SOFT X-RAY EMISSION AND X-RAY
PHOTOELECTRON STUDIES OP DISORDERED
ALUIMINIUM ALLOYS IN RELATION TO CPA
THEORY
P. Norris, D. Fabian, L. Watson, J. Fuggle, W. Lang
To cite this version:
P. Norris, D. Fabian, L. Watson, J. Fuggle, W. Lang. SOFT X-RAY EMISSION AND XRAY PHOTOELECTRON STUDIES OP DISORDERED ALUIMINIUM ALLOYS IN RELATION TO CPA THEORY. Journal de Physique Colloques, 1974, 35 (C4), pp.C4-65-C4-69.
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Submitted on 1 Jan 1974
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JOURNAL DE PHYSIQUE
Colloque C4, supplkment au no 5, Tome 35, Mai 1974, page C4-65
SOFT X-RAY EMISSION AND X-RAY PHOTOELECTRON STUDIES OF
DISORDERED ALUMINIUM ALLOYS IN RELATION TO CPA THEORY
P. R. NORRIS, D. J. FABIAN, L. M. WATSON, J. C. FUGGLE and W. LANG
Department of Metallurgy (Materials Physics Group),
University of Strathclyde, Glasgow, U. K.
RBsumB. - Nous avons examine la structure electronique d'alliages binaires desordonnb
par etudes spectrales d'emission de rayons X mous ainsi que par des mesures des photoelectrons
obtenus par rayons X.
Les transitions electroniques que ces deux processus impliquent, peuvent Etre considerees comme
(< locales )> dans le premier cas et comme (( moyennes )> dans I'autre cas. Ceci permet d'interprkter
la distribution des electrons dans divers alliages desordonnes selon I'approximation d'un potentiel
coherent ; ceci faisant particulihement reference aux recents developpements de la theorie de
Kudrnovsky, SmrCka et VelickJ; (1972).
Nos mesures ont port6 sur des alliages de solution A 1'6tat solide d'aluminium avec un metal
prtcieux, l'argent et un metal de transition, le vanadium. L'etude spectrale d'emission de rayons X
mous pour ces systkmes desordonnb indique une interaction effective avec la bande-d du metal
prkcieux ou de transition en solution. Le spectre des photoClectrons extraits de la bande de valence
par rayons-x permet de localiser la position de cette bande-d.
Abstract. - Experimental information on the electronic structure of disordered binary alloys
derived from soft x-ray emission spectra and x-ray photoelectron measurement is examined. The
electron transitions involved in the two processes can be regarded as <<localized>> in the one case
and <( averaged >) in the other. This leads to interesting interpretations of the electron distributions
in disordered alloys in terms of the coherent potential approximation, particularly with reference
to the recent extensions of the theory described by Kudrnovsky, SmrCka and Velickjl (1972).
Measurements for alloy solid solutions of aluminium with the noble metal silver and the transition metal vanadium are described. Soft x-ray emission spectra for these disordered systems
indicate the effective interaction with the d-band of the noble or transition metal component,
while x-ray photoelectron valence-band spectra serve to locate the position of the d-band.
1. Introduction. - With recent success in theoretical descriptions of the disordered metallic state,
the various experimental techniques for exploring
the electronic structure of metallic alloys are coming
each into their own. Moreover, taken as an interdependent whole they become extra powerful by providing complementary information.
Theoretical models for transition-metal alloys based
on the coherent potential approximation (CPA theory
[I-31 effectively provide a rationalization of the concept
of local electron densities, which concurrently have
become a necessary feature in the interpretation of
soft x-ray emission spectra of disordered alloys.
The matrix element determining the oscillator strength
for the emission of an x-ray photon, when a valence
electron is involved in the transition that fills a vacant
core level (arising in a given excited atom of the
solid), is dependent on the overlap of valence-electron
wavefunction with the core-level wavefunction, and is
therefore restricted essentially to the vacinity of the
excited atom. This localized property of the emission
process is of dominating importance when we study
alloys, where different forms of atom are available
for excitation. The core-level for different atoms
appear to (( see D different effective densities of valence-
band states ; current results and interpretation [4, 51
for binary alloys amply illustrate this effect.
CPA theory, whose application and approximations
we examine in this paper, as applied to soft x-ray
emission from binary alloys, provides a satisfying
framework for describing the cc two-band H picture
that emerges for transition and noble metal alloys.
We find close agreement between the predications
of the theory, within the simplifications adopted by
Kudrnovskf, SmrEka and Velickf [3], and the soft
x-ray band emission from disordered aluminiumsilver and aluminium-vanadium alloys. On the other
hand, these simplifications ignore changes in band
structure ; and we must keep in mind that chemical
shifts of the critical points in emission bands particularly of the Fermi edge - has generally been
noted experimentally when numerous inter-metallic
compounds have been compared with data for the
pure components. Similar, smaller, shifts in bandstructure features might well be expected in the formation of disordered alloys. Because the CPA Hamiltonian used in this model for soft x-ray emission
arbitrarily fixes the unperturbed energy levels, the
calculations by Kudrnovskf et al. can not be expected
to yield information on chemical shifts.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1974410
C4-66
P. R. NORRIS, D. J. FABIAN, L. M. WATSON, J. C. FUGGLE AND W. LANG
Soft x-ray emission measurements have proved not
to be the best form of experiment for the observation
of band and core-level shifts, nor for the location of
- for example - the d-bands in transition metals
or noble metals. The more recent technique of x-ray
photoelectron emission (XPS, or less descriptively
known as ESCA) is probably the most powerful
known to date for identifying sub-bands such as
valence-d or valence-f-bands in transition and rareearth metals. The essential difference in the electron
transition process, from that involved in soft x-ray
emission, is the non-localized nature of the initialstate valence-electron wavefunction. The high energy
final-state electron does not cc see )) any particular
atom in the solid from which the electron has been
excited, and only an (c averaged )) density of valenceelectron states can be sampled in the experiment making it a valuable complement to soft x-ray measurements. In general we find that the position of the
d-bands in alloys of noble metals and transition
metals with aluminium, located from XPS studies,
correlates well with the effect of the metal d-bands
on the soft x-ray A1 L2,,-emission bands for the
alloys.
2. Limitations of the model. - The model adopted
by Kudrnovskjr, SmrEka and Velickf assumes the
single-electron approximation, and also ignores changes of band structure on alloying. In fact, for an A-B
alloy it assumes that the sp components of the A
and B densities of states are identical. A crucial
approximation is the tightly-bound character of the B
d-band. This appears in two distinct parts of the
calculation ; in the determination of the alloy Green
function (;itself, and in the estimation of the electric
dipole transition matrix M: (Q = A, B) where it
yields the result that this matrix decomposes into an
sp block and a series of single-site d blocks. In the
case of non-degenerate d bands, considered by
Kudrnovsky et al., the d blocks are one-dimensional.
Another serious simplification is the assumption
of k independence of the sp sub-matrix of M:
(i. e. M&) :
<klM,I k' >
=
N -1 m2s
With these limitations, the expression for the
emission intensity is
where o is the energy relative to the bottom of the
band, w? is the absolute energy of the band of symmetry L from species Q, the factor N normalizes 12 to
the intensity emitted from a typical atom species Q
(it is a consequence of the CPA that all sites of a given
species become equivalent). As explained, the element
m& is independent of k, and m2Dis simply the element
representing the one-dimensional d block of the transition matrix at a particular site. g: is the corresponding
block of the Green matrix ; being one-dimensional,
it is the same as its trace, and consequently can be
shown to represent the partial density of d electrons
on a site of type Q. Furthermore, the term inside the
double summation may be shown to represent a
partial density of sp states on such a site - at least
in a certain sense - and thus eq. (2) expresses the
separation of the total intensity 12(o) into components
derived from each sub-band.
With an alloy of a simple metal and a transition
metal, there will be no second term in the expression
for the L band from the light metal (& disappears
when there are no d electrons), so that in the case of
the A1 L2,,-emission band, only the first term in
eq. (2) will contribute. At energies differing widely
from the energy of the d band the effect of concentrashould
tion on the site-averaged Green function
cA1
(1)
for some k-independent scalar m&. This can only
be a good approximation near the centre of the Brillouin zone, where k. r & l and consequently e&.' l
for all points r within an atomic volume. This is not
so in the region of the Fermi edge. The approximation
also breaks down on symmetry considerations.
Additionally, there are limitations of the CPA
itself; these probably are the least serious of all in
the context of the present model. For example, the
first significant departure from the CPA density of
states will occur at the boundaries of the sub-bands.
Since the state density in these regions is low, relative
to the maximum of the band, the soft x-ray emission
spectrum will not be greatly affected.
--
ENERGY a r b ~ t r a r yu n ~ t s
FIG. 1. - Soft x-ray L2,s-emission from the simple metal
component of a series of hypothetical binary alloys of a simple
metal and a transition metal, adapted from the calculations of
Kudrnovskf et al. The Fermi edge is envisaged as lying a short
distance above the energy of the d band in the transition metal
component.
SOFT X-RAY EMISSION AND X-RAY PHOTOELECTRON STUDIES OF DISORDERED ALUMINIUM
be slight, since the density of sp states will change
only where these are degenerate with the d-levels.
Thus, near the bottom of the sp band, not very much
change is expected for a small increase in the concentration of the heavy metal. Kudrnovskg et al. illustrate
(Fig. 1) the case of a heavy-metal concentration of
20 %, and it is noted that the bottom of the band is
very little different from that for pure light metal,
except for a small displacement to lower energy.
The decrease in L-emission intensity, at an energy
corresponding to the d levels of the transition metal,
is the result of an increased partial density of d states
with a resulting depletion of the local density of sp
states near the light metal site. Thus, we expect the
integrated intensity of A1 L,,,-emission from the alloy
to be lower than that from the pure metal, in the region
of the spectrum that corresponds to the energy of
the d-band.
3. Comparison with experiment. - To examine
the model and its applicability to suitable disordered
alloys, we require a system or systems for which the
component metals have near identical, or relatively
matched, sp-component bands, and also band structures that remain little changed on alloying. The first
requirement can be satisfied by choosing component
metals with significant free electron character, and the
second by restricting the system to relatively dilute
solid solutions. We confine the examination, for
convenience, to alloys of a simple metal with respectively a noble metal and a transition metal and study
the L-emission from the simple metal core-levels.
Silver in aluminium meets the requirements reasonably well for the case of a simple metal with a noble
metal ; the examination here is restricted (by dictates
of the phase diagram) to concentrations in the a solid
solution range. Vanadium in aluminium provides an
acceptable test in the case of a transition metal ;
the examination in this case is confined to vanadiumrich alloys, where there exists a broad enough range
of solid solution (it is not important which metal is
in excess since the sp band, which gives rise to the Lemission, is regarded essentially as common in the
alloy).
Careful choice in this way of suitable alloys for
testing the theory, provides a measure of the applicability of the CPA model to soft x-ray emission,
without implying acceptability of the assumptions
discussed above to alloys in general. Our examination
is then largely analogous to the theoretical test of CPA
made by Kirkpatrick, Velickf and Ehrenreich [6]
for the band structure of the rr ideal )) alloy coppernickel, except for their taking into account the multiplicity of the d-bands.
We have presented previously 17, 81 soft x-ray
emission data for aluminium-silver and aluminiumvanadium alloys, and we re-examine these spectra
here. In previous discussions the effect of alloying
on the L,,,-emission from aluminium atoms in the
(3-67
alloys has been noted and attributed to the d-band
of the noble-metal or transition-metal atoms respectively. This interpretation is reasonably well established,
particularly since apparent cr peaks )) in the L-emission
spectra become strongly pronounced in the case of
intermetallic compound formation. With aluminiumsilver solid solutions we claimed this peak, observable in the L,,,-emission, to reflect the s and d
character of the valence band, since it occurs at an
energy corresponding to hybridization of the lower
d-bands of silver with the s components of the aluminium atoms.
However, in earlier comparisons of emission spectra
for alloys of different composition, the emission band
intensities have been normalized to the maximum
intensity at the Fermi threshold. Some form of normalization is necessary because the emission intensity
from the aluminium falls off with composition ; the
fall-off moreover is not proportional to aluminium
concentration. For correct comparison, the emission
intensity from component A in an alloy, should be
expressed in the form
I," =
rate of emission of photons in a narrow energy
interval (dE)
rate of creation of type A core-holes x d E
This quotient would yield a concentration-dependent
integrated intensity, if self absorption is neglected.
If the experimental conditions can be accurately
controlled we can expect the denominator in the
expression to vary linearly with concentration. We
would then measure directly, not the quantity I,
but Ix (concentration). Thus we expect in general
the integrated intensity of the spectrum to be proportional to the concentration of the emitting species.
An alternative method for obtaining integrated
band intensities has been described by Wenger, Biirri
and Steinemann 191. This involves the monitoring
of a suitable emission line, one that arises from the
same core-level as the emission band investigated,
and is a powerful technique when for example both K
and L spectra are available, pointing once more at
the value of combining measurements by several
techniques.
In the present report we examine the A1 L,,,emission spectra, for different alloy concentrations
of aluminium, after simply scaling the intensity and
offsetting the zero. This allows just two variable
parameters and the curves are brought into coincidence at two arbitrarily chosen points in the region
of the tail. This is done because, on the assumption
that the CPA model applied to soft x-ray emission
is valid, it should be possible to obtain an accurate
match between the tails of the spectra for different
alloy concentrations. This indeed is found to be the
case (Fig. 2 and 3) for aluminium-silver and aluminiumvanadium solid solutions. The theory predicts then
that the intensity in higher-energy regions of the
C4-68
P. R. NORRIS, D. J. FABIAN, L. M. WATSON, J. C. FUGGLE AND W. LANG
at energies appreciably higher than the d bands is not
observed. However, there is no reason to expect a
close correspondence between the theory and experiment near the Fermi edge, especially since the transition
matrix element has been shown [lo] to exhibit rapid
variations in this region for pure aluminium.
To test properly that the fall-off corresponds to
the position of the d levels, we must experimentally
locate the latter. Here we turn to x-ray photoelectron
spectra.
4. x-ray photoelectron valence band spectra. Strictly, for the purpose of verifying the KudrnovskySmrEka-Velickf model, it is the position of the dband of the pure heavy metal that is to be examined
in relation to the soft x-ray emission band. We do this
in figure 4 for aluminium-silver, using the XPS valence
band measured for pure silver. However, we describe
here also the measurement of XPS valence band
spectra for the alloys themselves because it is imporFIG.2. - Experimentally recorded aluminium L2,3-emission tant to note experimentally the effect of alloying on
spectra from (top to bottom) pure aluminium, 8 % silver, 10 % the valence d-band of the pure heavy metal.
silver and 16 % silver. Intensities are normalized to bring the
low-energy extremities of the band into coincidence.
FIG.3. - Experimentally recorded aluminium L2,3-emission
spectra from (top to bottom) pure aluminium, 75 % vanadium
and 90 % vanadium. As for AI-Ag, the normalization constant
for each spectrum is chosen so that the low-energy sections of
the spectra match one another as closely as possible, but the
bands are also displaced in energy ; the theoretical justification
for such a displacement at high solute concentrations is clearly
demonstrated by the 40 % B curve in figure 1.
spectrum should fall progressively with heavy metal
concentration, the depletion of intensity setting in at
approximately the energy of the heavy-metal d levels.
This, too, appears to be confirmed in the measured
spectra, although the predicted recovery of intensity
FIG. 4. - The d band of pure silver, measured by XPS.
superimposed on two representative spectra from figure 2.
The energy scales have been displaced so that the soft x-ray
and XPS Fermi edges coincide.
To ensure cleanliness, the samples were prepared
by evaporation in vacuum. The method employed
in the case of alloys has been described previously [l 11.
The alloy is prepared in situ by evaporation and interdiffusion of the components. With aluminium-silver
required proportions of the two pure metals are
evaporated successively from separate tungsten filaments.
First, the silver is evaporated and its valence band
measured (Fig. 5), after monitoring the purity of the
sample using the carbon and oxygen 1s emission
SOFT X-RAY EMISSION AND X-RAY PHOTOELECTRON STUDIES O F DISORDERED ALUMINIUM
C4-69
silver shows clearly in the spectra. Comparison of the
spectra with those obtained for bulk specimens of
A1-Ag alloys (W. Lang et al., to be published) where cleanliness of the sample cannot be so well
controlled but the valence bands can nonetheless
be clearly identified - shows that in the initial stages
of diffusion (c to f in Fig. 5) the silver is in solid
solution in aluminium. As heating, and diffusion,
continue a separate phase ((( Ag,A1 B) is formed.
Splitting of the d-bands is clearly observable for
pure silver (spectrum a) ; it is absent for the Ag-A1
solid solutions (c - f), and appears again (although
reduced) as the (( Ag,Al>) phase is precipitated (formation of this phase is complete after 30 min at
140 OC). The d-band splitting in silver, as for gold
(Fuggle, Watson, Fabian and Norris [I 11) is attributed
predominantly to near-neighbour interaction and not
to spin-orbit effects. This is confirmed by recent
calculations by Keller [I21 (using a cluster model)
and Breeze A. (density-of-states calculation for pure
gold, unpublished communication).
INTER-DIFFUSION OF Ag-A1 FILMS
MONITORED AT THE At SURFACE
N
FIG.5. - X-ray photoelectron valence bands measured for (a)
pure silver, (b) pure aluminium, (c)-(h) silver-aluminium alloys
prepared by evaporation and interdiffusion of the pure metal
components.
peaks. Next, after retracting the sample into the
specimen preparation chamber, the aluminium is
evaporated onto the silver and the sample reintroduced
to the analyzer chamber. The spectrum of the double
layer is then measured. In figure 5, a is the valence
band for pure silver, and b the valence band for the
pure aluminium layer, showing no indication of the
silver. The sample is then heated in the analyzer
chamber and spectra recorded at suitable intervals
so that a series of valence bands (c to h in Fig. 5) are
obtained.
As the silver diffuses into the aluminium the intensity of photoemission increases and the d-band of the
5. Conclusion. - The results examined in this
paper show an impressive correlation between the
departure of the alloy soft x-ray spectra from that
of pure aluminium and the onset of an appreciable
density of silver d-states, as predicted by the model
under discussion. Additionally, the absence of a
significant shift with alloying of the silver d-band
is also consistent with the theoretical model, despite
the uncertainty in the photoemission matrix element.
Taken together the results provide strong evidence
that the electronic states of disordered alloys are
adequately described in terms of the ((averaged
medium x assumptions that underly CPA theory.
Acknowledgment. - We wish to thank the Science
Research Council for a grant in support of this
research ; and are indebted to F. Brouers and
B. Gyorffy for discussion and comments on the
manuscript.
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