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ATOMIC MAGNETIC MOMENT IN TERNARY ALLOY Fe-Co-Ni
N. Kunitomi, Y. Nakai, K. Yamasaki, N. Schibuya
To cite this version:
N. Kunitomi, Y. Nakai, K. Yamasaki, N. Schibuya. ATOMIC MAGNETIC MOMENT IN TERNARY ALLOY Fe-Co-Ni. Journal de Physique Colloques, 1974, 35 (C4), pp.C4-149-C4-151.
�10.1051/jphyscol:1974426�. �jpa-00215617�
JOURNAL DE PHYSIQUE Colloque C4, supplkment au no 5, tome 35, Mai 1974, page C4-149
ATOMIC MAGNETIC MOMENT IN TERNARY ALLOY Fe-Co-Ni
N. KUNITOMI, Y. NAKAI, K. YAMASAKI and N. SCHIBUYA Department of Physics, Faculty of Science,
Osaka University, Toyonaka, Osaka, 560, Japan
Rbsumb. - On a observk les moments magnetiques atomiques de Co et Fe dans l'alliage ternaire Fe-Co-Ni cubique & faces centrkes. Les rksultats sont expliques au moins qualitativement par une thkorie CPA.
Abstract. -The atomic magnetic moments of Co and Fe were observed in f.c.c. ternary Fe-Co-Ni alloys. The results are explained by CPA theory at least qualitatively.
Recently, the treatment of the non-dilute random substitutional alloys has become possible by the theory based on the coherent potential approximation (CPA). Jo, Hasegawa, and Kanamori have applied this method to obtain the physical properties of f. c. c. ferromagnetic ternary alloys [I]. In the present work, individual magnetic moment of each constituent atom in ternary f. c. c. alloy Fe-Co-Ni has been obtain- ed by means of the neutron diffraction and the Mossbauer effect. The results are compared with the conclusion of the above theory and the applicability of the CPA is discussed.
The experimental difficulty of determining the individual moments in the ternary system is that one has to know the three independent physical properties which relate to the individual moments, even if the single site approximation is assumed. In the present case, however, moment of Co atom has been almost uniquely determined from the values of the average moment and the polarized neutron difference cross section A(do/dQ), because there exists a fortunate condition that the coherent nuclear scattering ampli- tudes of Fe and Ni are approximately equal.
The polarized neutron difference cross section of the disordered scattering for a ternary system is expressed as
where ci, bi, and pi represent the concentration, the coherent nuclear scattering amplitude, and the atomic magnetic moment of atom i, respectively. The coeffi- cient a is the factor of the magnetic scattering ampli-
tude. If b,, is exactly equal to b,,, only the first term contributes to the cross section, and u,, can be deter- mined accurately. In the actual case of Fe-Co-Ni, b,, and b,, are slightly different, so the contribution of the second term was eliminated from the observed cross section by using the theoretical value of p,,.
The error for the determination of Co moment by this method is estimated to be less than 1
%
for every specimen.The measurement was made at room temperature by using a conventional type polarized neutron diffractometer and the difference cross section was observed by flipping the neutron spin direction. The background noise due to the multiple scattering was calculated by the computor simulation method [2].
In order to determine the absolute value of the cross section, the instrumental constant was determined by using the standard specimens of Ni, V and NH,Cl.
The specimens were prepared by melting in an argon arcfurnace and quenched from 1 000 OC after annealing for three hours. The specimens with various thickness up to 2 mm were examined in order to check the effect of the multiple scattering. Typical difference cross section patterns are shown in figure 1, in which the values before and after the subtraction of the multipIe scattering are shown. The corrected curves are usually smooth and show few effect of short range order. The cross section at angle zero was extrapolated by using averaged free atom HF form factor [3].
Magnetic moment of Co thus obtained is shown in figure 2 together with the theoretical values, being arranged along the equi-electron density lines. The experimental values for binary Ni-Co were obtained by interpolating experimental results by the previous workers [4, 51.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1974426
C4-150 N. KUNITOMI, Y. NAKAI, K. YAMASAKI AND N. SCHIBUYA
C O U N ~ S , F e C o OL 02 N i O L 1 1 = 2 m m l . F e , 0 C ~ O Z N ~ 0 7 1 t = 2 m m ~
e observed
.
corrected - multipleFIG. 1. - Observed polarized neutron difference intensity for typical two cases. The vertical axis represents the total difference counts accumulated during 120 min. The horizontal axis repre- sents 2 times the scattering angle. Curves in the upper figure show the strength of the multiple scattering obtained by computor
simulation.
FIG. 2. - Magnetic moment of cobalt shown along equi- electron number lines. The bottom line corresponds to the specimens with the same concentration of Fe and Ni. Open circles show the results obtained by the present investigation.
Black circles are obtained from the previous investigations [4,5].
Solid curves are the theoretical values calculated by CPA.
Along each line, the experimental values gradualIy increase with Co concentration rather than be constant.
This fact suggests that the CPA explains the experi- mental results better than the rigid band approxi- mation.
The contour lines of the Co moment are shown in figure 3. In order to see the general behavior of the concentration dependence of the Co moment, it is convenient to see the sequence of alloys with the same Co concentration but with the various concen- trations of Fe and Ni. If Fe concentration is increased, the theoretical and the experimental values of Co moment rapidly decrease in Ni side. In the intermediate
Exp.
FIG. 3. - Experimental and theoretical contour lines of Co moment. Dashed parts in the experimental patterns are uncertain due to the experimental error. The magnitude of the moment in the unit of PB, are shown by numbers attached to the curve.
concentration range, the theoretical value is rather unchanged while the experimental one increases after passing a minimum. Finally, if the concentration of the alloy approaches to the a-y phase boundary, the Co moment decreases again with increasing Fe concentration in both cases.
Inspecting the theoretical state density curves [I], it is clear that there are three causes which affect the magnitude of the Co moment : (1) Addition of Fe pushes down the atomic energy level of Co, thus the peak of the state density of Co shifts to lower energy side. I t causes the decrease of thenumber of the electron hole in the down spin band of Co and, therefore, the Co moment decreases. (2) Admixing of Fe pulls up the up-side edge of the Co band deforming its shape, and causes the rise of the Co moment. (3) In high Fe concentration range, the up-spin band of Co also has a hole. In this region, the Co moment rapidly decreases with the increase of Fe concentration.
Comparing the theoretical and the experimental maps, it is evident that the nature of both patterns are explained by the three origins described above.
However, in quantitatively, the second and the third origins are underestimated in the theory. Therefore,
ATOMIC MAGNETIC MOMENT I N TERNARY ALLOY Fe-Co-Ni
the curvature of the contour lines is smaller in the theoretical map than in the experimental one.
The atomic magnetic moment of Fe was evaluated from the hyperfine field of Fe measured by the Moss- bauer effect, by using the equation [6]
under the assumption that the coefficients a and b are constant throughout the whole region of the f. c. c.
structure. This assumption is supported by the fact that the magnetic form factor of Fe has nearly the same shape in various alloys containing Fe. The values of a and b used here are 63.3 and 94.4 kOe/y, respectively, which are determined by using the values of the observed hyperfine field and the observed moment of Fe and Ni in binary Ni-Fe system [7, 81 The moment of Fe thus obtained are shown in figure 4 together with the theoretical values being arranged along the equi-electron density lines. Expe- rimental and theoretical values increase with the increase of Co concentration contradicting to the conclusion of the rigid band approximation. However, the experimental value drops down near the y-e phase boundary deviating from the theoretical results.
This fact may suggest, the instability of the saturated ferromagnetism in this region.
FIG. 4. - Magnetic moment of Fe shown along equi-electron density lines. Open circles are the experimental values obtained by the present work. Black circles are those by the previous works [7, 81. Solid curves show the theoretical values calculated
by CPA.
References
[I] Jo, T., HASEGAWA, H., KANAMORI, J., J. Phys. Soc. Japan [5] COLLINS, M. F., WHEELER, D. A., PYOC. Phys. SOC 82.
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[2] NAKAI, Y., in press. 161 SHIRLEY, D. A., WESTENBARGER, G. A., Phys. Rev. 138 [3] WATSON, R. E., FREEMAN, A. J., Acta Cuystallogr. 14 (1961) (1965) A 170.'
27. [7] SHULL, C. G., WILKINSON, M. K., Phys. Rev. 97 (1955) 304.
[4] CABLE, J. W., WOLLAN, E. O., KOEHLER, W. C., Phys. Rev. [8] COLLINS, M. F., JONES, R. V., LOWDE, R. D., J. Phys. Soc.
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