Science, Faculty of
Physics and Astronomy, Department of
DSpace
UBCV
Shier, Richard Mowat
Master of Applied Science - MASc
University of British Columbia
A magnetic balance for the measurement of the saturation magnetization of alloys has been designed and built. The magnet develops a field strength of 21,000 oersteds in a gap approximately seven-eighths inch long and two inches in diameter, when consuming a power of 4.5 kilowatts. This field is sufficient to saturate solid metal samples of random shape. Specially shaped pole caps are used which produce a gradient in the direction of the axis of the gap which is constant to within two percent, within a volume cube three-sixteenths of an inch on edge. The ratio of saturation magnetizations of iron and nickel at room temperature agree closely with the accepted values. A new magnetic phase has been discovered in the manganese carbon system. It has been identified as ferromagnetic, but its composition and crystal structure remain unknown.
A MAGNETIC BALANCE AND ITS APPLICATION TO THE INVESTIGATION OF FERROMAGNETISM IN MANGANESE CARBON ALLOYS by RICHARD MOWAT SHIER A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED 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 APPLIED SCIENCE. Members of the Departments of Physics and Metallurgy THE UNIVERSITY OF BRITISH COLUMBIA OCTOBER, 1953 ABSTRACT. A magnetic balance for the measurement of the saturation magn-etization of alloys has been designed and built. The magnet develops a f i e l d strength of 21,000 oersteds i n a gap approximately seven-eighths inch long and two inches i n diameter, when consuming a power of 4«5 kilowatts. This f i e l d i s sufficient to saturate solid metal samples of random shape. Specially shaped pole caps are used which produce a gradient in the direction of the axis of the gap which i s constant to within two percent, within a volume cube three-sixteenths of an inch on edge. The ratio of saturation magnetizations of iron and nickel at room temperature agree closely with the accepted values, A new magnetic phase has been discovered in the manganese carbon system. It has been identified as ferromagnetic, but i t s composit-ion and crystal structure remain unknown. ACKNOWLEDGEMENT The. author, i s grateful to Mr, F.K. Bowers for many helpful suggestions contributing to a much more economical magnet design than had at f i r s t been thought possible. The Steel Company of Canada, Ltd., Hamilton, Ontario, very kindly contributed 1200 pounds of iron prepaid, for the magnet yoke. The author is also grateful to Mr, R. Richter for machine work done on the pole pieces and the suspension of the magnet. The design and construction of the magnet, up to but not includ-ing the design of the suspension and the shaping of the pole caps, was done in conjunction with Mr, CV, Kidson, Funds for the magnetic balance and certain other laboratory f a c i l i t i e s were provided by the Defence Research Board under Research Grant 281, The experimental work was done in the laboratories of the Dep-artment of Mining and Metallurgy, and the author i s grateful for the assistance offered and the f a c i l i t i e s available to him. The author received financial aid from The National Research Council i n the form of a Bursary during the winter of 1952-53, and a summer extension i n 1953» TABLE OF CONTENTS Page I o 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 e o o o o o II. THE MAGNETIC BALANCE Preliminary investigations . . . o o . . . . . . 7 Design of the magnet . . . . . . . . . . . . . 12 I n i t i a l tests of the magnet. . . . . . . . . . . . o . o o 20 Producing a uniform f i e l d gradient . . . . . . . 26 Final tests of the magnet. . . o a . o o . o . . . o . . . 3^ Gonclusions 0 . 0 0 0 . 0 0 0 0 0 0 0 0 0 . 0 . 0 . 0 . 0 0 46 III. FERROMAGNETISM IN MANGANESE CARBON ALLOYS Previous worko 0 * 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Pl*0C©dU.l*6 o o o o o o o o o o o o o o o o o o o o o e o « o 30 R6SU-LtS o O O O 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 * 0 0 0 0 0 0 5-^ ConCllXSXOTlSo o o o o o o o o o o o o o o o o o o o o o o o IV. APPENDICES 1. Detailed calculations for the magnet. . . . . . . . . . 56 2. Construction of the magnet. . o . a s o o o . o . . . o 62 3. Details of the successful pole caps . . . . . . . o . . 65 4. Wiring diagram of the magnet. . . . . . . . . . . . . . 66 5. Purity of the metals used . . . . . . . . . . . . . . . . 67 V © B I B L I O G R A P H Y o o o o o o o o o o o o o o o e o o o o o o o o o ILLUSTRATIONS Page 1 . Shnay's magnetic balance „ „ < . . < > » » < > « . . . . « » . o o . a . 6 2 . The magnetxc balance . o . o o . o o o . . o o « . . . . e . ' 0 ' o o 21 3 . The magnetic balance - suspension lowered. . . . . . . . . . . . . 2 2 4 o The magnetic balance - suspension raised , ;. . . . . . . . . . . . . 23 3 o Th© S U 3 pGIlSlOn 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 6o Hypothetical flux distribution between concave and convex pole caps 2 8 7 . Typical energy curve for stable rest position. . . . . . . . . . . 2 8 8 . Force curve due to a uniform f i e l d gradient. . . . . . . . . . . . 2 8 9 . Energy curve due to a uniform f i e l d gradient . . . . . . . . . . . 2 8 1 0 . Force curve due to the suspension. . . . . . . . . . . . . . . . . 2 9 1 1 . Energy curve due to the suspension . . . . . . . . . . . 29 1 2 . Total energy curve obtained by adding curves in Figures 9 and 1 1 . 29 1 3 . Force curve due to a non-uniform gradient. . . . . . . . . . . . . . 3 1 1 4 . Energy curve due to a non-uniform gradient . . . . . . . . . . . . 3 1 1 5 . Total energy curve due to a nonuniform gradient and a light suspsnsion 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 - 0 0 , 0 0 0 0 0 0 0 0 0 0 0 3 1 1 6 . Field distribution which would produce the non-uniform gradient of Fi^XlI*© X 3 o o 0 0 0 0 0 0 0 0 0 0 0 0 o o o o o o o o o o o 0 0 0 0 3-L 1 7 o Flux lines which would produce the non-uniform gradient of Fig. 1 3 32 1 8 o Typical non-uniform gradient which would produce an 'overstable' i*X 6 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 o 3 ^ 1 9 o First measurements of the f i e l d gradient . . . . . . . . . . . . . 3 5 2 0 . Effect of replacing the convex cap by a concave cap with success-ively smaller r a d i i of curvature . . . . . . . . . . . . . . . . . 36 2 1 o Effect of reducing the r a d i i of curvature of both caps . . . . . . 3 8 -(continued next page) ILLUSTRATIONS (continued) Page 2 2 , Effect of varying current . o . 0 « o o o . o o o o . o o o o . o o 4 0 2 3 o Variation of gradient 3 H s along y and z directions, - . , . , . 41 2 4 „ Field strength as a function of tot a l magnet current, . , , 0 . 0 4 2 17 2 5 . Vogel and Doring's phase diagram of manganese carbon, . . . , . 4 9 2 6 , Determination of whether the 1,8 weight percent carbon alloy i s ferromagnetic or paramagnetic „ » , , o o , , 0 0 0 0 , 0 0 a , , 5 3 2*7 o A c o i l SLSSGinbly 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 57 28 o Mctgn©"t» ciiniGnsions o o o o o o o o o o o o o o o o o o o » « o o o 6X TABLES Page 1 . Tests on Shnay's magnetic balance . . o . . o . . o . . . . „ , . . 1 0 2 , Dimensions of the pole caps o o o o o o o o o ° » ° o o o o o o ° o 3 3 3 o Effect of sample shape, o o o o o o . o s . o . . . . . . . . . . . 4 4 4 . Check of the line a r i t y of force vs. sample weight , „ . . . o . o o 4 4 5 „ Tests of saturation of iron and nickel powder samples . o . o . . . 4 6 6 „ Ratios of saturation magnetizations at room temperature for iron » and nxckelo o o o o o o o o o o o o o . o o o o . o o o o . o o o . 4 7 7 . Magnetic measurements of c h i l l cast alloys. . . . . . . . . . . . . 5 1 8 . Magnetic measurements of the 1.8$- carbon alloy, after heat tl*©&tlll6ntS e o o e 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 5^ 4-9 o COXX Winding d&^ Sl 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 5 9 l o A MAGNETIC BALANCE AND ITS APPLICATION TO THE INVESTIGATION OF FERROMAGNETISM IN MANGANESE CARBON ALLOYS 0INTRODUCTION i where The susceptibility of a substance i s defined as X ° M i s the magnetization, or dipole moment per unit volume., in the substance, when placed in a magnetic f i e l d H» The induction B i s given by the r e l -ation B s H + 4 TTlf. A diamagnetic substance has a small negative susceptibility, a paramagnetic substance a small positive susceptibil-i t y , and a ferromagnetic substance a large positive susceptibility. Further, the susceptibilities of diamagnetics and paramagnetics remain constant with H, while that of a ferromagnetic varies with f i e l d , Dia-magnetics and paramagnetics become non-magnetic i n zero applied f i e l d , — • whereas in a ferromagnetic, M is non-zero when an applied f i e l d i s decreas-ed to zero, and M reaches a maximum value as the applied f i e l d i s increased indefinitely. This behaviour of a ferromagnetic material is attributed to domains, which are small regions having a uniformly oriented and constant magnetization of the maximum value even in the absence of a f i e l d . As the f i e l d i s increased, the domains become oriented i n the direction of the applied f i e l d , so that when a l l the domains are aligned, the macroscop= i c body has a value of magnetization equal to that of each domain. The spontaneous magnetization of a substance i s defined as the magnetization of a domain in zero applied f i e l d . The absolute saturation moment, or saturation magnetization,is the spontaneous magnetization at absolute zero. The saturation magnetization i s a quantity dependent only upon the composition and crystal structure of the material, and is ind-2. icative of the electronic spin arrangement of the individual atoms, and the interactions between them. Properly, the variation of domain magnetization with f i e l d strength should be taken into account in any measurement, the saturation magnetization being obtained by extrapolation to zero f i e l d and zero temp-erature , Sucksmith^" has employed magnetization isothermals i n this way to determine the saturation magnetization. However, the variation of domain magnetization with f i e l d at low temperatures i s so slow that a close approximation to the saturation magnetization can be obtained merely by measuring the macroscopic magnetization of the sample in question, when saturated in a strong f i e l d , at various temperatures, and extrapolat-ing to absolute zero. In future, the saturation magnetization at a temp-erature other than zero refers to the value of the macroscopic magnetizat-ion of the material, when i t i s in a saturation f i e l d . The saturation magnetization of a sample at temperatures above absolute zero can be determined by measuring the force exerted on i t in a magnetic f i e l d having a gradient constant- pver the volume of the sample (magnetic balance method), or by measuring with a b a l l i s t i c galvanometer the charge induced in a c o i l containing the sample which i s connected in series opposition with an identical c o i l , when both coils are placed in the same homogeneous magnetic f i e l d , and the f i e l d i s suddenly reversed ( b a l l i s t i c method). The equations for the f i r s t method can be developed as follows. The energy of a magnetic dipole a i n a magnetic f i e l d H i s m 0 lf« Now the magnetization "M* i s the dipole moment per unit volume. Thus the energy of a magnetic body of; volume v i s w - "M „ "H V 3. If the magnetization and f i e l d are parallel, which i s the case i n a para-magnetic or diamagnetic body and i n a saturated ferromagnetic body, the energy becomes simply W = MHv The force on the body i s then F • - grad W The force component in the x direction i s F X = 3x Two cases now arise. For diamagnetic and paramagnetic bodies, M = %H where % the susceptibility i s constant, and F X - - dim) v 0 x = -tt* a(H2) d x dx For saturated ferromagnetic bodies, M i s a constant throughout the body and hence i s independent of x. Thus F x - - 9(m) v 9 x - - vM 0 H Thus oy measuring the force on an unknown sample and comparing i t with the force on a sample of a known material placed i n the same force f i e l d , one can determine the susceptibility of diamagnetic or paramagnetic materials, or the saturation magnetization of ferromagnetic materials. Now the force exerted on the sample must be constant over a f a i r region for two reasons. F i r s t , the force must be the same on a l l parts of the sample. Secondly, i f the force is constant over a f a i r volume, the posi«= 4. tioning of different samples w i l l not be so c r i t i c a l . These considerations indicate that for diamagnetic or para-magnetic measurements, a magnetic f i e l d must be produced having the pro-duct of f i e l d strength and f i e l d gradient constant over a f a i r region, and for ferromagnetic measurements, a magnetic f i e l d must be produced having a f i e l d gradient constant over a f a i r region. If a body i s placed in an applied magnetic f i e l d H ^ , the f i e l d produced by the body i t s e l f i s such as to oppose the applied f i e l d . This demagnetizing f i e l d i s proportional to the magnetization of the sample, the factor of proportionality, called the demagnetizing factor N, being dependent only on the geometry of the sample. The net internal f i e l d Hj i n the sample i s reduced to Hj - H A - NMo Long needles and ellipsoids of revolution have low demagnetizing factors. Flat plates held normally to the f i e l d direction have high demagnetizing factors. For a small applied f i e l d and a large demagnetizing factor, the net f i e l d may be reduced below that necessary to saturate a ferro-magnetic sample. In order to ensure saturation, the applied f i e l d must be made as large as possible. Thus two requirements of the magnet in a magnetic balance f o r ferromagnetic materials are a high f i e l d strength and a f i e l d gradient constant over a volume several times larger than the sample. The magnetic moment of a ferromagnetic material i s due to the 2 moments of the individual electrons. In Heisenberg's original theory of ferromagnetism, he postulated that the exchange energy between two atoms i n a ferromagnetic body must be positive, i n order for the ferro-magnetism to exist. The exchange energy i s a term i n the expression for the t o t a l energy of a number of atoms, that arises because of the coulomb attraction between the electrons themselves, and between each electron and a l l other atoms except the one to which i t belongs. It accounts for the fact that a linear combination of a l l possible configurations of atoms and electrons must be used to provide a wave function for the system which i s either symmetric or antisymmetric, Bethe then showed roughly that as two atoms are brought together from a distance, the exchange energy is at f i r s t positive (ferromagnetism) then changes sign and becomes negative (antiferromagnet ism). 3 Zener used a different approach in his theory of ferromagnetism He postulated that exchange energy between two atoms each having a net spin i s always negative, tending to align the spins in an antiferromagnetic manner, but that the coupling of the spins of the conduction electrons i n the 3d band tends to align- the spins; in.a ferromagnetic manner, whichever tendency i s the stronger determines whether the material i s ferromagnetic or antiferromagnetico If the atoms in an antiferromagnetic material are spaced farther apart, the exchange coupling diminishes and the indirect coupling via the, conduction electrons dominates, creating conditions conducive to ferromagnetism. Therefore no matter which theory i s used, i t is apparent that i f an element having atoms with a net unbalanced spin i s in an antiferro-magnetic condition, i t possibly can be made ferromagnetic i f the atoms are spaced farther apart. Using this concept, Morgan^ began investigations into manganese - rich ternary alloys composed of manganese, carbon, and a third element. Because the binary system manganese-carbon was one of the few not investigated, and because information on the binary manganese-6, carbon would be fundamental and necessary to any work on manganese-carbon ternaries, a more detailed study of the binary seemed i n order. II. THE MAGNETIC BALANCE Preliminary, Inv.estications». . 5 A magnetic balance had been built by Shnay to measure the magnetization of steels near the Curie point. See Figure 1. This instrument is of the type in which the force on a sample placed i n a magnetic f i e l d with uniform gradient is measured, and is constructed according to the design of Buehl and Wulff In Shnay's instrument, a d.c. electromagnet, consuming about 500 watts, provides a magnetic field, of about 3000 oersteds in a gap one inch long and two inches in diameter between the ends of two iron pole pieces. The faces of the pole pieces are specially shaped so that the f i e l d gradient is i n the direction of the axis of the gap, and i s f a i r l y constant over a part of the axis. The sample is placed i n a metal bucket on the end of a horizontal arm, which is suspended at its midpoint by a v e r t i c a l piano wire suspension. The bottom end of the suspension i s held fast| the top end i s connected by a worm gear to a d i a l which measures the amount of rotation of the suspension wire. A mirror i s attached to the horizontal arm. A light source sends the image of a hairline to the mirror where i t is reflected to appear on a distant scale. When the f i e l d i s switched on, the force caused by the f i e l d gradient tends to pull the sample towards the region of stronger f i e l d . The d i a l on the suspension i s then rotated u n t i l the sample i s returned to i t s i n i t i a l position. The force due to the suspension must then be equal and opposite to the force due to the f i e l d gradient. On the assumption of a linear stress-strain characteristic below the elastic limit of the suspension Figure 1„ Shnay's magnetic balance. 9 o wire, the amount of rotation of the d i a l i s proportional to the restoring force on the sample and hence also to the force on the sample due to the f i e l d gradient. Tests were begun to determine whether Shnay's magnetic balance was really satisfactory for the measurement of saturation magnetizations„ Because most of the alloys produced were extremely b r i t t l e , the samples could not be shaped into ellipsoids or cylinders by f i l i n g or grinding. Instead, samples were made up of powders cemented together with a binder made of gun cotton dissolved in butyl acetate, and extruded from a glass tube to form cylinders about 1/4 inch long, Shnay's balance had to be checked to see whether the f i e l d was sufficient to saturate powdered samples. Iron and nickel samples were prepared of the sol i d metals and of powders of various meshes. The d i a l rotations AO per unit weight of the various powders and of solid nickel were determined. The ratio of AO per unit weight of solid iron to AO per unit weight of solid nickel was compared with the ratio for solid iron 7 to solid nickel obtained by Weiss and Forrer , See Table 1, It i s evident that the nickel powder samples did not saturate well, and the iron powder samples not at a l l . Even the solid nickel and iron samples are not too satisfactory since the ratio i s appreciably d i f f -erent from the accepted value. The powdered samples were weighed after they were cemented together and no allowance was made for the weight of binder. However, since this i s less than one milligram, i t could not be responsible for the discrepancies observed. The only conclusion to be reached was that the f i e l d strength was insufficient to saturate powdered samples. The uniformity of the f i e l d gradient had next to be checked0 10. TABLE 1. Tests on Shnay's magnetic balance. Sample Weight AO AO weirfit Solid nickel .0729 gm. 117.8 1616 Powdered nickel, 80=200 mesh .0309 47.0 1520 " " , 200-270 M .0301 45.8 1525 w « , 270-325 " .0303 46,9 1550 « * , less than 325 mesh .0318 49.3 1552 Solid Norway iron .0104 64.7 6220 Powdered Norway iron, 80-200 mesh ,0151 71.2 4720 • • w , 200-270 w ,0152 71.3 4690 W M N ( 270-325 m .0156 71.7 4600 00 8 0 " , less than 325 mesh .0153 70.9 4630 AO per unit weight of Fe «• 6220 - 3.85 AQ per unit weight of Ni l6lo Weiss and Forrer's values 3.985 Buehl and Wulff had measured the f i e l d along the axis, presumably with a 8 fluxmeter, and found i t extremely linear (i.e.* uniform gradient). Piercy , using the analogy between electric and magnetic potentials, had checked the f i e l d gradient characteristics of Shnay's magnet by measuring the electric potential between the poles of the magnet which had been removed from the magnet and placed in an electrolytic tank. It was f e l t that neither of these, tests were conclusive. F i r s t , Buehl and Wulff's method w i l l not l l o show up variations i n the f i e l d gradient too well, because they w i l l be of second order compared to variations in the f i e l d . Secondly, Piercy's method is even worse in this respect because the f i e l d gradient w i l l be proportional to the second derivative of the potential. Also, the v a l i d i t y of a perfect analogy between the electric and magnetic case i s doubtful because, i n generalj>the f i e l d characteristics change with the magnitude of the f i e l d , and no allowance i s made for this in the electrolytic tank method. Thirdly, neither system makes measurements while a sample i s i n place in the f i e l d . It was decided that the only satisfactory way to check the uniformity of the gradient was actually to measure the force on a sample, as a function of position. No extensive tests of this type were made on Shnay's magnet, since the position of the sample was not easily variable. However, an i n s t a b i l i t y in the position of the sample was noted, indicating a non-uniform gradient. Some attempts were made to improve Shnay's balance by modifying the existing instrument. The sample bucket and suspension arm had been made of commercial brass, probably containing some iron impurity, and were found to be weakly magnetic. They were replaced with a copper bucket and a s i l v e r solder arm. Steel shields were placed above the tops of the coils to reduce the leakage flux, which would be normal to the useful flux of the gap. The i n s t a b i l i t y decreased somewhat. Two attempts were made to increase the f i e l d strength. The two coils were placed in parallel and the current doubled, but the f i e l d strength increased only a small amount. Specially tapered pole pieces were tried, following the method 9 of Bitter , but the maximum f i e l d strength obtainable was only 7000 oersteds. It was concluded that a l l possible improvements had been tried, and that a new,more powerful magnet was required, Sucksmith was unable to 1 2 , saturate powdered nickel samples in a f i e l d of 16,000 oersteds. It was decided to design the new magnet to develop a f i e l d of at least 18,000 oersteds in a gap one inch long and two inches i n diameter. Design.of the Magnet., The magnetic balance was chosen i n preference to the b a l l i s t i c method for the following reasons: 1, The equations for the b a l l i s t i c method show that the charge must be passed into a b a l l i s t i c galvanometer in a time that i s very short compared to the period of the galvanometer. This necessitates a rapid reversal of the f i e l d (the f i e l d must be reversed, not merely switched off, because of remanence). But a sudden collapse of f i e l d in an inductive load carrying such a large current would produce a tremendous back emf and consequent arcing at the switch contacts. The use of relays is not permissable because of the very short time allowed for reversal. For the magnetic.balance method, no f i e l d reversal i s necessary, and since switch-ing can be done i n the a„c„ cir c u i t while the d,c. circuit remains com-plete, no arcing problems w i l l arise, 2. The b a l l i s t i c method is not accurate ..for powdered samples,. The cross-sectional area of the sample must be accurately known, which is not possible with the powdered extrusions, Buehl and Wulff 9s magnetic balance was an adaptation of one designed by Fereday^, who built a magnet, and calculated the shape of pole pieces necessary to make the product of f i e l d and f i e l d gradient uniform along the axis of the gap for paramagnetic measurements. These theoretically designed pole pieces had to be empirically modified, because of fringihg effects, Buehl and Wulff, by trial-and-error methods, made 13« pole pieces which would give a constant field gradient along the axis of the gap, for ferromagnetic measurements,, Sucksmith ^ designed pole pieces having two inclined surfaces, which produced a gradient normal to the axis of the gap. The force on the sample was measured by a ring type balance, not a torsion suspension. Some information on magnet construction 12 is contained in Aaronson's design of a magnet for a Van de Graaff gen-erator. The factors which determined the size and shape of the new magnet were: (a) Number of ampere-turns required (b) Design of the yoke (c) Design of the coils (a) Number of ampere-turns required. In the magnetic circuit, which is the path followed by the flux lines, the magnetomotive force produces a certain flux through the various reluctances of the circuit. The basic equation i B NI - £ Hdl where N • number of turns of magnetizing coil I = current in amperes H B field strength in ampere-turns per inch in element^of length d l o The integration is carried out over any flux path in the magnetic circuit. If the path of integration is taken as a flux line which passes through the gap and then around the yoke, the integration breaks into two parts. NI - H i l i + H a l a where « field strength in the iron yoke 1^ 3 path length of flux line in the iron yoke. H o H - f i e l d strength in the a i r gap. fit l a = path length of flux line i n the a i r gap. Because of the high permeability of iron, the second term w i l l contribute a major part of the t o t a l ampere turns, i.e., most of the magnet-omotive force w i l l be "dropped across" the a i r gap. From the required f i e l d strength i n the gap of 18,000 oersteds, and a gap length of one inch, the second term becomes 36,400 ampere-turns. The f i r s t term i s un= known u n t i l the yoke i s designed, but from many t r i a l calculations, an app-roximate idea of i t s value can be obtained. Adding this to the known second term gave an estimated t o t a l ampere-turns of 4 5 , 0 0 0 . (b) Design of the yoke. A l l the flux lines produced by the coils pass through the coils themselves. After a flux line leaves the c o i l , many possible paths are available to i t D It can pass through the iron pole piece u n t i l i t reaches the gap, then cross the gap to the other pole a Or, i t can leave the iron before i t reaches the gap, pass through the a i r to rejoin the iron at an equivalent point on the other side of the gap. Such a flux line does not contribute to the useful flux in the gap and i s considered leakage flux. The ratio of the t o t a l flux to the useful flux through the gap i s called the leakage factor. It i s impossible to calculate exactly, and i s d i f f - , 13 i c u l t even to estimate, Roters gives methods of calculating leakage factors, involving the geometric shapes of the pole pieces used. The leakage factor w i l l vary with f i e l d strength, because as the permeability of the iron decreases with high f i e l d strengths, the reluctance of the iron paths increases, and so also does the leakage. 10 In Fereday's f i r s t maghet , the coils were placed on the 15. sides of the yoke, leaving a long path between the ends of the coil and the gap. Buehl and Wulff's design (and therefore Shnay's magnet) was also of this type. In view of the discussion in the preceding paragraph, i t is apparent that these designs are very poor, and that there will be a large leakage factor because of the many leakage paths available. This was borne out by the comparatively large field observed at the square corners of the yoke of Shnay's magnet. The best position for the coils is obviously as close to the gap as possible, with the only distance between them that necessary for gaining access to the gap. A flux line leaving the coil on the end away from the gap can travel entirely through the iron yoke to the other coil, or can bend around and travel through the air to the other coil, or can take a combin-ation '6f ' these paths. However, the air paths will be so long that the all-iron paths will have far less reluctance and almost a l l the flux will travel through the iron yoke. Consequently i t can be assumed that the total flux will pass through that cross-section of the pole piece where the pole piece joins the yoke. If the pole piece is then tapered from this cross-section to the two inch diameter required at the gap, the flux lines will converge to produce a high flux density at the pole face. The flux density at the pole ?ace, and hence the field strength in the gap(since B * v H in air and B is continuous across a surface of discontinuity, prov-ided B is normal to the surface) will be H - B a p f where B p = flux density at the large cross-section of the pole piece g = geometrical factor, the ratio of the areas of the large and small cross sections of the pole piece, f - leakage factor. 16. The faetor |? should be made as high as possible. It was decid-ed to attempt to make i t unity, so that the leakage would be exactly compensated for by the tapering of. the pole piece. The method of calc-ulation of the leakage factor of the pole pieces was suggested by Mr. F,K, Bowers. The following assumptions are made; 1. The field strength is uniform within the gap, 2. Outside the gap, the field strength falls off inversely as the distance from the axis of gap, 3. All flux lines can be neglected which f a l l outside the arc of a circle with centre at the midpoint of the gap, and radius equal to the distance from the midpoint of the gap to a point on the circumference of the larger cross-section of the pole piece. By trial-and-error calculation, a pole piece was found having suitable dimensions for | » 1, It turned out g - f = 9. This determined the large cross-sectional area of the pole piece. The cross-sectional area of the yoke then had to be at least as large. After the coils were designed, the length of the yoke was made sufficient to carry them. The impurities in the iron determine the ease of saturation. Low carbon iron is essential for a yoke which is to provide a low reluct-ance flux path. Most of the other elements merely dilute the iron insofar as magnetic properties are concerned. The advantages offered by magnetic alloy steels did not justify their cost, so high purity iron was employed. (c) Design of the coils. 14 De Haas and Westerdijk ' produced fields up to 250,000 oersteds by connecting a small copper wire coil immersed in liquid nitrogen to a large battery. Many magnets have been built using copper wire coils cooled 17. 12 by water, o i l , or forced a i r . The magnet designed by Aaronson uses copper tubing specially coated with asbestos. The cooling water flows inside the tubing, giving a high cooling efficiency. Smaller magnets have used copper wire coils with hollow discs, or 'pancakes', through which cooling water can flow, interspersed between the c o i l s . For reasons of economy, av a i l a b i l i t y of materials, and efficiency of cooling, the last method was employed. It was assumed that two thirds of the t o t a l cross-sectional area of the coils would be taken up by cooling pancakes and insulation, and one third by the copper wire i t s e l f . The number of ampere-turns N has been determined partly by the size of the gap and partly by estimation. The width of the coils was determined by the dimensions of the pole piece and the required space between the c o i l s . It then remained to determine the diameter of the co i l s . Now, to produce a given number of ampere-turns, i n a c o i l of a given size, the power required i s the same regardless of the wire size used. This can be seen from the following equations. NI = Nia = 2± F - ( H l ) 2 p i y O where N = number of turns, as before, I •» current in any one turn, a = cross-sectional area of cqils, i = current per unit cross-sectional area of copper wire, A = t o t a l cross-sectional area of coils, 1 p = fraction of t o t a l area of coils occupied by copper. 18 „ P = power input to magnet. p - resistivity of copper. Further, i t can be shown that for a given number of ampere-turns, the power dissipated increases as the volume of the coil decreases. Thus, for the most economical design of magnet the best procedure is to estimate the maximum power which can be dissipated by the cooling system, then calculate the volume of the coils required. Of course,if the power input is too high, the cost of the power supply becomes excessive, but for moderate power, the most important consideration is to reduce the size of the coils, since i f the coils are too large there will not be sufficient access to the gap available. A conservative estimate of 50 cc. per second was made of the rate that water could be drawn through the water cooling pancakes, under water tap pressure. An allowable temperature rise of 20°C. was assumed. This gave a power dissipation of 4180 watts. From this, the physical dimensions of the coils were determined. Ddfcble cotton covered square wire was found to have the best packing properties. The size was determin-ed only by the voltage of the power supply. Since these calculations were made before the question of a power supply had been investigated, the supply voltage was taken as 120 volts with a l l coils in series, or 30 volts with the four quarters of the coils in parallel. The closest commercial .wire.size was number 10. It was necessary to maintain F = 3, yet have an integral and even number of coils and water cooling pancakes„ Further, the coils had to be of such a width as to contain an integral number of thicknesses of wire. These requirements were met by having five water cooling pancakes 19. and four coils of three thicknesses of wire each, on each side of the gap. Henceforth, the five pancakes and four coils will be called a coil assembly. The water cooling pancakes consisted of two copper pans which f i t inside each other with an internal spiral of copper strip to force the water to follow a tortuous path through the pancakes. Each pancake has an inlet and outlet tube, and a l l ten pancakes were connected in parallel to inlet and outlet manifolds. The coils on Aaronson's Van de Graaff magnet were made of two layers of tubing each, consequently, both ends of each coil came \o the outside. In the present magnet with three layers to each coil, this could not be done. Instead, the inside ends of each layer were folded back inside the other coils, and laid along the surface of the conical pole piece, to be brought out at the end of the pole piece away from the gap. The suspension wire hangs from the bottom of a vertical shaft, on the upper end of which a vernier dial is mounted concentrically with the shaft. Each, suspension wire is of the same length and has a brass pin soldered to each end, making changing the suspension wire simple. On the lower end of the suspension wire is fastened the horizontal suspension arm, having the bucket for the sample on one end and a damping paddle in a pan of o i l on the other. A weight is suspended in a pan of heavy o i l by a wire connected to the bottom of the suspension arm, in line with the suspension wire. The weight keeps the suspension wire taut, and the o i l pan prevents lateral motion of the suspension arm during measurements. The shaft holding the suspension wire turns in a bearing which can be moved in two directions in the horizontal plane by a system of ways, and the shaft itself can be moved vertically to any position relative to the 20. bearing, by an adjusting collar. Thus the sample i n the bucket can be moved to any position i n the gap for plotting the f i e l d characteristics. As with Shnay's magnet, a mirror on the suspension arm reflects the image of a lighted hairline to a distant scale, to enable the bucket to be returned to i t s original position. The optical system was improved to make a more satisfactory image. The last half inch of each pole piece was made a removable pole cap which screwed onto the "remainder of the pole piece. The bearing for the v e r t i c a l shaft f i t s into a plate which can be moved ve r t i c a l l y about a foot, thus raising the whole suspension and bringing the bucket out from between the poles to above the co i l s , so that samples may be easily placed in the bucket. I n i t i a l tests of ...the, magnet. Before the magnet was assembled, one c o i l assembly was tested for cooling characteristics In the E l e c t r i c a l Engineering Department, where suitable power was available. The c o i l assembly was run entirely i n series from 60 volts d.c. with 100 cc, of water per second flowing through the water cooling pancakes. The f i n a l temperature rise of the copper wire coils was only 9°C. Several types of d„c„ generators were considered for the magnet. They f e l l into, two classes? 120 volt motor-generator sets, and 30 or 40 volt welding generators. The latter were far cheaper, so the magnet was operated with four quarters of the coils in parallel, at low voltage and high current. Two welding generators were tested; an A„0„ Smith 40 volt, 200 ampere welding r e c t i f i e r unit, and a Hobart ML-204-S 40 volt, 200 22. Figure 3° The magnetic balance - suspension lowered. 23. 2U 2 5 o ampere generator. The former had a 360 cycle ripple of about eleven volts, causing a great deal of hum in the magneto The Hobart welder had negligible r i p p l e 0 It also had a fine adjustment rheostat for the f i e l d which could be removed from the generator and mounted near the magnet, whereas the control on the A,0, Smith unit was integral with the machine. Since both machines were noisy and drafty, this last consideration was importanto Consequently, the Hobart welder was deemed more suitable. For these i n i t i a l tests, plane pole caps were screwed onto the pole pieces. The f i e l d strength was measured with a search c o i l and a Rawson fluxmeter. The search c o i l was fastened to the end of a long rod and drawn quickly out of the f i e l d . The c o i l was calibrated against another search c o i l which in turn had been calibrated by proton resonance techniques in a Van de Graaff generator. At 140 amperes ( 3 5 amperes through any turn) the f i e l d was 19,600 oersteds as compared with the design figure of 18,000 oerstedso The complete f i e l d strength against current curve was plotted, but w i l l not be reproduced here, since the plane pole caps are never used in practice« The curve for the pole caps actually used i s reproduced in Figure 2 4 » Steel suspension wires were found to be quite unsuitable, since the f i e l d gradient was strong enough to pull the whole suspension toward the gap. Copper was t r i e d next, but no matter how much the wire was f i r s t cold worked, creep effects were always present. The zero point and f i n a l readings would change slowly with time, for large rotations, Chromel wire was f i n a l l y t r i e d and found quite suitable. It i s non-magnetic and show-ed no creep effects. The bucket, was made of sheet copper and soft soldered together. 26, The bucket was diamagnetic, but this was offset by gluing small bits of commercial brass to i t which probably contained some ferromagnetic impurity. The most non-magnetic material f o r a suspension arm was alloy number sixteen, made by Eutectic Welding Alloys, I n c For f i e l d plotting, a small f l i p c o i l , 1/4 inch i n diameter, was made up so that i t was quickly turned 180° by a rubber band, when released. The f l i p c o i l frame was attached to the bottom of the shaft which normally held the suspension, so that the f l i p c o i l could be moved to any part of the f i e l d . The whole method, however, was abandoned i n favour of measuring the force on a metal sample,because the variations i n the f i e l d were only i n the order of a few percent, which was hardly better than the accuracy of the fluxmeter readings. Producing a uniform f i e l d gradient.. At f i r s t , i t appeared that a uniform f i e l d gradient in the gap could be produced very simply by using one concave and one convex pole cap with a common centre of curvature, the convex cap having a smaller face diameter. If the flux-lines l e f t one pole cap normal to the surface, and proceeded in straight lines to the other cap to strike i t normally, a uniform gradient would obviously occur. See Figure 6, Two pole caps were made of low carbon chain iron and were locally ground, one concave and one convex, on a lens grinding machine. The dimensions and curvatures were made such as to produce a gradient of about 1000 oersteds per inch. Although the radii of curvature of the two caps should have differed by the length of the gap, they were made the same r a d i i , v i z . 41 3/4 inches,since the lens grinding machine permitted only certain discrete r a d i i . With these pole caps in place, the f i e l d gradient was plotted, using a sample of pure nickel in the bucket. The results were disappointing. The only stable positions of rest were close to the pole caps5 in the middle of the gap the sample was quite unstable. Two defects were present in the caps. The convex cap had a small depres-sion in i t s exact centre. Also a mistake had been made in calculating the thickness before grinding of the convex cap, the effect being to decrease the gap by 0,012 inches. But neither of these two defects was held responsible for the poor results obtained. Instead, i t was f e l t an analysis of the conditions which would cause the observed i n s t a b i l i t y was necessary. With the f i e l d switched on and the suspension rotated a given amount, the sample w i l l move to that point between the poles at which i t s energy is a minimum. In order that the sample may come to rest midway between the poles, the energy of the sample,as a function of i t s position for a fixed d i a l setting, must be as i n Figure 7, It must now be seen whether the ideal pole pieces would produce this type of curve. If the f i e l d gradient is constant along the axis, then the force and energy due to the gradient alone w i l l be as in Figures 8 and 9, In these diagrams, the highest f i e l d i s at the right pole. The force due to the suspension w i l l vary linearly from one pole to the other, producing a parabolic vari-ation of energy with position. See Figures 10 and 11, The t o t a l energy function of the sample i s obtained by adding the two energy curves, as in Figure 12, This curve is seen to satisfy the condition for s t a b i l i t y in the middle of the gap. The conditions which produce i n s t a b i l i t y can arise as follows. 28. Figure 6. Hypothetieal f lux Figure 7« Typical energy:', curve d is t r i but ion . between concave; and, for stable rest position,, convex, pole caps0 imifeam-^eM^adi-ent-. a uniform field ^ gradient„. 29 o 30. If the suspension i s very light, the smaller is the slope of the force curve i n Figure 11, and the straighter the energy curve of Figure 12„ The result i s the t o t a l energy curve i s shallower, Now, i f in conjunction with a light suspension, the f i e l d gradient i s not constant, but has the form in Figure 13. giving an energy curve due to the gradient of the form in Figure 14, then the t o t a l energy curve would have a maximum i n the middle as i n Figure 15. The only stable positions of rest for the sample would be against the pole caps. Such a f i e l d gradient as that of Figure 13 implies a f i e l d distribution as i n Figure 16. This means a decrease in f i e l d strength below the required value i n the middle of the gap, which would be caused by the flux lines not converging, as i n Figure 17. The in s t a b i l i t y could thus be overcome by? I. Reshaping the pole pieces to make the flux lines converge more o If a truly linear f i e l d could not be produced, an'overstable.' f i e l d as in Figure 18 could be tolerated, although the advantages of a uniform gradient would then not be available, 2„ Using a heavier suspension,, The disadvantage i s that in the present magnet, the lower end of the suspension wire i s not anchored, and a heavy, suspension would cause l a t e r a l motion of the whole suspension arm as the d i a l turned. And as above, the advantages of a uniform gradient would be lost. It was decided to try reshaping the pole pieces, since this offered the best opportunity of achieving both s t a b i l i t y and a uniform f i e l d gradient, A 4,5 milligram nickel sample was used with a number 28 copper suspension wire. The chromel suspension wire was not used u n t i l 31. C UJ Figure 15 <, Total,-energycurve due^ to«-j.-,-?iMMn>«»aiti^ eCTi- «gradient», and a light ..suspension.,. I X Figure 16 0 Field distribution,, .• which would produce the non-uniform: gradient of Figure 13° 32 o Figure 17 o Flux lines which would produce • •. the nonuniform, gradient x>f Figure 13. " 3 3 o a l l tests were finished 0 A l l pole caps were made with the same large dia-meter and with the same angle of taper as the pole piece. The difference i n small face diameter was achieved by turning them to different thicknesses. The details of the caps are given in Table 2, Plots were made of the net angle of twist AQ of the suspension (which i s proportional to the force and hence to the gradient) against the co-ordinate of the sample. TABLE 2. Dimensions of the pole caps No. Original Face Diameter Original Radius of Curvature Final Radius of Curvature 1 2.010 inches oO inches oo inches 2 1 . 9 6 6 oo oo 3 1,996 - 4 1 3/4( convex) = 4 1 3/4 4 2.060 41 3/4(concave) 4 1 3/4 5 2.024 oo 6 1/2 6 1.715 co 2 8 1/4 Tests were begun at low currents because the in s t a b i l i t y made any measurements at high currents impossible. Replacing the convex cap no. 3 with the f l a t cap no. 2, which has only a slightly smaller diameter, smoothed out the gradient somewhat, since the flux lines would not diverge so much. Using f l a t cap no, 1, which has about the same diameter as no, 3 , did not affect the shape too much but, decreased the force everywhere, as would be expected, since the difference in areas of the two pole caps would 3 4 o be decreased, which would decrease the gradient also. Increasing the current from 40 amperes, through 60, 102,5, to 182,5 amperes increased the gradient and made i t less uniform. For the last two currents, the gradient actually decreased to zero and changed sign, across the gap. In this case, the sample shifted to the other end of the bucket, and the x values, read on the scale of the suspension, lost meaning. Consequently readings were taken only up to the point where the gradient changed sign. For the results of this series of tests, see Figure 19. In order to make the flux lines converge even more, the f l a t pole=cap no. 2, which had replaced the convex cap, was in turn replaced by cap ho„ 5, which was made concave with successively smaller r a d i i of curvature. The concave surface was produced by using a specially made j i g with a lathe, which allowed the tool bit to swing in an arc across the face of the pole cap, on the end of a long pivot arm. Curves showing the result of decreasing the radius of curvature are shown in Figure 20, The discontinuity i n the centre of each curve oc-curred because the sample moved from one end of the bucket to the other when the sign of the gradient changed. The gradient characteristic flatten-ed out as the caps were made more concave and the flux lines converged, but the sudden drop and reversal in centre of the gap was s t i l l present and could not be tolerated. The reason the gradient changed sign was that the flux lines did not always converge in the positive x direction. This could Be over-come by making a larger difference in the area of the pole caps, since the flux lines would then tend to converge more. Another pole cap, no, 6, was made up with a much smaller face diameter, to replace cap no, 5. A smaller 35. Cap 3, /?= -4/4: in. Cap4, T= 4-Ca/nps X (a) Cap 4/^in. Cap2, £= z~= 4-Oa/nps. (b) X Cap -f, Z=^fn. Cap /, T- ^ oamps. Cap 4 Cap 2, <*=» zr-60 amps. (c) (d) Cap -£>e= Cap 2, ^°*> T= /02.Sa/??ps. ,3 . Cap 4, fr=4ifm. Cap 2, /?=-oo J Z T = /82.5amps. x (e) (f) Figure 19o 36 „ Cap 4, R= 41$ In Cap 5 " ; / ? = ° o _T=- I82.Samps. (a) Cap4,l?=4/+/n, Cap SI R=29$h X= 182.5amps. (b) Cap 4, R~4/$ih. CapS, R=23$in. _T= 182.5amps. Cap 4, R=4/$fn. Cap 5,R=20in. Xx 182.5 amps. (c) ( d ) Figure 20o sample was used, so comparison with the previous curves, of the total force, is not possible 0 Only the shape of the curves can be compared. An immediate improvement occurred, using the originally optically ground concave cap no. 4, with a radius of 41 3/4 inches, on the left pole, and the new small cap no. 6 , s t i l l flat, on the right pole. But a large drop is s t i l l observed at the left end of the curve. In a successful attempt to remedy this, cap no. 4, having a radius of 41 3/4 inches, was replaced by cap no. 5, which had been dished to a radius of 18 inches. Further reductions of the radii of curvatures of both caps then improved the f a l -ling left end of the curve, but only at the expense of causing a slight hump in the middle. Modifications of a given cap affected both ends of the curve. See Figure 2 1 . The later curves are longer than the earlier ones because the original bucket, which could take samples 1/4 inch long, was removed, and the sample was fastened to the end of a suspension arm with scotch tape, so that a greater region of field could be plotted before the bucket hit the pole faces. Since i t appeared that the various types of pole caps tried had produced the best field gradient characteristics possible at 152,5 amperes, lower and higher currents were tried. At 90 amperes, the curve decreased monotonicallys at 227,5 amperes i t increased mbnotonically. At an intermediate current, the curve should have a plateau. Only two more trials were required to find that at 150 amperes, the curve was flat with-in less than 2% over a length of 3/16 inch. See Figure 2 2 . The field strength at this optimum current is about 21^000 oersteds. The exact, dimensions of the successful pole caps are given in Appendix III. The uniformity of the gradient in the y and.z directions was checked. The constancy was of the same order as in the x direction. See Figure 2 3 , 38. Cap f R=*fifin. Cap6,R=°<= T= i82Samps. (a). Cap 5,1?= 18 in. Cap <S, /?= o o X= /8Z.5 amps. (b) Cap 6, R=29in. T= I82.S amps. (o) C D CapS\R=/6in. Cap 6, R=29/n. T- /82. Samps. (d) Cap 5", /?=ft(n. Cap 6, /?=29in T~ I82.Samps. Cap 5] /?=/2fn. Cap 6, ^ -29/n T= /82,Saoips-X X (e) (f) Figure 21 0 Effect of reducing the ;radii of curvature.of (continued next page) Cap 5, R-(Om. Cap 6, R=29m, T= G/nps. (g) CapS,tf=8in. Cap 6, /x"=29/n. _T*= /82.Samps. (h) X Cap 5, R=8/n. Cap 6, R-28j/h. -7> 182.5 amps. X (i) Cap s; /?=7j/h. Cap 6, £=28j/h. T ~ /&•£. sramps. X 0 ) Cap 5, /?- 7'//?, Cap 6. /? = 28£/h. T= /82.S"amps. x (k) Cap S~, ff^6^/h. Cap 6, /?=28£/h. X =• J82.S amps. X (1) Figure 21„ (continued) Caps, R=6^/n. Cap 6 ,R=28^in. X = 90 amps. Cap S, R=6j/h Cap 6, R *2&f:/n. J - 227,5 amps. X (a) (b) C<7pS, R=6j/n Cap 6, R=28?:/n. T= l70<7/r>ps. (c) Caps, R3^6j-//7. Cap 6, R=2#$h. T = /SO amps. X (d) Figure 22„ Effect of. varying--::current.« <5 Cape, R-28iin. T- /SOa/nps. y (a) Caps, Cap-6, f?~-S&i/n. 1 - /SO amps z (b) Figure 23= Variation of gradient Ox along y and z directions. Figure 24„ Field strength as a function of t o t a l magnet currento SO 100 150 200 250 C u r r e n t in a m p e r e s 43 o Final.tests of the magnetic balance., With the successful pole caps in place, a curve of f i e l d strength against magnet current was plotted. See Figure 24 , It remained to check whether the f i e l d strength was sufficient to saturate both powdered samples and so l i d samples of random shape, to check that the deflection was proportional to sample weight, and to check that the ratio of saturation magnetizations at room temperature of pure iron and nickel corresponded with the accepted value. In order to investigate the effect of shape of the sample, specimens of pure nickel and Norway iron were made up in three shapes? needle-shaped, roughly spherical, and a f l a t plate. The needle and spheric-a l samples were placed i n the bucket, and the plate sample was stuck to the end of the bucket, with i t s largest cross section normal to the axis. Results are given i n Table 3 , The results for nickel show that shape need not be considered when measuring solid samples, 1 , 6 , ,the f i e l d strength of the magnet is sufficient to overcome the demagnetizing f i e l d due to the shape of the sample. But for iron, the magnetization i s too high, caus= ing the plate=like sample to have a significant demagnetizing f i e l d . But this i s not considered serious, because most of the alloys to be measured w i l l have magnetizations only of the order of nickel or less. Even i f the magnetization were high, no sample would be used that had such a high demagnetizing factor as the f l a t plate. The linearity of force with respect to sample weight was checked with a series of pure nickel samples of various weights. See Table 4° The AG per unit weight i s constant to within 2%„ The accuracy of weighing the lightest samples on a gold balance is probably no better than 2 $ , 4 4 . TABLE 3 c Effect of sample shape Sample Weight AO AO weight Nickel needle shaped 1 , 1 3 mg. 6 , 5 5 . 6 5 so ro 2 . 3 5 1 3 » 4 5 * 7 0 f» „ roughly spherical 7 o 2 8 4 1 . 8 5 . 7 5 f l a t , approx, 3 / 3 2 x 3 / 3 2 x , 0 0 7 7 o 4 0 4 2 . 2 5 . 6 ? Norway iron, needle shaped 1 . 1 5 2 6 , 4 2 2 . 9 » roughly spherical 1 . 8 7 4 2 . 4 2 2 , 7 OS > f l a t plate l o 3 4 2 2 , 6 1 6 . 9 TABLE 4. Check of the linea r i t y of force vs, sample weight Weight of Nickel sample 0 , 3 8 mg. 1 . 3 0 2 . 3 9 2 , 8 5 3 o l 4 4 » 1 5 5 . 8 6 6 . 5 0 7 . 2 8 A9 A6 weight 2 , 2 5 . 7 8 7 o 5 5 . 7 7 1 3 o 7 5 . 7 4 1 6 , 2 5 . 6 8 1 7 o 9 5 , 7 0 2 3 . 6 5 . 6 8 3 3 c 4 5 . 7 0 3 7 o l 5 , 7 1 4 1 o 9 5 . 7 5 45, The powdered samples were not cemented together as before because the amount of binder would not be negligible in samples so small„ Instead, dry powder was sealed into tiny v i a l s . The vials were made by sealing one end of a 1/8 inch long fine glass tube with Glyptal cement. The v i a l was weighed before and after f i l l i n g i t with powder. Then the open end was sealed with Glyptal cement. Considerable d i f f i c u l t y was encountered obtaining consistent results with the powders. F i r s t , samples were made up using powdered Norway iron and pure nickel which had been obtained by f i l i n g s olid pieces of the respective metals with new clean f i l e s . The AQ per unit weight • for solid Norway iron and four different grades of powder was erratic, with the values either the same as that of the solid metal, or sl i g h t l y lower. For nickel, the values increased as the powder became finer. These results could be explained by supposing that (l) small particles had become detached from the teeth of the new f i l e s and were contaminating the powders, 2) the magnetization of the f i l e material were slightly less than that of pure iron, and 3) the f i l e particles when f i l i n g iron were selective ac-cording to particle size and when f i l i n g nickel tended to increase in amount as the particle size decreased. Some iron powder and some nickel powder were then obtained which had not been produced by f i l i n g . Each powder size then gave exact-l y the same AO per unit weight, but unfortunately this figure was much less than that for the solid metals. As a conclusive check, new powders were made up with a well worn f i l e for the nickel, and (unfortunately) a clean but new f i l e for the iron. See Table 5 , The results for nickel were excellent% for iron, s t i l l erratic. 4 6 , TABLE 5 o Tests of saturation of iron and nickel powder samples. Sample Weight AO AO weight Solid nickel 3 . 1 4 1 8 , 0 5 . 7 3 Powdered nickel, annealed 6 1 0 ° C , 3 hrs., larger than 65 mesh 5 . 2 8 3 0 . 4 5 . 7 6 w w 65=200 w 5 . 4 7 3 1 . 7 5 , 7 6 n oo 200-270 90 4 . 9 4 2 8 . 3 5o74 ' • 00 - 00 270=325 0 0 3 . 2 3 1 8 , 7 5.78 00 50 less than 325 " 2 , 6 2 15.1 5,76 Solid Norway iron 1 . 4 0 3 1 . 6 22 . 6 Powdered Norway iron, annealed 6 l O ° C , 3 hrs larger than 65 mesh 1.50 3 3 . 2 22o2 19 0) JO 65-200 m 1,72 3 6 , 9 21 . 6 00 00 00 200-270 5 0 1 . 3 3 3 0 , 2 2 2 , 7 00 • 00 00 270-325 5 8 1 . 6 5 2 8 . 3 21 . 9 S 00 00 less than 325 00 1 . 2 9 2 3 . 7 21 . 9 Solid samples of pure iron wire and hydrogen reduced iron wire were used with the readings already obtained in Table 5 to obtain the ratio of the AO «s per unit weight for iron and nickel, which is proportional to the ratio of saturation magnetizations at room temperature. See Table 6. Agreement with Weiss and Forrer's value''' was quite good. Conclusions. It i s concluded that the magnetic balance i s satisfactory for 47. TABLE 60 Ratios of saturation magnetizations at room temperature for iron and nickel. Iron sample wt„, mg. AO AO for Ni, weight from Table 4 J0per unit wtoOf Fe weight AO per unit wt .of Ni Wire, H 2 reduced 0 . 5 5 2 1 o 8 5 o 7 4 3 . 8 0 Wire O 0 6 5 2 2 0 6 5 o 7 4 3-95. Wire 0 „ 8 5 2 2 o 5 5 . 7 0 3 . 9 5 Wire, H 2 reduced l o l l 2 2 0 7 5 0 6 8 3 o 9 9 Wire l o 5 3 2 2 0 6 5 o 7 0 3 . 9 7 Wire, H 2 reduced l o 6 5 2 2 . 7 5 o 7 1 3 . 9 7 Weiss and Forrer's values 3 o 9 8 5 measuring the saturation magnetizations of metal samples at room and low temperatureso The f i e l d gradient i s uniform enough so that the force on a sample i s constant to within 2% over a volume composed of a 3 / 1 6 inch cube. The f i e l d strength i s sufficient to saturate solid samples of any shape for alloys having magnetizations less than that of nickel, and can saturate samples of roughly spherical shape for alloys having magnetizations greater than that of nickel. Although the powdered samples could be expected to give quite f a i r accuracy, i t would be simpler and more reliable to use solid samples of the alloys of random shape. For determining Curie points higher than room temperature, Shnay's balance should be satisfactory, since near the Curie point, the magnetization should be low enough that the demagnetizing f i e l d i s negligible. I l l , FERROMAGNETISM IN MANGANESE CARBON ALLOYS Previous Work, 15 Heusler reported no ferromagnetic phases in the manganese carbon system. But Wedekind^ found manganese carbide to be consider-ably magnetic. However, Wedekind melted his alloys in a i r , which could have introduced nitrogen contamination (manganese nitride i s magnetic), Morgan'*' prepared an alloy of 20 atomic percent carbon which was magnetic after water quenching from 1050°C„ It had a face centred cubic l a t t i c e with a l a t t i c e parameter of 3,869 KX„ Morgan's programme was to attempt to space apart manganese atoms to produce conditions conducive to ferro-magnetism. Since the manganese atoms are quite far apart in y-manganese, carbon was added to space the atoms further apart, and another element was added to replace some manganese atoms i n an attempt to retain the y structure. The most recent phase diagram of manganese carbon i s that of 17 Vogel and Doring „ See Figure 25, The phase boundaries were determined by thermal and micrographic analysis. The S phase of manganese has been omitted entirely since i n 1935 only the a, B, and y phases of manganese were known. It is to be expected, then, that the y - f i e l d shown in the diagram i s r e a l l y subdivided into smaller regions to include the 8 phase 18 and some two-phase regions, Goldschmidt quotes this phase diagram, and mentions that the compounds Mn^Cg and MnyCa have also been identified. He gives considerable crystallographic information on similar compounds with iron instead of manganese, but with which the manganese compounds are iscnorphou,. In a later paper 1 9, he gives the interplanar spacings of these compounds and of Mn3C, for x-ray identification. 50. As seen in the phase diagram, there is an eutectoid decomp-osition of y -manganese into a-manganese and B-Mn3C. The eutectoid comp-osition is 1.8 weight percent carbon. It was decided to try to produce a ferromagnetic alloy by retaining some of the y solid solution by quench-ing an alloy of the eutectoid composition from above the eutectoid temp-erature. If the inter-atomic spacing of the manganese atoms were sufficient, a ferromagnetic alloy might result. Procedure. Because Vogel and Doring's figure of 1.8 percent for the eutectoid composition might not be exactly correct, a series of alloys with comp-ositions bracketing this figure was made up. Alloys were prepared under g an inert atmosphere in the vacuum melting unit described by Piercy . About 25 grams of constituents were placed in the unit, which was evacuated. The charge was thoroughly outgassed by heating to a dull red heat, by induction heating. Then the unit was flushed with argon several times. The charge was melted under one atmosphere of argon, and c h i l l cast into a cold mold. Chill casting produces far less coring than slow cooling. The cored structure was removed by homogenizing. A l l alloys were f i r s t measured on the magnetic balance in the as-cast condition. Carbon analyses were performed in case composition changes occurred during melting. De Bye-Scherrer x-ray diffraction photo-graphs were taken of most alloys after they had been powdered to .less than 325 mesh. Homogenizing and heat treating of alloys were carried out in controlled atmosphere annealing furnaces. Each furnace is a Vitreosil tube surrounded_by electrical heating elements. The tube was f i r s t evacu-51. ated, then argon was admitted and passed continuously over the specimen. However, oxide scale formed on the samples, either from oxygen impurities in the argon, or leaks from the a i r . To prevent this, the samples were f i r s t sealed in vacuum in small V i t r e o s i l tubes. The tubes themselves were put i n the tube furnaces i n case they became porous at high temperatures. But the d i s t i l l a t i o n of manganese inside the evacuated tubes was so severe that the tubes were f i l l e d with argon at one atmosphere pressure before sealitig, to reduce the rate of d i s t i l l a t i o n . Results. The alloys of Low carbon content, and those of high carbon content, were not magnetic. Those near 1.8 weight percent carbon were magnetic, with the 1.8 percent alloy the strongest. See Table 7 » But even this strongest alloy was only about one sixtieth as strong as nickel. Because manganese has a high susceptibility, the force on a sample of pure manganese in the magnetic balance, i s quite significant. The force per unit weight on even the strongest alloy was less than ten times that for pure manganese. The question then arose as to whether the magnetic alloy which was produced was ferromagnetic or paramagnetic. TABLE 7, Magnetic Measurements of C h i l l Cast Alloys. Sample % C AO weight Nickel 67,2 Manganese 0.234 Mh-C 0.8 0,235 .Mn-C 1.4 0,353 Mn-C 1.60 0.530 m~c 1,76 0.629 Mn-C 1.80 0.649 Mn-C 2,10 0.273 Mn^ C 3,3 0.325 52. Now, i t has been shown previously that the force on a paramagnetic substance i s proportional to the product of the f i e l d and i t s gradient and that the force on a ferromagnetic substance i s proportional to the gradient aloneo Thus pif the manner of variation of the force on an unknown i s invest-igated, i t can be identified as paramagnetic or ferromagnetic„ By measuring the force on a nickel sample for various f i e l d strengths, a curve showing the variation of gradient with f i e l d strength was obtained,, By multiplying the ordinates of this curve by the f i e l d strength, a curve showing the relative variation of the product of f i e l d strength and f i e l d gradient was drawn. This last curve was then compared with an experimental curve giving the dependence of force upon f i e l d strength f o r a sample of pure manganese. The two curves were almost identical. To determine whether the eutectoid alloy was paramagnetic or. ferromagnetic, measurements were taken on i t and a curve showing the relative variation of force with f i e l d strength was drawn. It f e l l between the ferromagnetic and paramagnetic curves obtained above, but much closer to the ferromagnetic curve. See Figure 26, X-ray diffraction analysis disclosed that a l l the c h i l l cast a l -loys were composed of a - manganese solid solution plus another phase which increased i n amount with carbon content. The a - manganese solid solution l a t t i c e was expanded from that of pure a - manganese. The alloy of the eutectoid composition was heated to various temperatures and water-quenched in an attempt to retain some of the high temperature phase. Samples quenched from 900°Go and below exhibited only a - manganese plus the second phase. Samples quenched from above 900°C, exhibited a complicated X-ray diffraction pattern. The structure was not Identified. The magnetic measurements showed that any sample quenched from below 800°C„ became almost completely non-ferromagnetic0 That i s , the force 53« 1—1 I ' l l I J I ) I 1 1 1 I 8 IO J2. 14- 16 IS ZO . 22 "• F~/eld strength H In kilo-oersteds Figure 26 „ Determination of whether the 108V weight, percent carbon a l l o y . i s . ferromagnet ic or paramagnet ic 54. per unit weight approached that of manganese. Samples quenched from 900°C. increased in magnetic strength to about one sixtieth of that of nickel. Samples heated at 1000°C. and 1100°C. decreased in magnetic strength, again approaching the paramagnetic strength of nickel. See Table 8. TABLE 8. Magnetic Measurements of the 1.8$ Carbon Alloy, after heat treatments. Al l samples sealed under argon in tubes. A l l water quenched. Temp, before Time at quenching Temperature weight not heated - 0.649 800°C. 114 hrs. 0.273 900°C. 114 hrs. 0.906 1000°Co 114 hrs. 0.300 1100°C. 48 hrs. 0.294 Discussion and Conclusiona. It has been established that a ferromagnetic phase does exist in the manganese carbon system in addition to the face centred cubic phase produced by Morgan; That the strongest magnetic alloy in the ch i l l cast condition occurs at 1.8 percent carbon is in accordance with Vogel and Ddring's phase diagram, because the eutectoid alloy would have the largest amount of the high temperature phase retained upon quenching. The magnetic phase is definitely ferromagnetic, because the curve in Figure 26 falls between the paramagnetic curve and the ferromagnetic 55. curve indicating a mixture of a paramagnetic substance and a ferromagnetic substance If either the magnetization of the ferromagnetic component or the fraction present were known, the other could be estimated, but both are unknown„ /V"- ' The expanded a - manganese, of course, is not responsible for the ferromagnetism, since i t is present in the non-magnetic samples. It is merely the a solid solution of the composition equivalent to the boundary between the a solid soltction and the two phase regions ..adjacent to i t . The high temperature phase which is ferromagnetic produced the unidentified X-ray pattern obtained in the alloy quenched from 900°C. The pattern is possibly due to y- or 5 - manganese solid solution. The decrease in magnetic strength for alloys quenched from above 1000°C. would indicate a phase change, probably involving 5 - manganese, which does not appear in Vogel and Doring"s diagram. The decrease for alloys quenched from below 800 oC is in accordance with the diagram. Although the eutectoid temperature is given as 740°C,, 800'C. might be too l i t t l e above i t to ensure retaining the high temperature phase. Furthermore, the samples must be removed from the interior of the tube furnace before they are quenched. As this takes one or two seconds, the samples have had time to cool below the furnace temperature, before they are quenched. 56„ IV. APPENDICES APPENDIX I DETAILED CALCULATIONS FOR THE MAGNET Ampere-turns required' NI - H il i= H a l a 18000 oersteds x 2o02 a mP-^ u^ n 3 x 1 i n c h oersted-inch = 36,400 ampere-turns Estimated t o t a l NI = 45,000 ampere-turns. Design of the, yoke. By trial-and-error, the pole pieces in Figure 27 were designed^ which had a geometrical factor g = 9 and a leakage factor f == 9. The cylindrical portion of the pole caps, 9/32 inch long, was neglected,, It was to support the brass plates. g = area of large end of pole piece = 9 area of small end of pole piece f ° flux,in gap • leakage flux flux in gap > A 2TTrHdr + l\ 27Tr \ dr / x 27frHdr Design of the c o i l s . Assuming an allowable temperature rise of 20°C, and a maximum flow of water of 50 cc. per second, the power dissipation, on the basis that a l l heat is removed by the water cooling system, i s Figure 2 7 , A c o i l .assembly. 58, P = 20°C„ x 50 cc. x 4.18 .joules x 1 calorie sec. calorie "C.cc. = 4180 watts. L = P A (NI)*5/? F = 4180 watts 45,000* amp-turns2 x 7.324 x 10~7 ohm-inch x 3 s O o 9 3 ^ o o o o o o o o o o o « * O O O O O O O 6 O O O O O O O « O O » O O O O O O O B O O O O O O O ( l) The width of the coil assembly is chosen as three inches, to allow sufficient access to the gap. The coils packed better than predicted however, and upon assembly, occupied only 2 3/4 inches. Wooden rings 3/3 inch thick separate the colls and the water pancakes from the pole piece. Let b be the height of the coil above the wooden ring. From Figure 27, the cross-sectional area of one coil assembly is A - 3b + 1/2 x 3 x 1.715 2 A 6ID ^ 50*L$ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 0 0 ( 2 ) * - i r OoD. • I.D a±Ls. (6 • 2b » 3/4) • (6 - I .71? • 3/4) S TT^D *^ 5 o ^ S^J o o o o 00000 00 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 < » ( 3 ) Solving equations (l ) , (2), (3) simultaneously yields A » 38.2 square inches L = 3508 inches b = 5.5 inches Area of copper alone in both coil assemblies = A = 38.2 - 12.7 square inches F 3 For a 120 volt generator, current I = P = 4JLS0 = 34.9 amperes V 120 59o Cross-sectional area of wire = 12.7 x 34.9 58 0.00985 square inches. 45,000 The nearest commercial square wire is number ten, having an area of 0.00984 square inches. Using number ten wire? Turns required » 12.7 - 1292-.00984 Current = I = 45.000 = 34.8 amperes. 1292 Resistance of coils = 1292 x 35.8 ft.x .824 x 1_ ohms = 3.42 ohms. . 12 .928 1000 f t . Voltage required =3.42 ohms x 34.8 amps. = 119.2 volts. Power dissipated = 34.8 amps x 119.2 volts « 4150 watts. A check is now made to see If when the coils are wound of number ten wire, with each successive coil along the pole piece having a different number of turns, whether the resistance and turns are correct to produce 20 the required number of ampere-turns. Using data for the space required by the double cotton covered square wire, the number of turns and resist-ance of each of the four coils in a coil assembly were calculated. See Table 9. TABLE 9. Coil winding data. Coil No.. Turns Inside Diam. Outside Diam. Mean Diam. Mean CIrcum. 0.D.-I.D, 2 Length in f t . Resist. afc40°C. 1 143.4 6.47 17.75 12.11 38.1 5.64 455 0.403 2 152.6 5.75 17.75 11.75 36.9 6,00 469 0,416 3 161.8 5.03 17.75 11.39 35.8 6.36 483 0.428 4 170.6 4.33 17.75 11.04 35.0 6.71 498 0.443 628.4 1.690 6 0 o The total number of ampere^turhs,then,is NI - 2 x 60 x 6 2 8 . 4 - 44,700. 1 . 6 9 0 Now,the rest of the yoke was made so that the cross-section at any point was not less than the larger area of the pole piece. The final dimensions are shown in Figure 28. The path length in iron is about 52 inches. The flux density in the iron at the larger area of the pole piece is B - H £ *= 1 8 , 0 0 0 x § - 1 8 , 0 0 0 gausses, g y In the rest of the yoke, B will be less, because the cross-sectional area is larger. But taking, conservatively, that the flux density is the same throughout the whole yoke, the field strength in the iron yoke, as given by 13 Roters for ingot iron, is 200 ampere-turns per inch. Then the total ampere-turns required NI - Hil, + H 1 1 i a a - 200 x 52 + 36,400 => 46,800. Thus the original estimate of 45 ,000 ampere-turns was quite reasonable. The inductance of the magnet is calculated as follows, L = N(P I • " 1 2 9 2 x 1 8 0 0 0 x 2 , 5 4 2 x 9 7 T 3 4 o 8 x 1 0 * = 1 , 2 henries where L = inductance in henries N = number of turns <p ~ total flux in we ber s 61. Figure 28. Magnet dimensions 62 0 APPENDIX II. CONSTRUCTION OF THE MAGNET Each coil was wound on a wooden bobbin, the three wires being laid on together. The wires were hand painted with glyptal air drying varnish as they were wound on. When the coil was removed from the bobbin, the outside was coated with glyptal, and thewhole allowed to dry. The wooden spacer rings for the coils and the cooling pancakes were turned on a wood lathe. Slots were cut on the insides of the rings to allow the inner ends of the coils to be led out. The water cooling pancakes were made, by a local firm, but consider-able patching and resoldering were required to make them watertight. Commercial insulating material to separate the coils from the water pan-cakes was priced, but was prohibitively expensive. Instead, a good quality tracing paper, coated with glyptal, was used. Rings of this material were placed on both sides of each coil. The coils and water pancakes were en-closed between two 5/16 inch brass plates, with eight 3/8 brass studs holding the assembly together. Brass plates of this thickness were needed because of the enormous force developed on the large surface area of the water pancakes. Even so, the plates bulged noticeably under a water pressure of 7 psi. The brass plates were notched to allow the inner ends of the wires to emerge. Connections were made according to the wiring diagram in Appendix IV, and the free ends brought out to terminal boards fastened to the brass plates. The yoke was forged from a square bar into the shape shown. Two holes were d r i l l e d to accomodate long studs to hold the pole pieces. The inner two faces of the yoke were milled plane and parallel. The tops of the yoke were notched to allow the wires to emerge. The pole pieces were machined and placed inside the c o i l assemblies, with conical pieces of glyptal coated tracing paper around them to insulate them from the wires which l i e along their surfaces. The entire c o i l assembly was then held verticalj the yoke on a platform with wheels was rolled underneath i t and the iron studs were tightened. With no pole caps i n place, the gap between the faces of the pole pieces i s 1.911 inches. Each c o i l assembly was held to the yoke by two angles of aluminum running down each side of the yoke. The water pancakes were joined by copper tubing to two pipe manifolds which lay along the base of the magnet. A pressure gauge was put i n the inlet line. A pressure of only 3 psi i s needed to operate the magnet intermittently at 150 amperes. For prolonged measurements or higher currents, 5 or 6 psi is required. Under no circumstances should the pres-sure be allowed to exceed 7 psi. Because of the position of the suspension, the inlet and outlet tubes of the pancakes had to be placed almost on a level with the axis of the magnet, instead of at the top of the magnet. Air pockets formed above the outlet, and serious heating resulted at the tops of the co i l s . To overcome this, a hole was d r i l l e d and tapped i n the top of each pancake. With the hose to the outlet held above the level of the pancakes, water was slowly poured into the i n l e t , forcing out the a i r . When the water reached the top of each pancake, a small screw with a rubber gasket was screwed into each hole, the seal being made tight with rubber cement. No further heating resulted. It i s recommended that this procedure be repeated 6 4 o every few months, to bleed off any air which has collected at the tops of the pancakeso The base platform was f i t t e d with three levelling screws. After the suspension had been f i t t e d to the brass plates, the screws were adjust-ed so that; (1) the axis of the pole pieces was level and (2) the axis of the shaft connecting the d i a l to the suspension wire was ve r t i c a l . 65 o APPENDIX III. 66. APPENDIX 17. Inner ends a b c Outer ends RIGHT COIL . ASSEM8L Y ©-Inner ends 3 2 a b c a b c Outer ends LEFT COIL ASSEMBLY Wiring diagram of the magnet. 67 o APPENDIX V o PURITY OF THE METALS USED. 1. Manganese used in alloys was electrolytic manganese, 99.9% pure. 2. Carbon used in alloys was spectroscopic carbon. 3. Nickel used in magnetic balance standards was Fisher Scient-i f i c Co. nickel powder, which was reduced under hydrogen and melted under 8 argon by Piercy . The powder had 0.1% Fe and less than 0.1% Co as the main impurities. 4. Iron wire used in some of the magnetic balance measurements, viz. Table 6, was Fisher Scientific Co. iron wire, 99.8% pure. 5» Iron used in the remaining magnetic balance measurements, and in pole caps 5 and 6, was Norway iron, containing 0.011% C, 0,01% P, 0.37% Mn, 0,026% Si. 6, Iron used in pole caps 1, 2, 3, 4 was chain iron, containing 0.06%C, 0.32% Mn, 7, Iron used in the yoke and pole pieces was donated by the Steel Co. of Canada, and contained 0,06% C, 0,015% P, 0,24% Mn, and 0,03% S, 68. V. BIBLIOGRAPHY. 1. W o Sucksmith, C.A. Clark, D „ J o Oliver, J.E. Thompson, Rev. Mod. Phys. 2£, 34, (1953). 2. R.M. Bozorth, Ferromagnetism. New York, D . Van Nostrand, 1951, p. 443. 3. C Zener, Phys. Rev. 81, 440, (1951),. 4 . E,R, Morgan', Progress report, University of British Columbia, (1953). 5. R.C. Shhay, Thesis, University of British Columbia,(1953). 6. R. Buehl and J . Wulff, Rev. Sci, Insts. -224, (1938). 7. P. Weiss and R, Forrer, Annales de Physique, L 2 , 279, (1929). 8. G.R. Piercy, Thesis, University of British Columbia,(1952). 9. F. Bitter, Rev, Sci. Insts, 2, 479, (1936), 10. R.A. Fereday, Proc. Phys. Soc. /£, 383, (1931). 11. R.A, Fereday, Proc, Phys. Soc, 44* 274, (1932). R.A. Fereday, Proc, Phys. Soc. £6, 214, (1934), 11. W, Sucksmith, Proc, Roy. Soc, A 170. 551,(1939). 12. D.A. Aaronson, Thesis, University of British Columbia, (1950). 13. H,C, Roters, Electromagnetic.Devices, New York, J. Wiley and Sons, (1941), 14. W.J, de Haas and J.B. Westerdijk, Nature 128, 271, (1946). 15. F, Heusler, Z, angew, Chem, 12, 260, (1904), 16. E. Wedekind, Berichte d. Deutsch. Chem, Gesell. 2663; (1911). 17. R, Vogel and W. Doring, Archiv fur das Eisenh'uttenwesen £, 247, (1935). 18. H, Goldschmidt, J, Iron and Steel Inst. 160. 345, (1948). 19. H, Goldschmidt, Metallurgia 40, 103, (1949). 20. Magnet and Radio Wire, Catalogue no, 246, Phillips Electrical Works, (1946),
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A magnetic balance and its application to the investigation of ferromagnetism in manganese carbon alloys
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