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2.6.6 Magnetic properties of materials

Many magnetic properties of materials are expressed in terms of the magnetic field strength H, magnetic flux density B and the magnetic polarization J. The SI units of H and B are, respectively, ampere per metre (A m⁻¹) and tesla (T).

The relation between the quantities expressed in SI units is:

              B= μ₀ H + J

in which µ₀ is 4π × 10⁻⁷ H m⁻¹, the magnetic constant (permeability of free space). The absolute permeability, μ( = B/H) and the volume susceptibility κ (= J/μ₀H), are thus related by the equation:

            μ = μ₀(1 + κ)

The mass susceptibility χ is equal to κ/ρ, where ρ is the density. The relative permeability μ_r = μ/μ₀ is the permeability of the material relative to that of a vacuum and is the value given in the tables.

In ferromagnetic materials as H is increased steadily from zero the permeability changes and is at first relatively small, its value being defined as the initial permeability, then reaches a maximum value, and finally decreases towards μ₀ as the polarization tends towards a limiting value (B − μ₀H). The flux density remaining when H is reduced to zero is the remanent flux density and the negative H needed to reduce B to zero is the coercive force. The remanent flux density and coercive force for a cycle which proceeds to saturation are called the remanence, B_r, and the coercivity, H_cB. In an open magnetic circuit the variation of J with H is usually measured and the coercivity is then denoted by H_cJ.

When a ferromagnetic material is taken through a cycle of magnetization there is a loss of energy as heat due to the combined effects of hysteresis, induced eddy currents and domain wall motion. The hysteresis loss per unit volume, Q_h = H dB, has been shown empirically to vary as B^1.6_max over a limited range of peak flux density of up to about 1 T for high saturation materials, and 0.5 T for low saturation materials. This relationship, known as the Steinmetz law, is nevertheless only approximate. Some indication of the second loss, namely the eddy current power loss, may be calculated from standard formulae once certain relevant physical parameters are known. In their present forms, however, these formulae are only approximate. The total power losses that will be dissipated in laminar material when an alternating flux is developed in it has a direct bearing on the efficiency that can be realized in equipment such as transformers and electric motors and should therefore be known accurately. Accordingly the power losses of representative forms of typical materials are measured and some of these are given in Table (3) in terms of power loss per unit mass.

Many magnetic properties of ferromagnetic materials depend greatly on previous history, state of strain, temperature, size, perfection and orientation of crystals, and the effect of small traces of impurity may be enormous.

When heated, ferromagnetic materials become paramagnetic at a temperature known as the (ferromagnetic) Curie point.

Ferrimagnetic materials (ferrites) have all of the above characteristics of ferromagnetic materials. However, due to their high resistivity, soft (low coercivity) ferrites are widely used in high frequency applications, in which case the following parameters are also of interest:

Apart from changes in their magnetic permeability, some materials have other responses to changes in magnetic field strength. All conducting materials exhibit the Hall effect, of which there are two forms. In the transverse Hall effect a voltage is developed in a direction at right angles to a current passing through the material when a magnetic field is applied in a mutually perpendicular direction. The relationship between the current flowing through the material I_x, the output voltage, V_y, the thickness of the material, t_z, and the applied magnetic field strength, H_z, is given by:

             V_y = (K_H I_x μ₀ H_z) /t_z

where K_H is the transverse Hall coefficient of the material. It has been found that some semiconducting materials have sufficiently high Hall coefficients to produce convenient, small size and low cost magnetic sensors. Indium arsenide having a Hall coefficient of 0.75 Vm/TA is a widely used material.

The same conditions that produce the transverse Hall effect also give rise to a voltage in the direction of the current and this is sometimes called the longitudinal Hall effect but more usually magnetoresistance. Until recently only small changes in resistance have been observed (up to 2% for the widely used Ni₈₀Fe₂₀ material at room temperature) but the so-called giant magnetoresistance (GMR) has been observed in multilayers of Fe/Cr (50% change in resistance) and Co/Cu (120% change in resistance). However, strong magnetic field strengths (≈ 800 kA/m) and a temperature of 4.2 K are required to observe GMR in a multilayer. In all cases the magnetoresistance of a material is a complex function of the applied magnetic field strength, temperature, material type and thickness.

Since the properties may vary considerably from specimen to specimen due to chemical composition and state of heat treatment, the values given are only to be regarded as typical of the materials mentioned. A range of values is indicated by a dash.

Symbols used in tables:

   B   = magnetic flux density
   B_r  = remanence
   H   = magnetic field strength
   H_cB = induction coercive force, coercivity
   H_cJ = magnetization coervice force, coercivity
   J    = magnetic polarization
   J_s   = (B − μ₀H)_s = saturation polarization
   Q_h  = hysteresis loss per unit volume per cycle
   μ_r   = relative magnetic permeability
   μ_i   = initial relative magnetic permeability

(1) Magnetic susceptibilities of paramagnetic and diamagnetic materials

Values are mass susceptibility per kilogram, χ, at 20°C.

	× 10−8			× 10−8			× 10−8
Common elements
Hydrogen   .  .  .  .  .	−2.49		Aluminium  .  .  .  .  .	+0.82		Germanium  .  .  .  .  .	−0.15
Oxygen.  .  .  .  .  .  .	+133.6		Copper      .  .  .  .  .	−0.107		Silicon   .  .  .  .  .  .  .	−0.16
Helium    .  .  .  .  .  .	−0.59		Silver      .  .  .  .  .  .	−0.25		Arsenic    .  .  .  .  .  .	−0.39
Neon   .  .  .  .  .  .  .	−0.41		Gold       .  .  .  .  .  .	−0.19		Indium  .  .  .  .  .  .  .	−0.14
Argon .  .  .  .  .  .  .	−0.60		Platinum  .  .  .  .  .  .	+ 1.22		Antimony .  .  .  .  .  .	−1.09
Krypton    .  .  .  .  .	−0.41		Mercury  .  .  .  .  .  .	−0.21		Tellurium  .  .  .  .  .  .	−0.39
Xenon    .  .  .  .  .  .	−0.40		Bismuth   .  .  .  .  .  .	−1.70		Gallium  .  .  .  .  .  .  .	−0.30
Nitrogen   .  .  .  .  .	−0.54		Sulphur   .  .  .  .  .  .	−0.62		Phosphorus .  .  .  .  .	−1.13
Sodium     .  .  .  .  .	+0.75		Lead   .  .  .  .  .  .  .	−0.15
Potassium .  .  .  .  .	+0.65		Uranium .  .  .  .  .  .	+2.19
Common compounds						Common materials
H2O     .  .  .  .  .  .	−0.90		NiSO47H2O   .  .  .	+20.1		Araldite  .  .  .  .  .  .	−0.63
NO      .  .  .  .  .  .	+59.3		NiSO4K2SO47H2O	+13.9		P.V.C    .  .  .  .  .  .	−0.75
CO2     .  .  .  .  .  .	−0.59		CuSO45H2O  .  .  .	+ 7.7		Perspex .  .  .  .  .  .	−0.5
NH3     .  .  .  .  .  .	−1.38		MnSO44H2O .  .  .	+81.2		Polyethylene   .  .  .	+0.2
HCl      .  .  .  .  .  .	−0.75		FeSO4(NH4)2   .  .
H2SO4    .  .  .  .  .	−0.50		SO46H2O   .  .  .	+40.6
NaCl    .  .  .  .  .  .	−0.64
NiCl2   .  .  .  .  .  .
(anhydrous)  .  .	+78.5
(in solution)  .  .	+43.0

    Notes:
    (1) To obtain values in CGS units per gramme, the SI values given should be multiplied by 10³ /4π.
    (2) For a more complete list of elements, see L. F. Bates, Modern Magnetism (CUP).

(2) Feebly magnetic steels and cast irons

    * In general, the relative magnetic permeability decreases at higher values of magnetic field strength.
    ^†  Low permeability reference materials available from National Physical Laboratory, Teddington, Middlesex, TW11 0LW, UK.
    ^‡ C. B. Post and W. S. Eberley, ‘Stability of austenite in stainless steels’, Trans. Am. Soc. Metals, 1947, 39, p. 868.

(3) Soft (low coercivity) materials

Material (approx. % composition , balance iron)	B/T for H/(A m−1) =		Relative permeability μr		Js T	HcB A m−1	Br T	Curie point °C	Resistivity 10−8 Ωm	Specific total loss for J = 1.5 T,   f = 50Hz W/kg	Specific apparent power for J = 1.5 T,   f = 50Hz VA/kg
	1000	5000	Initial μi 1000	Maximum μr 1000
Ferromagnetic elements
Iron, high purity (single
crystals in preferred direction)  .  .	2.01	2.01	—	1500	2.16	12	—	770	10	—	—
Armco iron      .  .  .  .  .  .  .  .  .  .  .	1.55	1.72	0.25	7	2.16	80	1.3	770	11	—	—
Cast iron (annealed)     .  .  .  .  .  .  .	0.60	0.86	—	—	1.70	400	—	—
Swedish iron (annealed)     .  .  .  .  .	1.52	1.72	—	—	2.16	70	—	770	—	—	—
Nickel      .  .  .  .  .  .  .  .  .  .  .  .  .  .	0.45	0.55	—	—	0.615	400	—	358	9	—	—
Cobalt      .  .  .  .  .  .  .  .  .  .  .  .  .  .	0.21	0.70	—	—	1.76	950	—	1115	9	—	—
Steels (solid)
Carbon steel (annealed) 1% C  .  .  .	0.75	1.54	—	—	2.00	600	—	—	—	—	—
Constructional steels:
0.3% C, 1% Ni	1.32	1.68	—	—	2.10	250	—	—	—	—	—
0.4% C, 3% Ni, 1.5% Cr  .  .  .  .	0.75	1.67	—	—	2.05	500	—	—	—	—	—
Mild steel, 0.1% C    .  .  .  .  .  .  .	1.46	1.74	—	—	2.15	150	—	—	10
Steels (sheet)†
Grain oriented silicon steels with
preferred magnetic properties in
direction of rolling of the parent strip
(d.c. magnetization):
Unisil-H, 103-27-P5, (27MOH) 2.9% Si	1.93	2.00	—	93	2.00	6	—	745	45	1.00 (J = 1.7T)	1.38 (J = 1.7T)
Unisil,089-27-N5,(27M4)              097-30-N5, (30M5) 3.1%Si            111-35-N5, (35M6)	1.86	1.96	—	75	2.00	7	—	745	48	0.84	1.16
	1.86	1.96	—	59	2.00	7	—	745	48	0.89	1.32
	1.84	1.94	—	58	2.00	7	—	745	48	1.00	1.39
Non-oriented silicon steels:
SURA   300-35-A5, (CK-37)    2.9% Si	1.46	1.65	—	8	2.00	40	—	745	48	2.95	28
400-50-A5, (CK-40)    2.4% Si	1.48	1.69	—	7	2.03	40	—	748	44	3.60	19
800-65-A5, (DK-70)    1.6% Si	1.53	1.73	—	5	2.08	70	—	758	34	6.50	14
Non-oriented, non-silicon steel:
Newcor 1000-65-D5  .  .  .  .  .  .  .	1.59	1.75	—	8	2.15	50	—	770	12	7.00	9.6