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The design and construction of a powerful electromagnet, and its application to magnetic measurements… Kidson, Geoffrey Victor 1953

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THE DESIGN AND CONSTRUCTION OF A POWERFUL ELECTROMAGNET, AND ITS APPLICATION TO MAGNETIC MEASUREMENTS OF THE ALLOY Mn6oAl2oC2o. by GEOFFREY VICTOR KIDSON, A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in the Departments of Physics and Metallurgy We accept this thesis as conforming to the standard required from candidates for the degree of MASTER OF SCIENCE, Members of the Departments of Physics and Metallurgy. THE UNIVERSITY OF BRITISH COLUMBIA OCTOBER 1953. SYNOPSIS. An electromagnet capable of producing:a magnetic field" intensity of greater than 21,600 gauss in a gap of one inch and over an area of 3.14 square inches has been designed and constructed. The structure of the ternary alloy of approximate composition Mn 6 oAl 2 oC 2 o has been investigated by X-ray methods, and shown to have an_ ordered perovskite structure, with a Q = 3,865 A0, The effective magnetic moment pit* manganese atom was measured, using the electromagnet, and a torsion balance method. The value of the ; magnetic moment at zero degrees Kelvin was found to be 1.2 Bohr magnetons per manganese atom. ACKNOWLEDGEMENT The author i s grateful for financial aid i n the form of a National Research Council Bursary during the winter of 1 9 5 2 - 5 3 , and the summer of 1 9 5 3 c Without such aid this work could not have been carried out. Mr. F. K. Bowers, of the Physics department made many valuable suggestions concerning the design of the magnet. The funds for the construction of the electromagnet were pro-vided by the Defense Research .Board. The iron for the yoke of the magnet was donated through the generosity of the Steel Co. of Canada, Hamilton. The author i s grateful to members of the staff of the Department of Mining and Metallurgy for helpful technical advice. TABLE OF CONTENTS page T I T I l E P A G E « o o « o a o e « o « o o o o o o « o o * « « « « « o « e « T A B U S O F C O N T E N T S » o o o o o o o o o o o o o o o o o o o o o o s o o * i i INDEX OF ILLUSTRATIONS AND TABLES. 0 . . . . . . . . i i i S Y N O P S I S o o o o o o o o o o o o o o o o o o o o o o o o o o e o o o o IV ACKNOWLEDGEMENT. . v PART 1; 'THE DESIGN, CONSTRUCTION AND PERFORMANCE OF THE ELECTROMAGNET1 I N T R O D U C T I O N o o o o o o o o o o o o e o o o o o t > o o o o o o o o o o ^ P R E V I O U S W O R K o o o o o o o o o o o o o o o o o o o o o o o o o o o o ^ TESTING OF SCHNAY MAGNET . 7 THE DESIGN- OF THE ELECTROMAGNET 10 THE CONSTRUCTION AND ASSEMBLY OF THE MAGNET. . . . . . . . . . . . . . . . . . 15 PERBM^HAN.^ .^Gffi..r.THE..MAGNEIi . ^  . . v . . . . . „ . . . . . . . . . . 17 D I S C U S S I O N ^ • o © o o o o o o - o o o o o o 0 O O 0 0 o o o • © O 0 o o o o • PART,2s, ?AN INVESTIGATION OF THE MANGANESE - RICH FERROMAGNETIC ALLOY OF APPROXIMATE COMPOSITION MneoAlzoCao.' I N T R O D U C T I O N o o o o « © o o o o o o o o o o o o o o o o o o O 0 0 o o 2 if P R E V I O U S W O R K o o o o o o o o o o o o o © o o o o o o o o o o o * « o e o P R O C E D U R E o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o a ^ R E S U L T S : 9 . . . o o o o o o o o o o o o o o o o o o o o o o o o o o o o e e o 3 2 DISCUSSION AND CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . . 37 A P P E N D I X I o o o o o o o o o o o o o o o a o o o o o o o o o o e o o o o o o o o o o o o o o o « « o e o « o o o o o « e « « o o « « A P P E N D I X I I o o o o o 4 o o o e « « o o o « o « o » » a » • • » » © • • l^] ILLUSTRATIONS AND TABLES Figure No. Plate No. Schnay M a g n e t 0 . 0 . 0 0 . 0 0 0 0 . 0 0 0 . e © o o o . o « . o . « o . o . . . . 1 I Final Design of New M a g n e t o o o . o o . . . o o . . 2 II Wiring Diagram of Coils 3 III Components of Coil Assembly..,...,.,.. 4 IV Completed Magnet..........................«.»....© 5*6 V, VI Field vso C u r r e n t o o o o o a o o o o o o e , « o o , o e « » . » . . . , , , , . . 7 VII Apparatus for Resistance Measurements. 8 VIII Magnetic Moments vs. Electrons per Atom........... 9 IX Debye-Sherrer X-ray Patterns... 4 10 X Pole Pxece D e s i g n . . o o . o » . . 0 0 0 0 0 . 0 0 0 0 0 0 0 . o . o o . . . . . . 11 XI Table No. Page No. Measurements, of Magnetic foments on Schnay MSL^nCit o a o o o 6> 0 - 0 0 o 0 e o o o o e 0 o o 0 0 o o e o o o a o « o o o o e « o o o o o 1 S Ratio of Interatomic Distance to Radius of 3d Shell 2 26 Heat Treatments of A l l o y . . . . . o , , . . . . 4 32 Analyses of S a m p l e s . 0 0 0 0 0 . o o o . . o o o o . a o o o o o o » o o , t t 5 33 Magnetic Measurements......... . 0 . . . . . . . . . . . . . . . . 6 35 Intensity J l G c L s x i r s m s n t s o « o o o o o o o o « o « « o e « o « o o « o « o e 7 35 Structure Factor C a l c u l a t i o n s 8 39 1. PART 1. •THE DESIGN, CONSTRUCTION, AND PERFORMANCE OF THE ELECTROMAGNET • Introduction Magnetism i s a universal property of matter. A l l substances respond to magnetic influence to a greater or lesser extent wheri placed i n a strong magnetic f i e l d of force, a3 near to a pole of an electromagnet. From the standpoint of magnetic susceptibility there are three general classes of substances: (a) Substances that are repelled by a magnetic pole are called diamagnetic. (b) Substances that are weakly attracted by a magnetife pole are palled paramagnetic. (c) Substances that are relatively very strongly attracted by a magnetic pole are called ferromagnetic. In addition to the elements Fe, Co, Ni, there are many alloys which are'.classified as ferromagnetic substances. For the present*/ may be assumed that within a ferromagnetic /Substance there are innumerable elementary magnet dipoles associated with the atoms or the molecules of the substance. Present theories regarding the nature of these elementary dipoles w i l l be considered later. 2. If the substance i s placed i n a magnetic f i e l d of force, the elementary dipoles w i l l tend to align themselves in the direction of the external f i e l d , thus causing the atoms to become polarized„ Within the substance, the negative side of one atom faces the positive side of the next atom, and the elementary dipoles w i l l cancel one another <= At the ends however, there w i l l be free poles and the bar as a whole w i l l be polarized„ If the surface densities of polarization at the ends are + s and - s, the magnetic moment of the bar as a whole i s sAl, where A = cross sectional area and 1 = length. Then the magnetic moment per,unit volume = sAl = s „ Al This quantity i s usually denoted by M0 If a measure of the magnetic moment per unit volume can be obtained, then knowing the number of atoms per unit volume,, the, magnetic moment,,per. atom.can. .be .detarminedf.. -The latter i s an important experimental quantity and i s useful i n any attempt to describe the ultimate nature of the elementary dipoles within the atomso One of the methods of determining M i s by measuring the f orce -Fx exerted on the &ampletof the.ferromagnetic substance ;;Whe a magnetic f i e l d H„ It can be shown that this force i s given by F x = KM _dH dx where K i s a constant of proportionality, and ^  H i s the gradient of the dx f i e l d i n the x-direction 0 If the f i e l d i s designed such that 73H = constant, and dx ?> H. = d,E = 0, then we have F = Yc^ M x Thus the requirements for a f i e l d suitable for making measurements of- M by 3. measuring the force on the sample are simply (a) That d> H. be constant over the sample where ffi d H = 0 o and d y !Tz (b) That the external applied field H be sufficiently strong so as to align a l l the elementary dipoles, thereby giving a true measure of M. Such a condition is known as satur-ation „ The first of these requirements can be met by suitable shaping of the pole pieces of the magnet. A simple and accurate method of measuring the force on the sample is that of the torsion balance. That is, by arranging that the angle of twist of a fine wire suspension required to return the sample to its i n i t i a l position in the field, before the field was on, be proport-ional to the force exerted on the sample, we have a direct proportional-ity between the angle of twist of the suspension and the magnetic moment of the sample. If comparison is then made to a standard sample whose magnetic moment is known, the moment of the unknown sample may readily be determ-ined,, The fulfillment of requirement (b) is hindered by what is ' known as the demagnetizing effect. This arises from the field produced by the free poles of the magnetic substajrice itse-li 1 and extends-through-out the sample in opposite direction to the applied external field, there-by acting, to reduce the effective applied field. The effect is dependent upon the geometry of the sample measured„ The resultant field within the bar can be expressed ass H i -• H e - NM-o where N = demagnetizing factor, = resultant internal field, H g 1 3 external f i e l d o The resultant field for a spherical specimen, for example, can be as small as 0„003 of the external field. Thus in order that saturation be produced in powdered samples, large fields must be used. 5 . PREVIOUS WORK A small electromagnet, whose design was adopted from that of Buehl and Wulff"*"s has been built and used in the department by Schnay^, Originally i t was intended for use in studies of phase trans-formations in ferrous alloys,, The pole pieces were designed so as to produce a constant field gradient along the axis of the pole pieces. The force exerted on a sample was found by means of a torsion balance; the angle of twist required to bring the sample back to its original position in the field being proportional to the force, 3 Piercy-^ investigated the characteristics of the magnet, and found them satisfactory for carrying out measurements of magnetic moment for cylindrically shaped specimens whose ratio of diameter to length was l : 5 o The Schnay magnet is shown in figure 1, Plate I. PLATE I 7. • NESTING OF THE SCHNAY -MAGNET The Schnay magnetic balance appeared capable of f u l f i l l i n g the requirements described on page 3, for carrying out measurements of the 3 magnetic moments of solid cylindrical specimens , however i t was not known i f saturation could be produced in powdered samples. Many-of the* alloye^^^ and i t was impossible to obtain samples in cylindrical form. Either irregular shapes or powdered samples had to be used. It was decided, therefore, that an investigation of the Schnay magnet be made, using powdered samples of standard iron and nickel, to determine i f the samples were saturated. A wide range of particle sizes was obtained by using screen meshes. The finely divided metal was mixed with a solution of guncotton dissolved in butyl acetate. Cylindrical samples were formed by an ex-trusion -method. The butyl acetate evaporated leaving a strong sample of the powdered metal bonded by the guncotton. The results of the measurements are shown in Table 1. It can be seen that the agreement between the solid and powdered samples is poor. The smallest difference occuring i s L$* 8. TABLE 1. Screen Size A 6/mg.. f or Ni . Q/mg:;for :Ee;;: Solid sample 1.616 80-200 .mesho 1.520 4.720 200-270 " 1.525 4.690 270-325 «» lo550 4.600 -325 " 1.552 4.630 Attempts were made to improve the measurements by modifying the magnetic balance. The small bucket used to hold the sample was found to give an appreciable deflection when no sample was in i t . Piercy had allowed for this by correcting his angle of twist. However i t was found that the amount of deflection due to the bucket was not constant. Suitable substitute materials were tested by suspending them by a fine thread in the field, and observing the resultant deflection when the field was applied„ A rod of commercial silver solder was thus found to be very nearly unaffected. A new sample holder using a copper bucket and solder arm was made up and used. An instability of the fiel d near the center of the gap was noted. This made consistent zero point readings difficult. It was as-sumed that the instability of the field was inherent in the design of the magnet, since any leakage flux from the coils was perpendicular to the flux between the pole pieces, causing a distortipn of the field. Steel plates were placed around the ends of the colls In an attempt to decrease the leakage flux. Although the shields were successful in improving the stability of the readings, the discrepancies between the solid.and powder-ed samples remained. Fluctuations of current in the coils due to resistance changes with heating, were eliminated by including a small rheostat in the circuit for fine adjustments of current„ It was concluded that the large discrepancies in readings for the different particle sizes were primarily due to the samples not reaching saturation., Two methods were used in attempts to increase the field strength in the gap. By connecting the coils in parallel, the current was increased from 4,0 amperes to a maximum of 8.0 amperes. The field strength was measured with a flux meter and search coil. The maximum field obtained in this way was only 3000 gauss. The notable lack of increase of the field strength in pro-portion to the increase in current, and hence in total ampere. - terms, was thought to be due to the poor placement of the coils. This resulted in the yoke of the magnet becoming saturated whereas the pole pieces were not. The effect of this upon the field strength in the gap will be more fully discussed on page 13 . Ewing^ has shown that the optimum,shape of pole piece to produce a maximum field is a cone, with an angle of taper of 54° 44*» Pole pieces were made up and the field strength measured, using various gap widths and currents0 The largest value of the field obtained in this way was 7000 gauss, using a gap of 3/881 and a current of 8 amps. 5 Since Sucksmith reported being unable to produce satur-ation of powdered samples in fields as 16000 gauss, i t was dec-ided that a more powerful electromagnet must be constructed for the magn-etic measurements of the new alloy systems. 10. THE .DESIGN. DE THE E L E C T R O M A G N E T . A starting point in the design problem of the electromagnet was provided by certain requirements that had to be fulfilled. In order that the powdered samples be saturated, a field strength of at least 18000 gauss was chosen„ The gap between the pole pieces had to be of sufficient size to permit measurements to be made at room temperature, -and-also .using a dewar flask for low temperatures. The one inch gap used in the Schnay magnet was considered satisfactory, and this value was adopt-ed for the new magnet.., Further considerations involved the available electrical power, the dissipation of heat from the coils and the availability of materialso Finally, of course, consideration had to be given to the over-a l l cost of the materials and construction. The details of the calculations are given in Appendix 1, how-ever the general scheme used will be outlined here. In the magnetic circuit, the energy required to produce the magnetic flux is provided by the magnetomotive force. The latter, in turn, is provided by the ampere-turns in the circuit, i o e 0 the product of the number of amperes times the number of turns in the coils„ An approximate determination of the total ampere-turns required can be obtained from the relation; NI - <^Hdl « H a l a + H j l ^ where N = number of turns H^  • field strength in iron I = current l a = path length in air Ha =» field strength in air 1^  = path length in iron 11. A major portion of the magnetomotive force will be dropped across the air gap, hence a fi r s t approximation of the total ampere-turns required can be obtained using (NI - ^1.) = H a l a . From this calculation, and many t r i a l and error designs, i t was estimated that the total number of ampere turns required was 45,000. Since the yoke had to be large enough to accomodate the coils, the latter were considered f i r s t . The method of dissipating the heat from the coils was one adopted from a number of alternatives. From considerations of the total size of the coil assembly, and the efficiency of cooling, a system of water cooling pancakes interspersed between the coils was chosen as that best suited to the requirements, and contributing to the most economical design. The size and shape of the coil assemblies were determined by the power which could be dissipated in them, which in turn was determ-ined by the rate of flow of water through the cooling pancakes. Assuming an allowable temperature rise of 20°C, and a rate of flow of water of 5 0 cc/sec, the power to be dissipated was found to be 4180 watts. From this figure and the estimated number of ampere-turns required, the effective parallel resistance of a l l turns was determined. It was decided that the cooling pancakes were to be of such a size that one-third of the total cross-sectional area of the coils was copper. The remainder of the space would be taken up by the cooling pan-cakes, insulation and the packing factor of the wire in the coils. Empirical values of the packing factor for various wire sizes were obtained from Roters^, , . 12. This choice of area allotted to the copper wire determined the ratio of the mean-turn length to total cross-sectional area of the coil assembly, as outlined in Appendix 1. The values of mean-tum length, cross sectional area, and the final dimensions of the coils were then found from the size of the pole piece. Considerations determining the choice of the shape arid size of the pole piece are discussed below. The choice of the wire size was determined by the voltage of the source. At the time of the design of the magnet, the d«c0. source had not been decided upon, hence a source giving 120 volts was assumed. Using this value, the closest commercial wire size was jjftLO wire. Square wire was chosen for its superior packing factor. Using #LQ wire, the following specifications were determined: Number of turns 1292 Current 34«8 amps. Resistance of coils (series) 3,42 ohms. Voltage required 119.2 volts. Power to be dissipated 4150 watts. One of the main difficulties encountered in the magnetic circuit calculations is that of the flux leakage. Not a l l of the flux from the pole pieces will be concentrated within the gap, but will tend to be spread out over a considerably larger area, resulting in a diminution of the field strength in the gap. It is therefore necessary to make the cross-sectional area of the pole piece face large enough to insure that a reasonably uniform field intensity will exist over the sample, perpendicular to the axis of the pole pieces and that this field intensity be sufficient to produce saturation in the sample. 13. The effect of the leakage factor can be nullified by making i I; 1 j use of a geometrical factor. That is, i f the pole pieces are tapered so that the ratio of the area of the large end to that of the small end is equal to the leakage factor, then the geometrical factor will tend to in-crease the flux density in opposition to the loss due to leakage. In this way, the flux density in the iron of the pole piece is known to be requir-ed to be 18000 gauss, since this is the value chosen for the gap field strength. On calculating the leakage factor of the pole pieces, the following assumptions were mades (a) All flux falling outside the arc of a circle whose center is at the gap center, and whose radius is equal to the distance from the gap center to the shoulder of the pole piece, can be neglected. (b) It is assumed that the field intensity across the gap is constant, and that i t falls off as ^ outside the gap, where r is the distance from the axis of the pole pieces. Using these assumptions, the leakage factor was found to be 9. It was pointed out on page 9 > that one of the faults in the design of the Schnay majgnet was that the yoke became saturated before the pole pieces did. In the magnetic circuit, the amount of magnetomotive force 'dropped8 across a given component will depend upon the reluctance of that component. It is desirable to have the maximum amount possible of the magnetomotive force produced by the coils to be dropped across the air gap. Thus the reluctance of the yoke should be kept small. The reluctance increases in the iron as saturation is approached. In order to avoid saturation the flux density should be kept small, and this can be 1 4 , done by using a large cross<=sectipnal area in the yoke. The placement of one coil assembly on each pole piece gave, further assurance that the pole pieces would be .saturated before the yoke. As was discussed on page 3 , i t is desirable, for the purpose of measuring the magnetic moment of the samples by the 'torsion balance' method, to have a constant field gradient along the axis of the pole pieces, and zero field gradient perpendicular to the axis,, In the design of a non-uniform field, having special charact-7 eristics, Fereday' pointed out that the flux lines can be assumed to leave and enter the pole pieces normal to the surfaces of the pole pieces. On the basis of this assumption, i t was proposed that a field gradient of the desired characteristics could be produQed^^by\vhavdA:g;rone'<'Cpncave';pp-le face and one convex, the two having a common center of curvature. The magnitude of the gradient, and hence the force exerted on the sample could be control-led by choosing a suitable ratio of poleface area. It was anticipated that the actual characteristics of the field would not follow the ideal case as discussed above. Hence the pole pieces were designed to have removable ca ps tp facilitate a change of the shape of the pole cap if. necessary,, The final design is shown in Figure 2, Plate II 0 15. THE CONSTRUCTION AND ASSEMBLY OF THE MAGNET„ The coils were wound into pancakes, each pancake consisting of three layers of double cotton covered wire„ The wires were coated with air-drying glyptal varnish, and wound on wooden bobbins, which were removed when the varnish was dry, leaving the coils self-supporting,. The water cooling pancakes were made of two copper pans, one fitted inside the other. An internal spiral of copper strip forced the cooling water to follow a circuitous path in the pancake, insuring good circulation. The coils and cooling pancakes were made up into two assemblies Each assembly consisted of four coils: and five cooling pancakes. An insul-ating sheet of drawing paper coated with glyptal varnish separated the coils from the cooling pancakes. The coil assemblies were fitted on to the pole pieces by using wooden rings, tapered on the inside to f i t the pole piece and flat on the outside to f i t the coil or cooling pancake. Matching slots in the wooden rings permitted the wires from the inside of the coils to be brought out along the surface of the pole piece. This facilitated the making of connections between the coils. A diagram of the wiring of the coils is Figure 3 , Plate III. In order to prevent the cooling pancakes from bursting due to the large force exerted over their surface;, the completed assembly was placed between two 5/8 inch brass plates, which Were bolted together. The pole pieces were secured to the yoke by a large bolt, passed through the yoke and screwed into the pole,piece. Figure 4, Plate I V shows the components of one coil assembly. 16. Originally the yoke was to be 6 inches square, however the only available iron suitable for the magnet was k 1/2" x 8'". It was necessary to have the iron forged to 685 x 6" at the top of the yoke to accomodate the 6" diameter pole pieces. The forging of the yoke was done by the B.C Marine Company, The inside faces of the yoke were machined at the Sumner Iron Works, The pole pieces were machined by Mr. R. Richter in the Met-allurgy shop. Special high purity iron was used for the pole caps. The assembled magnet was put on a portable base. Both hot and cold water could be mixed in the cooling system so as to provide any i n i t i a l temperature of cooling water desired. By this means, excessive condensation on the brass plates was avoided. The water was connected in parallel in the cooling system, by-using a common manifold, A pressure gauge was installed in the water line. It was found that an operating pressure of 3=5 p,s.i„ was adequate. The direct current was supplied by a Hobart Welding generator. This generator was chosen in preference to-others because of i t s small a,=c0 ripple, remote control rheostat and low cost. It is capable of giving a current range of 0 to 200 amperes at a voltage of k0 volts. The coils were connected in parallel to operate at low voltage and high current. Figure 5 , Plate V shows the completed magnet with the torsion balance. PLATE II Figure 2„ The Final design o f the-Tiew 'SHagnet,, PLATE.Ill Figure 3. Wiring.DiagramofqQpils ,,.; Coils 1, 2, 3, 4 (right) and coil 3 (left) are wound in the same direction.' Coils / 1, 2, 4 (left) are wound in the opposite direction to these; The diagram of'each coil assembly shows the coils in the physical order in which they are assembled' on the magnet. Insulating Cooling Plate Figure 4, Component parts of one coil assembly are shown. See page 15 for f u l l description .of the coil assemblies. 17. PERFORMANCE OF THE ELECTROMAGNET, A preliminary test of the rate of flow of water in the pancakes was made by enclosing the pancakes in two heavy plywood boards, which were bolted together. Using the'"pressttre;.*directly-'f rom--t-he''tapy--a--f low of 50 c C o / s e c , was easily obtained, and up to 200 c.c/sec, was possible. The coils and .cooling.pancakes .were assembled, using a %.<:•. dummy wooden pole piece. The cooling of the coils was tested by taking the readings of voltage across and the current through the coils. From this the resistance changes, and hence the temperature changes were plotted against time. Runs were continued for periods of one hour, at currents up to 50 amperes. The maximum temperature rise was only 9°C0 Thus the coils were found capable of taking large currents, producing up to 6 5 , 0 0 0 ampere turns. The field strength of the magnet was measured with a flux meter and search coil, borrowed from the Physics department. These had been calibrated using a proton resonance method. The maximum field strength measured, using a current of 52.5 amperes and flat pole caps was 21 ,500 gauss. The field strength in the center of the gap is plotted against the current in Figure 7, Plate VIlo 18„ DISCUSSION, The work thus far described was carried out jointly by Mr. Ro Mo Shier, and the author. The remainder of the work, namely the production of a constant field gradient along the axis of the pole pieces, and the design and: construction of the torsion balance, was carried out independtly by Mr. Shier 8. ' . ; The rather large field strength obtained indicated that the magnet would be capable of producing saturation in the powdered samples. Subsequent work verified this to be so, When the cooling pancakes were first tested, they were lying horizontally. It was observed that in the assembled position, in which the pancakes were vertical, the top of the coils became quite warm. This was attributed to air being trapped in the cooling pancakes, preventing water from circulating properly, and dissipating the heat. To overcome this difficulty, small holes were drilled in the tops of the cooling pancakes. This permitted the air to escape. The pan-cakes were f i l l e d with water, the holes were tapped, and sealed.using small screws, a rubber gasket and sealing cement. Prolonged running of the magnet produced no further h e a t i n g o P L A T E V PLATE V/II 25,000 20,000 _ 15,000 _ 01 3 C5 C c CO 0) • H 10,000 5,000 -Current in Amperes Figure 7,. The field intensity in the ga'p>"o»f'•>? the magnet, using plane pole piece caps, for varying current., The current indicated is that measured in any one turn. 2 4 . PART .2 p.. AN INVESTIGATION OF THE MANGANESE-RICH FERROMAGNETIC ALLOY OF APPROXIMATE COMPOSITION Mn 6 o Al 2 o C20» INTRODUCTION, Langevin was the fir s t to give an electron theory of para= magnetism which s t i l l forms a valuable introduction to its study. He was able to show that for weak fields and high temperatures the susceptibility of a paramagnetic gas is given by X.. s M - C , o . o , l H T where X^ is the susceptibility^ T is the absolute temperature and C is a constant for the material concerned. On the whole^ , paramagnetic susceptibilities tend to follow a modified form of equation 1, known as the Curie Weiss law. This may be written as X = C , or T - 0 M - CH 0 0 0 0 0 where © is a characteristic constant of the substance considered, 9 Weiss pointed out the significance of © in equation 2s i t means that the material behaves magnetically as i f there were an ad<= ditional field NM aiding the true field H„ If we replace © by NC in equation 2 we get M = C(H * ..NM) ..... 3 T 25. The quantity represented by NM is called the molecular field, and N is the molecular field constant. It is interpreted as supposing that the element-ary magnet does have an influence on its neighbors, contrary to the assumpt-ions of the simple Langevin theory. From the assumption of the existence of a molecular field, Weiss was able to show that below a given temperature, the magnetic moment of a ferromagnetic substance has a definite value even when no field is applied. It can be shown that the molecular field is some thousands of times as great as the field which can arise from forces of purely magnetic origin. It was concluded therefore, that the molecular field must be electrostatic in nature. The modern explanation of the large value of N was provided x) by Heisenberg , who discovered what are known as the interchange inter-action forces, or exchange forces of electrons in atoms. These forces depend upon the alignment of the electron spins in the atoms of ferro-magnetics although the forces between the spins themselves are not responsible for N„ In the quantum mechanical expression for the total energy of a system of nuclei and their associated electrons, a term arises which is called the exchange integral. It takes into account the possibility that the electrons of adjacent nuclei may exchange places in the system. For the simple case of two hydrogen atoms, the integral has the form ff i 2 1 2 V^ef 2ef ef_ e£_ ef_ e 2 1 i j The existence of the exchange interaction wastdiacovered:. independently by Dirac, -Since the Dirac paper is in English, i t is given here as a references P„ Diracs, Proc, Roy0 Soc, 2 6 . where k, 1 refer to the two electrons, and 1 , 2 , to the two nucleic The *^ V's are the;w*twe-functions of the unperturbed systems (i.e. no interaction between electrons) and the clT'S elements of the configuration space of the specified electrons0 Heisenberg related the exchange interaction to the molecular field constant by N OC zJ o o o a o o 5 where z = co-ordination number of the lattice» It is seen that for ferromagnetism to occur N, and consequently J must be positive,, In general, J is negative,, Equation 4 shows that i f J is to be positive, the term involving r must be relatively large. The kl necessary conditions are found to be that the ratio of the interatomic distance to the effective mean radius of the electron density distribution of the electrons involved in the interaction shall be large, and also that the orbital: quantum number for these electrons shall not be too small. There is the further basic condition that the atoms must contain incomplete groups of electronso Slater^ has shown that these conditions are fulfilled in the ferromagnetic metals Fe, Co, and Ni, and in some of the rare earths. He gives the following data for the ratio of interatomic distance to the mean radius of the unfilled shell, and concludes that for TABLE 2 „ Metal , Fe Co .Ni .. Cr. Mn Gd D/r 3 o 2 6 3 o 6 4 3 o 9 4 2 . 6 0 2 . 9 4 3 d ferromagnetism to exist:, D/r must be greater than 3 . 0 but not much greater. 27. This raises the interesting point that atoms with uncompens-ated electron spins which do not in the pure state exhibit ferromagnetism because the value of D/r is not suitable may combine with othea? non-fferro* -magnetic elements to form crystals whose lattice constant or distance between neighboring atoms permits a suitable value of D/r, and thus give a ferromagnetic compound., For example, metallic manganese which exhibits a paramagnetism more or less independent of temperature has a lattice constant of 2„58 A° whereas MnAs and MnSb with 2„85 and 2„89 A° respectively, are ferromagn-e t i c The structure sensitivity of ferromagnetism in Mn alloys requires that a careful determination of the interatomic distances between Mn atoms be made. In a ternary alloy system i t becomes imperitive that a degree of order be attained by the atoms i f the measurement of the magn-etic moment of the Mn atoms is to have any significance„ A random array of atoms in the crystal lattice would result in some of the Mn atoms having the ferromagnetic condition fu l f i l l e d and others not, thereby masking the true effective moment» It was proposed to determine the crystal structure and degree of order of the ternary system Mn-Al-C, by X-ray methods, and to measure the effective moment of the manganese atoms, using the new electromagnet„ 28. PREVIOUS WORK. A survey of experimental investigations of ferromagnetic mangan-11 ese alloys has been given by Bozorth „ Of the ternary alloys, one of the earliest and most important systems reported was the Heasler alloy of composition C^MnAl . In this, and most other ternarys, the atomic percentage of Mn is not large. 12 Recently a group under the supervision of E„R. Morgan , has made a survey of manganese-rich ferromagnetic alloys. These alloys are based on a interstitial solution of carbon in manganese0 In each of the systems investigated, the ferromagnetic phase was reported having a face-centered cubic structure. Preliminary magnetic measurements, made on the Schnay magnetic balance indicated that the effective magnetic moment of the manganese atoms in the alloys was at least 1„0 Bohr magneton per atom,. One of the systems investigated in the survey was Mn=Al~C, Morgan suggested that these alloys were based on the composition M^AIC. which in turn, was assumed to be a stabilized form of a high temperature face-centered cubic phase of Mn^C 29o PROCEDURE. The compositions of the materials used in making up the alloy-are listed in appendix II. In order to avoid contamination of the alloy by nitrogen or hydrogen, the melting was done under an atmosphere of -purified argon 3 in a high frequency vacuum melting unit designed and built in the departs ment. The manganese and carbon were placed in an R 84 Norton Alundum crucibleo The aluminum was suspended in the furnace above the crucible by a light thread, and added to the manganese and carbon after the latter had been melted. The furnace was evacuated and the material heated for degassing. Argon was admitted after the vacuum had been restored following the degassing. The manganese and carbon were melted, and the aluminum added by raising the crucible up to the aluminum slug. This procedure was adopted as the most successful way of obtaining a clean melt. The alloy was ch i l l cast into a cold brass mold. A metallographic examination of a sample of the ch i l l cast alloy showed evidence of segregation. This was removed by homogenizing the alloys. Heat treatments were carried out in a standard quartz tuba furnace, with a sixteen inch heating element. Purified argon was passed continuously through the furnace during the annealing. The-annealed samples were found to have a thick layer of green crystals form on them, in spite of the fact that the furnace had been ini t i a l l y evacuated, and the heat-ing carried out in an argon atmosphere. The crystals were identified by 30. their X-ray pattern as MnO„ It was assumed that oxygen was entering with the argon. An attempt to prevent the formation of the oxide was made by placing the samples in a small quartz tube and evacuat.ing_jand^ placed in the furnace, and,the annealing continued as before. This prevent-ed further formation of MnO; however, the high vapor pressure of both Mn and Al resulted in the loss of these two constituents to the walls of the tube. Finally, by placing small pieces of manganese and aluminum in the tube with the sample, the losses were reduced. In this case, however, the pure Mn and Al condensed on the samples. It was decided to f i l l as much of the tube as possible with the alloy, in the hope that the vapour pressures of the manganese and aluminum would reach equilibrium with negligible loss to the tube walls. Subsequent analysis for the Mn and carbon content of the samples indicated that the latter method was success-ful. Debsre^Sherrer powder patterns were taken of a l l samples, using Fe radiation and a Mn f i l t e r . The cell parameters were calculated for a l l samples. Intens-ity measurements of a l l visible lines-were. made.using a Phillips goniometer, a geiger tube and a scalar. Each line was scanned from 20 - 30 times to provide a statistical average of the counts. Background corrections were made by measuring the background count on both sides of the lines. Intensity calculations were made for three assumed structures, and compared to the experimental values. To check that the correct unit cell had been chosen, the density was calculated using the atomic weights and measured parameters. The results 3 1 . checked with the measured density, within the experimental error of the density measurement0 Magnetic measurements were carried out for a l l samples at 293°K, 200°K, and 70°K, using the new electromagnet and torsion balance. Results were compared to a standard sample of nickel, and the effective moment per manganese atom was calculated, assuming a value of 0 „ 6 l Bohr magnetons for the standard nickel. Since the demagnetizing effect is proportional to M, the magnetic moment per unit volume, and since M decreases rapidly near the Curie • temperature, i t was assumed: that the Schnay magnet was capable of saturating the samples near the Curie temperature. Therefore the Schnay magnetic balance was used in the Curie point determinations0 The samples were heated in a small furnace, in the field of the magnet. Temperatures were measured using a Chromel=Alumel thermocouple0 The readings were taken as the samples cooled, and the Curie temperatures determined by extrapolating to zero magnetic moment on a plot of temperature against M. Manganese assays were done in the department by Mr. R„ Butters Carbon analyses were done by the Vancouver Steel Co„, and checked in the department by Mr0 M. Swanson<> 3 2 . RESULTS, The various heat treatments of the samples are shown in Table Sample,No, Heat Treatme nt... ( 1 ) Chill cast o ( 2 ) Homogenized at 1 1 0 0°C for 1 0 0 hr„ Slow Cooled. ( 3 ) Ot 09 w 99 00 03 Water Quenched. (4) 05 00 oo 98 408 00 Slow Cooled,, ( 5 ) 00 00 00 » 2 1 6 08 Annealed 00 800°C " 4 8 00 00 0» 6 5 0°C w 2 4 00 00 00 480° C 9 0 4 8 09 08 00 2 0 0°C M 4 8 n The results of the manganese and carbon analyses are shown in Table 5 o The weight per cent of aluminum was determined as ( 1 0 0 % =• Mn - C), since the presence of the manganese made i t difficult to determine the amount of aluminum by chemical means. 33, TABLE .. 5o Sample Wt. fc, Mn wt. ic... Mn6oAl2oC2o 80,8? 5,89 13,24 1 82,00 5,90 12.10 2 80,90 5,90 13,20 3 80,00 6,20 13,80 4 ' 82,30 6,21 11.49 5 81,00 2,09 16,91 Table 6 gives the measured lattice parameter, Gurie temperature, and the effective magnetic moment per manganese atom, extrapolated to zero degrees Kelvin, The moment is given in terms of Bohr magnetons. One Bohr magneton is the dipole moment associated with the spin of one electron. The values of the lattice parameter were obtained by assuming a cubic perovskite structure,' Corrections were made according to the 13 methods described by Henry, Lipson and Wooster , The calculated and measured intensities of the X-ray lines are compared in Table 7, In presenting the relative values of intensities i t was thought that the adopted method of using ratios of the different lines, as shown, was a more reliable comparison than one in which a l l intensities are compared to one arbitrarily chosen line, say the line with the lowest intensity is assumed to be unity. In the latter case, i f the experimental value of the line chosen as a standard should be incorrect, i t would tend to spoil the values of the other lines. Table 7 shows only the calculated values assuming atoms i n t.he 34. unit c e l l occupied the following positions; Al 000 C Hi Mn HO, OH This structure i s known as the perovskite structure, and accounts for a l l the lines seen on the X-ray films. Calculations for the structure having the positions of Al and C reversed give very poor agreement with experiment-a l values. The method of calculation, and significance of the results w i l l be, described more f u l l y under the heading of Discussion. • G Assumed perovskite structure. 35. TABLE .60 Sample No. a. i n A° Effective magnetic moment i n Bohr magnetons Curie Temp. 1 3.865 1.20 Bohr mag. 127 °CL 2 3.873 0.99 w 57 3 3.873 1.08 57 4 3.874 1.12 «» 55.5 5 3.870 1.03 " 104.0 TABLE.. 7. .Ratio .of. lines,.. Calculated Measured-I l l s 100 5.90 6.00 Ills200 1.70 1.82 1115 220 3.28 3.34 Ills 2 2 2 6„95 6.55 I l l s 311 3.00 2.87 200s100 3.46 3.-30 200s220 1.93 1.84 200s222 4.10 3.60 200s311 1.80 1.56 220s100 1.79 1.79 220s222 2.12 1.95 311s220 1.07 1.18 100s222 1.17 1.09 36. If maximum order i s to be produced by a heat treating process, i t i s convenient to know the c r i t i c a l ordering temperature of the alloy. According to Sykes and Jones'^, the required annealing time can be greatly reduced by annealing the sample just below the c r i t i c a l order-disorder temperature to obtain the equilibrium degree of order at that temperature. Continued annealing at a lower temperature w i l l then produce the degree of order desired. An attempt to determine the c r i t i c a l ordering temperature by plotting the el e c t r i c a l r e s i s t i v i t y against temperature, was carried out, using a Kelvin Double bridge to measure the resistance changes. The c r i t i c a l temperature can be found from the discontinuity in el e c t r i c a l r e s i s t i v i t y ^ . A photograph of the apparatus i s shown i n Figure 8> Plate VIII. In this way i t was hoped that a systematic heat-treating routine could be devised. g Unfortunately, the results were not reliable. The samples were obtainable, in short lengths only, due to their brittleness. Changes in resistance due to end effects and the development of cracks in.the specimen as i t was heated were sufficient to invalidate the results. Fortunately, as described-on pages 37 - 41,;-a remarkable degree of order existed even in the c h i l l cast sample. PLATE VIII Figure 80 The apparatus used in making the resistance versus temperature measurements„ 37. DISCUSSION AND CONCLUSIONS. Under certain circumstances, i t is possible to determine the degree of order in a crystal lattice by means of X-ray intensity measurements. The term that dominates the intensity calculation is the so-called structure factor. This term is directly dependent upon tha geometrical array of atoms or molecules in the lattice. In general, the structure factor may be written as where -£ ^  is the atomic scattering factor of the atom at position (U^, V^ , W^ ) in the unit cell, and h, k, 1 are the Miller indices for the plane concerned. Consider the alloy Cu3Au, which forms a face-centered cubic lattice. In the completely disordered state the atoms are distributed at random among the lattice sites and the effective atomic scattering factor is taken as the average, Now because of the trigonometric terms in F, the structure factor for the planes whose indices are a l l even or a l l odd reduces to 4 x £ a u = + 3 "FQu5 whereas for the planes whose indices, are mixed, the structure factor reduces to zero in the disordered state. In the fully ordered lattice, the atomic scattering factor of each atom in its particular position in the unit cell is used. In this case, the structure factor for the lines corresponding to reflections from planes whose indices are homogeneous, remain unaffected, whereas the 38, lines corresponding to inhomogeneous indices become different from zero 9 Suck lines are called superlattAce..lines, and appear only when some degree of order exists. Hence they can be used as a measure of the degree of order. The situation i s quite different for the case.of ..the. perovak-it e structure, however. Here the unit c e l l is effectively face-centered cubic, with an extra atom in the body=centered position. Assuming f i r s t , a completely ordered structure, with atoms at the positions A l 000 C 4 4 f t Mn £|0, J0|, 044, the structure factors reduce to the terms given i n column two of Table 8; the evaluated result i s given in column three. For the fully, diso.Kd«pedv.lattica>..,.|.^...? 1/5( ^  + £Q + -3? M n ) must be used. The structure factors are given i n column four, and evaluated i n column fi v e . Since F appears as a squared term i n the intensity calcul-ation, the absolute values of F are given. 39. TABLE g» Line F ordered (F ord.) F disordered : (F dis.) 10G ?A1 - M^n * 1 2 . 1 l / 5 ( f A 1 + £ c + 1 13 .86 110 f«l - f Mn + f C 2 . 3 »» 0 1 1 2 . 0 2 111 f i l + 3 f M n ^ \ i 4 7 . 8 0 «• 0 3 3 2 . 5 8 200 f i l + 3 FMn + f ( l 50.55 w o 5 5 0 . 5 5 2 1 0 f i l - P - f rMn 1 C 5 . 9 0 w 0 1 9 . 0 6 211 fAl f * * < 0 > 2 . 3 m o 1 7 . 8 0 220 f A l + 1 3 6 . 5 5 w 0 5 3 6 . 5 5 2 2 1 ?A1 - '^ Mn " $C 7 2 . 3 w 0 1 6 . 7 8 222 fAl + 3^Mn + ^ ( / 2 8 . 1 «» 0 5 2 8 . 1 300 fAl M^n = i > 2 . 3 m 0 1 -310 f A l _ ^ Mn + ^ C 72.3 0 1 311 f i l + "^Mn " "^C 2 6 . 0 0 m 0 3 1 8 . 0 0 It is seen that under the assumption of complete disorder, the lines 1 0 0 . 110 etc., not only remain non-zero, but actually increase over the ordered state. Unfortunately there is no way of determining the value of the order parameter for the system under consideration, since the line intens-ities do not change in a linear way with the degree of order. It is inter-esting to note that the lines 2 0 0 , 220 and 222 are unaffected by the degree of order in the lattice. Significant information can be obtained from a consideration of line 1 1 0 . In the completely ordered alloy, the intensity is seen to 40. be very low, whereas in the disordered state its value is comparable to that of line 100. The experimental intensity of the 110 line was too small to measure. Similarily, the intensity of line 211 in the ordered state is lower than that of 110, whereas in the disordered state i t is close to that of line 210. Again, the intensity measurements were unable to detect 211, It is indicated therefore, that a fairly high degree of order exists even in the chill cast sample. This conclusion, however, can only be stated from the results of the intensity measurements. To say that ordering exists because of the appearance of the «superlattice lines', as 12 reported by Morgan , is quite erroneous. Indeed, as already pointed out, this could lead to the con-clusion that the order is increasing when in reality i t is decreasing, since the intensity of the 100, 110, and 211 lines increase with disorder. The calculations of density from the considerations of the unit cell led to good agreement with the experimentally determined value. 16 Goldsmidt has shown that a criterion of the stability of the peroyskite structure can be obtained from the fact that maximum stabil-ity occurs when the parameter t is equal to unity, where t is defined ass t = r A l 4 r M n Here r is the ionic radius. The calculated value for Mn3AlC was 1.002. It is-interesting to note that a perov3kite structure of Mn^ C, which Morgan reported as unstable leads to a value of 1,10 for t. An examination of Table 6 reveals that the Curie temperatures decrease as the lattice parameters increase. This would indicate that the ratio of interatomic distance to the ionic diameter of the manganese atom is somewhat too large for the maximum energy of magnetization. In the ch i l l cast sample, the interatomic distance was 3.865 A0, Assuming a 3d ionic radius of 0.9117 A0, the ratio of D/r - 3.865 - 4.24 0.91 This also indicates, that the radius is too large for maximum exchange interaction, as seen by referring to Table 2, page 26, and confirms the conclusion drawn from the Curie temperature measurements. It is interesting to note that the value of 1.2 Bohr magnetons per manganese atom for the c h i l l cast alloy is in agreement with the value IS deduced by Pauling-1-0 who attempted to account for the experimental values of saturation magnetization of the elements. The experimental curve is shown in Figure 9 , Plate IX. This, of course, makes i t difficult to account for the values of saturation magnetization of the other samples, unless i t is assumed that a greater degree of disorder exists, than for the c h i l l cast specimen, resulting in fewer Mn atoms in the ferromagnetic state. Some justification for this assumption is given by the faint appearance of line - 110 in the X-ray pattern of samples 2 and 3, as seen on Plate X„ No indication of the presence of line 110 is given in the chi l l cast X-ray film, thereby indicating a higher degree of order In the ch i l l cast sample. PLATE IX S' 3 .5 -+ Fe-Cr Fe-Ni c Fe-Co p Ni-Co & Ni-Cu 7 Ni-v:is <? Ni-Cr Ni-Mh Co-Cr 0 Cb-Mn '< Pure A Metals ELECTRONS PER ATOM Figure 9. A plot of magnetic moment per atom against atomic number..,.,.„<The. solid line is ...the .theoretical value; the dotted lines show the experimental measurements, 18 PLATE X Figure lbO. The Debye-Sherrer X-ray powder pattern for sample number 1. 43. APPENDIX I. Design Calculations. 1, Estimate of ampere-turns required (NI - H^) = H a l a amp-turns-• = 18000 gauss x 2o02 gauss-inch x 1 inch. m 36,400 ampere turns. From t r i a l designs, final estimated ampere-turns = 45,000, 2, Power to be dissipated. Assumed temperature rise = 20°C n rate of flow of water = 50cc/3ec, cc „ ipules; cal .% Power dissipation = 20°C x 50 iec. x ^ o l° c a l — x 1 ° » 4180 watts, 3, Effective resistance of copper in the coilss -6 R = power. ^ = 4180 _ = 2„06 x 10 ohms, ^ampere-turns) Specific resistance of copper at 20°C is —7 yV = 6,79 x 10 ohm-inch. Temperature coefficient of resistance of copper = a ,0„ Specific resistance at 40°C = <?„( I 4-=?At ) = 6,79 x IO"7 ohm inch (1 + 3,93 x 10~3 x 20) i.e, ?w°c - 7.324 x 10° 7 ohm-inch. Let L = mean circumference of the coil, A = total cross-sectional area of coil assemblies "P » space factor of the windings. 44. Assume ~i" • 3. Then R = ^  L ' I T T L = R_ = 2.Q6 x 10~6 0.938 «,.»,, „ 1 A ^ 7.324 x IO"7 x 3 The shape of the pole piece is shown in Figure \0, Plate 3 3 The width of each coil assembly will be 3 inches, which" provides a wo.rking space of 2 inches between the coil assemblieso From Figure 16 we have tan 0 = 3-1 = x 3$ • 3 o°o X = 1.715 A = 3b + | x 3 x 1.715 2 o°o A = 6 b + 5.15 L = ^ :o.p.+ i.D.1 2 J -^(6 2b.+ 3/4) • (6. - 1 . 7 1 5 . + 3/4) "tt[b + 5 o 8 9 ] 6 0 0 * 0 © From equations 1 , 2 and 3 » w e can.evaluate A2 L, and b 0 A = 38.15 square inches L = 35|08 inches b «= 5o5 incheso Area of copper - A = 38 .15 = 1 2 . 7 1 square inches. 3 If we assume one turn of solid wire, then the copper density per ampere k 6 Area of copper = TT x 1 0 x 1 2 . 7 1 Total amperes ~±~irr~~ 4 .5 x K r .amperes ' - 36O c i r C o mils/amperes. Assume the source voltage is 120 volts. Then current s Power => 4180 » 34.8 amperes, volts 120 o ° 0 Area of the wire • 35 amperes x 360 circmils.. ampere - 12,600 c l r c milso . /IO commercial wire size - 12,535 circ.mils, = .00984 square inch. Number of turns required = 12.7-1 = 1292. .00984 Current required = 450CO = 34.8 amperes. 1292 Resistance of coils = 1292 x 35.8 f t . x .824 x 1_ o h m a 12 .928 1000 f t . » 3o42 ohms. Voltage required for series connections = 3.42 ohms x 34»8 amps. = 119.2 volts. Power dissipated = 34,8 amps, x 119.2 volts = 4150 watts. From the diagram shown,.in. Figure 2 9 P l a t e n , the mean path length in the iron port of the magnetic circuit is 46 inches. To determine the value of the field in the iron, H^ , the following relation is used: B i = B a g l where = flux density in iron BQ 88 flux density in air gap » 18000 gauss. g = geometrical factor area of small .diameter of pole-?piece. to o» large ' m w 59 " - 1 9 1 - leakage factor s total flux, through largest :part of pole*?piece flux through air gap 2-vrr H dr o'o B„ = B gl = B = 18000 gauss< i a a From Roters, for B i » 18000 gauss, H„ = 200 ampoturns. 1 inch o .°„ Total ampere turns required - NI - Hal + H 1 i i a a - 200 x 46 + 36,400 - 451,600 ampere turns. PLATE X ~ 3 — Figure 10 a 0 Dimensions of pole piece and coil assembly0 V 2 1 X / L 3 _ H Figure 10 b 0 Detail of pole piece0 47 = APPENDIX. II. The following base materials were used for the alloys: Manganeses 99«.9 percent purity, donated by the Electromanganese Corporation of America. Aluminums 99° 99 percent purity, donated by the Aluminum Company of Canada6 Carbons Spectroscopic purity e BIBLIOGRAPHY 1, R o Buehl and J. Wulff, Rev, Sci, Inst, £ 224,(1938) 2, R„ Schnay, Masters Thesis, University of British Columbia, 1951, 3 , R, Piercy, i • . » i n n »» »• 1952. 4, .JSwiag,...-'-Magnetic Induction i n Iron, and .other. Metals! , 5, W„. Sucksmith, Proc, Roy. Soc, A170- 551, 1939. 6 , Roters, 'Electromagnetic Devices'0 7, R, Fereday, Proc. Roy, Soc, Zj6 214, 8, R, Shier, Thesis, University of British Columbia, 1953, 9, P, Weiss, Jour, Phys. (4), 6 , 661, 1 0 , J, Slater, Phys. Rev,, 3.6 57, 1930, 11, R, Bozorth, 'Ferromagnetism*, D. Van Nostrand Co,, 1951, 12, E o R , Morgan, Progress Report, 13, Henry, Lipson and Wooster, 8Interpretation of X-^ ray Diffraction Photographs,' McMillan Co, London, 1951o 14, C o Sykes and F, Jones, Proc Roy, Soc, AI06 376,1938. 15, Kurnakov and Agnew, Jour, Inst, Metals, 4Ji 484. 16, M. Goldschmidt, 'Geochim, Verlungsgesetze der Elemente VII, 1927, 17, J, Smithells "Metals Reference Book' Butterworth, London, 1949, 18, L. Pauling, Phys, Rev, 5Jt 899, 


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