Magnetic susceptibility

5.8.1 Magnetic susceptibility

When a metal is placed in a magnetic field of strength H , the field induced in the metal is given by

B = H + 4πI, (5.16) where I is the intensity of magnetization. The quantity I is a characteristic property of the metal, and

is related to the susceptibility per unit volume of the metal, which is defined as κ = I/H .

(5.17) The susceptibility is usually measured by a method which depends upon the fact that when a

metal specimen is suspended in a non-uniform transverse magnetic field, a force proportional to κ V · H · dH/dx, where V is the volume of the specimen and dH/dx is the field gradient measured transversely to the lines of force, is exerted upon it. This force is easily measured by attaching the specimen to a sensitive balance, and one type commonly used is that designed by Sucksmith. In this balance the distortion of a copper–beryllium ring, caused by the force on the specimen, is measured by means of an optical or electromechanical system. Those metals for which κ is negative, such as copper, silver, gold and bismuth, are repelled by the field and are termed diamagnetic materials. Most metals, however, have positive κ values (i.e. they are attracted by the field) and are either paramagnetic (when κ is small) or ferromagnetic (when κ is very large). Only four pure metals – iron, cobalt and nickel from the transition series, and gadolinium from the rare earth series – are ferromagnetic (κ ≈ 1000) at room temperature, but there are several ferromagnetic alloys and some contain no

274 Physical Metallurgy and Advanced Materials

Figure 5.30 B–H curves for soft (a) and hard (b) magnets.

metals which are themselves ferromagnetic. The Heusler alloy, which contains manganese, copper and aluminum, is one example; ferromagnetism is due to the presence of one of the transition metals.

The ability of a ferromagnetic metal to concentrate the lines of force of the applied field is of great practical importance, and while all such materials can be both magnetized and demagnetized, the ease with which this can be achieved usually governs their application in the various branches of engineering. Materials may be generally classified either as magnetically soft (temporary magnets) or as magnetically hard (permanent magnets), and the difference between the two types of magnet may be inferred from Figure 5.30. Here, H is the magnetic field necessary to induce a field of strength

B inside the material. Upon removal of the field H , a certain residual magnetism B r , known as the remanence residual, is left in the specimen, and a field H c , called the coercive force, must be applied in the opposite direction to remove it. A soft magnet is one which is easy both to magnetize and to demagnetize and, as shown in Figure 5.30a, a low value of H is sufficient to induce a large field B

in the metal, while only a small field H c is required to remove it; a hard magnet is a material that is magnetized and demagnetized with difficulty (Figure 5.30b).