NEW DETERMINATION OF MAGNETIC ANISOTROPY CONSTANTS OF ALNICO MAGNET ALLOYS

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NEW DETERMINATION OF MAGNETIC

ANISOTROPY CONSTANTS OF ALNICO MAGNET ALLOYS

Y. Iwama, M. Takeuchi, M. Iwata

To cite this version:

Y. Iwama, M. Takeuchi, M. Iwata. NEW DETERMINATION OF MAGNETIC ANISOTROPY

CONSTANTS OF ALNICO MAGNET ALLOYS. Journal de Physique Colloques, 1971, 32 (C1),

pp.C1-556-C1-557. �10.1051/jphyscol:19711189�. �jpa-00214012�

JOURNAL DE PHYSIQUE Colloque C I , supplkment au no 2-3, Tome 32, Fkvrier-Mars 1971, page C 1 - 556

NEW DETERMINATION OF MAGNETIC ANISOTROPY CONSTANTS OF ALNICO MAGNET ALLOYS

Y. IWAMA, M. TAKEUCHI and M. IWATA

Department of Applied Physics, Nagoya University, Nagoya, Japan

R6sum6. - On donne une mkthode pour analyser les courbes de couple magnktique &Alnico monocristallin avec le champ applique comme parametre. Elle permet la separation distincte de l'anisotropie uniaxiale induite ^(&!) de I'ani- sotropie cristalline cubique ( K ; ) . Pour Alnico 5 et Alnico 6 trait6 optimalement, KL = 15,6 et 15,O 105 erg.cm-3, et K: = 1,5 et 1,2 105 erg.cm-3, respectivement. En outre, on a trouvk que si les kchantillons 6taient traitks dans un champ deviant de la direction [100], l'anisotropie induite montre un changement perceptible en grandeur et direction.

Abstract. - A method is given to analyse a magnetic torque curve of monocrystalline Alnico with a parameter of measuring field. It allows a distinct determination of the induced uniaxial anisotropy (&) from the cubic crystalline ani- sotropy ( K ; ) . For optimally treated Alnico 5 and Alnico 6, K: = 15.6 and 15.0 105 erg.cm-3, and ^{K ; =} 1.5 and 1.2 105 erg.cm-3, respectively. Furthermore, it has been found that when they are treated under a field in a direction deviated from [100], the induced anisotropy shows noticeable changes in magnitude as well as in direction.

A high coercivity of Alnico-type magnet alloys is generally recognized as due t o a shape anisotropy of ferromagnetic precipitates which are finely dispersed in a non-magnetic matrix of the alloys subjected to an appropriate treatment. Since a real. material consists of an assembly of the particles packed in fairly high density, a mutual interaction between them may greatly alter the overall anisotropy from a shape anisotropy which can be estimated for an isolated particle [I]. This work is to experimentally determine the overall shape anisotropy with a separation from the crystalline anisotropy of the precipitate phase.

I. Principle of Analysis. - The specimen used is a disk-shaped monocrystal with (001) surfaces. After an appropriate treatment it is assumed to consist of an assembly of similar prolate spheroids of precipitates aligning in a certain direction with a packing fractionp.

A series of magnetic torque curves are measured on the specimen under various higher intensities of magnetic field. In such a situation it can be reasonably assumed that uniform magnetizations of the particles may rotate in unison accompanied with a rotation of the measuring field. In addition, the particles as a whole may contribute a well-defined cubic anisotropy which is proper to the precipitate phase, because they are precipitated coherently with the monocrys- talline matrix.

Then, the torque exerted by a unit volume of the specimen is

L(8) = - pKu sin 2(8 - a - cp) - p - Kl sin 4(8 - q) 2

= - PHI, sin cp , (1)

where Ku, K, and I, are the shape anisotropy constant (uniaxial), the crystalline anisotropy constant (cubic) and the magnetization, all of which are taken as per a unit volume of the precipitate. And H i s the apparent effective field under consideration of only the shape of the specimen and the angles 8, cp and a are illustrated in figure 1. The last equation has been derived from the equilibrium condition for I,. The particle inter- action is assumed to be included implicitly in the Ku so

that it should be fairly different from a shape aniso- tropy constant for an isolated prolate spheroid, or K,* = I?(N, - N,)/2 [I].

If considered that ^q should tend to 0 as H goes to co in!Bq. (1) and assumed K,, % K,, the torque can be approximated under sufficiently high field by

pKu ( ^{1 - -} 2;) ^{sin 2(8 - a) +}

N K1

+ pKu ² sin 4(8 - a) - p - sin 4 8 -

2 H 2

- pKu sin 6(8 - a) ,

8 H~

where Ha = 2 Ku/Is. Therefore, if we rearrange it into L(8, H) ⁼ a,(H) cos 2 8 + a2(H) cos 4 8 +

+ a,(H) cos 6 8 + b,(H) sin 2 8 +

+ b,(H) sin 4 8 + b,(H) sin 6 8 , ₍₃₎

we obtain

a,/b, = - ^{tan 2 a ,} (5)

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19711189

NEW DETERMINATION OF MAGNETIC ANISOTROPY CONSTANTS C 1 - 557 and

The last equation implies that b,(H) - vs. - ^(l/H)

plot may give the value of pK, from the intercept of the line on the ordinate.

11. Experimental Results with Discussion. - Mono- crystalline Alnico 5 (8.0 % Al, 14.0 % Ni, 23,9 % Co, 3.1 % Cu) and Alnico 6 (8.2 % Al, 14.3 % Ni, 24.0 % Co, 3.1 % Cu, 1.0 % Ti) have been investigated in the way above described. In the first place the disk- shaped specimens have been cooled from 1 250 OC at a rate of about 0.5 0C.s-I under the magnetic field in a crystallographic [I001 direction, followed by annealing at 600% for 16 hr. For the alloys it is known as the optimal magnet treatment. In such a case the uniaxial anisotropy K, is induced along the [loo], so that all the ai's are to be 0 in Eq. (3). The magnetic torque has been measured under various fields up to about 17 kOe. The harmonic wave analyses of the curves have proved that they can be fitted close to the finite Fourier series of Eq. (3), giving b,, b2 and b, as functions of H. In addition the

b,(H) - VS. - (1/H)

plot has given a well-defined straight line to determine the value of pK,. The results obtained are shown in Table I with other data obtained from a magnetization measurement.

TABLE I

PKU PKI I H ~

Material (105 erg.cm-3) (105 erg .cm-3) (Oe) ( G )

-- - - - -

Alnico 5 15.6 1.5 710 1140

Alnico 6 15.0 1.2 785 830

For both alloys K,/Ku - 0.1, which seems to be consistent with the previous assumption. It is to be noted that these results involve unavoidably the unknown factor of p, which must be determined by another experiment, say, an electron-microscopic observation of the precipitate structure. If assumed p = 0.57 -- 0.63 for Alnico 5 according to the previous

works [2, 31, we obtain

Ku = 27.4

24.8 x lo5 erg.cm-, .

If it is considered that the Ku should involve the particle interaction, this value seems to be quite large, because the coercive force is rather low as shown in Table I.

It may be suggested, therefore, that on the ordinary magnetization reversal there should occur any other mechanism than the rotation in unison. On the other hand, the value of K , is 2.6 - ^{2.4 x} lo5 e r g . ~ m - ~ , which seems to be reasonable, because according to Hall [4], K , is neraly 2.5 x 105 erg.cm-, for a binary Fe-Co alloy with the composition of Fe2Co.

By the way it has been proved that the values of

anisotropies would not appreciably change even if the particles grew so larger as to lead to a considerably low coercive force. Further measurements have been carried out for the (001) disk specimens treated under a field in the direction deviated from [I001 by 15O, 30° and 45O, respectively. The resulta are shown in Table I1 with the coercive forces measured in their optimal directions. As the field direction deviates from [loo], the induced anisotropy decreases together with the coercive force, though a decrease in the former is much more marked. It should be also noticed that the uniaxial anisotropy has been induced not in the treatment field direction, but in a certain direction closer to the nearest [loo], except for the case of 45O.

This fact may suggest that with Alnico alloys there is a strong tendency of precipitation in the crystallogra- phic < ¹⁰⁰ > direction as suggested by Cahn [5]. If based on a model shown in figure 2, a calculation is

made for each precipitate like as in the chain-of-sphere model [GI, the observed variations in magnitude and direction of the induced anisotropy can be qualitatively explained. Indeed, a ratio of K, in the case of optimal treatment (Fig. 2a) to that in the case of 450 treatment (Fig. 2c) is estimated as 3.0, which well agrees with the observed value of 3.5.

Angle between [loo]

and field direction during treatment

-

0 15 30 45 References

TABLE I1

I H ~ in optimal pKu Angle between [loo] direc- (105 erg. and induced aniso- tion

cm-3) tropy direction

(Oe)

- - -

15.6 0.2 710

14.9 3.7 680

10.3 12.0 620

4.4 43.3 520

[I] STONER (E. C.) and WOHLFARTH (E. P.), Phil. Trans. [4] HALL (R. C.), J. Appl. Phys., 1959,30,816.

Roy. Soc., 1948, A240, 589.

121 LUBORSKY (F. E.), MENDELSOHN (L.T.) and PAINE (T. O.), [5] CAHN (J. W.), J. Appl. Phys., 1963, 34, 3581.

J. Appl. Phys., 1957, 28, 344. 161 JACOBS (I. S.) and BEAN (C. P.), Phys. Rev., 1955, 131 YERMOLENKO (A. S.) and SHUR (Ya. S.), Fiz. Metal. ^{100, 1060.}

Metalloved, 1964, 17, 31.