energy is equal:

(4)

where - parameter equal to width of domain border.

Equating this size of density of crystallographic energy equal which appears in a transitive layer, it is possible to admit, чтo they are equal at , where

. (5)

By means of the formula (5) it is possible to estimate density of energy of domain border on area unit:

. (6)

Further supposing that the particle has the cubic form, with the party, we will find the critical sizes the one - domain - and its energy we will define under the formula:

(7)

Let now the same particle is broken into two domains then energy is equal:

(8)

Equating we will find expression for the critical size the one - domain:

. (9)

However, at an estimation in weak anisotropy minerals it is necessary to proceed first of all from a parity between exchange and magnetostatic energy. It is necessary to consider energy of magnetic crystallographic anisotropy still. As it is distributed homogeneously on all volume of grain, therefore it is unprofitable, when the total density exchange and crystallographic energy will be comparable with density magnetostatic energy:

₍₁₀₎ where - a multiplier defining rest of magnetic poles "has disappeared" as a result of disorder of an one-domain condition. Believing, it is possible to estimate roughly that

(11)

Considering that we consider particles in the form of a cube (N=1/3) the critical size of an one-domain condition of rock basalt it is equal

The literature:

1. Urusova B. I, Uzdenova F.A., Lajpanov U.M., Energy of a magnetostriction in magnetic ores//In сб. «The Science. Formation. Youth» Maikop. 2008. С.57-61.

2. Belov K.P., Magnetic transformations//M. 1959.