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Magnetomechanical properties of rapidly quenched materials
MATERIALS SCIENCE & EHGINEERING MaterialsScienceand Enaneering A226-228 (1997)614-625
A
Magnetomechanical properties of rapidly quenched materials Zbigniew Kaczkowski Polish Academy of Sciemes Institute of Physics> al. Lotnikdw
32146, 02-668 Warsaw, Poland
Abstract Magnetomechanical properties of rapidly quenched materials are discussed. The magnetomechanical coupling and AE effect depend on magnetostriction and anisotropy. A crystallization reduced the magnetostriction and the magnetomechanical coupling practically vanishes. 0 1997 Elsevier Science S.A. Elasticity moduli; AE effect; Heat-treatment(influence);Mapletomechanicaicoupling; Magnetostriction;Piezomagnetic equations; Piezomagneticcoefficients;Rapidly quenchedalloys
Keywords:
1. Introduction Magnetomechanical properties of the magnetic materials are very important in the theory and applications. Magnetomechanical and mechanomagnetic phenomena in solids have a long, nearly 400 year history [l-23J.
2. Magnetostriction and other magnetomechanical interactions Magnet&&ion embraces the phenomena involving the interaction between magnetization and mechanical stresses and strains and refers both to the changes in
dimensions (linear magnetostriction, longitudinal (Fig. 1) and transverse magnetostriction,
‘I’L= - (l/2)$ [l&23]. The magnetostriction may have a positive (elongation, Fig. 1) or negative (contraction) sign. When the magnetization M (or induction B) approaches a saturation (MS or B,), the magnetostriction approaches its limiting value: a saturation magnetostriction (A,) (Fig. l), which belongs to the basic parameters of the magnetic materials [20-301.
Magnetostriction usually decreases in magnitude with increasing temperature. In the most of magnetic materials the saturation magnetostriction is proportionai to ca. squared magnetization,
i.e. R, N Mi. Mag-
netostriction may be increased or decreased by stress, depending on its sign and the direction of the acting
Joule’s effect [3],
volume magnetostriction, Barrett’s effect [9]) and to the changes in elastic properties (AE effect [13]) that occur in magnetic materials in the presence of imposed magnetic fields and to the magnetization changes (magnetoelasticity, Villari’s effect [S]) that occur in magnetic materials exposed to mechanical stresses[l&23]. The linear longitudinal and traverse relative changes of dimensions, i.e. length (I), width (w, or diameter d or radius r) or thickness (t), in the applied magnetic field (H) are known as a linear longitudinal (2 = ,I1= ,111 = Al//), or transverse (2, = 2, = At/t, or = Awjw, or Au/r)
magnetostrictions (or longitudinal or transverse Joule’s effects). In many materials, e.g. in nickel or in some of
metallic glasses,the changes in the length measured at right angles to the applied field are about half of the longitudinal magnetostriction and opposite in sign, i.e. 0921-5093/97/$17.00 0 1997ElsevierScienceS.A. All rights reserved. PIISO921-5093(96)10695-X
Fig. 1. Even effect of the magnetostriction [A( + H) = %( - H)] and forced piezomagnetism[,I _ ( + H) = - R_ ( - H) at constant static &,>i,,]. When&=O, &(+H,)=R,(-H,).
Z. Kaczkowski / Matettals Science and Engineering A226-228 (1997) 614-625 PERMEUDUR
I3
JO%PERMALLOY ALfER,ALCOfER FeRlCl.~ETAL.GL~SS
C~~?%:;~T.GLASS $%lTES
M
Fig. 2. Villari’s effect.
forces. When /z> 0, tension usually decreases 1, and when /2< 0, tension increases an absolute magnitude of the /z making it more negative, e.g. [19,23]. In strong magnetic fields the linear magnetostriction approaches a limiting value (3.,), superposed on which is a relative small length change. Then the material expands or contracts equally in all directions and its volume is changing (volume magnetostriction or Barrett’s effect, w = AVIV= Al/l+ At/t + Awjw) [l&23]. The Joule’s effect (discovered in 1842) has its inverse in Villa& effect, i.e. changes of the magnetization produced by an external tension, discovered in 1865 [8]. Magnetostrictive materials exhibit either an increase (positive Villari’s effect in Alfers, Alcofers, Permendurs and iron-rich metallic glasses) or a decrease of the magnetization (negative Villari’s effect in nickel, nickel ferrites and in some cobalt-rich metallic glasses) with increasing of the strains, depending on the sign of the magnetostriction and the direction of the applied forces (Fig. 2). In iron and some other iron-rich alloys, e.g. steels, the permeability increases with the strain in weak magnetic fields (H) and decreases in higher fields H. Between these states is a point on the magnetization curve (Villari’s Reversal-JR in Fig. 2) where the magnetostriction is unaffected by the strain. Villari discovered also that an iron bar lengthen when magnetized by a weak magnetic field but contracts when a particular field is exceeded. So Villari’s effect also means the change of the magnetostriction sign in iron (Villa& point) [S]. In transverse Villari’s effect is a change in the magnetization (or permeability) that occurs in a direction transverse to that of the mechanical strain [8]. With the fundamental magnetomechanical effects, as the magnetostriction, AE effect and magnetoelasticity (Villari’s effect) there are associated other magnetomechanical phenomena, e.g. Page’s clicks effect (magnetoacoustics) [Z], Wertheim’s effects (a generation of the voltage in the twisted rod immersed in a magnetic field) [4], Guilemin’s effect (straigthenning of the bent rod exposed to a magnetic field) [5], Mateucci’s effects
615
(change of the magnetization in twisting rod) [6], Wiedemann’s effects (twisting of the wire subjected an axial and a circular field) [7], Nagaoka-Honda effect (change of magnetization in hydrostatic pressure) [ll], magnetostrictive-piezoelectric effect, magnetostrictive detection effect, Barkhausen jumps or noisses (jump changes of magnetization order of magnitute of 10 nT) [15], magnetoacoustic emission [17], AG, AK and AC effects, Guillaume’s Invar effect (invariant thermal expansion) [I21 and Elinvar effect (elasticity invariable with the temperature) [16], piezomagnetic effect [14]. All magnetostrictive phenomena are connected with magnetic structure [l&-23]. The changes of the dimensions and other magnetostrictive phenomena depend on non-180” Bloch-wall movements and on domain vector rotations. The magnetostrictive may exhibit a hysteresis as a function of magnetic field (Fig. 1, Rozing’s effect, discovered in 1894 [lo]) or induction, stress, strain and temperature [l&23]. 3. Piezomagnetism, piezomagnetic equations and coefficients Piezoelectric phenomena have an analogy in piezomagnetism [14,23-261. In 1910 Voigt pointed out that a true piezomagnetic effect is theoretically possible in 29 of the 32 crystal classes [14]. In 1957 Dzialoshinski from a consideration of the magnetic symmetry, drew an attention to several antiferromagnetic materials in which piezomagnetic effect should be observed 1271. The first observation of a natural piezomagnetism of the antiferromagnetics was made by Borovik-Romanov in MnF, and CoF, [28]. When variations in mechanical and magnetic parameters are small compared with initial values of these parameters and reversible, the magnetomechanical interactions can be represented as effective linear phenomena. In the biased magnetostrictive materials is observed phenomenologically equivalent to piezomagnetism phenomenon, i.e. proportionality between a magnetization and stress. This forced piezomagnetism is observed in the all magnetostrictive materials when they are polarized by the bias magnetic field or at the magnetic remanence (Fig. l), The magnetically polarized magnetostrictive materials as an analogy to the piezoelectric ceramics can be termed piezomagnetic materials (resonators or transducers). The properties of the piezomagnetic materials are characterized by piezomagnetic coefficients occurring in the piezomagnetic equations, e.g. [23-26,31-341. In many cases, mechanical, thermal, electrical, and magnetic properties are treated in isolation from the others. Connections between them, i.e. between electric
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(E) and magnetic (H) fields and magnetic inductions (B) or electric displacement (D), strains (S), stresses (T), heat or entropy per unit volume (S,) and temperature (T> for the simplest interactions thermodynamically reversible are shown in Fig. 3. The magnetomechanical interactions are represented by the top face of the cube, presented in Fig. 3 with four variables: two mechanical, i.e. T and S, and two magnetic, i.e. H and B (or magnetization M or magnetic polarization J = p,,M). Starting points of the piezomagnetic (or magnetostrictive) equations are: a relation for the magnetization curve (B = pH) and Hooke’s Law (T = ES) to which the terms representing magnetomechanical interaction should be added, i.e. B=p,,(H+M)+AB=,@?+J+AB,
(1)
B=p&H+dT=,ul,H+dT,
(2)
where M is the magnetization, J-the magnetic polarization, $ = p/p0 is the relative value of the permeability y, and cl0= 471.10 - 7 H m-l is magnetic constant (defined in an old MKSA system as the vacuum permeability), the increment AB (positive or negative according to the sign of the magnetostriction and of the direction of the acting force) represents a change of the induction caused by the magnetomechanical interaction, e.g. by stress T, and coefficient of the proportionality d is the piezomagnetic (or stress) sensitivity [29-371, and S=;+AS=;+dH,
(3) H where AS represents a change of the S, and EH is the modulus of elasticity at constant magnetic field (H), connected with the magnetomechanical interactions caused by the changes of the H. If the thermal terms are omitted, the application of suitable magnetic bias field and resulting mechanical STRESS
PIEZOMAGNETICC0EF. eg
T
MAGNETIC FIELD
P
STRAIN
\
ELEKTRICFIELD
-
D ELECTRIC POlARlZATlON
+
ELEC~XA~OIK
Fig. 3. The relations between the thermal, electrical, magnetic and mechanical properties.
bias magnetostriction allows the use of four possible simple sets of the linear equations of state between four harmonic variables: the magnetic variables H and B (or M or J) and mechanical variables S ( = g) and T ( = E), whilst one magnetic and one elastic variables are chosen as independent variables, Using this assumptions and taking into a consideration thermodynamic relations, it is possible to derive corresponding identities and in the case of Eq. (2) and Eq. (3) one piezomagnetic coefficient d (stress sensitivity or piezomagnetic sensitivity) will be in the both equations [37]. The differentiation of the functions: B = f(H, T) and S= F(H, T> with respect to each magnetic field and stress components gives first set equations in Table 1. Changing the variables B, H, T and 5’ after differentiating the other combinations of the functions for changed independent and dependent variables we have three new sets of piezomagnetic equations [22,29-34,361 (Table 1). The coefficient of the proportionality d in Eq. (3) is identic with the piezomagnetic sensitivity from Eq. (2) [29-34,371, because the second order mixed partial derivatives of the perfect differential of the thermodynamical potential q are equal each other, e.g. [22,29,37]. In such case one should state precisely definitions of the magnetic and mechanical coefficients and thus the permeability should be determined at constant stresses j+, i.e. permeability of the free vibrating sample, and
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the elasticity moduli EH at constant magnetic field H, what corresponds an electrical source with internal impedance going to i&ity (Zi+ a), i.e. at constant current 1, to which is proportional magnetic field (i.e. H= d/l, where n is the number of turns of the coil and I is the length of magnetic path), e.g. [22,29,34,36,37]. The total differentials of the magnetic and mechanical functions (2) and (3) are given in Table 1 as the first set. Changing the variables B, H, T, and S the next three sets of the piezomagnetic equations may be derived, e.g. [22,24-26,29-34,36,37] (Table 1). In each set of piezomagnetic equations there are three piezomagnetic or magnetomechanical coefficients, e.g. ,u=, EH and d in the first set in Table 1. When a small alternating field and small alternating tensile stress are applied to a freely vibrating magnetically polarized sample, processesbecome reversible, the induction B and strain S will be linear functions of the both independent variables, i.e. B= f(H, r> and S= F(H, T>. The perfect
f,=f, , f.=f,
Fig. 4. Equivalent circuits of the piezomagnetic transducer and its impedance (Z) and characteristics plotted against frequency (f) and the equivalent motional impedance circle diagram. E is voltage applied to transducer and Z-electric current. Z, is the transducer impedance and Z, is the electrical (magnetic) impedance representing the series (or parallel) form of the equivalent circuit of electrical losses R = R,, + A, (where RCu are the losses in the winding and R, the losses in magnetic core) and reactance component joL, (where L, is inductance of the coil with the core). Z, is the mechanical impedance transformed to the electrical circuit, R, = D (diameter of the motional impedance circle), C, and L, represent internal friction losses, mass and elasticity of transducer, respectively. Z,,, and Z,, are maximum and minimum values of the impedance for resonance (f, =:fH) and antiresonance (f, zjJ frequencies and f0 and f, are mechanical resonance frequencies (without or with magnetic losses), f,, f2,f,, f;‘, f; and j’; are quadrantal frequencies.
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Fig. 5. Saturation magnetostriction (%,) of the Fe-Co-Ni-B metallic glasses [50].
differentials of these variables (changing in each set the independent variables) will have in the 5’1 units the matrix forms presented in second parts of the Table 1 [22,25,26,29-34,371. The Eq. (2) and Eq. (3) cannot be applied to a more general problem, since coupling between displacements in orthogonal directions has been completely neglected, e.g. [25]. For the general case, the coefficients in Eq. (2) and Eq. (3) are the matrix quantities rather than the scalar quantities, e.g. [22,24-26,29-34,371. In the matrix form these Eq. (2) and Eq. (3) are presented in Table 1 as the first set. The piezomagnetic equations are valid for the adiabatic changes [22,32-34,371. The partial derivatives evaluated at the bias values:one magnetic, one mechanical and one magnetomechanical (piezomagnetic) are the linear parameters, which are functions of these bias quantities but they are constaa for given operation points for small signal analysis. The differentials in Table 1 may be then replaced by their small signal values, i.e. ac vector quantities of the magnetic field (H) and magnetic induction (B) [or magnetic polarization (J) or (I), or magnetization (M)] and two second-order tensor quantities: dynamical stress (T or g) and strain (S or E). The choice of the independent variables is arbitrary [22,24-26,29-341. The piezomagnetic coefficients: d, e, g, h, denoted respectively to piezoelectric constants [30-331, and the permeabilities ,+ of the free vibrating sample (at constant stressesY’) and pS of the clamped sample (at constant strain S), the elasticity moduli EH at constant magnetic field H, what corresponds an electrical source with internal impedance going to infinity (&-+ co, Fig. 4), i.e. at constant current 1, and EB at constant magnetic induction B, what
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Table 2 Satuiation induction (B,) and magnetostriction (A,), Curie point (rd and density co) of the selectedrapidly quenched alloys Alloy
Fesobo Fe80P16CB 3 1 Fe7.&B14 Fe7&% Fe7&d9 Fe&A7 kdLd%o %Ni40Pd% Fe3C072P16A13B6 %%&%. ~osoB,o Fe,.,Co35.2Ni3,.8B,., Co~dJi3d22.3 Nii42.8C036.5Fe3.9B16.8 Fe73Pl~3%.5B9 h7Cr8% Fe74.5CulW2%.5B7 %jSi15,5B7 Fe73.jCWWid% Fe~&Mb& LO%, b&@b&.&
4
33
Tc
P
T
10-6
“C
Mg mw3
1.6 1.49
30 30 31.6 28.9 34 46 13.5 11 -0 -0 -6 -11.5 -9.0 -8.5 20.0 8.5 21 42 24 14 26
374 282
7.4 1.7
389 247 270 400
7.14 7.52 7.10
1.0 0.82 ~0.71 1.18
1.24 1.2 1.5 1.2 0.98 1.2
570 111 315 440 320 280
corresponds an electrical short circuited source, i.e. with impedance going to zero (Z-O), and the magnetomechanical coupling coefficient (1~)are variables dependent not only on the temperature, stress, pressure but also on the ac and dc magnetic fields, e.g. [22,2426,29-34,37]. Dynamical properties of the magnetostrictive materials (and transducers) are characterized by their piezomagnetic coefficients occurring not only in piezomagnetic equations, presented in Table 1, but also in other versions of these equations and units and by other coefficients [22-26,29,32,33,36]. 4. Magnetomechanical coupling coefficient Although each piezomagnetic coefficient characterizes some properties of piezomagnetic materials as a function of the magnetic bias field, magnetization, amplitude, or temperature, but none of them is itself a sufficient parameter for describing the usefulness of the piezomagnetic materials or transducers [22,2426,29,32,33]. It is only the set of three coefficients occurring in each pair of the system of piezomagnetic equations, e.g. EH, ,LL~and 4 that gives almost enough information, e.g. [22,24-26,29-341. None of them, however, can be a measure of the effectiveness of energy conversion. This function is fuElled by the magnetomechanical coupling coefficient (k), which, in
Remarks
- 3.0 x -2.5 x - 5.5 x 2.1 x
Ref.
41 41 54 54 54 79 41 41 59 59 18 14 74 74 78 71 48 16 76 76 80
10v6 kr 10m6kr 10e6 kr 10-6 kr
1.2 -0 kr 1.2-O kr 4x lop6 kr -0 kr
addition to the mechanical (Q), or magnetomechanical (& and QB), and electrical (Q3 quality factors, electroacoustical efficiency (II), vibration amplitude (A) etc., permits to compare properties of the piezomagnetic materials and transducers with those of the piezoelectric materials, components and transducers [24-261. Its analogy in piezoelectric materials is the coefficient of the electromechanical coupling [24-261. A part of energy (Aw) supplied to a transmitting transducer is converted to the energy of elastic oscillation (W) and radiated into medium loading the transducer. The opposite process occurs in a receiving transducer. The measure of this transformation is a squared coefficient of magnetomechanical coupling (1~~).It defines which part of the magnetic energy is converted into mechanical energy [22,24-26,29-361,
iB,H-iB,H k2= !?= 2 w
=-1-Ps PT
’
(4)
where the magnetic induction B = ,uH, and ,Uis, respectively, the magnetic permeability of the freely vibrating sample (at constant mechanical stressesT), i.e. for BT is pT, or of the clamped sample (at constant strains S), i.e. for B, is ,U~,and H is magnetic field. In a receiver the mechanical energy is partly converted to the magnetic energy,
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=I-
where stressesT = 0 = ES = EE,and S and E are strains and moduli of elasticity at constant magnetic field (S, and EH = 412c&= 412fip for rods and EH = n2d2c& = n2d2fip for toroids) or at constant magnetic induction 6% and EB =412ci = 4E2xp for rods and EB = n2d2c2,= n2d2Ep for toroids), respectively [because ultrasound velocities cs3= (E33/p)1/2]and p is the vibrator density. I is the length of the half-wave longitudinally vibrating rod and d is mean diameter of the radial vibrating resonator. fr and f, are the resonant and antiresonant frequencies, respectively [40-451 (Fig. 4) and a is a shape coefficient (for the half-wave resonator or transducer a = 7r2/8 and for toroidal resonator a = 1). The relations between the magnetomechanical coupling coefficient and coefficients occurring in each set of the piezomagnetic equations are following [23-26,2934]:
The magnetomechanical coupling coefficient (k) is connected with magnetostriction (A), elasticity moduli (I&J and terms of energies: magnetocrystalline ( R7;3,magnetostatic ( W’n) and magnetoelastic ( W,) by the following dependence: (7) The magnetomechanical coupling coefficient (k) [22,24-26,29-371 is calculated from resonant (f,> and antiresonant (~‘3 frequencies (Eq. (5), Fig. 4) [2426,29,32-36]. Using this method it is also possible to obtain mechanical and magnetomechanical quality factors. Generally: Q = f,i( f2 -fr). The mechanical quality factor Q, and the mechanical internal friction coefficient (Q-l) are calculated using the impedance circles (Fig. 4) from the mechanical resonancef. and the quadrantal frequencies fi and fi, i.e.
Qm=fiA--fl
*
(8)
The magnetomechanical interaction is connected with the magnetomechanical quality factor QH which can be obtained from the quadrantal frequencies f; and fr and the resonant frequency f, (for maximum impedance, Fig. 4), e.g. [32,33,36] f,
QH=Q=~-~~.
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The magnetomechanical quality factor at constant magnetic induction (B) may be obtained from admittance characteristics [36]. The mechanical and magnetomechanical internal friction coefficient Q - l may be calculated from the Eq. (8) or Eq. (9). The classic lumped element equivalent circuits of piezomagnetic transducers were discussed by many authors [22,24-26,29,33-361. Author uses series (or parallel) [29,33,36] magnetic circuit connected with the parallel mechanical circuit (Fig. 4). In Fig. 4, there are also presented connections between resonant-antiresonant characteristic and motional impedance circle. The motional impedance circle is more universal and possessesmore information. It is possible to obtain from the motional impedance circle not only the frequencies of the magnetomechanical resonances for maximum and minimum impedance, i.e. fr andf,, how it is in classical resonant-antiresonant method, but also the frequencies of the mechanical resonance for maximum resistance (f. for the circuit without magnetic losses, or f, for the circuit with magnetic losses) [24,29,33,36]. There are limitations for using these methods, e.g. when the magnetomechanical coupling coefficient is higher than 0.8 or the quality factor (Q) is lower than 20, e.g. [34,36]. 5. Requirements for the piezomagnetic materials For good piezomagnetic materials may be proposed the following mechanical, magnetic, piezomagnetic and other physical requirements [22,24-26,29,33,39]: 1. The-magnetostriction shbuld be greater than 15 x 10-6. 2. The magnetocrystalline energy (EK) should be very low. 3. The high induction saturation (B, > 1 T) should permit operations at the high power signals. 4. The Curie (TC) or Neel (TN) temperatures should be higher than 200-300°C. 5. The magnetomechanical coupling coefficient (k) should be higher than 0.15. 6. The mechanical quality factor (Q) should be higher than 20. 7. The electrical resistivity (p,J should be higher than 1 ~0 m to keep down the eddy current lossesup to the frequencies of 100 kHz. 8. The temperature coefficients of magnetomechanical coupling coefficient, permeability and elasticity moduli and sound velocity should be very low. 9. The material should have the stable magnetic, mechanical and piezomagnetic properties. 10. The corrosion resistance should be very high. These properties depend on the chemical composition, thermal, magnetic and/or mechanical treatment and their history, magnetic bias field (polarization), ampli-
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tude of ac magnetic field, temperature, pressure and coupled environment etc. The most known from the piezomagnetic materials is a nickel, practically used from 60 years. Next are Alfers (1 l-14% Al-Fe alloys), nickel based ferrites, Permalloys (containing from 45 to 60% Ni), Permendurs (4050% Co-Fe) alloys, containing also l--2% V), Hiperco (Co-Cr-Fe alloys), Ni-Co alloys, Alcofers, iron-rich metallic glasses and rare-earth compounds and alloys, e.g. [l&26,29,32-34,38-48]. In the nickel [;1,= - (30-40) x lo-‘], nickel-ferrites [ - (26-28) x 10W6]and polycrystalline cobalt [ - (1850) x 10m6] and some rare elements (RE) [e.g. in holmium 3,,= -(160-3500) x lO-‘j at 45 K], compounds and alloys the magnetostriction is negative [23,29,33,40-451. In the iron and some steels there are a change of the sign of a to negative when these materials are magnetized [8,18-26,29,33]. The iron-nickel alloys (Permalloys up to 78% Ni) and Fe-Co (Permendurs), Fe-Pt, Fe-Al (Alfers to 14% Al), Fe-Al-Co (Alcofers) alloys, iron-rich metallic glasses and some rare-earth elements, compounds and alloys exhibit the positive magnetostriction [l&26,29,33,40-45]. Piezomagnetic properties of the magnetostrictive materials are determined, generally, from electrical impedance characteristics, using the resonant-antiresonant method and/or from the motional impedance circles, e.g. [22,24-26,29,3 l-37,43], and from the dynamical magnetic measurements, e.g. [ 18-22,2426,29,32-36]. These parameters are investigated versus bias magnetic field, ac magnetic field amplitude, chemical composition, temperature etc., e.g. [18-26,29,31481. Very important in these investigations are mechanical, thermal and magnetic histories of materials or transducers, e.g. [18-26,33,36,40,43]. The influence of the heat-treatment-especially above the Curie temperature, but in the case of metallic glasses below the crystallization or nanocrystallization temperature-is very useful, also annealing in magnetic fields and/or with applied stresses. The internal stresses (or their great part) are then removed and better magnetic structure is formed [19,40]. In the case of the typical piezomagnetic materials the absolute values of the saturation magnetostriction are changing from 20 x 10m6(ferrites, metallic glasses and 45-50% Permalloys) to 1500 x lo- 6 and above for RE alloys. The Curie temperature of these materials changes from 200°C (RE alloys) to 970 and 980°C (Hiperco and 2V-Permendur). The density is ranging from about 5 to about 9.5 Mg mW3.The resistivity is in the range from 0.07 ~.IQm-i (Ni) to 1.2- 1.4 @2 m (Alfers, Alcofers and metallic glasses) and 10 mR m (ferrites) [19,22,24-26,33,39,40]. The relative values of the initial permeability (,q) change from 2- 100 (RE alloys and ferrites) to 20 000 (metallic glasses).The relative values of the maximum permeability are in the range of 10 (RE alloys and ferrites)
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- 100000 (50% Permalloys and metallic glasses).Magnetocrystalline anisotropy constants are equal to zero or nearly zero in metallic glasses, nickel, Alfers, Alcofers and Ni-Co ferrites, and are very high in RE alloys and compounds. The bias magnetic field for providing the maximum values of the magnetomechanical coupling coefficient (k) changes from 3-200 A m-i (metallic glasses, Alfers) to 20 kA m-l (rare-earth alloys). Ultimate (yield) strength changes from 20-700 MPa for ferrites and Terfenols to 1OO-1600 MPa for Alfers, Alcofers, Permendurs and metallic glasses [2326,33,39]. 6. Magnetostrictive properties of rapidly quenched materials Magnetocrystalline anisotropy arising from longrange crystallinity is absent in amorphous alloys. In amorphous materials with random distribution of the local symmetry axes and alloy components the crystalline anisotropy should be averaged out to zero, what in practice gives about two orders of magnitude smaller anisotropies in amorphous materials than in crystals. This conclusion for averaging of the local magnetocrystalline anisotropy may be confirmed by the macroscopic observation of 3D-based transition-metalmetalloid amorphous alloy, e.g. [23,38,49]. The investigation of the magnetostriction in amorphous materials is valuable from the theoretical and practical point of view [18-26,29,33-36,38-41,491. The local field is effective in nanocrystalline materials on a scale of a part of the nanometer. O’Handley and Grant proposed a model in which they had taken into account the strong structural short-range order [49]. It is important, in theory and practice, to know the relation between the local magnetostrictive strains associated with the atomic scale structural properties and the macroscopic magnetostriction constant 1, [23,38,49]. The sign and magnitude of the magnetostriction depend sensitively on the chemical composition (Fig. 5, Table 2). Iron-rich metallic glassesexhibit good magnetostrictive properties, e.g. Fig. 5 and Table 2. The magnetostriction depends on temperature. Theory of one-ion character of the magnetostriction, given by O’Handley, is a good explanation of the temperature dependenceof the /z [38,49]. Heat-treatment has also great influence on the magnetostriction [42,54]. Its characteristics depend on the temperature and the time of annealing. Directional characteristics of the magnetostriction were presented for Fe-P-C alloys [55,56]. The characteristics of the ,?r and 1, as functions of magnetic field for Fe-C alloy at temperatures of 77 and 300 K were presented by Kazama and Fujimori [57] and characteristics of the /2i, 2, and w for Fe-S-B metallic glassesafter different heat-treatments were investigated by Vlasak and
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Kaczkowski [54]. The magnetostriction of iron-rich amorphous alloys depends on the cooling rate [58]. In the amorphous materials magnetocrystalline anisotropy is absent and, in this case, on the magnetic properties decisive influence may have the magnetoelastic energy, connected with structural and induced internal stresses, introduced during cooling, and the linear magnetostriction, e.g. [23,33,38-42,49,50,54,59-801. Hysteresis loops in amorphous metallic glasses, because of excellent magnetic properties, are very narrow, e.g. [50,60,62]. Laser annealing has somewhat different influence on the changes of magnetostriction than classical heat treatment. A magneto-volume effect (spontaneous and forced volume magnetostriction) of the amorphous alloys is connected with the thermal expansion and the Invar and Elinvar properties, e.g. [52]. A stress dependence of the magnetic properties of amorphous alloys is, generally, in good agreement with a model proposed by Vgzquez, Fernengel and Kronmiiller 163,641.
;,H;
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7”“-“a’
f,
k =0.182 0.177j
0.6 0.4 r\* 01 40
I 41
I 42
'Q
1 I 43 44f [kHz]
Fig, 7. Impedance (Z) vs. frequency (j) of the Fe,,Si,,Bg asquenched strip at bias field H = 400 A m - ’ at amplitudes of the ac field equal to 1 and 2 A m-l [81].
4l-/hi
-38Ah-n
Correlations between magnetic domain walls and tension in Fe-Ni-P-B amorphous alloys investigated Williams and Bishop [65]. The Wiedemann effect, i.e. the influence of twisting on the magnetic properties, and the Mateucci effect were investigated by Barandiaran and Hernando and their school, e.g. [66,67]. The Barkhausen effect in the amorphous alloys was discussed in some papers, e.g. [68]. The magnetoacoustic emission was observed in F-Cu-Nb-Si-B alloys [69]. The magnetic after-effect or disaccommodation is investigated in metallic glasses very intensively, e.g. [7073]. The results and theories of the magnetostriction in partially or full crystallized alloys are presented in some papers, e.g. [41,48,49,74,76,80].
7. Piezomagnetic properties of the rapidly quenched magnetostrictive materials
Fig. 6. Impedance moduli (Z) vs. frequency (jJ and motional circles for bias fields equal to 38, 100 and 900 A m-’ for the 60 mm long strips of the as-quenched Fe,,Si,B,, alloy [81].
When a magnetostrictive material is placed in an alternating field the mechanical vibrations occur because of the dimension changes (Fig. 4). If the frequency of the ac applied to the polarized magnetostrictive resonator is equal to its mechanical resonance frequency the magnetomechanical coupling coefficient may be calculated from Eq. (5) (Figs. 4, 6 and 7). The piezomagnetic properties are investigated as a function of magnetic bias field (Figs. 8-l 1) or
622
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I
z 1 I9.
rA7L 1 7
370°C Ih Si&,
Fe,, 5Cu,Nb3Si,6 ,B,
180
i
-
160
2 ; 140 w 2 120 0 =
100
-0-
--O--
-A-
--A--480°Cann.1 h --V-- 480% am. 2h
-v-
asquenched
80
0
400
800
1600
1200
Magnetic Field H [ Aim 1
01 0
I 400
I I 800H[Alm]
Fig. 8. Maximum (Z,,J and minimum (Zmin) impedance moduli (2) vs. magnetic bias field (H) for the annealed in air for 1 h at 370°C strip of the Fe,,Si,B,, alloy.
amplitude of ac magnetic field (Fig. 12), chemical composition, temperature, pressure etc., e.g. [32,33,36,39, 40,45-47,81-861. Dynamical properties of the magnetostrictive materials (and transducers) are characterized not only by the piezomagnetic coefficients occurring in piezomagnetic equations (Table 1) and by the magnetomechanical coupling coefficient and quality factors (or internal friction coefficients) [(Eq. (4) Eq. (5) Eq. (6) Eq. (7) Eq. (8) Eq. (9)] but also by a magnetoacoustical efficiency and piezomagnetic dynamics (Z, = Z,,, Zti,) (Fig. 8). The maximum potential efficiency occurs at the mechanical resonancefm (Fig. 4). The electromechanical efficiency is determined by the product of the dynamical coefficients I&&,(2,, i.e. y = l/(1 + I/ k*Q,Q,). The magnetoacoustical efficiency is a product of the magnetomechanical (or electromechanical) effi-
EH GPa]
ciency (q,J and mechanoacoustical efficiency (yl& i.e. Y = vemx TIna- The influence of the amplitude of ac magnetic field (h) on the internal friction (Q-l), magnetomechanical coupling coefficient (1~) and Young’s modulus (I&) is very high at the range over 1 A m-l (Figs. 7 and 12), e.g. [81]. Young’s modulus changes as a function of the amplitude of ac magnetic field, for the bias magnetic fields lower than 200 A m-r for the Fe,,Si,B,, alloy strips may be related to the internal friction coefficient Q-r by the formula: Q-r M 0.424 AE/E, which is valid for the magnetomechanical Rayleigh’s law [81].
-0-460~c -A-4480'% -v--5oo~c -i--520'?
-1 Q Sld31
150
0
140
4
130
Fig. 10. Elasticity moduli (L$., and .&J of the Fe,,.,Cu,Nb,Si,,,,B, alloy strips, in as-quenched state and annealed in vacuum at the temperature of 480°C for 1 and next for 2 h at magnetic field, vs. magnetic bias field (H) [82].
0
Fig. 9. Magnetomechanical coupling coefficient (k), internal friction coefficient (Q- ‘) and elasticity modulus (En) vs. magnetic bias field (H) for the strip of the as-quenched of the Fe,,Si,Br, alloy [81].
od 0
400
800
1200
I 1600
Magnetic Field H [A/m ] Fig. 11. Magnetomechanical coupling coefficient (1~)of the 50 mm long Fe,,,,Cu,Nb,Si,,,,B, alloy strips, annealed in vacuum at temperatures of 460, 480, 500 and 520°C for 1 h vs. magnetic bias field (H) 1471.
Z. Kacrkowski
/Materials
Science and Engineering A226-228
-a
2 4 6 8 h[Alm~
r-460 i
Fig. 12. Internal friction (Q-r) and Young’s modulus (E&I dependences on the amplitude of magnetic field at various polarization for the Fe,,Si,B,, alloy strip [81].
8. Final remarks and conclusions It is very important in the piezomagnetic measurements to define the amplitude of the ac magnetic field because of the nonlinearity of the magnetic, mechanical and piezomagnetic properties (Figs. 7 and 12) [81]. Another condition is connected with demagnetizing before measurements the investigated samples. Otherwise, as a staring point will be remanence for major or minor loops with different signs, i.e. B, or - 3,. In very sensitive materials, as amorphous and nanocrystalline alloys, it is necessary to eliminate an influence of the external magnetic and electromagnetic fields, also magnetic earth field, or to put the investigated samples in screen chambers or boxes. A heat-treatment is a fundamental source of the improvement magnetic and piezomagnetic properties of the magnetic materials, especially of the amorphous alloys, e.g. [19,40,46, 47,82-X8]. In the normal heat-treatment process important is not only a time of annealing at the chosen temperature but also heating and cooling rates and atmosphere. The special heat treatment is conducted using external stresses (stress-annealing), e.g. [84] or
(1997) 614- 625
623
longitudinal or transverse magnetic fields, e.g. [53,57,82-851. Generally, annealing over the Curie temperature removes a great part of internal stresses and improves the magnetic and piezomagnetic properties of the amorphous alloys. A disadvantage of the annealing at the high temperatures over about 400-550°C depending on the chemical composition, is worsening of their mechanical properties. The ribbons become then very brittle. This heat treatment in the case of the piezomagnetic alloys should be about 50-100°C below the crystallization temperature (Fig. 13). The magnetomechanical coupling coefficient of the as-quenched iron-rich amorphous alloys is equal to 0.1-0.2. After annealing above the Curie temperature this value increases to 0.30-0.96 depending on the composition, temperature, time and atmosphere of the heat-treatment, e.g. [40,46,82-881 (Figs. 6- 13). Great influence on the magnetomechanical coupling coefficient have a quality of the ribbons, their uniformity, homogeneity etc. The internal stresses may be in great part removed by the heat treatment, but defects and impurities will be a reason of the Bloch-wall pinning. The stress-annealing and annealing in the transverse magnetic field also improved piezomagnetic properties because of the changes of the magnetic structure arrangement. The rotation of the magnetization vectors and non-180” Bloch wall movement are responsible for the excellent piezomagnetic properties. Values of Q factor of the amorphous alloys are changing from about 20 to 2500, depending on the chemical composition, mechanical imperfections, temperature, frequency, mechanical, magnetic and thermal history
and magnetic
structure,
and bias and ac fields,
e.g. [19,32,62,81-851. A majority of magnetic materials in the presence of the magnetic field lower than that
Annealing
TetnperatureT['C
1
Fig. 13. Saturation magnetostriction (A,), elasticity moduli at demagnetization (E,,) and saturation (ES) and their minimum values (Emin) and maximum values of the magnetomechanical coupling coefficient (k) of the Fe,,,,Cu,Nb,Ta,Si,,,,B, alloy strips, annealed in vacuum for 1 h vs. annealing temperature (r) [SS].
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providing the magnetic saturation show a deviation from Hooke’s law [Eq. (3) and Table l] which in amorphous materials may overpass 5000% [88]. The diszidvantage in the soft magnetic materials, i.e. the high magnetostriction, is very useful in some fields of the metrology, radioelectronics, as sensors and in the ultrasonic devices in the hydrolocation, technology and medicine, e.g. [24-26,29,32-34,511. References [l] W. Gilbert, De magnete, magneticisque corporibus et de magno magnete Tellure, Physiologia nova, P. Short, Londini, 1600. [2] C.G. Page, Amer. J. Sci., 32 (1837) 396. [3] J.P. Joule, Ann. Electr. Magn. Chem., 8 (1842) 219. 143G. Wertheim, Ann. Phys. Chemie, 12 (1844) 610. [S] A. Guilemin, Compt. Rend. Acad. Sci., 22 (1846) 264. 161C. Matteucci, Compt. Rend. Acad. Sci., 24 (1847) 301. [7] G.H. Wiedemann, Ann. Phys. Chanie, I17 (1862) 193. [S] E. Villarri, Ntlovo Cimento, 20 (1865) 317. [Y] W.F. Barrett, Nature, 26 (1882) 585. [lo] W.L. Rozing, ZI?RFHO {Fiz.), 26 (1894) 253. [ll] N. Nagoaka and K. Honda, Phil. Mag., 5 (1896) 46, 261. [12] C.E. Guillaume, Compt. Rend. Acad. Sci., 170 (1897) 1433. [13] K. Honda, S. Shimizu and S. Kusakabe, Phil. Mug., 4 (1902)
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Wisia, 1994, Upper Silesian Division of the Polish Acoustical Society, Gliwice, 1994, pp. 29-40. 1371 Z. Kaczkowski, J. Magn. Magn. Muter., 41 (1984) 341. 1381 R.C. O’Handley, Phys. Reo. B, 18 (1978) 930. 1391 Z. Kaczkowski, Akustyka Molekularna i Kwantowa, 16 (1995) 97. 1401 Z. Kaczkowski, Int. J, Appl. Electromagn. Mater., 5 (1994) 229. [411 F.E. Luborsky, in E.P. Wohlfarth (ed.), Ferrotnagnetic Materia/s, North-Holland Publ. Co., Amsterdam 1980, pp. 451-529. 1421 Z. Kaczkowski, L. Kraus, G. VlasBk, and P. Duhaj, J. Magtl. Magn. Mater., 160 (1996) 275. [431 Savage, A.E. Clark and J.M. Powers, IEEE Trans. Magn., MAC-11 (1975) 1355. [441 K.P. Belov, G.I. Kataev, R.Z. Levitin, S.A. Nikitin and V.I. Sokolov, Uspekhi Fiz. Nauk, 140 (1983) 271. [451 R.D. Greenough, T.J. Gregory, S.J. Clegg and J.H. Purdy, J. Appl. Phys., 70 (1991) 6534. [461 P.M. Anderson III, J. Appl. Phys., 53 (1982) 8101. [471 Z. Kaczkowski, L. Lanotte and M. Miiller, J. Magn. Magn. Mater., 140-144 (1995) 325. [481 M. Miller and N. Mattern, J. Magn. Magn. Mater., 136 (1994) 79. [491 R.C. O’Handley and N.J. Grant, in S. Steeb and H. Warlimont (eds.), Rapidly Quenched Metals, Elsevier Science Publ, B.V.,
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Akademia Nauk, Warszawa, 1972, pp. l-378. [23] E. du Tritmolet de Lacheisserie, Magnetostriction: Theory and Applications of Magnetoelasticity, CRC Press Inc., Boca Raton, 1993, pp. l-409. [24] Y. Kikuchi (ed.), Ultrasonic Transducers, Corona Publ. Co. Ltd., Tokyo, 1969. 1251D.A. Berlincourt, D.R. Curran and H. Jaffe, in W.P. Mason (ed.), Physical Acoustics, Vol. lA, Academic Press, New York, 1964, pp. 169-270. [26] W. Pajewski, Z. Kaczkowski and E. Stolarski, in Handbtrch de1 Elektronik, Franzis-Verlag, Miinchen, 1979, pp. 132-155. [27] I.E. Dzialoshinski, 5’0~.Phys. JETP, 6 (1958) 621. [28] A.S. Borovik-Romanov, Sov. Phys. JETP, If (1960) 786. [29] Z. Kaczkowski (ed.), Materialy piezomagizetyczne i ich zastosowania (Piezomagnetic Matesials and their Applications), PWN, Warszawa, 1978, pp. 1-813. [30] Z. Kaczkowski, Proc. Yibr. Probl., 2 (1961) 457. [31] z. Kaczkowski, Archiu. Acoust., 6 (1981) 385. 1321Z. Kaczkowski, Mater. Sci. Forum, 119-121 (1993) 591. [33] Z. Kaczkowski, VI. Vedeckd Konferencia Elektrotechuickej Fakulty, Zbornik PrednriSok, Fyrika, Technicka Univerzita v KoSicach, Elektrotechnickh Fakulta, KoSice, 1992, pp. 132-155.
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A
Magnetomechanical properties of rapidly quenched materials Zbigniew Kaczkowski Polish Academy of Sciemes Institute of Physics> al. Lotnikdw
32146, 02-668 Warsaw, Poland
Abstract Magnetomechanical properties of rapidly quenched materials are discussed. The magnetomechanical coupling and AE effect depend on magnetostriction and anisotropy. A crystallization reduced the magnetostriction and the magnetomechanical coupling practically vanishes. 0 1997 Elsevier Science S.A. Elasticity moduli; AE effect; Heat-treatment(influence);Mapletomechanicaicoupling; Magnetostriction;Piezomagnetic equations; Piezomagneticcoefficients;Rapidly quenchedalloys
Keywords:
1. Introduction Magnetomechanical properties of the magnetic materials are very important in the theory and applications. Magnetomechanical and mechanomagnetic phenomena in solids have a long, nearly 400 year history [l-23J.
2. Magnetostriction and other magnetomechanical interactions Magnet&&ion embraces the phenomena involving the interaction between magnetization and mechanical stresses and strains and refers both to the changes in
dimensions (linear magnetostriction, longitudinal (Fig. 1) and transverse magnetostriction,
‘I’L= - (l/2)$ [l&23]. The magnetostriction may have a positive (elongation, Fig. 1) or negative (contraction) sign. When the magnetization M (or induction B) approaches a saturation (MS or B,), the magnetostriction approaches its limiting value: a saturation magnetostriction (A,) (Fig. l), which belongs to the basic parameters of the magnetic materials [20-301.
Magnetostriction usually decreases in magnitude with increasing temperature. In the most of magnetic materials the saturation magnetostriction is proportionai to ca. squared magnetization,
i.e. R, N Mi. Mag-
netostriction may be increased or decreased by stress, depending on its sign and the direction of the acting
Joule’s effect [3],
volume magnetostriction, Barrett’s effect [9]) and to the changes in elastic properties (AE effect [13]) that occur in magnetic materials in the presence of imposed magnetic fields and to the magnetization changes (magnetoelasticity, Villari’s effect [S]) that occur in magnetic materials exposed to mechanical stresses[l&23]. The linear longitudinal and traverse relative changes of dimensions, i.e. length (I), width (w, or diameter d or radius r) or thickness (t), in the applied magnetic field (H) are known as a linear longitudinal (2 = ,I1= ,111 = Al//), or transverse (2, = 2, = At/t, or = Awjw, or Au/r)
magnetostrictions (or longitudinal or transverse Joule’s effects). In many materials, e.g. in nickel or in some of
metallic glasses,the changes in the length measured at right angles to the applied field are about half of the longitudinal magnetostriction and opposite in sign, i.e. 0921-5093/97/$17.00 0 1997ElsevierScienceS.A. All rights reserved. PIISO921-5093(96)10695-X
Fig. 1. Even effect of the magnetostriction [A( + H) = %( - H)] and forced piezomagnetism[,I _ ( + H) = - R_ ( - H) at constant static &,>i,,]. When&=O, &(+H,)=R,(-H,).
Z. Kaczkowski / Matettals Science and Engineering A226-228 (1997) 614-625 PERMEUDUR
I3
JO%PERMALLOY ALfER,ALCOfER FeRlCl.~ETAL.GL~SS
C~~?%:;~T.GLASS $%lTES
M
Fig. 2. Villari’s effect.
forces. When /z> 0, tension usually decreases 1, and when /2< 0, tension increases an absolute magnitude of the /z making it more negative, e.g. [19,23]. In strong magnetic fields the linear magnetostriction approaches a limiting value (3.,), superposed on which is a relative small length change. Then the material expands or contracts equally in all directions and its volume is changing (volume magnetostriction or Barrett’s effect, w = AVIV= Al/l+ At/t + Awjw) [l&23]. The Joule’s effect (discovered in 1842) has its inverse in Villa& effect, i.e. changes of the magnetization produced by an external tension, discovered in 1865 [8]. Magnetostrictive materials exhibit either an increase (positive Villari’s effect in Alfers, Alcofers, Permendurs and iron-rich metallic glasses) or a decrease of the magnetization (negative Villari’s effect in nickel, nickel ferrites and in some cobalt-rich metallic glasses) with increasing of the strains, depending on the sign of the magnetostriction and the direction of the applied forces (Fig. 2). In iron and some other iron-rich alloys, e.g. steels, the permeability increases with the strain in weak magnetic fields (H) and decreases in higher fields H. Between these states is a point on the magnetization curve (Villari’s Reversal-JR in Fig. 2) where the magnetostriction is unaffected by the strain. Villari discovered also that an iron bar lengthen when magnetized by a weak magnetic field but contracts when a particular field is exceeded. So Villari’s effect also means the change of the magnetostriction sign in iron (Villa& point) [S]. In transverse Villari’s effect is a change in the magnetization (or permeability) that occurs in a direction transverse to that of the mechanical strain [8]. With the fundamental magnetomechanical effects, as the magnetostriction, AE effect and magnetoelasticity (Villari’s effect) there are associated other magnetomechanical phenomena, e.g. Page’s clicks effect (magnetoacoustics) [Z], Wertheim’s effects (a generation of the voltage in the twisted rod immersed in a magnetic field) [4], Guilemin’s effect (straigthenning of the bent rod exposed to a magnetic field) [5], Mateucci’s effects
615
(change of the magnetization in twisting rod) [6], Wiedemann’s effects (twisting of the wire subjected an axial and a circular field) [7], Nagaoka-Honda effect (change of magnetization in hydrostatic pressure) [ll], magnetostrictive-piezoelectric effect, magnetostrictive detection effect, Barkhausen jumps or noisses (jump changes of magnetization order of magnitute of 10 nT) [15], magnetoacoustic emission [17], AG, AK and AC effects, Guillaume’s Invar effect (invariant thermal expansion) [I21 and Elinvar effect (elasticity invariable with the temperature) [16], piezomagnetic effect [14]. All magnetostrictive phenomena are connected with magnetic structure [l&-23]. The changes of the dimensions and other magnetostrictive phenomena depend on non-180” Bloch-wall movements and on domain vector rotations. The magnetostrictive may exhibit a hysteresis as a function of magnetic field (Fig. 1, Rozing’s effect, discovered in 1894 [lo]) or induction, stress, strain and temperature [l&23]. 3. Piezomagnetism, piezomagnetic equations and coefficients Piezoelectric phenomena have an analogy in piezomagnetism [14,23-261. In 1910 Voigt pointed out that a true piezomagnetic effect is theoretically possible in 29 of the 32 crystal classes [14]. In 1957 Dzialoshinski from a consideration of the magnetic symmetry, drew an attention to several antiferromagnetic materials in which piezomagnetic effect should be observed 1271. The first observation of a natural piezomagnetism of the antiferromagnetics was made by Borovik-Romanov in MnF, and CoF, [28]. When variations in mechanical and magnetic parameters are small compared with initial values of these parameters and reversible, the magnetomechanical interactions can be represented as effective linear phenomena. In the biased magnetostrictive materials is observed phenomenologically equivalent to piezomagnetism phenomenon, i.e. proportionality between a magnetization and stress. This forced piezomagnetism is observed in the all magnetostrictive materials when they are polarized by the bias magnetic field or at the magnetic remanence (Fig. l), The magnetically polarized magnetostrictive materials as an analogy to the piezoelectric ceramics can be termed piezomagnetic materials (resonators or transducers). The properties of the piezomagnetic materials are characterized by piezomagnetic coefficients occurring in the piezomagnetic equations, e.g. [23-26,31-341. In many cases, mechanical, thermal, electrical, and magnetic properties are treated in isolation from the others. Connections between them, i.e. between electric
616
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(E) and magnetic (H) fields and magnetic inductions (B) or electric displacement (D), strains (S), stresses (T), heat or entropy per unit volume (S,) and temperature (T> for the simplest interactions thermodynamically reversible are shown in Fig. 3. The magnetomechanical interactions are represented by the top face of the cube, presented in Fig. 3 with four variables: two mechanical, i.e. T and S, and two magnetic, i.e. H and B (or magnetization M or magnetic polarization J = p,,M). Starting points of the piezomagnetic (or magnetostrictive) equations are: a relation for the magnetization curve (B = pH) and Hooke’s Law (T = ES) to which the terms representing magnetomechanical interaction should be added, i.e. B=p,,(H+M)+AB=,@?+J+AB,
(1)
B=p&H+dT=,ul,H+dT,
(2)
where M is the magnetization, J-the magnetic polarization, $ = p/p0 is the relative value of the permeability y, and cl0= 471.10 - 7 H m-l is magnetic constant (defined in an old MKSA system as the vacuum permeability), the increment AB (positive or negative according to the sign of the magnetostriction and of the direction of the acting force) represents a change of the induction caused by the magnetomechanical interaction, e.g. by stress T, and coefficient of the proportionality d is the piezomagnetic (or stress) sensitivity [29-371, and S=;+AS=;+dH,
(3) H where AS represents a change of the S, and EH is the modulus of elasticity at constant magnetic field (H), connected with the magnetomechanical interactions caused by the changes of the H. If the thermal terms are omitted, the application of suitable magnetic bias field and resulting mechanical STRESS
PIEZOMAGNETICC0EF. eg
T
MAGNETIC FIELD
P
STRAIN
\
ELEKTRICFIELD
-
D ELECTRIC POlARlZATlON
+
ELEC~XA~OIK
Fig. 3. The relations between the thermal, electrical, magnetic and mechanical properties.
bias magnetostriction allows the use of four possible simple sets of the linear equations of state between four harmonic variables: the magnetic variables H and B (or M or J) and mechanical variables S ( = g) and T ( = E), whilst one magnetic and one elastic variables are chosen as independent variables, Using this assumptions and taking into a consideration thermodynamic relations, it is possible to derive corresponding identities and in the case of Eq. (2) and Eq. (3) one piezomagnetic coefficient d (stress sensitivity or piezomagnetic sensitivity) will be in the both equations [37]. The differentiation of the functions: B = f(H, T) and S= F(H, T> with respect to each magnetic field and stress components gives first set equations in Table 1. Changing the variables B, H, T and 5’ after differentiating the other combinations of the functions for changed independent and dependent variables we have three new sets of piezomagnetic equations [22,29-34,361 (Table 1). The coefficient of the proportionality d in Eq. (3) is identic with the piezomagnetic sensitivity from Eq. (2) [29-34,371, because the second order mixed partial derivatives of the perfect differential of the thermodynamical potential q are equal each other, e.g. [22,29,37]. In such case one should state precisely definitions of the magnetic and mechanical coefficients and thus the permeability should be determined at constant stresses j+, i.e. permeability of the free vibrating sample, and
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the elasticity moduli EH at constant magnetic field H, what corresponds an electrical source with internal impedance going to i&ity (Zi+ a), i.e. at constant current 1, to which is proportional magnetic field (i.e. H= d/l, where n is the number of turns of the coil and I is the length of magnetic path), e.g. [22,29,34,36,37]. The total differentials of the magnetic and mechanical functions (2) and (3) are given in Table 1 as the first set. Changing the variables B, H, T, and S the next three sets of the piezomagnetic equations may be derived, e.g. [22,24-26,29-34,36,37] (Table 1). In each set of piezomagnetic equations there are three piezomagnetic or magnetomechanical coefficients, e.g. ,u=, EH and d in the first set in Table 1. When a small alternating field and small alternating tensile stress are applied to a freely vibrating magnetically polarized sample, processesbecome reversible, the induction B and strain S will be linear functions of the both independent variables, i.e. B= f(H, r> and S= F(H, T>. The perfect
f,=f, , f.=f,
Fig. 4. Equivalent circuits of the piezomagnetic transducer and its impedance (Z) and characteristics plotted against frequency (f) and the equivalent motional impedance circle diagram. E is voltage applied to transducer and Z-electric current. Z, is the transducer impedance and Z, is the electrical (magnetic) impedance representing the series (or parallel) form of the equivalent circuit of electrical losses R = R,, + A, (where RCu are the losses in the winding and R, the losses in magnetic core) and reactance component joL, (where L, is inductance of the coil with the core). Z, is the mechanical impedance transformed to the electrical circuit, R, = D (diameter of the motional impedance circle), C, and L, represent internal friction losses, mass and elasticity of transducer, respectively. Z,,, and Z,, are maximum and minimum values of the impedance for resonance (f, =:fH) and antiresonance (f, zjJ frequencies and f0 and f, are mechanical resonance frequencies (without or with magnetic losses), f,, f2,f,, f;‘, f; and j’; are quadrantal frequencies.
(1997) 614-625
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Fig. 5. Saturation magnetostriction (%,) of the Fe-Co-Ni-B metallic glasses [50].
differentials of these variables (changing in each set the independent variables) will have in the 5’1 units the matrix forms presented in second parts of the Table 1 [22,25,26,29-34,371. The Eq. (2) and Eq. (3) cannot be applied to a more general problem, since coupling between displacements in orthogonal directions has been completely neglected, e.g. [25]. For the general case, the coefficients in Eq. (2) and Eq. (3) are the matrix quantities rather than the scalar quantities, e.g. [22,24-26,29-34,371. In the matrix form these Eq. (2) and Eq. (3) are presented in Table 1 as the first set. The piezomagnetic equations are valid for the adiabatic changes [22,32-34,371. The partial derivatives evaluated at the bias values:one magnetic, one mechanical and one magnetomechanical (piezomagnetic) are the linear parameters, which are functions of these bias quantities but they are constaa for given operation points for small signal analysis. The differentials in Table 1 may be then replaced by their small signal values, i.e. ac vector quantities of the magnetic field (H) and magnetic induction (B) [or magnetic polarization (J) or (I), or magnetization (M)] and two second-order tensor quantities: dynamical stress (T or g) and strain (S or E). The choice of the independent variables is arbitrary [22,24-26,29-341. The piezomagnetic coefficients: d, e, g, h, denoted respectively to piezoelectric constants [30-331, and the permeabilities ,+ of the free vibrating sample (at constant stressesY’) and pS of the clamped sample (at constant strain S), the elasticity moduli EH at constant magnetic field H, what corresponds an electrical source with internal impedance going to infinity (&-+ co, Fig. 4), i.e. at constant current 1, and EB at constant magnetic induction B, what
618
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Table 2 Satuiation induction (B,) and magnetostriction (A,), Curie point (rd and density co) of the selectedrapidly quenched alloys Alloy
Fesobo Fe80P16CB 3 1 Fe7.&B14 Fe7&% Fe7&d9 Fe&A7 kdLd%o %Ni40Pd% Fe3C072P16A13B6 %%&%. ~osoB,o Fe,.,Co35.2Ni3,.8B,., Co~dJi3d22.3 Nii42.8C036.5Fe3.9B16.8 Fe73Pl~3%.5B9 h7Cr8% Fe74.5CulW2%.5B7 %jSi15,5B7 Fe73.jCWWid% Fe~&Mb& LO%, b&@b&.&
4
33
Tc
P
T
10-6
“C
Mg mw3
1.6 1.49
30 30 31.6 28.9 34 46 13.5 11 -0 -0 -6 -11.5 -9.0 -8.5 20.0 8.5 21 42 24 14 26
374 282
7.4 1.7
389 247 270 400
7.14 7.52 7.10
1.0 0.82 ~0.71 1.18
1.24 1.2 1.5 1.2 0.98 1.2
570 111 315 440 320 280
corresponds an electrical short circuited source, i.e. with impedance going to zero (Z-O), and the magnetomechanical coupling coefficient (1~)are variables dependent not only on the temperature, stress, pressure but also on the ac and dc magnetic fields, e.g. [22,2426,29-34,37]. Dynamical properties of the magnetostrictive materials (and transducers) are characterized by their piezomagnetic coefficients occurring not only in piezomagnetic equations, presented in Table 1, but also in other versions of these equations and units and by other coefficients [22-26,29,32,33,36]. 4. Magnetomechanical coupling coefficient Although each piezomagnetic coefficient characterizes some properties of piezomagnetic materials as a function of the magnetic bias field, magnetization, amplitude, or temperature, but none of them is itself a sufficient parameter for describing the usefulness of the piezomagnetic materials or transducers [22,2426,29,32,33]. It is only the set of three coefficients occurring in each pair of the system of piezomagnetic equations, e.g. EH, ,LL~and 4 that gives almost enough information, e.g. [22,24-26,29-341. None of them, however, can be a measure of the effectiveness of energy conversion. This function is fuElled by the magnetomechanical coupling coefficient (k), which, in
Remarks
- 3.0 x -2.5 x - 5.5 x 2.1 x
Ref.
41 41 54 54 54 79 41 41 59 59 18 14 74 74 78 71 48 16 76 76 80
10v6 kr 10m6kr 10e6 kr 10-6 kr
1.2 -0 kr 1.2-O kr 4x lop6 kr -0 kr
addition to the mechanical (Q), or magnetomechanical (& and QB), and electrical (Q3 quality factors, electroacoustical efficiency (II), vibration amplitude (A) etc., permits to compare properties of the piezomagnetic materials and transducers with those of the piezoelectric materials, components and transducers [24-261. Its analogy in piezoelectric materials is the coefficient of the electromechanical coupling [24-261. A part of energy (Aw) supplied to a transmitting transducer is converted to the energy of elastic oscillation (W) and radiated into medium loading the transducer. The opposite process occurs in a receiving transducer. The measure of this transformation is a squared coefficient of magnetomechanical coupling (1~~).It defines which part of the magnetic energy is converted into mechanical energy [22,24-26,29-361,
iB,H-iB,H k2= !?= 2 w
=-1-Ps PT
’
(4)
where the magnetic induction B = ,uH, and ,Uis, respectively, the magnetic permeability of the freely vibrating sample (at constant mechanical stressesT), i.e. for BT is pT, or of the clamped sample (at constant strains S), i.e. for B, is ,U~,and H is magnetic field. In a receiver the mechanical energy is partly converted to the magnetic energy,
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=I-
where stressesT = 0 = ES = EE,and S and E are strains and moduli of elasticity at constant magnetic field (S, and EH = 412c&= 412fip for rods and EH = n2d2c& = n2d2fip for toroids) or at constant magnetic induction 6% and EB =412ci = 4E2xp for rods and EB = n2d2c2,= n2d2Ep for toroids), respectively [because ultrasound velocities cs3= (E33/p)1/2]and p is the vibrator density. I is the length of the half-wave longitudinally vibrating rod and d is mean diameter of the radial vibrating resonator. fr and f, are the resonant and antiresonant frequencies, respectively [40-451 (Fig. 4) and a is a shape coefficient (for the half-wave resonator or transducer a = 7r2/8 and for toroidal resonator a = 1). The relations between the magnetomechanical coupling coefficient and coefficients occurring in each set of the piezomagnetic equations are following [23-26,2934]:
The magnetomechanical coupling coefficient (k) is connected with magnetostriction (A), elasticity moduli (I&J and terms of energies: magnetocrystalline ( R7;3,magnetostatic ( W’n) and magnetoelastic ( W,) by the following dependence: (7) The magnetomechanical coupling coefficient (k) [22,24-26,29-371 is calculated from resonant (f,> and antiresonant (~‘3 frequencies (Eq. (5), Fig. 4) [2426,29,32-36]. Using this method it is also possible to obtain mechanical and magnetomechanical quality factors. Generally: Q = f,i( f2 -fr). The mechanical quality factor Q, and the mechanical internal friction coefficient (Q-l) are calculated using the impedance circles (Fig. 4) from the mechanical resonancef. and the quadrantal frequencies fi and fi, i.e.
Qm=fiA--fl
*
(8)
The magnetomechanical interaction is connected with the magnetomechanical quality factor QH which can be obtained from the quadrantal frequencies f; and fr and the resonant frequency f, (for maximum impedance, Fig. 4), e.g. [32,33,36] f,
QH=Q=~-~~.
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The magnetomechanical quality factor at constant magnetic induction (B) may be obtained from admittance characteristics [36]. The mechanical and magnetomechanical internal friction coefficient Q - l may be calculated from the Eq. (8) or Eq. (9). The classic lumped element equivalent circuits of piezomagnetic transducers were discussed by many authors [22,24-26,29,33-361. Author uses series (or parallel) [29,33,36] magnetic circuit connected with the parallel mechanical circuit (Fig. 4). In Fig. 4, there are also presented connections between resonant-antiresonant characteristic and motional impedance circle. The motional impedance circle is more universal and possessesmore information. It is possible to obtain from the motional impedance circle not only the frequencies of the magnetomechanical resonances for maximum and minimum impedance, i.e. fr andf,, how it is in classical resonant-antiresonant method, but also the frequencies of the mechanical resonance for maximum resistance (f. for the circuit without magnetic losses, or f, for the circuit with magnetic losses) [24,29,33,36]. There are limitations for using these methods, e.g. when the magnetomechanical coupling coefficient is higher than 0.8 or the quality factor (Q) is lower than 20, e.g. [34,36]. 5. Requirements for the piezomagnetic materials For good piezomagnetic materials may be proposed the following mechanical, magnetic, piezomagnetic and other physical requirements [22,24-26,29,33,39]: 1. The-magnetostriction shbuld be greater than 15 x 10-6. 2. The magnetocrystalline energy (EK) should be very low. 3. The high induction saturation (B, > 1 T) should permit operations at the high power signals. 4. The Curie (TC) or Neel (TN) temperatures should be higher than 200-300°C. 5. The magnetomechanical coupling coefficient (k) should be higher than 0.15. 6. The mechanical quality factor (Q) should be higher than 20. 7. The electrical resistivity (p,J should be higher than 1 ~0 m to keep down the eddy current lossesup to the frequencies of 100 kHz. 8. The temperature coefficients of magnetomechanical coupling coefficient, permeability and elasticity moduli and sound velocity should be very low. 9. The material should have the stable magnetic, mechanical and piezomagnetic properties. 10. The corrosion resistance should be very high. These properties depend on the chemical composition, thermal, magnetic and/or mechanical treatment and their history, magnetic bias field (polarization), ampli-
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tude of ac magnetic field, temperature, pressure and coupled environment etc. The most known from the piezomagnetic materials is a nickel, practically used from 60 years. Next are Alfers (1 l-14% Al-Fe alloys), nickel based ferrites, Permalloys (containing from 45 to 60% Ni), Permendurs (4050% Co-Fe) alloys, containing also l--2% V), Hiperco (Co-Cr-Fe alloys), Ni-Co alloys, Alcofers, iron-rich metallic glasses and rare-earth compounds and alloys, e.g. [l&26,29,32-34,38-48]. In the nickel [;1,= - (30-40) x lo-‘], nickel-ferrites [ - (26-28) x 10W6]and polycrystalline cobalt [ - (1850) x 10m6] and some rare elements (RE) [e.g. in holmium 3,,= -(160-3500) x lO-‘j at 45 K], compounds and alloys the magnetostriction is negative [23,29,33,40-451. In the iron and some steels there are a change of the sign of a to negative when these materials are magnetized [8,18-26,29,33]. The iron-nickel alloys (Permalloys up to 78% Ni) and Fe-Co (Permendurs), Fe-Pt, Fe-Al (Alfers to 14% Al), Fe-Al-Co (Alcofers) alloys, iron-rich metallic glasses and some rare-earth elements, compounds and alloys exhibit the positive magnetostriction [l&26,29,33,40-45]. Piezomagnetic properties of the magnetostrictive materials are determined, generally, from electrical impedance characteristics, using the resonant-antiresonant method and/or from the motional impedance circles, e.g. [22,24-26,29,3 l-37,43], and from the dynamical magnetic measurements, e.g. [ 18-22,2426,29,32-36]. These parameters are investigated versus bias magnetic field, ac magnetic field amplitude, chemical composition, temperature etc., e.g. [18-26,29,31481. Very important in these investigations are mechanical, thermal and magnetic histories of materials or transducers, e.g. [18-26,33,36,40,43]. The influence of the heat-treatment-especially above the Curie temperature, but in the case of metallic glasses below the crystallization or nanocrystallization temperature-is very useful, also annealing in magnetic fields and/or with applied stresses. The internal stresses (or their great part) are then removed and better magnetic structure is formed [19,40]. In the case of the typical piezomagnetic materials the absolute values of the saturation magnetostriction are changing from 20 x 10m6(ferrites, metallic glasses and 45-50% Permalloys) to 1500 x lo- 6 and above for RE alloys. The Curie temperature of these materials changes from 200°C (RE alloys) to 970 and 980°C (Hiperco and 2V-Permendur). The density is ranging from about 5 to about 9.5 Mg mW3.The resistivity is in the range from 0.07 ~.IQm-i (Ni) to 1.2- 1.4 @2 m (Alfers, Alcofers and metallic glasses) and 10 mR m (ferrites) [19,22,24-26,33,39,40]. The relative values of the initial permeability (,q) change from 2- 100 (RE alloys and ferrites) to 20 000 (metallic glasses).The relative values of the maximum permeability are in the range of 10 (RE alloys and ferrites)
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- 100000 (50% Permalloys and metallic glasses).Magnetocrystalline anisotropy constants are equal to zero or nearly zero in metallic glasses, nickel, Alfers, Alcofers and Ni-Co ferrites, and are very high in RE alloys and compounds. The bias magnetic field for providing the maximum values of the magnetomechanical coupling coefficient (k) changes from 3-200 A m-i (metallic glasses, Alfers) to 20 kA m-l (rare-earth alloys). Ultimate (yield) strength changes from 20-700 MPa for ferrites and Terfenols to 1OO-1600 MPa for Alfers, Alcofers, Permendurs and metallic glasses [2326,33,39]. 6. Magnetostrictive properties of rapidly quenched materials Magnetocrystalline anisotropy arising from longrange crystallinity is absent in amorphous alloys. In amorphous materials with random distribution of the local symmetry axes and alloy components the crystalline anisotropy should be averaged out to zero, what in practice gives about two orders of magnitude smaller anisotropies in amorphous materials than in crystals. This conclusion for averaging of the local magnetocrystalline anisotropy may be confirmed by the macroscopic observation of 3D-based transition-metalmetalloid amorphous alloy, e.g. [23,38,49]. The investigation of the magnetostriction in amorphous materials is valuable from the theoretical and practical point of view [18-26,29,33-36,38-41,491. The local field is effective in nanocrystalline materials on a scale of a part of the nanometer. O’Handley and Grant proposed a model in which they had taken into account the strong structural short-range order [49]. It is important, in theory and practice, to know the relation between the local magnetostrictive strains associated with the atomic scale structural properties and the macroscopic magnetostriction constant 1, [23,38,49]. The sign and magnitude of the magnetostriction depend sensitively on the chemical composition (Fig. 5, Table 2). Iron-rich metallic glassesexhibit good magnetostrictive properties, e.g. Fig. 5 and Table 2. The magnetostriction depends on temperature. Theory of one-ion character of the magnetostriction, given by O’Handley, is a good explanation of the temperature dependenceof the /z [38,49]. Heat-treatment has also great influence on the magnetostriction [42,54]. Its characteristics depend on the temperature and the time of annealing. Directional characteristics of the magnetostriction were presented for Fe-P-C alloys [55,56]. The characteristics of the ,?r and 1, as functions of magnetic field for Fe-C alloy at temperatures of 77 and 300 K were presented by Kazama and Fujimori [57] and characteristics of the /2i, 2, and w for Fe-S-B metallic glassesafter different heat-treatments were investigated by Vlasak and
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Science and Engineering A226-228
Kaczkowski [54]. The magnetostriction of iron-rich amorphous alloys depends on the cooling rate [58]. In the amorphous materials magnetocrystalline anisotropy is absent and, in this case, on the magnetic properties decisive influence may have the magnetoelastic energy, connected with structural and induced internal stresses, introduced during cooling, and the linear magnetostriction, e.g. [23,33,38-42,49,50,54,59-801. Hysteresis loops in amorphous metallic glasses, because of excellent magnetic properties, are very narrow, e.g. [50,60,62]. Laser annealing has somewhat different influence on the changes of magnetostriction than classical heat treatment. A magneto-volume effect (spontaneous and forced volume magnetostriction) of the amorphous alloys is connected with the thermal expansion and the Invar and Elinvar properties, e.g. [52]. A stress dependence of the magnetic properties of amorphous alloys is, generally, in good agreement with a model proposed by Vgzquez, Fernengel and Kronmiiller 163,641.
;,H;
621
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7”“-“a’
f,
k =0.182 0.177j
0.6 0.4 r\* 01 40
I 41
I 42
'Q
1 I 43 44f [kHz]
Fig, 7. Impedance (Z) vs. frequency (j) of the Fe,,Si,,Bg asquenched strip at bias field H = 400 A m - ’ at amplitudes of the ac field equal to 1 and 2 A m-l [81].
4l-/hi
-38Ah-n
Correlations between magnetic domain walls and tension in Fe-Ni-P-B amorphous alloys investigated Williams and Bishop [65]. The Wiedemann effect, i.e. the influence of twisting on the magnetic properties, and the Mateucci effect were investigated by Barandiaran and Hernando and their school, e.g. [66,67]. The Barkhausen effect in the amorphous alloys was discussed in some papers, e.g. [68]. The magnetoacoustic emission was observed in F-Cu-Nb-Si-B alloys [69]. The magnetic after-effect or disaccommodation is investigated in metallic glasses very intensively, e.g. [7073]. The results and theories of the magnetostriction in partially or full crystallized alloys are presented in some papers, e.g. [41,48,49,74,76,80].
7. Piezomagnetic properties of the rapidly quenched magnetostrictive materials
Fig. 6. Impedance moduli (Z) vs. frequency (jJ and motional circles for bias fields equal to 38, 100 and 900 A m-’ for the 60 mm long strips of the as-quenched Fe,,Si,B,, alloy [81].
When a magnetostrictive material is placed in an alternating field the mechanical vibrations occur because of the dimension changes (Fig. 4). If the frequency of the ac applied to the polarized magnetostrictive resonator is equal to its mechanical resonance frequency the magnetomechanical coupling coefficient may be calculated from Eq. (5) (Figs. 4, 6 and 7). The piezomagnetic properties are investigated as a function of magnetic bias field (Figs. 8-l 1) or
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I
z 1 I9.
rA7L 1 7
370°C Ih Si&,
Fe,, 5Cu,Nb3Si,6 ,B,
180
i
-
160
2 ; 140 w 2 120 0 =
100
-0-
--O--
-A-
--A--480°Cann.1 h --V-- 480% am. 2h
-v-
asquenched
80
0
400
800
1600
1200
Magnetic Field H [ Aim 1
01 0
I 400
I I 800H[Alm]
Fig. 8. Maximum (Z,,J and minimum (Zmin) impedance moduli (2) vs. magnetic bias field (H) for the annealed in air for 1 h at 370°C strip of the Fe,,Si,B,, alloy.
amplitude of ac magnetic field (Fig. 12), chemical composition, temperature, pressure etc., e.g. [32,33,36,39, 40,45-47,81-861. Dynamical properties of the magnetostrictive materials (and transducers) are characterized not only by the piezomagnetic coefficients occurring in piezomagnetic equations (Table 1) and by the magnetomechanical coupling coefficient and quality factors (or internal friction coefficients) [(Eq. (4) Eq. (5) Eq. (6) Eq. (7) Eq. (8) Eq. (9)] but also by a magnetoacoustical efficiency and piezomagnetic dynamics (Z, = Z,,, Zti,) (Fig. 8). The maximum potential efficiency occurs at the mechanical resonancefm (Fig. 4). The electromechanical efficiency is determined by the product of the dynamical coefficients I&&,(2,, i.e. y = l/(1 + I/ k*Q,Q,). The magnetoacoustical efficiency is a product of the magnetomechanical (or electromechanical) effi-
EH GPa]
ciency (q,J and mechanoacoustical efficiency (yl& i.e. Y = vemx TIna- The influence of the amplitude of ac magnetic field (h) on the internal friction (Q-l), magnetomechanical coupling coefficient (1~) and Young’s modulus (I&) is very high at the range over 1 A m-l (Figs. 7 and 12), e.g. [81]. Young’s modulus changes as a function of the amplitude of ac magnetic field, for the bias magnetic fields lower than 200 A m-r for the Fe,,Si,B,, alloy strips may be related to the internal friction coefficient Q-r by the formula: Q-r M 0.424 AE/E, which is valid for the magnetomechanical Rayleigh’s law [81].
-0-460~c -A-4480'% -v--5oo~c -i--520'?
-1 Q Sld31
150
0
140
4
130
Fig. 10. Elasticity moduli (L$., and .&J of the Fe,,.,Cu,Nb,Si,,,,B, alloy strips, in as-quenched state and annealed in vacuum at the temperature of 480°C for 1 and next for 2 h at magnetic field, vs. magnetic bias field (H) [82].
0
Fig. 9. Magnetomechanical coupling coefficient (k), internal friction coefficient (Q- ‘) and elasticity modulus (En) vs. magnetic bias field (H) for the strip of the as-quenched of the Fe,,Si,Br, alloy [81].
od 0
400
800
1200
I 1600
Magnetic Field H [A/m ] Fig. 11. Magnetomechanical coupling coefficient (1~)of the 50 mm long Fe,,,,Cu,Nb,Si,,,,B, alloy strips, annealed in vacuum at temperatures of 460, 480, 500 and 520°C for 1 h vs. magnetic bias field (H) 1471.
Z. Kacrkowski
/Materials
Science and Engineering A226-228
-a
2 4 6 8 h[Alm~
r-460 i
Fig. 12. Internal friction (Q-r) and Young’s modulus (E&I dependences on the amplitude of magnetic field at various polarization for the Fe,,Si,B,, alloy strip [81].
8. Final remarks and conclusions It is very important in the piezomagnetic measurements to define the amplitude of the ac magnetic field because of the nonlinearity of the magnetic, mechanical and piezomagnetic properties (Figs. 7 and 12) [81]. Another condition is connected with demagnetizing before measurements the investigated samples. Otherwise, as a staring point will be remanence for major or minor loops with different signs, i.e. B, or - 3,. In very sensitive materials, as amorphous and nanocrystalline alloys, it is necessary to eliminate an influence of the external magnetic and electromagnetic fields, also magnetic earth field, or to put the investigated samples in screen chambers or boxes. A heat-treatment is a fundamental source of the improvement magnetic and piezomagnetic properties of the magnetic materials, especially of the amorphous alloys, e.g. [19,40,46, 47,82-X8]. In the normal heat-treatment process important is not only a time of annealing at the chosen temperature but also heating and cooling rates and atmosphere. The special heat treatment is conducted using external stresses (stress-annealing), e.g. [84] or
(1997) 614- 625
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longitudinal or transverse magnetic fields, e.g. [53,57,82-851. Generally, annealing over the Curie temperature removes a great part of internal stresses and improves the magnetic and piezomagnetic properties of the amorphous alloys. A disadvantage of the annealing at the high temperatures over about 400-550°C depending on the chemical composition, is worsening of their mechanical properties. The ribbons become then very brittle. This heat treatment in the case of the piezomagnetic alloys should be about 50-100°C below the crystallization temperature (Fig. 13). The magnetomechanical coupling coefficient of the as-quenched iron-rich amorphous alloys is equal to 0.1-0.2. After annealing above the Curie temperature this value increases to 0.30-0.96 depending on the composition, temperature, time and atmosphere of the heat-treatment, e.g. [40,46,82-881 (Figs. 6- 13). Great influence on the magnetomechanical coupling coefficient have a quality of the ribbons, their uniformity, homogeneity etc. The internal stresses may be in great part removed by the heat treatment, but defects and impurities will be a reason of the Bloch-wall pinning. The stress-annealing and annealing in the transverse magnetic field also improved piezomagnetic properties because of the changes of the magnetic structure arrangement. The rotation of the magnetization vectors and non-180” Bloch wall movement are responsible for the excellent piezomagnetic properties. Values of Q factor of the amorphous alloys are changing from about 20 to 2500, depending on the chemical composition, mechanical imperfections, temperature, frequency, mechanical, magnetic and thermal history
and magnetic
structure,
and bias and ac fields,
e.g. [19,32,62,81-851. A majority of magnetic materials in the presence of the magnetic field lower than that
Annealing
TetnperatureT['C
1
Fig. 13. Saturation magnetostriction (A,), elasticity moduli at demagnetization (E,,) and saturation (ES) and their minimum values (Emin) and maximum values of the magnetomechanical coupling coefficient (k) of the Fe,,,,Cu,Nb,Ta,Si,,,,B, alloy strips, annealed in vacuum for 1 h vs. annealing temperature (r) [SS].
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providing the magnetic saturation show a deviation from Hooke’s law [Eq. (3) and Table l] which in amorphous materials may overpass 5000% [88]. The diszidvantage in the soft magnetic materials, i.e. the high magnetostriction, is very useful in some fields of the metrology, radioelectronics, as sensors and in the ultrasonic devices in the hydrolocation, technology and medicine, e.g. [24-26,29,32-34,511. References [l] W. Gilbert, De magnete, magneticisque corporibus et de magno magnete Tellure, Physiologia nova, P. Short, Londini, 1600. [2] C.G. Page, Amer. J. Sci., 32 (1837) 396. [3] J.P. Joule, Ann. Electr. Magn. Chem., 8 (1842) 219. 143G. Wertheim, Ann. Phys. Chemie, 12 (1844) 610. [S] A. Guilemin, Compt. Rend. Acad. Sci., 22 (1846) 264. 161C. Matteucci, Compt. Rend. Acad. Sci., 24 (1847) 301. [7] G.H. Wiedemann, Ann. Phys. Chanie, I17 (1862) 193. [S] E. Villarri, Ntlovo Cimento, 20 (1865) 317. [Y] W.F. Barrett, Nature, 26 (1882) 585. [lo] W.L. Rozing, ZI?RFHO {Fiz.), 26 (1894) 253. [ll] N. Nagoaka and K. Honda, Phil. Mag., 5 (1896) 46, 261. [12] C.E. Guillaume, Compt. Rend. Acad. Sci., 170 (1897) 1433. [13] K. Honda, S. Shimizu and S. Kusakabe, Phil. Mug., 4 (1902)
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