The specific heats of ferromagnetic...

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The Specific Heats o f Ferromagnetic Substances.By L. F. B ates, B.Sc., Ph.D.

(Communicated by A. W. Porter, F.R.S.—Received October 4, 1927.)

Introduction.It is well known that a close relation must exist between the thermal and

the magnetic properties of a ferromagnetic substance. On the basis of his theory of the internal molecular field, Weiss* predicted a discontinuity in the specific heat of a ferromagnetic substance in the region of its critical point. His reasoning may be briefly summarised as follows. The mutual potential energy, E, of a number of elementary magnets, each of moment ji and making an angle 6 with the applied field H, is given by E — — p. H cos 6; so that when ■we consider a cubic centimetre of the given substance we may write E = —|H .I, where I is the intensity of magnetisation. Since the substance is ferromagnetic, we must suppose, according to Weiss, the existence of a molecular field of considerable magnitude, equal to N I, where N is a constant which is obtainable from a knowledge of the Curie constant and the critical point of the substance. Thus we may further write E = — 4NI2, and, since E is negative, we must provide heat in order to demagnetise the substance. The amount of heat

1 Nnecessary to demagnetise 1 gm. of the substance is therefore — . —, I2, where p2J p

is the density of the substance. Now I varies with the temperature, so that the heat necessary to demagnetise a substance results in an apparent increase of its specific heat by an amount

_0_/J_ N T2 \ 1 N 0P0T \2J ' p ’ 1 2J ‘ p ’ 0T

From curves showing the variation of magnetisation with temperature, W eiss concluded that the specific heat of a ferromagnetic substance should rise to a maximum at the critical temperature, and should then decrease discontinuously, owing to the sudden disappearance of the magnetic term at that temperature. Experiments on the specific heats of nickel, iron and magnetite were made by Weiss and Be clef' by the method of mixtures, which was later refined by Weiss

* See Weiss and Foex, “ Le Magnetisme,” p. 145, or Weiss and Beck, ‘ J. de Physique,’ vol. 7, p. 249 (1908).

t ‘ J. de Physique,’ vol. 7, p. 249 (1908).

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and his collaborators.* They heated the material under investigation to a temperature T° C., and then plunged it into a calorimeter containing water. In this way they found the mean specific heat of the substance between 16° C. and T° C. A curve was plotted with the value of this mean specific heat against T, and from this curve the value of the true specific heat at any given temperature was deduced. Their results were not completely in accord with theory, the best agreement being obtained in the case of nickel. We need not consider their results in detail, for it has been pointed out that these experiments were not altogether above criticism. For example, Sucksmith and Pottery have drawn attention to the effect of the continual quenching of their material, and to the high degree of accuracy, namely, 1 part in 16,000, which would be necessary in these experiments if the specific heat of nickel were to be accurate to 1 per cent, in the range of the temperature from 350°-C. to 354° C. Sucksmith and Potter also emphasised the importance of determining magnetic and calorimetric data for the same specimen simultaneously, and they carried out experiments on specimens of nickel and Heusler alloy in which the specific heat was measured at different temperatures by a modification of the Nernst-Eucken method, and the magnetisation was simultaneously measured by a ballistic method. Measurements were thus made at temperatures up to 410° C. Their results were markedly different from what would be expected on the Weiss theory. They found that change in specific heat was not confined to a limited region around the critical point, but was spread over a considerable range of temperature. In fact, they suggested that the critical point indicates a certain stage in a transition which takes place over a range of temperature of some hundred degrees and which is not complete at the critical temperature.

The publication of an article on magnetism by P. DebyeJ drew the writer’s attention to the existence of a group of compounds of manganese discovered by Hilpert and Dieckmann§, namely, manganese phosphide, manganese arsenide, manganese antimonide, manganese bismuthide. These substances have critical temperatures at 26°, 45°, 330° and 380° C. respectively I t will be observed that two of these substances have critical points which are conveniently low so that the writer considered that they would form excellent materials for an examination of the variation of the specific heat in the neighbourhood of the

* Dumas, ‘ Arch. Sci. Phys. Nat.,’ vol. 27, pp. 352, 453 (1909); Weiss, Piccard and Car- rard, ibid., vol. 42, p. 378 (1916), and vol. 43, pp. 22, 113 and 199 (1917); Piccard and Carrard, ibid., p. 451 (1915).

t ‘ Roy. Soc. Proc.,’ A, vol. 112, p. 157 (1926).% ‘ Handbuch der Radiologie,’ VI, p. 668 (1926).§ ‘ Jahr. der Rad. und Electrok.,’ vol. 10, p. 91 (1913).

Specific Heats o f Ferromagnetic Substances. 681



682 L. F. Bates.

critical point, and it was decided to make first measurements with manganese arsenide.

Preparation of Material.—The manganese arsenide used in these experiments was made in the manner described by Hilpert and Dieckmann* who state that this method gives rise to a single compound of the form MnAs. An amalgam of mercury and manganese was formed by electrolysis of a concentrated solution of manganese chloride. A piece of so-called pure metallic manganese, made by the thermal process was placed inside an extraction thimble and used as anode, and a pool of mercury as cathode. The resulting amalgam was quickly washed with distilled water, pressed through a linen cloth and placed in a pyrex distillation flask which was quickly evacuated. The mercury was then driven off by heating, so that finally pure manganese in the form of a black pyrophoric powder remained1 in the flask. The powder was rendered non- pyrophoric by allowing a little coal gas to enter the flask before air was admitted. The manganese was then placed in a clear silica tube together with metallic arsenic in the proportions of about 2-7 gm. and 5*6 gm. respectively, with excess arsenic. The tube was evacuated, sealed and heated to 750° C. for 10 to 12 hours in a muffle furnace. On cooling, the excess arsenic condensed at the end of the tube which cooled first, and was removed. The compound, which probably contained some free arsenic, appeared as a hard compact mass. This was finely powdered and digested in concentrated hydrochloric acid for some days. I t was then washed in water and alcohol and dried. Mr. H. Terrey, B.Sc., Lecturer in Chemistry, kindly analysed a sample of the final product and found that it consisted almost exactly of one part of manganese combined with one part of arsenic. This, of course, does not tell us whether we are dealing with a simple compound or with a solid solution of manganese and arsenic.

Preliminary Experiments. —In a footnote to their paper,f Hilpert and Dieckmann stated that these compounds of manganese showed a temperature hysteresis. The temperature hysteresis was examined in a series of preliminary experiments in which the magnetic induction of a specimen, placed in a constant field, was measured at various temperatures. The way in which the magnetic induction varies is shown in fig. 1. The substance ceases to be ferromagnetic in the neighbourhood of 45° C. If, however, the temperature is reduced after the specimen has been rendered paramagnetic, it is seen that the induction changes but slightly until a temperature between 33-5° and 34° is reached,

* ‘ Ber. d. Chern. Ges.,’ vol. 44 (2), p. 2380 (1911).t ‘ Ber. d. Chem. Ges.,’ vol. 44, p. 1615 (1911).



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when the substance rapidly regains its ferromagnetic properties. If the temperature is raised to some point below 45° C., e.g., to 42° C., then on reducing

Specific Heats o f Ferromagnetic Substances.

F ig. 1.

the temperature, the induction changes very little until in the neighbourhood of 34° C. when the substance again begins to regain its initial ferromagnetic properties very rapidly.

Apparatus for Thermal Measurements.—For an accurate examination of its thermal properties it was obvious that heat had to be supplied to the substance very slowly, and the following modification of the Nernst-Eucken method was used. The substance was placed in a copper calorimeter A, fig. 2, made of tubing 5 cm. long, 1-85 cm. internal diameter and 0-97 mm. thick. I t was closed at one end by a thin copper plate and at the other end by a copper cover which fitted over the tubing and which could be soldered in position. Inside A was placed a light frame of copper wire, of the shape shown in E, fig. 2, which served as a former on which were wound a heating wire and a thin wire for the measurement of temperature. The heating wire was of No. 42 double silk covered manganin, and was wound round the straight wire of the frame and passed between the portions xx of the arms of the frame. The temperature filament was of No. 44 double silk covered platinum wire and was wound on the portions yy of the frame. The wires were held in position by touches of shellac. In this way the heating and temperature filaments were distributed as efficiently as possible throughout the interior of the containing vessel. As the rate of supply of heat was always low, there was little doubt that the substance changed uniformly throughout its mass and that the temperature as recorded by the



684 L. F. Bates.

platinum wire was trustworthy. The heating and temperature filaments were provided with leads of No. 32 double silk covered copper wire. In filling the

calorimeter A, a layer of the substance was first placed at the bottom of the vessel, the copper wire frame was placed inside, and the remainder of the substance added slowly. In all, 42-15 gm. were used. During the filling the vessel was repeatedly tapped by a large bar magnet and the substance was thus closely packed. When the vessel was full, the copper leads were threaded through two small holes in the copper cover, and the latter was soldered in position. The small holes through which the leads emerged were filled with molten shellac, so that the calorimeter should have been airtight, although this provision could not be tested and was probably not necessary. Three small copper hooks soldered to the outside of the calorimeter permitted it to be suspended by threads from the cover of the thin walled brass vessel B. The cover

of B could be cemented in position with hard wax. I t was provided with a brass tube inside which was cemented a glass tube C which permitted the outer vessel to be connected to a two-stage Hyvac pump. The thin copper leads to the calorimeter passed along the glass tube and emerged at D where a glass stopper was cemented in position. Just outside D the thin leads to the temperature filament were soldered to heavy copper leads and connected to a very excellent form of Callendar and Griffith’s bridge, for the loan of which I am greatly indebted to Mr. N. Eumorfopoulos. A pair of compensating leads were provided, and for convenience the thin ends of these leads were not placed inside the brass vessel, but were placed in contact with the brass tube, and the slight departure from the usual practice in this case could not have introduced any perceptible error. The brass vessel was mounted in a tank of water which was kept in violent agitation. The heating filament was connected in series with a battery, rheostat and milliammeter.

Procedure.—The temperature filament was first calibrated by noting its



resistance when the brass vessel contained air, and the water was kept at constant temperatures for long periods by means of an electrical heater. In each experiment the brass vessel was thoroughly evacuated and surrounded with melting ice until the resistance of the filament corresponded to a temperature of 2° to 3° C. This was done in order to ensure that the initial state of the substance was the same in each experiment, and to be able to heat the substance in a perfectly definite manner. A definite value of the heating current was chosen, and since the resistance was of manganin, it was only necessary to maintain this current constant in order to ensure a constant rate of supply of heat. The heating current was switched on and the times at which the temperature filament attained consecutive values differing by 0 • 1 ohm (or 0 • 05 or 0 • 025 ohm when necessary) were noted. An increase of resistance of 0-1 ohm corresponded to an increase of temperature of about 1° C. Hence the amounts of heat necessary to cause definite rises of temperature of the calorimeter system were knowfi. The specific heat of the copper of which the calorimeter was made was found by the method of mixtures, so that the thermal capacity of the copper case and wires was known. To ensure that the radiation correction was negligible, the temperature of the water surrounding the brass vessel was raised at the same rate as the temperature of the calorimeter. Thus, at the moment when the filament acquired a temperature corresponding to a resistance of R ohms, the temperature of the bath was raised to correspond to a resistance of R + 0-05 ohm, and this temperature was maintained until a resistance of R + 0 • 1 ohm was attained by the filament, whereupon the temperature of the water was again adjusted.

Results.—The specific heat of the compound could thus be found over a series of small temperature intervals. To be free from accidental errors the mean values of the times were taken for 10 such experiments, in which heat was supplied at the constant rate of 0-03243 calorie per second. To give an idea of the accuracy attained, it may be mentioned that the times for which heat was supplied in the separate experiments to raise the temperature of the system from 25-5° to 53-8° were respectively 8917, 9124, 8924, 8819, 8958, 8864, 9044, 8815, 8656 and 8998 seconds. The mean value was 8912 seconds, corresponding to the supply of 289-0 calories. All these experiments gave graphs which showed the same variation of specific heat with temperature. The values for the complete set of experiments are shown in fig. 3, where it will be seen that the specific heat rises slowly from a value of 0-122 at 28° C. to a value of 0-14 at 36° C., then rises with increasing rapidity to a value of about 0-8 in the neighbourhood of 42° C., then falls rapidly to a value of 0 • 13 at 45° C., and thence

VOL. CX V II.— A. 3 A




686 L. F. Bates.

to a slightly defined minimum value of 0-10 at 46*5° C., after which it slowly rises with increase in temperature. This minimum was presumably due to the sudden change in the rate at which the temperature of the calorimeter system rose.

2 8 3 0

F ig. 3.

Now, the above results were obtained with a value of the heating current such that the temperature of the calorimeter and its contents rose from 25° C. to 52 • 8° C. in approximately 2 | hours. The chief errors likely to arise were those due to non-uniform heating of the specimen and to radiation. I t was possible to ascertain the order of magnitude of these errors by repeating the experiments with different rates of supply of heat. Accordingly, six experiments were made with a heating current of 54*0 milliamperes, corresponding to a rate of supply of heat of 0*04929 calorie per second, so that the time taken to raise the temperature of the system through the above range was now 1 hour 40 minutes instead of 2|- hours. The times for which heat was supplied to produce this rise in temperature in the several experiments were 5892, 5863, 5872, 5956, 5984 and 6009 seconds respectively. The mean value is 5929 seconds, which corresponds to the supply of 292 • 3 calories, which is in satisfactory agreement with the value 289-0 obtained in the first experiments. The specific heat curve in this case was very similar to fig. 3, but the initial specific heat was somewhat larger than in fig. 3. Thus at 28° C. the specific heat in the first case was 0-122, whilst in the second case it was 0-129, and the rate of increase of specific heat between 28° and 36° was greater in the second case. The maximum



value of the specific heat was somewhat less, and the minimum was more pronounced, but the position of the maximum was the same in both curves, and the values of the specific heat above 46° C. were practically identical in both. These features show that the radiation effects in these two sets of experiments must have been very small. The results indicated that in the second case heat was being supplied to the system rather too quickly, so that in the region below the critical point the material did not change its state as uniformly as in Curve I.

Some experiments, which were tedious, were also made with extremely slow rates of supply of heat to the system. For example, in one experiment the heating current was 32*74 milliamperes, and the time required to raise the temperature of the system from 25° to 53*8° was nearly 5 hours. Naturally, a high order of accuracy would not be expected with such a slow rate of heating. The results of this experiment are given in fig. 4.


F ig. 4.

It will be seen that the value of the specific heat from 28° C. to 38° C. is in good agreement with the value obtained in the first case, but the rise of specific heat between 38° and 42° is much more rapid, and the final value of the specific heat above 46° C. is higher. The minimum is, however, much less pronounced. The position of the maximum value of the specific heat, found by producing the ascending and descending arms until they meet, was the same in all experiments within the limits of experimental error. In the three cases the maximum occurred at 42*16, 42*21 and 42*26° C. respectively, the mean value of which may be taken as 42 • 2° C.

The real difference between these three cases lies in the shape of the peak. There is no doubt that the slower the heat is supplied to the system, the more

3 a 2



688 L. F. Bates.

pronounced does the peak become, although it is difficult to believe that the peak could become much more pronounced than in fig. 4, if the rate of supply of heat were still further decreased.

A few experiments were made in which the calorimeter and its contents were first heated to about 55° C. and were then allowed to cool, whilst the temperature of the surroundings was constantly adjusted to be 15° C. less than that of the temperature filament. The results showed that the specific heat of the compound rose slowly with fall in temperature between 45° and 35°, probably due to non-uniform cooling of the material. A rapid increase in specific heat then occurred, and a maximum was reached. This maximum was poorly defined because of the limitations of the cooling method. Between 28° and 25° the specific heat fell rapidly, and finally approached a value which was nearly constant. Experiments were also made in which the calorimeter system was heated to 54° C. and then allowed to cool slowly to 35°, when it was again heated. The specific heat over the range 35° to 54° was found to. be nearly constant under these conditions.

Magnetic Properties.—We now have to examine the magnetic properties of the substance more fully. I t was felt that the best mode of attack was to examine the magnetic induction of the substance when placed in a strong magnetic field. Some of the substance was therefore packed tightly in a copper tube 6 cm. long and 0 • 55 cm. in internal diameter. Of this tube a solenoid of No. 32 double silk covered copper wire wras wound. The tube was mounted at right angles to a brass rod and placed between the poles of an electromagnet. An exactly similar solenoid, wound on an empty tube, was mounted side by side with the first. The tubes were placed in a bath of paraffin oil which was heated electrically and vigorously stirred. The solenoids were connected in series with a ballistic galvanometer of long period. The tubes were placed with their axes parallel to the lines of force of the electromagnet. The deflection of the galvanometer was observed, either when the tubes were suddenly turned through 180° or when a known current was switched on and off in the magnet coils. The solenoids were connected in opposition, so that the galvanometer deflection was a measure of the magnetic induction in the substance. Special experiments were made to prove that the introduction of this ferromagnetic substance did not appreciably upset the applied magnetic field.

The tubes were first cooled and determinations of the ballistic deflections were made as the temperature was increased. The apparatus was maintained at a given temperature until the ballistic deflection was constant, and owing to the nature of the substance the determinations in the region of 41° and 42° were



made very slowly. I t was felt that by using a copper tube of smaller bore to contain the compound, any errors due to the movement of the powder and to inequalities of temperature would be lessened. Further experiments were therefore made in which the substance was enclosed in a tube of 0-25 cm. internal diameter, but there was no apparent difference in the nature of results obtained. The magnetic field used in these experiments was 1960 gauss.


Fia. 5.

In fig. 5 are plotted a typical set of experimental observations, together with a curve showing the rate of change of the magnetic induction, I, with temperature found from these observations, in arbitrary units. The latter curve exhibits a maximum at 42-2° C., and it is clear that there is a marked resemblance between the curves showing the variation of the specific heat with temperature and that showing the variation of magnetic induction with temperature. If, however, we plot dl2[dT against temperature, we obtain a somewhat similar curve, but dI2/dT reaches a maximum at 41*5° C. and becomes extremely small at 44° C.

Discussion of Results.—There are several interesting features about the curves which are given in this paper. In the first place the heat curves very definitely suggest that the thermal changes which occur when this ferromagnetic compound is heated are associated with molecular changes. For it is clear that whenever the magnetic properties are changing, there is also a corresponding thermal change, and when the substance has become paramagnetic there is very little further change in its specific heat. Again, the rate at which the substance absorbs heat is a maximum, within the limits of experimental



690 L. F. Bates.

error, at the temperature at which the magnetic changes occur at the maximum rate ; although in view of the method which had to be used in investigating the magnetic induction, perhaps this coincidence should not be stressed too far. The problem, then, becomes analogous to the question of the specific heat of dissociating gases. We may obtain an approximate value of the energy necessary to produce these molecular changes. In the case represented in fig. 3, the heat supplied to 1 gm. of the compound to raise its temperature from 25 • 5° to 53-82° was 5-19 ealories. The mean specific heat from 25*5° to 42-2°, found by producing the initial portion of the curve, was 0-130, and the mean value from 42 • 2 to 53 • 82, found by producing the end portion of the curve, was 0 • 106. Therefore the actual quantity of heat required to change the state of the compound was approximately 1-79 calories per gram.

The curves given in this paper have many features in common with those obtained by Sucksmith and Potter* for nickel and Heusler alloy, where it is clear that similar heat phenomena must occur, but must extend over a considerable range of temperature. Their curves of the variation of specific heat with temperature showed in several cases, however, that pronounced heat changes occurred even at temperatures considerably above that at which the substance became paramagnetic. This was not so evident in the case of nickel, but in the case of Heusler alloy the heat phenomena appeared to exist at temperature, 15° to 20° above the critical point. In the experiments described here the relation between the thermal and magnetic properties is more intimate than in the cases investigated by Sucksmith and Potter. The two sets of experiments may satisfactorily be explained if we assume that in ferromagnetic materials the atoms are associated in groups, and that the rearrangement of the electron systems in these groups is responsible for the loss of ferromagnetism. Stonerf has used this conception, in order to account for the fact that the values of the magnetic moment per atom of ferromagnetic substances deduced from low temperature saturation intensity measurements differ considerably from the values obtained from the variation in susceptibility above the critical points and that, moreover, these values bear no apparent relation to the values of the moments of the ions of ferromagnetic metals found by measurements on salts and solutions. Stoner showed that the experimental differences could be accounted for on the basis of the quantum theory, by assuming that the atoms in crystals are associated in groups and that the magnetic properties are due to ions within these groups which have the same moments as ions in solid

* Loc. cit.t ‘ Proc. Leeds Phil. Soc.,’ Jan., 1926.



salts and in paramagnetic solutions. Thus in the case of nickel, the group is supposed to consist of five atoms consisting of one Ni++, one Ni+ and three neutral nickel ions. Presumably such a group would be held together by some kind of electron sharing, and there appears a priori no reason why the electron orbits should not be rearranged as the temperature of the group rises. This rearrangement would be associated with definite thermal changes, and the change from the ferromagnetic to the paramagnetic state might be due to a particular stage in the rearrangement process, but there appears no reason why the rearrangement process and its associated thermal effects should not continue above the critical temperature. The experiments described in this paper presumably deal with the comparatively simple case where the rearrangement process ends at the same temperature as the change in magnetic properties, and it is hoped that future experiments will enable us to say more about the nature of this rearrangement.

Summary.

The thermal and magnetic behaviour of a simple ferromagnetic compound of manganese and arsenic has been studied. This compound has a critical point at 45° C. It is found that heat is very rapidly absorbed when the substance changes from the ferromagnetic to the paramagnetic state. The thermal and magnetic phenomena are intimately connected, and the conclusion is reached that with the magnetic change there is associated a heat of transformation. I t is considered that magnetic phenomena in the region of the critical point are evidence of a transformation which in this case appears to be complete at that temperature, but which, in general, may reach only a particular stage at the critical point.

Further experiments on this and other compounds of manganese are in progress.

It gives me much pleasure to acknowledge the kind interest with which Prof. A. W. Porter, F.R.S., has followed the course of this investigation.




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