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MAGNETIC POLARISATION CLOUDS IN
FERROMAGNETIC NICKEL-CHROMIUM ALLOYS
B. Rainford, A. Aldred, G. Low
To cite this version:
B. Rainford, A. Aldred, G. Low. MAGNETIC POLARISATION CLOUDS IN FERROMAGNETIC NICKEL-CHROMIUM ALLOYS. Journal de Physique Colloques, 1971, 32 (C1), pp.C1-575-C1-576.
�10.1051/jphyscol:19711198�. �jpa-00214022�
JOURNAL DE PHYSIQUE Colloque C I, supplkment au no 2-3, Tome 32, Fkvrier-Mars 1971, page C 1 - 575
MAGNETIC POLARISATION CLOUDS IN FERROMAGNETIC NICKEL-CHROMIUM ALLOYS (*)
B. D. RAINFORD (**), A. T. ALDRED (***) and G. G. LOW Atomic Energy Research Establishment Harwell, Didcot, Berks., England
R6sum6. - On mesure la diffusion magnktique de neutrons de grande longueur d'onde dans les alliages B - C r contenant 10,O d 12,5 at. % de Cr. Tenant compte de prwdents rksultats de Collins et Low pour des alliages de 1,5,6,0 et 9,O at. % Cr, les rksultats montrent que la section efficace de diffusion varie rapidement avec la concentration en Chrome.
Nous attribuons cet effet B l'existence de grands nuages de polarisation magnktique dans les alliages dont la concentra- tion en chrome est proche de celle pour laquelle le ferromagnbtisme disparait.
Abstract. - The diffuse magnetic scattering of long wavelength neutrons from E - C r alloys containing 10.0 and 12.5 at. % Cr has been measured. When combined with the earlier results of Collins and Low for 1.5,6.0 and 9.0 at. % Cr alloys, the data show that the diffuse cross section changes rapldly w~th chrorn~um concentration. We attribute thls effect to the existence of large magnetic polarisation clouds in those alloys that have a chromium concentration close to the critical concentration at which ferromagnetism disappears.
The magnetic moments of dilute Ni-Cr alloys have been studied by Sadron [I] and Van Elst et al. [2], and, more recently, by Gardner and Smith [3] and Besnus [4]. These studies show that the addition of chromium to nickel produces a rapid decrease in the magnetization ; the change of magnetic moment per added chromium atom (dp/dc) is initially about
- 6.0 pB. Low and Collins [5, 61 have measured the diffuse magnetic scattering of long wavelength neu- trons from a dilute (1.5 at. %) Ni-Cr alloy, and find that the moment defect around isolated chromium impurities extends about 5 A into the nickel matrix.
These features have been discussed by Comly et al. [7]
and by Low [8] in the light of Friedel's [9] bound impurity state description of magnetic defects in alloys such as Ni-Cr.
The results obtained by Gardner and Smith [3]
and Besnus [4] for more concentrated Ni-Cr alloys show that the high field susceptibility increases rapidly with chromium concentration to a very large, sharp maximum in the vicinity of the critical concentration (C, - 11 at. % Cr) a t which the alloys cease to be ferromagnetic.
In this paper we present measurements of the magne- tic diffuse scattering of neutrons from two Xi-Cr alloys, with chromium concentration of 10.0 and 12.5 at. %,
in the region of the critical concentration. These data supplement the earlier measurements of Collins and Low [6] for alloys containing 6.0 and 9.0 at. % chro- mium. The experimental technique has been described by Low and. Collins [5]. Our measurements were made with the polycrystalline alloy specimens held at 4.2 OK in a neutron beam of 4.8 A mean wavelength.
The observed angular distributions are plotted in figure 1 with Collins and Low's data for the 6.0and 9.0 % Cr alloys, included for comparison.
The two sets of data are in good agreement, and
(*) Work supported in part by U. S. Atomic Energy Com- mission.
(**) Attached from Imperial College London. Present address : A. E. K., Riso, Roskilde, Denmark.
(***) On assignment from Argonne National Laboratory.
show that the forward diffuse cross section diminishes rapidly with increasing chromium concentration.
Collins and Low attributed the rapid fall in the diffuse cross section, as the impurity concentration increases, to the overlapping of the widespread moment distur- bances from neighbouring impurity atoms, which would also produce a more uniform distribution of magnetization. In fact, as the chromium concentra- tion increases, the angular distributions in figure 1 become more sharply peaked in the forward direction, which corresponds to an increase in the range of moment fluctuations. It appears that, as the critical concentration is approached, the increasing exchange enhancement favours the formation of a highly non- uniform magnetization distribution.
Similar effects have been observed recently in Ni-Cu [lo] and Pd-Ni [Ill alloys near the critical composition. Following the approach of Hicks et al. [lo], we describe the inhomogeneous distribution of magnetization in these x - C r alloys in terms of magnetic polarisation clouds that have an average moment density p(r) and a concentration C. Then the diffuse magnetic scattering cross section may be expres- sed as
d o - -
dQ - 0.049 C ( l - C ) [ M ( K N ~ b/sr atom ( 1 ) where
is the Fourier transform of the moment density within a cloud and K is the scattering vector. The value of M(K) in the forward direction, M@), corresponds to the average total moment (in pB) per cloud. In order to apply eq. (1) to the analysis of the experimental data, we assume that away from the centre of a polari- sation cloud the spherically averaged moment density may be described by a Yukawa function l/r exp[- K , r].
Then M(K) has a Lorentzian form,
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19711198
C 1 - 576 B. D. RAINFORD, A. T. ALDRED AND G. G. LOW This assumption is justified in systems with large
exchange enhanced susceptibilities at small scattering vectors [8]. Substituting M(K) from eq. (3) into eq. (1) we have fitted the experimental data, with the forward cross section (do/dB), and the inverse range parame- ter K , as disposable parameters. The best values for these parameters are listed in. Table, L and the fitted, curves are shown in figure 1. The value of K , decrea- ses uniformly as the chromium content increases, reflecting an increase in the range of the polarisation disturbances. For comparison K , has the value 0.63 A-1 in the dilute limit (1.5 at. % Cr). Table I also lists the values of the mean moment per atom of alloy p taken from Gardner and Smith's measure- ments, except the value for the 10 % alloy, which is an extrapolation. If p for an alloy is taken as the sum of the individual cloud moments, so that
Magnetic properties of Ni-Cr alloys : forward cross section (do/dQ), and range parameter K , are obtained f r o m 5 t t e d curves in figure 1 ; concentration C and total moment M(0) of polarisation clouds deduced from ji and (do,IdQ),.
Alloy (do/dQ)o KI - P c M(O)
(at. % Cr) (b/sr atom) (A-9 slatom om) (%I (PB)
- - - - - -
6.0 0.091 0.52 0.27 3.7 7.2
9.0 0.068 0.45 0.14 1.3 10.3
10.0 0.067 0.36 0.09 0.6 15.4
12.5 0.020 0.23 - - -
then this relation combined with the expression for the forward cross section (do/dQ), from eq. (1) allows us to estimate the concentration of polarisation clouds C and their average total moment M ( 0 ) ; these are also listed in Table I. From these values we obtain a concept of the polarisation clouds that is very similar to that deduced by Hicks et al. for the clouds in Ni- Cu alloys near the critical concentration. Namely, the clouds have a large average total moment, of the order of 10 pB, and a low concentration, of the order of 1 %. The concentration C decreases approximately linearly with chromium content, and would extrapo- late to zero at a chromium concentration of about 10.7 %, which is very close to the critical composition.
Although the 12.5 % Cr alloy is paramagnetic, it has a large susceptibility and so the alloy has a signi- ficant magnetic diffuse cross section (Fig. 1). This intensity presumably arises from the quasi-elastic scattering of the neutrons from slow critical fluctua- tionr.
[I] SADRON (C.), Ann. Phys., Paris, 1932, 17, 371.
[2] VAN ELST (H. C.), LUBACH (B.) and VAN DER BERG (G. J.), Physica, 1962, 28, 1297.
[3] GARDNER (W. E.) and SMITH (T. F.) (private commu- nication).
[4] BESNUS (M.' J.) (private communication).
[5] Low (G. G.) and COLLINS (M. F.), J. Appl. Phys., 1963,34,1195.
[6] COLLINS (M. F.) and Low (G. G.), Proc. Phys. Soc., 1965, 86, 535.
[7] COMLY (J. B.), HOLDEN (T. M.) and Low (G. G.), J. Phys. C., 1968, 1, 458.
SCATTERING VECTOR, K (I-')
FIG. 1. -Diffuse magnetic cross sections for scattering of neutrons from Ni-Cr alloys at 4.2 O K . The data for 6.0 and
9.0 % Cr alloys are taken from ref. [6].
Our experiments also determine the diffuse nuclear cross section, which yields a measure of the atomic non-randomness. The results for the 10 % and 12.5%
Cr alloys indicate the presence of a small amount of residual short range ordering and are consistent with an order parameter, a,, of - 0.02. These observations are in contrast to recent measurements [12, 131 on Ni-Cu alloys which indicate a tendency for clustering of the atomic species. I t may be inferred from the presence of similar polarisation clouds in Ni-Cu and Ni-Cr alloys that the existence of this phenomenon
-
does not depend specifically on composition fluctua- tions in the alloys.
Acknowledgments. - We would like to thank V. Rainey for experimental assistance. We have also benefited from discussions with Professor E. P. Wohl- farth and Drs. W. E. Gardner, T. F. Smith and J. Mathon.
,nces
[8] Low (G. G.), Adv. Phys., 1969, 18, 371.
[9] FRIEDEL (J.), NUOVO Cim. (Suppl.), 1958, 7 , 287.
[lo] HICKS (T. J.), RAINFORD (B. D.), KOUVEL (J. S.), Low (G. G.) and COMLY (J. B.), Phys. Rev.
Lett., 1969. 22. 531.
[ I l l ALDRED -(A. T.), RAINFORD (B. D.) and STRING-
FELLOW (M. W.), Phys. Rev. Lett., 1970, 24, 897.
1121 MOZER (B.), KEATING (D. T.) and .MOSS (s: C.), Phys. Rev., 1968, 175, 868.
[13] ALDRED (A. T.) et al. (to be published).
