上海交通大学：《材料与文明》课程教学资源（参考资料）Understanding Mater_Chapter 12 - Magnetic Properties of Materials

12 Magnetic Properties of Materials 12.1·Fundamentals Modern technology would be unthinkable without magnetic ma- terials and magnetic phenomena.Magnetic tapes or disks(for computers,video recorders,etc.)motors,generators,telephones, transformers,permanent magnets,electromagnets,loudspeak- ers,and magnetic strips on credit cards are only a few examples of their applications.To a certain degree,magnetism and elec- tric phenomena can be considered to be siblings since many com- mon mechanisms exist such as dipoles,attraction,repulsion, spontaneous or forced alignment of dipoles,field lines,field strengths,etc.Thus,the governing equations often have the same form.Actually,electrical and magnetic phenomena are linked by the famous Maxwell equations,which were mentioned already in Chapter 10. At least five different kinds of magnetic materials exist.They have been termed para-,dia-,ferro-,ferri-,and antiferromagnet- ics.A qualitative as well as a quantitative distinction between these types can be achieved in a relatively simple way by utiliz- ing a method proposed by Faraday.The magnetic material to be investigated is suspended from one of the arms of a sensitive bal- ance and is allowed to reach into an inhomogeneous magnetic field(Figure 12.1).Diamagnetic materials are expelled from this field,whereas para-,ferro-,antiferro-,and ferrimagnetics are at- tracted in different degrees.It has been found empirically that the apparent loss or gain in mass,that is,the force,F,on the sample exerted by the magnetic field,is: FVxH盟 (12.1)

12 Modern technology would be unthinkable without magnetic ma￾terials and magnetic phenomena. Magnetic tapes or disks (for computers, video recorders, etc.) motors, generators, telephones, transformers, permanent magnets, electromagnets, loudspeak￾ers, and magnetic strips on credit cards are only a few examples of their applications. To a certain degree, magnetism and elec￾tric phenomena can be considered to be siblings since many com￾mon mechanisms exist such as dipoles, attraction, repulsion, spontaneous or forced alignment of dipoles, field lines, field strengths, etc. Thus, the governing equations often have the same form. Actually, electrical and magnetic phenomena are linked by the famous Maxwell equations, which were mentioned already in Chapter 10. At least five different kinds of magnetic materials exist. They have been termed para-, dia-, ferro-, ferri-, and antiferromagnet￾ics. A qualitative as well as a quantitative distinction between these types can be achieved in a relatively simple way by utiliz￾ing a method proposed by Faraday. The magnetic material to be investigated is suspended from one of the arms of a sensitive bal￾ance and is allowed to reach into an inhomogeneous magnetic field (Figure 12.1). Diamagnetic materials are expelled from this field, whereas para-, ferro-, antiferro-, and ferrimagnetics are at￾tracted in different degrees. It has been found empirically that the apparent loss or gain in mass, that is, the force, F, on the sample exerted by the magnetic field, is: F
V $ 0 H d d H x , (12.1) Magnetic Properties of Materials 12.1 • Fundamentals

224 12.Magnetic Properties of Materials FIGURE 12.1.Measure- ment of the magnetic susceptibility in an in- homogeneous mag- netic field.The mag- netic field lines (dashed)follow the iron core. where V is the volume of the sample,uo is a universal constant called the permeability of free space (1.257 X 10-6 H/m or Vs/Am), and X is the susceptibility,which expresses how responsive a ma- terial is to an applied magnetic field.Characteristic values for X are given in Table 12.1.The term dH/dx in Eq.(12.1)is the change of the magnetic field strength H in the x-direction.The field strength H of an electromagnet (consisting of helical windings of a long,in- sulated wire as seen in the lower portion of Figure 12.1)is pro- portional to the current,I,which flows through this coil,and on the number,n,of the windings (called turns)that have been used to make the coil.Further,the magnetic field strength is inversely proportional to the length,L,of the solenoid.Thus,the magnetic field strength is expressed by: H=I L (12.2) The field strength is measured(in SI units)in "Amp-turns per meter"or shortly,in A/m. The magnetic field can be enhanced by inserting,say,iron,into a solenoid,as shown in Figure 12.1.The parameter which ex- presses the amount of enhancement of the magnetic field is called the permeability u.The magnetic field strength within a mate- rial is known by the names magnetic induction!(or magnetic Calling B "magnetic induction"is common practice but should be dis- couraged because it may be confused with electromagnetic induction, as shown in Figure 10.3

where V is the volume of the sample, 0 is a universal constant called the permeability of free space (1.257 106 H/m or Vs/Am), and $ is the susceptibility, which expresses how responsive a ma￾terial is to an applied magnetic field. Characteristic values for $ are given in Table 12.1. The term dH/dx in Eq. (12.1) is the change of the magnetic field strength H in the x-direction. The field strength H of an electromagnet (consisting of helical windings of a long, in￾sulated wire as seen in the lower portion of Figure 12.1) is pro￾portional to the current, I, which flows through this coil, and on the number, n, of the windings (called turns) that have been used to make the coil. Further, the magnetic field strength is inversely proportional to the length, L, of the solenoid. Thus, the magnetic field strength is expressed by: H
I L n . (12.2) The field strength is measured (in SI units) in “Amp-turns per meter” or shortly, in A/m. The magnetic field can be enhanced by inserting, say, iron, into a solenoid, as shown in Figure 12.1. The parameter which ex￾presses the amount of enhancement of the magnetic field is called the permeability . The magnetic field strength within a mate￾rial is known by the names magnetic induction1 (or magnetic 224 12 • Magnetic Properties of Materials X L N S FX I FIGURE 12.1. Measure￾ment of the magnetic susceptibility in an in￾homogeneous mag￾netic field. The mag￾netic field lines (dashed) follow the iron core. 1Calling B “magnetic induction” is common practice but should be dis￾couraged because it may be confused with electromagnetic induction, as shown in Figure 10.3.

12.1·Fundamentals 225 TABLE 12.1.Magnetic constants of some materials at room temperature Type of Material X(SI)unitless X(cgs)unitless u unitless magnetism Bi -165×10-6 -13.13×10-6 0.99983 Ge -71.1×10-6 -5.66×10-6 0.99993 Au -34.4×10-6 -2.74×10-6 0.99996 Diamagnetic Ag -25.3×10-6 -2.016×10-6 0.99997 Be -23.2×10-6 -1.85×10-6 0.99998 Cu -9.7×10-6 -0.77×10-6 0.99999 Superconductorsa -1.0 ~-8×10-2 0 B-Sn +2.4×10-6 +0.19×10-6 1 Al +20.7×10-6 +1.65×10-6 1.00002 Paramagnetic W +77.7×10-6 +6.18×10-6 1.00008 Pt +264.4×10-6 +21.04×10-6 1.00026 Low carbon steel 5×103 Fe-3%Si (grain-oriented) Approximately the same as u 4×104 Ferromagnetic Ni-Fe-Mo (supermalloy) because of x=u-1. 106 a See Sections 11.3 and 12.2.1 Note:The table lists the unitless susceptibility,x,in SI and cgs units.(The difference is a factor of 4m,see Appendix Il.)Other sources may provide mass,atomic,molar,volume,or gram equiv- alent susceptibilities in cgs or mks units. Source:Landolt-Bornstein,Zahlenwerte der Physik,Vol.11/9,6th Edition,Springer-Verlag,Berlin (1962). flux density)and is denoted by B.Magnetic field strength and magnetic induction are related by the equation: B=u uoH. (12.3) The SI unit for B is the tesla(T)and that of uo is henries per me- ter (H/m or Vs/Am);see Appendix II.The permeability (some- times called relative permeability,ur)in Eq.(12.3)is unitless and is listed in Table 12.1 for some materials.The relationship be- tween the susceptibility and the permeability is u=1+X. (12.4) For empty space and,for all practical purposes,also for air,one defines X=0 and thus u=1 [See Eq.(12.4)].The susceptibility is small and negative for diamagnetic materials.As a conse- quence,u is slightly less than 1 (see Table 12.1).For para-and antiferromagnetic materials,X is again small,but positive.Thus, u is slightly larger than 1.Finally,X and u are large and positive for ferro-and ferrimagnetic materials.The magnetic constants are temperature-dependent,except for diamagnetic materials,as

flux density) and is denoted by B. Magnetic field strength and magnetic induction are related by the equation: B
 0H. (12.3) The SI unit for B is the tesla (T) and that of 0 is henries per me￾ter (H/m or Vs/Am); see Appendix II. The permeability (some￾times called relative permeability, r) in Eq. (12.3) is unitless and is listed in Table 12.1 for some materials. The relationship be￾tween the susceptibility and the permeability is 
1 $. (12.4) For empty space and, for all practical purposes, also for air, one defines $
0 and thus 
1 [See Eq. (12.4)]. The susceptibility is small and negative for diamagnetic materials. As a conse￾quence,  is slightly less than 1 (see Table 12.1). For para- and antiferromagnetic materials, $ is again small, but positive. Thus,  is slightly larger than 1. Finally, $ and  are large and positive for ferro- and ferrimagnetic materials. The magnetic constants are temperature-dependent, except for diamagnetic materials, as 12.1 • Fundamentals 225 TABLE 12.1. Magnetic constants of some materials at room temperature Type of Material $ (SI) unitless $ (cgs) unitless  unitless magnetism Bi 165 106 13.13 106 0.99983 Ge 71.1 106 5.66 106 0.99993 Au 34.4 106 2.74 106 0.99996 Diamagnetic Ag 25.3 106 2.016 106 0.99997 Be 23.2 106 1.85 106 0.99998 Cu 9.7 106 0.77 106 0.99999 Superconductorsa 1.0 8 102 0 -Sn 2.4 106 0.19 106 1 Al 20.7 106 1.65 106 1.00002 Paramagnetic W 77.7 106 6.18 106 1.00008 Pt 264.4 106 21.04 106 1.00026 Low carbon steel 5 103 Fe–3%Si (grain-oriented) 4 104 Ferromagnetic Ni–Fe–Mo (supermalloy) 106 a See Sections 11.3 and 12.2.1 Note: The table lists the unitless susceptibility, $, in SI and cgs units. (The difference is a factor of 4, see Appendix II.) Other sources may provide mass, atomic, molar, volume, or gram equiv￾alent susceptibilities in cgs or mks units. Source: Landolt-Börnstein, Zahlenwerte der Physik, Vol. 11/9, 6th Edition, Springer-Verlag, Berlin (1962). Approximately the same as  because of $
  1.

226 12.Magnetic Properties of Materials we will see later.Further,the susceptibility for ferromagnetic ma- terials depends on the field strength,H. The magnetic field parameters at a given point in space are, as explained above,the magnetic field strength H and the mag- netic induction B.In free (empty)space,B and uoHl are identi- cal,as seen in Eq.(12.3).Inside a magnetic material the induc- tion B consists of the free-space component (uoH)plus a contribution to the magnetic field (uoM)which is due to the pres- ence of matter [Figure 12.2(a)],that is, B=uoH uoM, (12.5) where M is called the magnetization of the material.Combining Egs.(12.3)through (12.5)yields: M=XH. (12.6) H,B,and M are actually vectors.Specifically,outside a mater- ial,H(and B)point from the north to the south pole.Inside of a ferro-or paramagnetic material,B and M point from the south N N N HoH H (a) (b) (c) (d) FiGURE 12.2.Schematic representation of magnetic field lines in and around different types of ma- terials.(a)Para-or ferromagnetics.The magnetic induction (B)inside the material consists of the free-space component(uoH)plus a contribution by the material (uoM);see Eq.(12.5).(b)The magnetic field lines outside a material point from the north to the south poles,whereas inside of para-or ferromagnetics,B and poM point from south to north in order to maintain continuity. (c)In diamagnetics,the response of the material counteracts (weakens)the external magnetic field. (d)In a thin surface layer of a superconductor,a supercurrent is created (below its transition tem- perature)which causes a magnetic field that opposes the external field.As a consequence,the magnetic flux lines are expelled from the interior of the material.Compare to Figure 11.27

we will see later. Further, the susceptibility for ferromagnetic ma￾terials depends on the field strength, H. The magnetic field parameters at a given point in space are, as explained above, the magnetic field strength H and the mag￾netic induction B. In free (empty) space, B and 0H are identi￾cal, as seen in Eq. (12.3). Inside a magnetic material the induc￾tion B consists of the free-space component (0H) plus a contribution to the magnetic field (0M) which is due to the pres￾ence of matter [Figure 12.2(a)], that is, B
0H 0M, (12.5) where M is called the magnetization of the material. Combining Eqs. (12.3) through (12.5) yields: M
$ H. (12.6) H, B, and M are actually vectors. Specifically, outside a mater￾ial, H (and B) point from the north to the south pole. Inside of a ferro- or paramagnetic material, B and M point from the south 226 12 • Magnetic Properties of Materials N S N S N S N S 0H 0H B S N 0M 0M 0M 0M (a) (b) (c) (d) FIGURE 12.2. Schematic representation of magnetic field lines in and around different types of ma￾terials. (a) Para- or ferromagnetics. The magnetic induction (B) inside the material consists of the free-space component (0H) plus a contribution by the material (0M); see Eq. (12.5). (b) The magnetic field lines outside a material point from the north to the south poles, whereas inside of para- or ferromagnetics, B and 0M point from south to north in order to maintain continuity. (c) In diamagnetics, the response of the material counteracts (weakens) the external magnetic field. (d) In a thin surface layer of a superconductor, a supercurrent is created (below its transition tem￾perature) which causes a magnetic field that opposes the external field. As a consequence, the magnetic flux lines are expelled from the interior of the material. Compare to Figure 11.27

12.2.Magnetic Phenomena and Their Interpretation 227 to the north;see Figures 12.2(a)and (b).However,we will mostly utilize their moduli in the following sections and thus use light- face italic letters. B was called above to be the magnetic flux density in a mate- rial,that is,the magnetic flux per unit area.The magnetic flux is then defined as the product of B and area A,that is,by 中=BA. (12.7) Finally,we need to define the magnetic momentn(also a vector)through the following equation: M=0, (12.8) which means that the magnetization is the magnetic moment per unit volume. A short note on units should be added.This book uses SI units throughout.However,the scientific literature on magnetism(par- ticularly in the United States)is still widely written in electro- magnetic cgs(emu)units.The magnetic field strength in cgs units is measured in Oersted and the magnetic induction in Gauss. Conversion factors from SI into cgs units and for rewriting Eqs. (12.1)-(12.8)in cgs units are given in Appendix II. 12.2.Magnetic Phenomena and Their Interpretation We stated in the last section that different types of magnetism ex- ist which are characterized by the magnitude and the sign of the susceptibility (see Table 12.1).Since various materials respond so differently in a magnetic field,we suspect that several funda- mentally different mechanisms must be responsible for the mag- netic properties.We shall now attempt to unfold the multiplicity of the magnetic behavior of materials by describing some perti- nent experimental findings and giving some brief interpretations. 12.2.1 Ampere postulated more than one hundred years ago that so- Diamagnetism called molecular currents are responsible for the magnetism in solids.He compared these molecular currents to an electric cur- rent in a loop-shaped piece of wire which is known to cause a magnetic moment.Today,we replace Ampere's molecular cur- rents by orbiting valence electrons. To understand diamagnetism,a second aspect needs to be con- sidered.As explained in Chapter 10 a current is induced in a wire loop whenever a bar magnet is moved toward (or from)this loop

to the north; see Figures 12.2(a) and (b). However, we will mostly utilize their moduli in the following sections and thus use light￾face italic letters. B was called above to be the magnetic flux density in a mate￾rial, that is, the magnetic flux per unit area. The magnetic flux  is then defined as the product of B and area A, that is, by 
B A. (12.7) Finally, we need to define the magnetic moment m (also a vector) through the following equation: M
 V m , (12.8) which means that the magnetization is the magnetic moment per unit volume. A short note on units should be added. This book uses SI units throughout. However, the scientific literature on magnetism (par￾ticularly in the United States) is still widely written in electro￾magnetic cgs (emu) units. The magnetic field strength in cgs units is measured in Oersted and the magnetic induction in Gauss. Conversion factors from SI into cgs units and for rewriting Eqs. (12.1)–(12.8) in cgs units are given in Appendix II. We stated in the last section that different types of magnetism ex￾ist which are characterized by the magnitude and the sign of the susceptibility (see Table 12.1). Since various materials respond so differently in a magnetic field, we suspect that several funda￾mentally different mechanisms must be responsible for the mag￾netic properties. We shall now attempt to unfold the multiplicity of the magnetic behavior of materials by describing some perti￾nent experimental findings and giving some brief interpretations. Ampère postulated more than one hundred years ago that so￾called molecular currents are responsible for the magnetism in solids. He compared these molecular currents to an electric cur￾rent in a loop-shaped piece of wire which is known to cause a magnetic moment. Today, we replace Ampère’s molecular cur￾rents by orbiting valence electrons. To understand diamagnetism, a second aspect needs to be con￾sidered. As explained in Chapter 10 a current is induced in a wire loop whenever a bar magnet is moved toward (or from) this loop. 12.2.1 Diamagnetism 12.2 • Magnetic Phenomena and Their Interpretation 227 12.2 • Magnetic Phenomena and Their Interpretation