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X-RAY K ABSORPTION EDGES IN BINARY SOLID SOLUTIONS OF COBALT, IRON, AND NICKEL
L. Azároff, R. Donahue
To cite this version:
L. Azároff, R. Donahue. X-RAY K ABSORPTION EDGES IN BINARY SOLID SOLUTIONS OF COBALT, IRON, AND NICKEL. Journal de Physique Colloques, 1971, 32 (C4), pp.C4-312-C4-316.
�10.1051/jphyscol:1971457�. �jpa-00214658�
JOURNAL DE PHYSIQUE Colloque C4, supplkment au no 10, Tome 32, Octobre 1971, page C4-312
X-RAY K ABSORPTION EDGES IN BINARY SOLID SOLUTIONS OF COBALT, IRON, AND NICKEL
(*)L. V. AZAROFF (**) and R. J, DONAHUE (*
*
*)Institute of Materials Science, University of Connecticut Storrs, Connecticut, U. S. A.
R6sum6. - Dans les solutions binaires solides a structure cubique face-centree, les modifications de structure line des discontinuites K des mCtaux de transition suggkrent que la densite de trous locaux augmente prks des sites des atomes Ni dans Ni-Fe et des sites des atomes Co dans Co-Fe.
Une diminution correspondante s'observe dans les autres sites atomiques.
Dans les solutions cubiques centrees, la discontinuite K de Fe n'est pas modifike par la compo- sition de I'alliage dans Fe-Ni alors que premier maximum dans la discontinuite K du Ni augmente puis decroit aprks un somrnet correspondant a 15 % de Ni. Dans la solution solide Co-Fe c'est la discontinuit6 KCo qui reste inchangee dans I'alliage alors que le p~emier maximum de la discon- tinuite K du Fe augmente avec la concentration en Co puis dkroit. L'absorption elevQ par les atomes de fer dans la region de la discontinuite K de Co, rend cependant sa determination difficile.
Les caractkristiyues genbrales des discontinuites Kde Co, Fe, et Ni se ressemblent dans les solu- tions solides bcc et sont tres differentes de leurs formes dans les solutions solides fcc. Les variations de structure Blectronique des atomes absorbants dkduites de leur spectre d'absorption K sont en bon accord avec leurs moments magnCtiques dans ces alliages.
Abstract. - In binary solid solutions having the face-centered cubic structure, changes in the fine structures of the transition metal Kedges suggest that the densiy of localized holes increases at Ni atom sites in Ni-Fe and Ni-Co and at Co atom sites in Co-Fe. Corresponding decreases are noted at the other atomic sites.
In body-centered cubic solid solutions, the Fe K edge appears to be unchanged with alloying composition in Fe-Ni whereas the first maximum in the Ni Kedge grows in size and then declines after peaking at about 15 at. % Ni. In Co-Fe solid solutions it is the Co Kedge that remains unaf- fected by alloying while the first maximum in the Fe K edge increases with increasing Co concen- tration and then declines. The high absorption by iron atoms in the region of the Co K edge, however, makes its determination more difficult.
The general features of the Kedges of Co, Fe, and Ni resemble each other in the bcc solid solu- tions and are characteristically different from their shapes in fcc solid solutions. The variations in the electronic structures of the absorbing atoms inferred from their K absorption spectra are in good agreement with their magnetic moments in these alloys.
Introduction. - The iron-group elements : Fe, Co, and Ni have been the subjects of numerous studies because of their intrinsic interest as well as their practical role in alloys and compounds. Despite this attention, considerable uncertainty remains about their electronic structure, even in simple solid-solution alloys. As is well-known, the fine structure appearing in the vicinity of the X-ray absorption edge of a metal is related to the availability of empty quantum states and the probability that a photoejected electron will undergo a transition to one of these states. A study of the X-ray absorption spectra of Fe, Co and Ni, therefore, should disclose information regarding the
(*) Research supported by the National Science Foundation.
(**) Department of Physics.
( * * *) Department of Metallurgy.
electronic structure of the absorbing atoms. The direct interpretation of X-ray absorption spectra is compli- cated, however, by our inability to calculate the tran- sition probabilities exactly. Nevertheless, it has been demonstrated [I] that semiquantitative interpre- tations can be made provided that a single parameter is varied (e. g. composition) which causes systematic changes to take place in the fine structure. Solid- solution alloys provide a n excellent vehicle for such studies because the constancy of crystal structure (symmetry) assures that the transition probabilities should vary in a monatonic way with composition, if at all.
The system Co-Ni forms a continuous solid solu- tion series having a face-centered cubic (fcc) structure and no tendency toward ordering a t room tempera- ture. By comparison, both Fe-Co and Fe-Ni form fcc
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1971457
X-RAY K ABSORPTION EDGES I N BIN ARY SOLID SOLUrIONS OF COBALT C4-313 solid solutions at elevated temperatures but it is
possible to quench in the fcc structure in cobalt containing up to 10 at. % Fe and in nickel containing up to about 65 at. % Fe, with a strong tendency toward ordering in the vicinity of the composition FeNi,. These two systems also form body-centered cubic (bcc) solid solutions, a-Fe dissolving up to 25 at. % Ni and up to 75 at. % Co, the latter showing a strong tendency toward ordering in alloys contain- ing more than 25 % cobalt. The electronic structures of the fcc solid solutions for all three systems show a linear variation between the number of unpaired spins (3 d vacancies) and the average number of elec- trons per atom in the solution [2], [3]. This depen- dence is definitely not linear for the two bcc solid solutions. It has been suggested 121, [4] that those ele- ments that show a linear relation probably share a common 3 d band, while deviations from linearity indicate that this rigid-band model does not apply.
Because X-ray absorption spectra have been useful in shedding light on just this question in the past [5], it is of interest to examine the solid-solution alloys of Fe, Co, and Ni by this means.
Experimental procedures. - The iron-nickel, iron- cobalt, and cobalt-nickel solid solutions were prepa- red from electrolytic Co and Fe of 99.99 % purity and Ni of 99.95 %purity by melting accurately weighed samples in a previously baked-out alumina crucible.
Approximately 40 g of each composition was placed in a high-vacuum melting furnace, evacuated to at least microns pressure, and slowly heated to the melting point of the charge. The molten alloys were agitated during a slow cooling to minimize segrega- tion effects and to prevent the crucible from cracking.
The cooled ingots were found to have lost no weight and subsequent chemical analyses confirmed the starting compositions to within 0.5 %. All samples were cold worked slightly and vacuum annealed for 100 h at 1800 OF. They were subsequently reduced to foils by cross rolling and vacuum annealing and all foils were examined metallographically, by X-ray diffraction, and under a strong light to check their compositional and physical homogeneity.
The actual test specimens were placed in a special holder that allowed two samples to be examined suc- cessively with a background measurement inserted between each pair of readings. A two-crystal spectro- meter previously described [6] was equipped with two silicon crystals whose 11 1 reflection halfwidths were of the order of 10 s. The stability of the X-ray source, detectors, and counters was such as to assure an overall statistical accuracy of better than f 1 %
for the individual measurements. The absorption coefficients determined were corrected for instrumental effects using a previously described procedure [7]
suitably modified.
The experimentally measured linear absorption coeffi- cient ,u of an AB alloy can be expressed as
where p, and pB are the weight percent and pmA and pmB the mass absorption coefficients, respectively, of the two constituents, while p is the density of the alloy. Since it is desired to observe the variation of only one of the two absorption co&cients as a func- tion of the incident X-ray energy, it is necessary to predetermine the values of the mass absorption coeffi- cient of the other component in the same energy range. This was done using the foils of the pure metals. Knowing the absorption coefficient of one constituent, it is possible to rearrange the terms in eq. (1) to solve for the linear absorption coefficient of the other element, say pA directly in terms of the measured p values of the alloy.
The advantage in normalizing the experimental data in this way is that eq. (2) yields a value << per atom u rendering the absorption coefficient magnitu- des independent of alloy composition and directly comparable to other like values. It should be noted that in practice, however, the absolute determination of p is complicated by uncertainties in the foil thickness and porosity. Moreover, as is well known from Moseley's Law, an element of atomic number Z absorbs more strongly radiation having energies near the absorption edge of element Z
+
1 or Z+
2 so that this imposes an additional limitation on the accuracy, particularly when the heavier ele- ment is present in small amounts. The influence of errors introduced in the data-reduction process by incorrect evaluation of the instrumental factors affect- ing the measurements were also independently tested and found to be negligibly small. Since carbon is a frequent contaminant of iron, the effect of the presence of up to 0.45 % carbon on the iron absorption curve was investigated using several iron foils and found to be negligible. Despite these precautions, changes observed to be taking place in the fine structure at the absorption edge of a metal as a result of alloying were deemed to be significant only when they clearly exceed- ed the magnitudes of all possible experimental errors and when they displayed some kind of regular varia- tion with composition.Cobalt-nickel. - Pure cobalt consists of a mixture of 60 % atoms having the 3 d8 4 s1 and 40 % having the 3 d9 4 so electronic structure while the same pro- portions of atoms in pure nickel have the configura- tions 3 d9 4 s1 and 3 d l 0 4 so, respectively. If cobalt and nickel atoms share the 3 d-4 s bands in the alloys, then the addition of cobalt to nickel should increase the 3 d hole density proportionately. As previously pointed out [I], a K electron, photoejected by the X-ray absorption process, is sensitive only to the electronic states localized in the vicinity of the absor-
21
bing atom. Thus the fine structure of an absorp- tion edge reflects the density of states derived from the band model by reflecting a probability that, say, in pure nickel 60 % of the time the electron can go to an empty 3 d or 4 s state and 40 % of the time to an empty 4 s state only (exclusive of higher states). It is, of course, necessary to satisfy the dipole selection rules but, as shown by Burdick for copper [8], in fcc metals there is considerable admixture of d-s-p sym- metry to meet this requirement. Accordingly, one would expect that the addition of cobalt to nickel will increase the number of atoms having one or two 3 d vacancies and cause a rise in the absorption curve at energies corresponding to transitions to these states.
Such an alteration actually has been observed [9]
and figure 1 shows the systematic changes taking place in the nickel edge of five alloys. The actual scale along the ordinate is expressed in terms of the average number of 3 d holes per nickel atom by assuming that the area under the appropriate absorption maximum
I I I I I I I I
20 40 6 0
Cobalt ( a t . 010)
FIG. 1. - Relative area changes in portions of the nickel K absorption edge expressed in units reflecting the estimated density of 3 d holes at nickel atoms in Ni-Co solid solutions.
in pure nickel corresponds to 0.6 holes. By measuring the same maxima in each of the alloys it is then possi- ble to prorate their relative areas accordingly [I]
and to construct figure 1. Clearly, the rigid-band pic- ture appears to hold true for these Co-Ni solid solu-
tions.
Iron-nickel. - According to Crangle [2], the fcc solid solution of Ni-Fe shows a linear variation bet- ween the number of unpaired spins and average atomic number from Z = 28 (100 % Ni) to Z = 27 (50 % Ni) and then a gradual deviation, peaking at 40 % Ni, followed by a sharp decline. The nickel K absorption edge shows a corresponding change, as can be seen in figure 2, except that the peaking appears to set in closer to 50 % nickel. The relative changes in the area of the first absorption maximum have been scaled by comparison to the same area in pure nickel in
1 I I I I 1
0 20 40 6 0
Iron (at. O/o)
FIG. 2. - Relative changes in 3 d holes at nickel atoms in fcc Fe-Ni solid solutions.
deriving the numerical values used in plotting figure 2.
For bcc solid solutions Crangle [2] shows an initial rise in the total number of unpaired 3 d
+
4 s elec- trons from 2.0 in pure Fe to nearly 2.2 when slightly more than 10 % Ni has been added. A comparable change is seen to occur in the Ni K absorption edge.In constructing figure 3, a wider energy region in the
Nickel ( a t .
FIG. 3. - Relatives changes in 3 d - 4 s holr;b at nickel atoms in bcc Fe-Ni solid solutions.
absorption spectrum was prorated so as to make certain that all 3 d and 4 s states were included. It must be emphasized here, as previously pointed out [I], the scaling process employed is very crude so that relative changes with alloying composition may be deemed meaningful but not the actual magnitudes assigned t o the ordinate axis. It is interesting to note that no relative change larger than experimental (statistical) errors was observed in the iron Kedge in all the fcc and bcc alloys containing nickel that were examined.
Iron-cobalt. - In cobalt it is the bcc or alpha phase of iron that has the large solid solubility for cobalt.
X-RAY K ABSORPTION EDGES I N BINARY SOLID SOLUTIONS O F COBALT C4-315
Only three fcc alloys, respectively, containing 7.0, 8.3 and 10.0 at. % Fe were examined. As in the other two systems, fcc solid solutions show a regular varia- tion in the first absorption peak. In the Co Kedge, the addition of 7 at. % iron doesn't seem to affect the spectrum, but thereafter, the density of holes (peak area) increases in a regular way as more iron is added.
In the Fe Kedge, the spectrum of an alloy containing 10 at. % Fe (maximum possible) duplicates the spec- trum of pure gamma iron within experimental error but as the iron content decreases, so does the area of the first maximum, indicating a linear decline in the empty 3 d states at iron atoms.
The bcc solid solutions behave quite differently.
The cobalt K edge shows no significant variations among six alloys spanning 15-65 % cobalt. The iron K edge, on the other hand, behaves as shown in figure 4.
ground-state structures are examined, therefore, changes in the observed fine structure should reflect changes in the distribution or occupation of the available states.
The three solid-solution systems examined in the present paper have been referred so far only to the previous analysis of Crangle [2], which was based on data from magnetic susceptibility, polarized neutron, and related measurements. In a later study, Collins and Forsyth [3] employed polarized neutron diffrac- tion to measure the magnetic moment distributions in Ni-Fe and Fe-Co solid solutions. In Ni-Fe they found a general increase in the iron moments and a more regular decline in the nickel moments with increasing nickel content. (Note that the moments of nickel atoms (( decline )) to the value appropriate for pure nickel, i. e., they increase with iron content.)
Cobalt (at. 010)
FIG. 4. - Relative changes in area of first maximum in the Fe Kedge in bcc Fe-Co solid solutions.
Because the appropriate energy distribution among 3 d and 4 s electrons in iron is subject to some contro- versy, only the relative peak areas are plotted in figure 4, without attempting to deduce the correspon- ding numbers of holes. The increase in hole density (peak areas) appears to maximize at about 35 at. %
cobalt. This can be compared to a rather broad maxi- mum (in the number of unpaired spins) ranging from 20 to 35 % Co reported by Crangle [ 2 ] .
Discussion. - An interesting feature of the shapes of the absorption edges of Co, Fe, and Ni is that they resemble each other very closely when the atoms are in a bcc or fcc solid solution but are characteristically different when the unlike structures are compared.
This has been pointed out in an earlier study of absorp- tion edge shapes [lo] where it was suggested that the like shapes reflected similarities in the absorbing atom's environment, i. e., similar energy distributionof empty quantum states. When atoms having closely similar
This can be compared with figure 2 in this paper which shows a similar progression except for the apparent peaking at about 50 %. In bcc Fe-Co, they found no significant change in the magnetic moments of cobalt atoms but a progressive rise in the moments of Fe atoms to a value of nearly three Bohr magnetons in the presence of 50-70 % cobalt. This can be compared with figure 4 where it is seen that the density of 3 d holes at iron atoms reaches a maximum at about 35 % Co while the cobalt Kedge remains unaffected by alloying.
It is tempting to speculate why the area in the absorp- tion peak declines as more cobalt is added whilst the magnetic moment per iron atom remains cons- tant. Until a more exact interpretation of X-ray absorption spectra becomes possible, however, it is better to resist such temptations.
Acknowledgments. - We wish to express our appreciation to Mr. J. A. Reffner for preparing the final illustrations appearing in this paper.
References
[ I ] AZ~ROFF (L. V.), J. Appl. Phys., 1967,38,2809. [5] AZAROFF (L. V.), Science, 1966,151,7$8.
121 GUNGLE (J.), Electronic Structure and Alloy Che- [6] AZAROFF (L. V.), Advan. X-Ray Annul., 1965, 9, 242.
mistry 'f the lYansition P.
*'
[7] PORTEUS (J. O.), J. Appl. Phys., 1962, 33, 700.Ed. (Interscience Publishers, New York, 1963),
pp. 51-68. [SJ BURDICK (G. A.), Phys. Rev., 1963, 129, 138.
131 C O L ~ S ( M . F.) and FORSYTH ( J . B.), Phil. Mag., [91 D o ~ m (R. J.) and AZ~ROFF (L. V.), J. APP~. Phys.,
1963, 8, 401. 1967,38,2813.
[4] M o n ( N . F.), Advan. Phys., 1964, 13, 325. [lo] AZAROFF (L. V.), Mat. Res. Bull., 1967,5 137.
DISCUSSION Mr. ULMER.
-
HOW was the zero of energy definedon your absorption spectra ?
Does this inflexion point represent the Fermi edge of spectra by definition ?
Mr. AZAROFF. - The Fermi energy was located by determining the inflection point in the initial absorp- tion rise by the usual arctangent approximation. This is also the crossover point between the absorption edge and the KP emission curve.
Mr. NIKIFOROV. - In the interpretation of K-absorp- tion spectra of the 3 d-elements alloys prof. Asaroff makes an assumption about the number of 3 d elec-
trons per atom in solids. He thinks that the atom has a configuration 3 dn 4 sX where X is equal to 1 or less. This correlates with our results presented here by prof. Blotern. We have calculated the number of 3 d-electrons per atom using experimental data KB,-
integral intensity. The result is that 3 d-transition metals have a configuration 3 dn 4 sl.
Mr. AZAROFF.
-
If I may make a small addendum, the band model for nickel, of course, predicts an<< average )> atom having 3 d9.4 4 soe6, that is, one-
and-half more times is there one 4 s electron present.
Since an absorbing atom cannot have a non integral number of electrons, it is necessary to consider the actual electronic structures of individual atoms.
