A Mössbauer effect study of the structural and magnetic properties of Co-Ga alloys

A Mössbauer effect study of the structural and magnetic properties of Co-Ga alloys

64 Journal of Magnetism and Magnetic Materials 28 (1982) 64-76 North-Holland Publishing Company A MOSSBAUER EFFECT STUDY OF THE STRUCTURAL AND MAGNE...

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64

Journal of Magnetism and Magnetic Materials 28 (1982) 64-76 North-Holland Publishing Company

A MOSSBAUER EFFECT STUDY OF THE STRUCTURAL AND MAGNETIC PROPERTIES OF Co-Ga ALLOYS G.L. W H I T T L E , P.E. C L A R K * a n d R. C Y W I N S K I + Department of Solid State Physics, Research School of Physical Sciences, Australian National University, Canberra, ACT 2600, Australia

Received 5 November 1981; in revised form 21 January 1982

Mrssbauer spectra have been recorded from Co:,Gal0o_,(45 <~x ~<65) alloys at room temperature (RT) and 4.2 K in order to study the structural and magnetic properties of this system. The nonmagnetically split RT spectra are analyzed with the use of a lattice simulation model that predicts the effect of the antistructure Co atoms. The measured vacancy concentration ((p:, p)/p~ ) and corresponding calculated number of AS Co atoms ([(100- x)( F - 1) + 50] where F = fraction of vacancies) were used in establishing the near neighbour atomic distributions around a Co atom. It was established that the large number of vacancies present (as high as 8% of total sites) exist solely on the Co sublattice. The effect of heat treatment on the vacancy concentration and atomic distributions is also studied. Spectra recorded at 4.2 K proved to be in agreement with previous magnetic studies on this system and on the Fe-substituted Co-Ga alloys, in which slow cooled alloys exhibit spin glass characteristics while the quenched alloys are best explained by a superparamagnetic model. Slow cooled alloys display smaller magnetic clusters and lower spontaneous magnetisation compared to quenched alloys of the same concentration. As the concentration is increased to near the limit of the phase boundary, the heat treatment was found to become unimportant.

1. Introduction Since a p r e l i m i n a r y study by Booth a n d Marshall [1] of the magnetic b e h a v i o u r of Co-rich C o - G a alloys, a great deal of interest has been shown in both the m a g n e t i c a n d structural properties of this intermetallic series. The r - p h a s e of C o - G a exists between 40 a n d 65 at% cobalt a n d has the B2(CsC1) structure [2,3]: two i n t e r p e n e t r a t i n g simple cubic lattices, one of cobalt a n d the other of gallium. Structurally the m a i n interest lies in the u n u s u a l l y high vacancy c o n c e n t r a t i o n o n the Co sublattice a n d the diposition of a n t i s t r u c t u r e (AS) Co atoms (i.e. those Co atoms displaced to G a sites [4-6]). Such defects occur even at the equiatomic composition. Since these h o m o g e n e o u s r - p h a s e c o m p o u n d s exist over

* Department of Applied Physics, Capricornia Institute of Advanced Education, Rockhampton, Qld. 4700, Australia. + Neutron Division, Rutherford-Appleton Laboratories, Didcot, Oxfordshire OX 11 OQX, England.

a wide c o n c e n t r a t i o n range, deviations from stoichiometry result in even more structural disorder. It is precisely these deviations from perfect order that influence the magnetic properties of the system. In addition, different heat treatments not only produce a different n u m b e r of defects [5], b u t also quite different magnetic behaviour. However, the differences in the observed magnetic properties with heat t r e a t m e n t c a n n o t be consequence of the n u m b e r of defects alone. Magnetisation measurements and neutron scattering experiments have helped to resolve the m a g n e t i c b e h a v i o u r of these alloys by revealing the presence of s u p e r p a r a m a g n e t i c assemblies formed b y the magnetic clustering of m o m e n t b e a r i n g Co atoms on the G a sublattice. The measurements show that the onset of ferromagnetic order is due to a percolation of these superparam a g n e t i c clusters. The critical c o n c e n t r a t i o n for f e r r o m a g n e t i s m is reported to be 55 at% cobalt for the C o - G a system [7,8].

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G.L. Whittle et al. / Structural and magnetic properties of Co-Ga alloys

More recently, magnetic studies have focussed on the behaviour of the magnetic clusters in the composition range just below the critical concentration. Slowly cooled alloys in the concentration range 51-55 at% cobalt exhibit a sharp cusp in the temperature dependence of the ac susceptibility [9] indicative of a single cluster blocking temperature typical of spin glasses [10,11]. Even beyond this intermediate magnetic regime, Grover and coworkers [12,13], from NMR and ac susceptibility measurements, have labelled slow cooled alloys in the concentration range 58.5-63 at% cobalt as belonging to the "cluster spin glass" category. In contrast, for a quenched Co54Ga46 specimen Cywinski and Gray [14] claim superparamagnetic behaviour manifests itself as determined by the frequency dependence of the alternating magnetisation. Low dc field susceptibility measurements confirm this picture through a broad peak in the zero field cooled suspectibility and a thermoremanence that persists to temperatures beyond the peak temperature. The details of the behaviour of the magnetic dusters are therefore still open to question. In addition, a Mrssbauer effect study [16] of three Co-Ga alloys (50, 58.5 and 60 at% cobalt, measured at 293 and 78 K) prepared as Mrssbauer effect sources, investigated the local atomic environment and its effect on the magnetic behaviour. This will be discussed in more detail in later sections. We have previously reported some results of Mrssbauer effect absorber experiments on the pseudobinary Co(Ga, Fe) system. The site preference of the atoms was determined, and the unusually high vacancy concentration examined [17]. The nonmagnetically split room temperature (RT) spectra of this investigation were computer fitted on the basis of a lattice simulation model which used the measured vacancy concentration to determine the number of Fe atoms having 0,1,2, etc., vacancies in their nearest neighbour (NN) shell. A complete study of the magnetic behaviour of the Fe-substituted Co-Ga alloys, from MOssbauer effect and low dc field magnetisation measurements, has also been reported [18,19]. The results confirm the dependence of the magnetic behaviour on heat treatment.

65

In this paper, we present the results of a Mrssbauer effect investigation of CoxGa~0o_x (45 ~
2. Experimental details Alloys both for density measurements and to be used in the preparation of Mrssbauer sources were fabricated from 6 N gallium and 5 N cobalt by arc melting in an argon atmosphere. Weight losses during melting were typically 0.2%, actual compositions thus being close to the nominal ones. The resulting ingots were then given a heat treatment of 830°C for 24 h followed by either a water quench, or a slow cool (15°C/h). The 57Co-doped Co-Ga Mrssbauer sources were prepared by spark machining a thin disc from the appropriate alloy, and polishing this down to approximately 50/~m. Thin foils could not be obtained due to the brittleness of the alloys. The 57Co activity (supplied by Radiochemical Centre, Amersham in the form of carrier free 57COC12 in dilute HC1) was electropolated onto these discs using standard techniques (see, for example, refs. [20,21]). After plating, the sources were heat treated at 830°C for 2 h in a hydrogen environment to diffuse in the activity. Spectra were recorded from the sources in this condition, but the discs were then melted in quartz tubes, crushed and remade as powder sources with a calculated optimum thickness [17]. This procedure was to ensure the proper dispositon of the 57Co probe. The sources were examined at RT in a standard Mrssbauer spectrometer, with a thin K4Fe(Cn)6-3H20 absorber (0.1 mg 57Fe/cm2 and denoted KFCN) utilized in recording the Mrssbauer spectra. Full width at half maximum height (fwhm) of the spectral components against the single line KFCN

G.L. Whittle et aL / Structural and magnetic properties of Co-Ga alloys

66

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Fig. 1. (a) Lattice parameter versus cobalt concentration; (b) bulk density versus cobalt concentration, where • this study, • Berner et al. [5], x7 A m a m o u and Gautier [23]; (c) vacancy concentration versus cobalt concentration where • this study, • Q alloys Bemer et al. [5], V SC alloys Bemer et al. [5].

G.L. Whittle et al. / Structural and magnetic properties of Co-Ga alloys

absorber were typically 0.26 mm -~, indicating thickness effects were not a problem. A helium cryostat with an external MiSssbauer drive transducer was employed for the low temperature measurements. The sources were cooled to 4.2 K inside the cryostat, with the KFCN absorber vibrated externally. This is the opposite arrangement to that used for the RT spectra where the Doppler shift was applied to the sources. X-ray and density measurements were performed on selected CoxGal00_ ~ alloys in only the quenched condition. These measurements were considered sufficient to deduce all near neighbour environments, and vacancy concentrations. X-ray powder diffraction spectra using Fe-Ka radiation were taken for all alloys. In every case the alloys were found to be single phase with the expected B2 structure. Lattice parameters were determined by a Nelson-Riley extrapolation [22] of the lattice parameters corresponding to each line, and X-ray densities, Px, were calculated from these. Measurements of the bulk density, p, of the powdered samples were performed by the usual displacement method using carbon tetrachloride. The fraction of vacancies was set equal to ( p x p)/p~ (see appendix). This differs from Berner et al. [5] where they claim the fraction of vacancies is equal to (p~- p)/p. A full discussion of this difference is given in the appendix. Lattice parameters, X-ray and bulk densities, and corresponding vacancy concentrations are listed in table 1. Lattice

parameters, bulk densities and vacancy concentrations are also plotted as a function of cobalt concentration, x, in fig. 1, with similar data from other investigations [5,23]. Vacancy concentrations for SC CoxGal0o_ x alloys, which were not measured here, are also included.

3. Lattice simulation

A lattice simulation model was previously used to predict the extent of the effect of vacancies in the Co(Ga, Fe) alloys [17]. The main purpose of the model was to provide assistance in the interpretation of the M6ssbauer spectra by predicting the contributions from various sites to the spectra. To again assist in determining the distribution and type of near neighbours a similar procedure was adopted. The lattice simulation of the pseudobinary Co(Ga, Fe) alloys was quite simple. A vacancy concentration of, say 100F simply resuited in 50F (F-fraction of vacancies) Co atoms moving to Ga sites. An identical approach is, of course, applicable to the equiatomic CoGa alloy, but in nonstoichiometric C o - G a alloys the calculation of site occupancies becomes more difficult. The appendix also deals with this problem in detail. In constructing a CoxGal00_ x alloy, a perfectly ordered equiatomic CoGa alloy was simulated initially employing the largest three-dimensional array possible (403 = 64000 lattice sites) on a Burroughs

Table 1 Lattice parameters, X-ray densities, #x, bulk densities, p, and corresponding vacancy concentrations for the series CoxGal0o_ ~ alloy

lattice parameter

X-ray density Px (g c m - 3)

Bulk density, p (g c m - 3)

2.863( ---+0.001 ) 2.869 2.880 2.879 2.878 2.877 2.877 2.875

Vacancy concentration

[(px - p)/px)]x lOO

(A) Co45 Ga 55 Co4sGas2 CosoGaso Co52Ga4s Co55Ga45 Co57Ga43 CossGa42 Coc,4Ga 36

9.18 9.08 8.94 8.92 8.89 8.87 8.85 8.78

67

8.38( ---0.05) 8.55 8.57 8.66 8.68 8.81 8.85 8.78

8.7( -4-0.5) 5.8 4.6 2.9 2.3 0.6 0 0

G.L. Whittle et al. / Structural and magnetic properties of Co-Ga alloys

68

~

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(iii) the total number of As Co atoms can be set equal to [(100 - x ) ( F - 1) + 50] where F is the fraction of vacancies and x the atomic percent of cobalt (see appendix).

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6700 computer. Then to obtain the required alloy, vacancies and AS Co atoms were introduced according to the following assumptions (i)

the Co and G a sublattice remain discrete. Ga atoms are never found on the Co sublattice. (ii) Fe atoms are randomly distributed on G a sites only.

The corresponding lattices were constructed using this information and the measured vacancy concentrations. All Co atom NN environments were checked, and the number of times each site occurred was recorded. Again the expected contributions to the MOssbauer spectra could be deduced. In these alloys the main component of the spectra is expected to be from the normal Co atoms with an 8 G a atom environment. Instead of the vacancies being important as in the previous investigation, it is the AS Co atoms that have a large effect on the spectra. Fig. 2 shows a plot of the change in fractional contribution of the various sites calculated from the model for the cobalt concentrations of 45 to 65 at% for quenched alloys. Fig. 2a shows the most probable calculated environments around normal Co atoms (on Co sites), whereas fig. 2b shows the environments of AS Co atoms. In the Co55Ga45 alloy, for example, it is readily seen that the main contributions to the MOssbauer spectra are expected to be from the 8 G a atom, the 7 G a atom and 1 Co atom, the 6 Ga atom and 2 Co atom, and the 8 Co atom N N environments. The expected percentage contributions to the spectra for selected Q C o - G a alloys were calculated based on the measured vacancy concentrations, and are shown in table 2. Again the small number of defects (AS atoms in this case) has quite a large effect. This concept was completely

Table 2 E x p e c t e d n e a r - n e i g h b o u r distributions a r o u n d a C o b a l t a t o m , c a l c u l a t e d f r o m the lattice s i m u l a t i o n m o d e l for q u e n c h e d CoxGal00 ~, MOssbauer sources

Site Alloy

Co45Ga55 C o s o G a 5o Co55Ga45 Co58Ga42 Co65Ga35

8 Ga

92.4 64.4 29.7 20.2 3.9

7 Ga I Co

6 Ga 2 Co

5 Ga 3 Co

4 Ga " 4 Co

3 Ga 5 Co

8 Co

7 Co 1 vac

6 Co 2 vac

5 Co 3 vac

6.9 25.6 34.5 31.8 14.0

0.1 4.4 17.6 22.2 22.1

0.5 5.2 8.9 19.7

0.9 2.2 11.2

0.1 0.3 4.1

0.2 2.3 7.7 14.3 23.9

0.1 1.9 3.5 -

0.1 0.7 0.7

0.1 0.1

G.L. Whittle et al. / ~tructuraland magneticproperties of Co-Ga alloys

69

I

ignore o - ~ a MOSSbauer investi' d ' 111 h t e previous ' u,,1 , ,, gation by Rao and Iyengar [16]. They simply assumed that only one site (the 8 Ga atom NN) was present in the CosoGas0 spectrum, and that the Co58.sGaal.5 and Co6oGa4o source spectra consisted of components from the 8 Co atom and 8 G a atom N N environments only. Their corresponding M6ssbauer parameters are therefore open to question. As in our previous investigation, it must be stressed that these expected contributions cannot be set equal to the fractional areas of the components obtained directly from the spectra, due mainly to the different recoil-free fractions of the various sites. However, the model is extremely useful in indicating the relative importance of the major contributions to the overall spectra; a task that is otherwise extremely difficult in such alloy systems.

j-=

Co x Ga 1O0 -x

X

4. Results and discussion 4.1. Structural properties

CoxGal0o_ x M6ssbauer sources with x = 45, 50, 54, 55, 56.5 and 58 were studied in the quenched and slow cooled condition. The Co6sGa3s sample will be omitted from this section since it magnetically orders in the vicinity of 300 K [7]. The Lorentzian lineshape approximation is considered valid in the fitting of the M6ssbauer spectra. Selected RT spectra for alloys in the Q condition are shown in fig. 3. These spectra are representative of all RT spectra recorded. Visually there is little difference between the spectra of the SC and Q specimens and the alloys with x = 54, 55 and 56.5. Based on the lattice simulation model the major N N environments for all Co atoms (fig. 2 and table2) may be predicted. The major components are expected to be: (i) 8 Ga near neighbours - configurations which have cubic symmetry will contribute a single Lorentzian line to the spectra. Rao and Iyengar [15] have reported the isomer shift of this singlet component to be 0.58 mm s -~. However, this value will not be the isomer shift of the 8 Ga N N site, but rather the centroid of the Co5oGas0 spec-

l a bsorption

1

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Vetocity(rams-I ) Fig. 3. RT spectra for Q CoxGaloo_x alloys.

trum, which has other components that these authors have neglected. Also the high velocity used ( - 8 mm s - 1) in recording their spectra introduces considerable uncertainty into the determination of the peak position, and corresponding into their isomer shift value. (ii) 7 Ga plus 1 Co atom near neighbours combinations of Ga and Co atoms will result in charge asymmetry, producing either a discrete doublet component or a distribution of doublets depending on the arrangement of the atoms. The 7 Ga and 1 Co atom N N environment should contribute a discrete quadrupole doublet to the spectra. Parameters for components (i) and (ii) should be easily found from the Co45Ga55 M6ssbauer

G.L. Whittle et a L / Structural and magnetic properties of Co-Ga alloys

70

source spectrum since only these two components are predicted to be present. (iii) 6 Ga plus 2 Co atom near neighbours - the parameters of this quadrupole doublet may be determined by subtracting all other known components from the CosoGas0 spectrum. Since this doublet is completely unresolved it is difficult to decide if a discrete orientation of the two Co atoms exists. (iv) 5 Ga plus 3 Co atom near neighbours similarly, all known components can be subtracted from the Co55Ga45 source spectrum leaving the approximate parameters of this doublet. (v) 8 Co .atom near neighbours - from the lattice simulation model this site is quite significant even in the Cos0Gaso spectrum, and should be incorporated into the fit. This site, of course, results from AS Co atoms, and its parameters have already been fully determined [17]. The fractional occurrence of these sites in the various spectra is predicted by the lattice simulation model. Sites with greater than three Co atoms

in the Ga NN shell have been omitted from this analysis since the number of these sites is not of significant magnitude. The small number of AS Co atoms with vacancies in their N N shell can also be neglected. The fractional occurrence of these contributions is shown in fig. 2. The best fits to the experimental data based on this model, comprising these predicted contributions, are shown by the full lines through the data in fig. 3. The corresponding Mrssbauer parameters for all Q and SC specimens, determined by the subtracting and fitting of various components, are listed in table 3. The positions of the individual spectral components, labelled N (singlet), P (doublet), Q (doublet), R (doublet) and K (singlet), are also marked above the appropriate spectrum in fig. 3. Components N and K represent the 8 Ga N N and 8 Co N N site, respectively, while doublets P, Q and R can be ascribed to normal Co sites in which the Ga N N shell contains 1, 2 or 3 AS Co atoms. Normally fitting this many unresolved components to a spectrum would result in quite meaningless parameters, but using the lattice simu-

Table 3 MOssbauer parameters for Q and SC CoxGal0o_ x source spectra where column labelled A indicates fractional areas (+0.02), IS indicates isomer shift in m m s - 1 relative to a-Fe at R T (-+0.01 m m s - l ) and QS indicates quadrupole splitting in m m s i ( + 0 . 0 2 mm s-t ) Alloys

Singlet N (8 Ga)

Doublet P (7 G a - I Co)

Doublet Q (6 G a - 2 Co)

Doublet R (5 G a - 3 Co)

A

IS

A

IS

QS

A

IS

QS

'0.86 0.62 0.44 0.34 0.29 0.24

0.23 0,24 0.22 0.23 0.22 0.22

0.14 0.28 0.30 0.33 0.35 0.34

0.46 0.46 0.46 0.48 0.45 0.46

0.15 0.16 0.15 0.14 0.15 0.15

0.06 0.19 0.21 0.20 0.15

0.38 0.38 0.38 0.39 0.38

0.24 0.25 0.24 0.23 0.26

0.90 0.70 0.49 0.39 0.35 0.26

0.23 0.24 0.24 0.22 0.23 0.23

0.10 0.24 0.29 0.33 0.33 0.35

0.46 0.46 0.47 0.47 0.46 0.46

0.15 0.15 0.14 0.15 0.15 0.16

0.04 0.18 0.22 0.20 0.14

0.38 0.37 0.37 0.39 0.39

0.25 0.26 0.26 0.24 0.25

A

IS

Singlet K (8 Co) QS

A

IS

0.76 0.78 0.80

0.04 0.07 0.08 0.10 0.18

0.14 0.14 0.14 0.15 0.14

0.78 0.80

0.02 0.04 0.06 0.08 0.16

0.14 0.14 0.14 0.14 0.14

a) Quenched Co4sGass Cos0Gas0 Cos4Ga ~ Co55Ga4s Co56.5Ga43.5 Co~8Ga42

0.04 0.06 0.09

0.32 0.30 0.30

b) Slow cooled Co45Ga55 CosoGa 50 Co54Ga~ CossGa45 Co56.5 Ga43.5 CossGa42

0.04 0.09

0.30 0.30

G.L. Whittle et al. / Structural and magnetic properties of Co-Ga alloys

lation and the subtraction of components, reasonably accurate parameters can in fact be obtained. The parameters of the 8 Ga atom NN (N) and 7 Ga and 1 Co atom NN (P) components were determined from the Co45Ga55 spectrum. Singlet N has a positive isomer shift of (0.23--+ 0.01) mm s -I, while doublet P has an isomer shift of +0.46 - 0 . 0 1 and a quadrupole splitting of ( 0 . 1 5 - 0.02) mm s-1. As predicted, this spectrum is fully described by incorporating only these two components. This proves vacancies do not exist on the Ga sublattice. Doublets Q and R were then determined in turn from the C%0Gas0, Co55Ga45 and Co58Ga42 spectra. It is impossible to determine if these doublet components correspond to discrete atomic orientations, however, it is more likely they are merely representative of a distribution of doublets. For this reason no significance will be attached to these doublet parameters. In table 3 the fractional areas, A, isomer shifts, IS, and quadrupole splittings, QS, are shown. All isomer shifts and quadrupole splittings of the various components are consistent throughout the samples. In most cases the agreement between the measured fractional areas and the predicted ones is quite good. A comparison between Q and SC specimens is readily observed in the table. In general the SC alloys have a decreased number of vacancies and correspondingly fewer Co antistructure atoms. This is obvious from an increase in singlet N, and a decrease in singlet K and the doublet components. In the C%8Ga42 alloy there is almost no difference in the measured site occupancies between the Q and SC specimens. At this concentration vacancies are no longer present, and one would expect site occupancies to be equivalent. Again it is obvious a small amount of defects can have a large effect on site environments. The parameters of the 8 Ga atom NN and 7 Ga and 1 Co atom NN spectral components have been accurately determined, and although it was difficult to obtain as accurate values for the unresolved doublets Q and R, some important points have still resulted from this investigation of the C o - G a sources. The fact that no vacancies are present on the Ga sublattice is one of the main premises in

71

establishing the lattice model. This has been unambiguously verified for the first time. Also, identification of the various sites may assist in the analysis of the low temperature magnetically split MOssbauer spectra. The large positive isomer shift values found for the 8 Ga atom NN site and sites consisting of NN of Ga and Co atoms also adds further support to the migration of Fe atoms to fill vacancies in the Co 2_yGa 1.92+y Fe0.08 (Y = 0.15 and 0.20) alloy series [17]. Also, it must be remembered that the spectra of fig. 3 are Mrssbauer source spectra, and although all velocity scales are with respect to a-Fe at RT, isomer shifts obtained directly from these source spectra are of opposite sign to the same site from an absorber experiment.

4.2. Magnetic properties To gain information on the magnetic behaviour of the CoxGal00_ x system, spectra were recorded at 4.2 K for all alloys in both the Q and SC condition. In this system, the magnetic ordering is completely determined by the AS Co atoms, and is not a combination of added magnetic impurities and magnetic AS Co atoms, as in the previously studied Co(Ga, Fe) system [ 18,19]. The results are best summarised in fig. 4a and b and fig. 5. Fig. 4a contains spectra for the x = 54, 56.5 and 58 Q alloys, while fig. 4b shows the same concentrations in the SC condition. The spectra for both the Co45Ga55 and C%0Gas0 alloys were unchanged at 4.2 K except for the temperature dependent shift, and have not been included. Fig. 5 shows the spectra for the Q Co65Ga35 alloy at RT and 4.2 K. In our previous investigations of the Co(Ga, Fe) alloys, the magnetically split spectra were fitted using a computer programme based on a method developed by Window [24]. This method is applicable to systems displaying a range of hyperfine fields, and produces the corresponding hyperfine field distribution (P(B) curve) based on the fit. However, spectra such as those of this study, with a distribution of hyperfine fields, as well as a wide distribution of isomer shifts and quadrupole splittings are extremely difficult to fit due to their large asymmetry. The P ( B ) programme was therefore of

G.L. Whittle et al. / Structural and magnetic properties of Co-Ga alloys

72

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Fig. 4. (a) Spectra for Q CoxGamo_x alloys recorded at 4.2 K; (b) spectra for SC CoxGa~0o_x alloys recorded at 4.2 K.

little use and the spectra were left unfitted. Any relevant information can still be easily extracted from the data. Below the accepted onset of ferromagnetism ( x - - 5 5 ) the only evidence of moment formation, as observed by the presence of magnetic splitting in the wings of the M0ssbauer spectra was in the Q C054Ga46 alloy. In this intermediate magnetic regime ( ~ 48-55 at% Co), the M0ssbauer spectra are quite insensitive to any cluster formation due to the small number of magnetic Co atoms compared to nonmagnetic Co atoms. The nonmagnetic Co atoms therefore dominate the spectra in this concentration range. However, the presence of a small number of moment bearing Co atoms cannot be denied, as observed by magnetisation measurements [23,25], neutron scattering [7] and Hall

effect measurements [19]. It is worthwhile to note the appreciable cluster formation in the Q Co54Ga46 compared to the SC specimen. A difference between the Q and SC C%4Ga46 alloy is also found in the magnetisation measurements of Meisel et al. [9] on the SC alloy, and Gibbs and Cywinski [15] and Cywinski and Gray [14] on the Q specimen. Meisel et al. have shown distinctive spin glass behaviour, whereas Cywinski and coworkers have preferred a superparamagnetic model to describe the Q alloy data. Both approaches appear well justified from the spectra of this investigation, and the magnetisation and M6ssbauer effect data reported for the Q and SC Co(Ga, Fe) alloys [ 19]. The magnetic splitting evident in the wings of the Q Co54Ga46spectrum is evidence for the for-

G.L. Whittle et al. / Structural and magnetic properties of C o - G a alloys

.... t*/0

.¢'

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/

~,~.

..~.: ~ t:

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ri. . 7"~'Z.'~.:,." ". ,%,: •

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Fig. 5. Spectra for Q Co65Ga35 alloy recorded at RT and 4.2 K.

mation of magnetic moments which are static for periods of time of the order of at least 10 - 7 S. These dusters are considered to be eventually responsible for the formation of the first infinite cluster at x = 55. The corresponding average hyperfine field value is 25.5 (--+5%) T. In a system with a distribution of magnetic clusters, a wide range of anisotropies, and therefore cluster relaxation rates may exist. The broadness of the lines is also believed to be indicative of a distribution of cluster relaxation rates present in the alloy• The spectrum of the SC alloy does not display any such magnetic splitting, which is not surprising since the SC alloy will not only have fewer AS Co atoms, but smaller cluster sizes as well [7]. The Q alloys of fig. 4a, beyond the onset of ferromagnetism (x = 56.5, 58), have very similar spectra at 4.2 K. A unique hyperfine field of 27.3 ( - 5 % ) T is apparent in both spectra, plus a distribution of smaller fields causing the broadening of the nonmagnetic central peaks. The magnetic split-

73

ting in the spectra masks any information concerning which sites have contributed to the cluster formation. However, the formation of a moment on an AS atom will depend not only on the immediate environment, but its next neighbour shell as well [23]. The similarity of the two spectra may be expected, since the number of AS atoms, which are responsible for the magnetic splitting, is quite similar in these two alloys. In the x = 56.5 alloy there are 6.8% AS Co atoms, comprising those from the compositional excess of cobalt and those from the presence of vacancies, while the vacancy-free Co58Ga42 alloy has 8.0% due to the concentration dependence. The M6ssbauer spectra are revealing the presence of the static clusters in the alloys, and it appears this has not changed very much with the addition of a further 1.2% AS atoms. A comparison of these two Q alloys to the same SC alloys (fig. 4b), again suggests a greater tendency for clustering in the Q alloys. The spectra of these SC alloys show a definite hyperfine field contribution beyond a concentration of x = 55. The corresponding average hyperfine field values in the Co56.5Ga43.5 and Co58Ga42 alloys are 26.0 and 26.8 ( - 5 % ) T, respectively, still lower than the Q alloys• The velocity of the contribution on the side of the main paramagnetic peak in the SC x = 56.5 and 58 alloys indicates that this component is part of the magnetic splitting. From the structural investigation it was found that no nonmagnetic peak exists at this position. The C%8Ga42 alloy in both the Q and SC condition has exactly the same number of AS Co atoms, since no vacancies exist in either alloy• However, the fractional area of the magnetically split component in the spectra is still significantly lower in the SC alloys. This establishes that the number of AS atoms alone does not uniquely determine the magnetic behaviour. In fig. 5 it is seen that the Co65Ga35 alloy exhibits magnetic ordering in the vicinity of 295 K. There is no detectable difference between these Q alloy spectra and those of the SC alloy at the same temperatures. A quite unique hyperfine field of 29.6 (--+5%) T was found in both 4.2 K spectra, as witnessed by the narrow outer field peaks. obviously, the spontaneous magnetisation in-

74

G.L. Whittle et al. / Structural and magnetic properties of Co-Ga alloys

creases as the number of magnetic atoms in the large cluster increases. It is clear, even at this concentration, a distribution of cluster relaxation rates is present, as shown by the overlapping hyperfine peaks inside these outer field lines. A nonmagnetic contribution is still clearly observed. As the concentration is increased to x = 65, the thermal history of the alloys appears to be rendered irrelevant by the sheer number of AS Co atoms.

5. Summary The RT Mrssbauer spectra of both Q and SC CoxGal00_ x alloys allowed the Co atom environment to be full determined. The spectra were analysed with the use of a lattice simulation model that predicted the effect of the AS Co atoms on the spectra. The measured vacancy concentrations and corresponding calculated number of AS Co atoms were used in establishing the appropriate atomic distributions. The parameters of the 8 G a atom N N environment, and doublets corresponding to Co atoms with 1, 2 and 3 AS Co atoms in the G a N N shell, were determined. For the first time it was verified that vacancies do not exist on the G a sublattice. The large positive isomer shifts of the components added further support to the migration of Fe atoms to fill Co sublattice vacancies in the previously investigated CO2_yGal.92+yFe0.08 alloys. In addition, spectra were recorded ~,t 4.2 K to help resolve the magnetic behaviour of the Q and SC alloys. The measurements were found to be consistent with previous magnetic studies on C o Ga, and Fe substituted C o - G a alloys. It was unfortunate that the study of the C o - G a sources proved relatively insensitive to cluster behaviour below the onset of long-range ferromagnetic order. However, evidence of larger clusters was found in the Q alloys compared to the SC. Since this was also observed in the Co58Ga42 alloy, it was proved that the presence of larger clusters in the Q alloys was not just a consequence of a greater number of AS Co atoms. In this Q alloy, there must obviously be a much wider distribution of cluster sizes. As the Co concentration is increased to near the limit

of the phase boundary, the heat treatment was found to become unimportant.

Appendix Vacancy and antistructure atom distribution ConGa loo- x alloys

in

The concept of vacancy and antistructure atom distribution in nonstoichiometric binary alloys is not as straightforward as one might think. This appendix deals with this problem in relation to the lattice simulation model discussed previously. However, in order to establish the site distribution, the correct vacancy concentration must first be calculated. Berner et al. [5] have calculated vacancy concentrations in C%Gamo_ x alloys using the formula ( p ~ - p ) / p where Px and p are the X-ray and bulk densities, respectively. This differs from our analysis and is also discussed in this appendix. A. 1. Calculation of vacancy concentrations A.I.1. The Ga rich CoxGalo o , alloys (x < 50) If we denote the average mass of C o + G a atoms as ~ , and let there be a total of 100 atoms, the total mass is 100N. Then assuming all sites to be fully occupied, there will be 50 unit cells each with a volume of a 3, where a is the lattice parameter. The density would then be Px = 100m/50a3.

(A.1)

It is now necessary to consider the real material with Co sublattice vacancies. If we now assume 100 - x G a atoms, y Co AS atoms, and the presence of Co sublattice vacancies only, the G a sublattice must contain 100 - x + y atoms or sites. There must also be an equivalent number of sites on the Co sublattice, giving the total number of lattice sites, S, as S = 2(100 - x + y ) .

(A.2)

However, there are only x Co atoms in total, and as there are y of these on the G a sublattice, only ( x - y ) are available for the Co sublattice. The total number of vacancies on the Co sublattice, v,

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G.L. Whittle et al. / Structural and magnetic properties of Co-Ga alloys

then becomes v = 100 - 2x + 2y.

(A.3)

Therefore, in the real material there are 100 - x + y unit cells, but still 100 atoms, giving p = 1 0 0 ~ / ( 1 0 0 -- x + y ) a 3.

(A.4)

This, of course, is the bulk density. Now Berner et al. [5] claim that the fraction of vacancies is given by (Px - P ) / P . Using (A.1) and (A.4) this becomes ( O ~ - O) _ 5 0 - x + y 0 50

(A.5)

(A.6)

using (A.2) and (A.3). Clearly Berner et al. are wrong. The fraction of vacancies, F, is actually F-

(Px-P)

_

,ox

50-x+y 100--x+y"

(A.7)

Following a similar argument as above, again with the number of Co atoms being x and the number of Ga atoms (100 - x), the value of F can be found and shown to be equal to (px - P)fOx. In the Co rich alloys, the total number of Co AS atoms can be thought of as comprising a number y due to vacancies, as in A. 1.1, plus x - 50 due to the excess in cobalt concentration. There are now (x-50+y)Co atoms on the Ga sublattice, together with the (100 - x) Ga atoms, giving a total number of Ga sites of (50 + y ) . The total number of lattice sites is therefore

v = 50 + y - (50 - y ) = 2y.

(g.9)

Using (A.8) and (A.9) the fraction of vacancies, F, becomes Y

50 + y

A.2.1. The Ga rich CoxGaloo_ x alloys (x < 50)

Y=

(100 - x ) ( F - 1) + 50 (1--F)

_ Px-- P

Px

(A.11)

The total number of lattice sites on one sublattice, given by 1 0 0 - x + y , using (A.11) becomes 50/(1 - F ) , giving the total number of sites in an alloy of 100 atoms as

(A.10)

(A.12)

Distributing these between the Co and Ga sublattices, and scaling the distribution to provide for 100 sites (i.e. 50 Co and 50 Ga lattice sites), instead of the 1 0 0 / ( 1 - F ) , the site occupation can be easily determined, and is shown in table 4. A.2.2. The Co rich CoxGaloo_ x alloys (x > 50)

It can again be shown that s = 1 0 0 / ( 1 - F), and similarly the site occupation is found. The

Table 4 Site occupanciesfor Ga rich CoxGal0o_x alloys,where F is the fraction of vacanciesand x is the atomic percent of cobalt

(A.8)

The number of vacancies on Co sites must then be

F--

Based on the measured vacancy concentration and the known atomic percent of cobalt, x, in an alloy, the site occupation can be established. An expression for the number of AS Co atoms can be derived to be used in the lattice simulation computer programme.

s = 100/(1 -- F ) .

A.1.2. The Co rich CoxGaloo_ x alloys (x > 50)

s = 100 + 2y.

A.2. Site occupation

From the vacancy concentration expression (A.7), y can be written as

However, the fraction of vacancies is really V _ 50 - x + y S 100-x+y'

Obviously to calculate the correct vacancy concentration ( P x - P)/Px should be used.

Co sublattice

Ga Co COAs Vacancies

Ga sublattice

(100- x)(l - F) x(1 - F) --((100-- x) (F-- 1)+50) + 100F

+(100-- x) (F-- 1)+50

50

50

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G.L. Whittle et al. / Structural and magnetic properties of Co-Ga alloys

Table 5 Site occupancies for Co rich CoxGal00 x alloys Co sublattice Ga Co COAs Vacancies

50(1 - F ) -- 50F + 100F 50

Ga sublattice ( 1 0 0 - x)(l - F ) + ( x -50)(1 - F ) + 50F

50

distribution for the Co rich alloys is shown in table 5. In summary, for both x > 50 and x < 50, on a lattice containing two sublattices, each of 50 sites, there are 100F vacancies randomly placed on Co sites, and [(100 - x)(F-- 1) + 50] Co atoms on Ga sites. Therefore, given the correct measured fraction of vacancies, F, the number of AS Co atoms can be easily found for any concentration x. This was used in the lattice simulation model.

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[5] D. Berner, G. Geibel, V. Gerold and E. Wachtel, J. Phys. Chem. Solids 36 (1975) 221., [6] A.H. van Ommen, A.A.H.J. Waegemaekers, A.C. Moteman, H. Schlatter and H. Bakker, Acta Met. 29 (1981) 123. [7] R. Cywinski, J.G. Booth and B.D. Rainford, J. Phys. F7 (1977) 2567. [8] G.U Whittle, G.C. Fletcher, P.E. Clark and R. Cywinski, J. Phys. F12 (1982) 303. [9] M.W. Meisel, W.P. Halperin, Y. Ochiai and J.O. Brittain, J. Phys. FI0 (1980) LI05. il0] J.A. Mydosh, J. Magn. Magn. Mat. 7 (1978) 237. [11] J.A. Mydosh, J. Magn. Magn. Mat. 15-18 (1980) 99. [12] A.K. Grover, S.K. Malik, C. Radhakrishnamarty and R. Vijayaraghaven, Solid State Commun. 32 (1980) 1323. [13] A.K. Grover, L.C. Gupta, R. Vijayaraghaven, M. Matsumura, M. Nakano and K. Asayama, Solid State Commun. 30 (1979) 457. [14] R. Cywinski and E.M. Gray, Phys. Lett. 77A (1980) 284. [15] P. Gibbs and R. Cywinski, Solid State Commun. 33 (1980) 553. [16] K.R.P.M. Rao and P.K. Iyengar, Phys. Stat. Sol. (a) 30 (1975) 397. [17] G.L. Whittle, P.E. Clark and R. Cywinski, J. Phys. F10 (1980) 2093. [18] G.L. Whittle and P.E. Clark, Solid State Commun. 33 (1980) 903. [19] G.L. Whittle, P.E. Clark and R. Cywinski, J. Magn. Magn. Mat., to be published. [20] I. Dezsi and B. Molnar, Nucl. Instr. and Meth. 54 (1967) 105. [21] S.M. Qaim, P.J. Black and M.J. Evans, J. Phys. CI (1968) 1388. [22] N.F.M. Henry, H. Lipson and W.A. Wooster, The Interpretation of X-ray Diffraction Photographs (McMillan, London, 1960). [23] A. Amamou and F. Gautier, J. Phys. F4 (1974) 563. [24] B. Window, J. Phys. E4 (1971) 401. [25] A. Parthasarathi and P.A. Beck, Solid State Commun. 18 (1976) 211.