Perature Change with Temper

PERATURE CHANGE WITH TEMPER- material. Below the Curie point ATURE FOR NICKEL a ferromagnetic substance has, in addition to the ordinary energy possessed by a non-magnetic substance, a magnetic energy depending on the spontaneous mag netization. The spontaneous magnetization decreases with increas ing temperature, corresponding to a change from a state in which the elementary magnets are alined parallel to each other to one in which they are orientated at random ; and energy must be sup plied to bring about this change. The internal molecular field, Hi, is proportional to the intensity of magnetization, so that the magnetic energy per unit mass is given by U = — —I f NMI = — NI' 2 p Let o- be the magnetic moment per unit mass; let n=N p; then For the part .9„, of the specific heat due to the change in magnetic energy with change in temperature, dTNow the magnetization decreases more and more rapidly as the temperature increases up to the Curie point (see fig. 34), above which the spontaneous magnetization (and also the part of the specific heat depending on it) becomes zero. The variation in the specific heat of nickel with temperature, as measured by Weiss, is shown in the upper curve of fig. 43.

There is an

abrupt change at the Curie temperature, the mag nitude of which is in good agreement with that calculated from the spontaneous magnetization curve. For other ferromagnetics similar changes are found, but some accurate specific heat meas urements on nickel and Heusler alloys by W. Sucksmith and H. H. Potter (1926) show that the changes are not in general so abrupt as the Weiss theory would indicate, though with manganese arsenide (a ferromagnetic with the low Curie temperature of about C) L. F. Bates (1928) has found that the specific heat rises to a maximum and then falls to a steady value within a few degrees. The fact that there is an intimate relation between the specific heat and the magnetic changes affords strong support of the general outlook of the Weiss theory; though in some cases the changes are less simple than would be expected if the change at the critical temperature was purely of a magnetic character.

A further

confirmation of the theory of spontaneous magnetiza tion is afforded by the magnetocaloric effect. When a strong magnetic field is applied to a ferromagnetic substance, the magnet ization is accompanied by a reversible change of temperature (which may be of the order of 1 °C, and so is much larger than the irreversible temperature change, which is usually not more than a few thousandths of a degree, accompanying a hysteresis cycle). It may be shown that the change of temperature AT associated with a change of field AH is given by T AT dT where S is the specific heat, and a the specific intensity of mag netization. The magnetocaloric temperature change should thus

a rise to a maximum where d — is greatest, i.e., at the Curie point, dT and that it does so is shown by the results of Weiss and Forrer for nickel, shown in the lower curves in fig. 43. From the fore Fig. 44.-CHANGE IN LENGTH IN A LONGITUDINAL MAGNETIC FIELD going equation the specific heat S may be calculated from the magnetocaloric data (giving 77AH) and purely magnetic data (which give dol dT). The specific heat so calculated agrees remarkably well with that determined directly (fig. 43). It may be shown that the magnetocaloric change of temperature should be proportional to the change in the square of the magnetization, AT= — The apparent magnetization may be zero, though the elementary domains are spontaneously magnetized; and gives a measure of this "true" magnetization. Its magnitude, as deduced from the magnetocaloric effect, is in agreement with that obtained by other methods. A consideration of the various magneto-thermal effects seems to render it impossible to avoid the conclusion that in ferro magnetics below the Curie point spontaneous magnetization occurs throughout certain domains of the substance, though the exact size and nature of these domains is still obscure.

Magneto-mechanical Effects.

A vast amount of experi mental work has been carried out on the way in which the magnetic characteristics of ferromagnetic materials are influenced by different mechanical stresses, and on the mechanical effects of magnetization. The simplest phenomenon, discovered by J. P. Joule in 1842, is the change in length accompanying longitudinal magnetization. This "magnetostriction" effect has been exten sively investigated by S. Bidwell and other experimentalists. Some of the results are shown in fig. 44.

It will be seen from the curves that different materials behave very differently, and that it is in consequence not possible to account for the deformation as due in any simple manner to a purely magnetic stress. Iron at first lengthens and then contracts. The critical value of the field (and the magnetization) varies with the hardness of the iron ; it is decreased if the wire is under tension. Magnetostriction in single iron crystals has recently been investigated by W. L. Webster (1925) and also by K. Honda and Y. Mashiyama (0926). The results are shown in fig. 44. Along the tetragonal axis there is a continuous increase in length, along the trigonal a continuous decrease. The shape of the curve for ordinary soft iron (which is a mass of small crystals) can be explained as a combination of the effects found along the differ ent axes of single crystals. In connection with the remarkable properties of permalloy (the iron-nickel alloy with 78.5% Ni) 20 0 .00 .0 600 000