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ATOMIC AND MAGNETIC SHORT RANGE ORDER IN Cu-Mn ALLOYS
H. Sato, S. Werner, R. Kikuchi
To cite this version:
H. Sato, S. Werner, R. Kikuchi. ATOMIC AND MAGNETIC SHORT RANGE ORDER IN Cu-Mn ALLOYS. Journal de Physique Colloques, 1974, 35 (C4), pp.C4-23-C4-26. �10.1051/jphyscol:1974404�.
�jpa-00215595�
JOURNAL DE PHYSIQUE Colfoque C4, suppKment au no 5, Tome 35, Mai 1974, page C4-23
ATOMIC AND MAGNETIC SHORT RANGE ORDER IN Cu-Mn ALLOYS
H. SAT0 and S. A. WERNER Scientific Research Staff, Ford Motor Company,
Dearborn, Michigan 48121, U. S. A.
and R. KIKUCHI
Hughes Research Laboratories, Malibu, Calif. 90265, U. S. A.
RBsumB. - Dans cette publication, nous abordons quatre points fondamentaux du comporte- ment de l'alliage Cu(Mn) :
1) L'evolution du fond de diffusion de neutrons avec la tempdrature, en relation avec la structure Clectronique.
2) La persistance d'un ordre a courte distance elevd dans un large domaine de tempkrature.
3) La valeur &levee de la concentration critique nkcessaire pour atteindre I'ttat antiferromagnk- tique dans les rkseaux c. f. c.
4) Le comportement mictomagnetique des alliages c. f. c.
Abstract. - In this paper we discuss four interesting features of the Cu(Mn) alloy systems : 1) The character and temperature dependence of the diffuse neutron scattering and its relation to electronic structure.
2) The persistence of the short-range atomic ordering over a broad temperature range.
3) The high critical concentration for antiferromagnetism in fcc systems.
4) Mictomagnetic behavior in these fcc alloys.
1. Introduction. - The possibility of the existence of long range atomic order in Cu(Mn) alloys has attracted a great deal of attention over the last 40 years or so, and in fact has remained controversial until very recently [I, 21. Our neutron diffraction data on this alloy system has shown that short range order develops over a very broad temperature range, but that long range order does not occur even under extensive annealing [3, 41. In retrospect, the failure to detect any proof is mainly due to the fact that the (electron and X-ray) scattering powers of Cu and Mn are so nearly equal ; consequently diffuse scattering due to short range order could not be detected. Positive proof of the existence of the well developed short range order could only be made by neutron diffraction.
Recently this alloy system has attracted attention in connection with spin glass behavior [ 5 ] , which is a general characteristic of more or less disordered alloys irrespective of the concentration of magnetic atoms. The magnetic properties of Cu(Mn) have been known to depend intimately on the spatial distribution of atoms. Consequently, a simultaneous analysis of the atomic and magnetic correlations, along with the macroscopic magnetic properties, is necessary in order to obtain a quantitative understanding of spin glass behavior in alloys.
In this report, we first discuss some important characteristics of the atomic short range order in this
alloy system and then discuss how these are related to the spin glass or mictomagnetic behavior of this system based on the data so far obtained.
2. Experimental neutron results on the short range order. - In this section we present data which summarizes the salient features of the diffuse scattering due to the creation of short range order in this system.
In figure 1, neutron diffraction results on an initially well-annealed 25 at. % Mn polycrystalline specimen at various temperatures are shown. A characteristic feature is the existence of a pronounced diffuse peak around the { 1 4 0 } reflection position. Similar observa-
FIG. 1. - Neutron diffraction pattern from an initially well- annealed polycrystalline Cu-Mn alloy of 25 at. % Mn at various
temperatures.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1974404
C4-24 H. SATO, S. A. WERNER AND R. KIKUCHI
tions were made by Meneghetti and Sidhu [6] and Vance et al. [7]. We have found a sloping background towards low scattering angle, indicating the existence of magnetic disorder scattering. The intensity at { 1 + 0 ) still increases down to liquid nitrogen temperature indicating that the magnetic scattering is included in this peak. A most interesting feature is that this peak cannot be suppressed by a quenching of the specimen from 800 OC into water, indicating that the formation of the short range order is relatively rapid.
Results of a scan at room temperature of the diffuse intensity along the [h 101 line in reciprocal space on a well-annealed single crystal of Cu-25 % Mn is shown in figure 2 [4]. The broad peaks centered at the (3 10)-
FIG. 2. - Diffuse intensity along the line [h 101 in reciprocal space. The circles are the data obtained at room temperature on a well-annealed sample, and the triangles are the results of the same scan obtained after cooling the sample rapidly back
to room temperature (from 440 OC) [4].
type positions (A, B, C, D) are characteristic of the short range order in these alloys and have the symmetry of the M = 1 type superlattice (DO,,) [8]. The width indicates that the range of atomic correlation is about 3 fcc unit cells.
The decrease in the intensity with wave-vector in going from (+ 10) to ii \ 10 is due to three things ,1 : 1) Debye-Waller factor, 2) increase of the spectrometer resolution volume in k-space with wave-vector k, 3) the decrease of a possible magnetic contribution to the peaks resulting from a decreasing form factor f (k). By calculation, a subtraction of 1) and 2) from the experimental decrease of intensity indicates that about 25 % of the intensity at A is due to magnetism [9]. A preliminary attempt to separate the magnetic diffuse scattering from the total scattering was made by Wells and Smith [lo]. It is, however, our position that this separation is not reliable for this alloy system in an unpolarized beam experiment.
The temperature dependence (for increasing tempe- rature) of the intensity of these peaks is shown in figure 3 for Cu-25 % Mn [4]. The measured variation of intensity is more rapid in the single crystal than in
FIG. 3. - Temperature dependence of the diffuse intensity at A, B, and C in figure 2. (( x )) indicates the intensity upon
cooling the sample back to room temperature [4].
the polycrystal as can be seen by comparing the data of figures 1 and 3. The reason is that the experimental integration over the volume in k-space containing the diffuse intensity is different in the case of a single crystal from that of a polycrystal. Also, the width, T,
2 7c 2 TL
changes from .33 - at room temperature to .48 -
a a
at 440 OC, indicating a decrease of the correlation range in this direction of 50 %. That appreciable short range order persists over a very large temperature range (up to -- 600 OC) is quite important as will be discussed later. Upon cooling the sample back to room temperature, the intensity of the (3 10) peak had decreased by 30 % as shown by the (( x )) in figure 3. This was accompanied by a broadening such
2 TL
that r = .38 - in the direction of the scan. This a
indicates that, although the formation of the short range order is rapid, it still requires a considerable amount of annealing time to reach the fully developed state of the short range order.
Other important results to be mentioned here are : 1) the distribution of the diffuse scattering around the (3 10) type position is approximately ellipsoidal, elongated somewhat towards the [h 101 direction, 2) the shape of the intensity distribution of the diffuse peaks essentially does not change by decreasing the Mn content, although the distribution becomes more diffuse and appears to have a tendency of becoming more spherical [4].
ATOMIC AND MAGNETIC SHORT RANGE ORDER IN Cu-Mn ALLOYS C4-25
3. Discussion. - The fact that the shape of the diffuse intensity distribution does not change with composition requires attention. The distribution of diffuse intensity generally reflects the shape of Fermi surface of the alloy, especially if the Fermi surface has flat parts. In other words, diffuse peaks are expected at 2 k, which calipers the Fermi surface of the alloy in a < 110 > direction where the Fermi surface is flat (fcc alloys) [ll]. Since Mn is expected to be tri- valent in the Cu-Mn alloys [12, 131, the size of the Fermi surface is such that the location of diffuse scattering at (3 1 0 ) positions at 25 at. % Mn can be justified [13]. However, as the Mn content decreases, the Fermi surface shrinks and the diffuse peak should split into two, and it should eventually reach the position expected for the M = 2 structure (DO,,) [8]
at 15 at. % Mn. This was actually observed in the Cu-A1 system [14] where Al behaves as trivalent atom as Mn. No such tendency, however, is found in the Cu-Mn system. This seems to indicate that the origin of the interaction which creates the short range order is in part due to the core interactions and is not solely through the conduction electrons.
The existence and the development of the short range order extends over a wide temperature range, but the annealing at low temperature does not create long range order. The existence of well developed short range order is generally understood as evidence for the critical point of order being not far away in temperature. The failure to induce the long range order by annealing in such a case is generally inter- preted as the sluggishness of the atomic movement at the annealing temperature. However, in face cen- tered cubic alloys this persistence of short range order should be considered as a fundamental characteristic [15]. To understand this, consider first a simple AB alloy. At high temperatures fcc symmetry requires that the coordination number of a given atom is 12 ; however, since it is not possible to have all A-B pairs in an ordered state (i. e. there must also be A-A and B-B pairs), the effective coordination number becomes less as ordering develops. Because of this decrease, the transition temperature is lowered and the short range order persists to low temperatures.
Magnetism in alloys can also be thought of as result- ing from the sum of pair interactions. Experimental evidence indicates that the Mn-Mn interaction is strongly negative (antiferromagnetic) at the nearest neighbor distance, but is ferromagnetic at the second nearest neighbor distance in common alloys. Although a strong nearest neighbor antiferromagnetic interaction exists, the Cu(Mn) alloys do not become antiferro- magnetically ordered until a very high concentration of magnetic atoms is reached [16, 171. This type of beha- vior can be understood from arguments which are completely analogous to the discussion given above for the AB alloy. In figure 4 the concentration depen- dence of the critical point for an Ising model ferro- magnet and an Ising model antiferromagnet calculated
FCC ANTI FERRO FIRST ORDER
0 I I
DENSITY OF MAGNETIC ATOMS pB
FIG. 4. - Concentration dependence of the critical point for an Ising model ferromagnet and an Ising model antiferromagnet in a magnetically dilute face centered cubic system, calculated by the tetrahedron approximation of the cluster-variation method. The energy parameter E is defined as 2 E = 8,- - E++ [IS].
by the tetrahedron approximation of the cluster variation method are compared [18]. It should be pointed out that in a fcc ferromagnet the effective coordination number does not change with ordering, while in an antiferromagnet it decreases. This lowering of the effective coordination number in an anti- ferromagnet depresses the critical point and raises the critical concentration [19, 201. It should, paren- thetically, be noted that in a bcc lattice the critical behavior of a ferromagnet and an antiferromagnet are equivalent. Therefore, in the composition range we are dealing with in these fcc Cu-Mn alloys, it is not necessary t o even consider the antiferromagnetically ordered state. At the same time, this indicates that the face centered cubic alloys are in general a favo- rable system for spin-glass studies.
The M = 1 type ordering tends to eliminate the nearest neighboring Mn pairs in favor of second neighboring pairs. This means that, in the short range ordered state where we can regard the system as an assembly of statistical clusters with a prepon- derence of second neighbor Mn pairs ; the system can be thought of as an assembly of ferromagnetic clusters since the moments of the Mn atoms tend to align in a parallel fashion inside the clusters. This explains the superparamagnetic behavior of the Cu- Mn alloys above the freezing temperature [5]. There-
C4-26 H. SATO, S. A. WERNER AND R. KIKUCHI
fore, as the short range order of M = 1 type develops by annealing, the total cluster magnetization increases in any composition range. However, the nearest neighbor Mn pairs, which cannot be eliminated com- pletely by the short range ordering, tend to cancel out the magnetic moment of the clusters. As long as the concentration of Mn atoms is low, nearest neigh- boring Mn pairs can be easily eliminated from the cluster and therefore, the total cluster magnetization increases with the Mn content. On the other hand, at higher concentrations of Mn atoms, more and more nearest neighbor Mn pairs are included in the cluster and tends to cancel out the cluster moment.
In other words, the maximum in the total cluster magnetization can be expected to occur below the
Cu,Mn stoichiometric, M = I, composition. As the degree of short range order increases, the maximum would be shifted to a higher Mn content for the same reason. This qualitatively explains the result of Beck et al. [5] that a sharp maximum in the total cluster magnetization exists at around 20 % Mn when well annealed, but the maximum is shifted to a lower concentration of Mn for quenched alloys. A quanti- tative explanation, however, must await a more precise separation of atomic and magnetic scattering utilizing polarized neutrons.
Acknowledgment. - Valuable discussions with Pro- fessor P. A. Beck of the University of Illinois are highly appreciated.
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