This document discusses the influence of conduction electrons on the electric field gradient (EFG) in amorphous intermetallic alloys. It presents a model that incorporates a screening term for the electronic contribution to the EFG using Thomas-Fermi screening. Mossbauer spectroscopy experiments were conducted on amorphous FeZr and (FeCu)Zr alloy ribbons and films prepared by meltspinning and coevaporation. The results show that screening must be considered to understand the quadrupole splitting observed in alloys where the density of states at the Fermi level varies with concentration.

1. Hyperfine Interactions 27 (1986) 437-440 437
THE INFLUENCE OF THE CONDUCTION ELECTRONS
ON THE EFG IN AMORPHOUS INTERMETALLIC
ALLOYS
P.M.L.O. SCHOLTE(1), M. TEGZE(2), F. VAN DER WOUDE(1), K.H.J. BUSCHOW (3)
and I. VINCZE
(1) Solid State Physics Laboratory, Materials Science Center, University of Groningen,
1 Melkweg, 9718 EP Groningen, The Netherlands
(2) Central Research Institute for Physics, P.O.Box 49, H-1525 Budapest, Hungary
(3) Philips Research Laboratories, 5600 MD Eindhoven, The Netherlands
The quadrupole splitting in alloys is determined by the structural
and electronic properties of the alloy. Only in cases where the
density of states at the Fermi level is constant or known as a
function of the concentration, relevant structural information can be
obtained from the quadrnpole splitting.
i. INTRODUCTION
The electric field gradient (EFG) is often used to study the local
configurations in amorphous metals. The EFG usually is decomposed into aelattice
iat . I
contribution V and a contrlbution of the conduction electrons V . In a
zg . . . z
large number of Intermetalllc systems the electronlc part is proportlona~ to the
lattice contribution /1,2/. Therefore the EFG in amorphous metals often is
calculated using a simple point charge model with a Coulomb potential # between
the constituent atoms /3/.
1 qn
= ~ ! r~ (I)
vt~ (l-7oo)Vlzz + Velzz
at (2)
where 7~ is the Sternheimer antishielding factor, qn and r are the charge
and radial distance of atom n. Furthermore n
V el = -K V lat (3)
zz zz
with K=-2 for IIIB and IV and K=+3 for the other elements /2/.
However not all intermetallic systems follow the trend of the universal
correlation. Verma et al. observed in STFeZr a large value of K=9 /4/. In this
paper we will show the importance of---a screening term for the electronic
contribution of the EFG. The possible role of screening can also be concluded
from the observation of Moruzzi et al. /5/ that the Fermi level in amorphous
TM-TM alloys is located at, or near, a maximum in the density of states. The
screening term s(rn) will modify the potential ~ as expressed in
1 qn s( (4)
n n
Consequently in alloys where screening is important an independent source for
s(r ) is necessary if one wants to obtain structural information from
qua~rupole splittings as obtained from MES.
9 J.C. Baltzer A.G., Scientific Publishing Company

2. 438 P.M.L.O. Scholte, et al., Influence of the conduction electrons on the EFG
0.6
-
---
---
-
.....
Fc c.
Dodec.
B cc-12
Bcc-8
J
- - Tetra.
0,41
0.4
0.3g
E
E
// / /
~ 0.37 // I I
E ,'// /
s
0.2 ,!,: I / /
///
/// /
03~ ,!///
~,'x /
,,2/
0,33 2'0 4 6'0 do loo ~ i , i ,
k/Ann
i i ,
10-1
, i i I i i
100
at% Zr
Fig.2. Quadrupole splitting as a func-
tion of screeninglength ~ in a number
Fig.l. Quadrupole split- of "quasi-crystalline" models. Ann is
ting in a statiscally the nearest neighbour distance; Bcc-12
disordered alloy without resp. -8 is a Bcc structure with 12,
chargetransfer, resp. 8 neighbours.
2. EXPERIMENTAL
2.1. Sample preparation
Amorphous ribbons ( F e . ~ Zr , x=]0,60-80) of about 1 mm wide and
9 I U--X X
20 pm thick were prepared ~y means of meltspinning in an atmosphere of purified
Argon. Amorphous films ( F e 1 ~ Zr , X=IO-80; (Fel00_vCUv)lOO~xZrx ,
x,y=lO,20,40,80) of about 5006UUA x w~re produced by coevaporatiOn ot the
elements onto an aluminium substrate in UHV-equipment /6/. The noncrystallinity
of these samples was confirmed by X-ray diffraction.
2.2. Mossbauer experiments
The room temperature Mossbauer spectra were recorded using a conventional
constant acceleration type spectrometer with a moving source ( STCo in Rh) and
a stationary absorber.
To eliminate substrate effects and to reduce the measuring time we used
conversion electron Mossbauer spectroscopy to obtain the spectra of the thin
films. Some films were measured also in transmission geometry, but the spectra
were identical to the CEMS spectra.
The spectra were analysed using the deconvolution method of Vincze /7/.
3. RESULTS AND DISCUSSION
3.1. The model
We calculated the EFG using a Thomas-Fermi screening, i.e. in (4)
s(r) = exp(-r/~) (5)

3. P.M.L.O. Scholte, et al., Influence o f the conduction electrons on the EFG 439
~I O
8
8,,
A
0.7
~20
Y (Fe 100-yCUy ) 100-xZTx
A40
o60
oz~ 80 /
O3 A < o
/
/
E 0.4 E 05 /
/
E AA AA o
iI
___./
i 0.3 I
~ 20 8b loo o 20 0 60 80 100
Fe Zr x (at% Zr)
x (Qt % Z r )
Fig.3. Average quadrupole splitting in Fig.4. Average quadrupole splitting in
amorphous Fe-Zr alloys prepared by amorphous (Fe,Cu)-Zr alloys. The dashed
meltquenching ( 0 ) and by coevaporation line indicates the splittings in
(A). amorphous Fe-Zr alloys.
where ~ is the screening length. The EFG-tensor can be expressed as
X - r2
1 3Xnl nj n~ij
Vii - 4~s0 ~ qn S(rn) rs (6)
n n
with the screening term S(r)
S(r) = (I + rlX + ~<r/%) 2) exp(-r/X) (7)
are the coordinates of atom n and 6 . is the Kronecker delta.
Xni The summation is calculated o v ~ the nearest neighbours surrounding a
central Fe atom. In crystalline materials with long range order (LRO) this may
lead to erroneous results, but because of the absence of LRO in amorphous
alloys the symmetry of the next coordination shells becomes more spherical. As a
consequence the contribution of these shells will be small. Also the
introduction of the screening term causes the lattice sum in (6) to converge
more rapidly.
The amorphous "quasi-crystalline" and DRPHS clusters are constructed as
described in /8/. The charge transfer and the changes in the interatomic
distances as a function of the concentration were calculated using the
Miedema-Niessen theory /9/.
In fig. 1 the concentration dependence of the quadrupole splitting in a
statistically disordered alloy is shown, assuming an infinite screening length
and no charge transfer. One obtains a parabolic-like behaviour. In fig. 2 we
plot the quadrupole splitting as a function of the screening length. The
quadrupole splitting shows a clear sensitivity to small changes in the
screening length, when X is not too large. In the free electron model the
screening length is connected to the density of states at the Fermi level
n(Ef)

4. 440 P.M.L.O. Scholte, et aL, Influence of the conduction electrons on the EFG
1 e 2 n(Ef) (8)
~2- ~0 Vm
Where V is the molar volume. Consequently a decrease of n(Ef) will cause an
9 m
increase of the quadrupole splitting.
Additional information about the concentration dependence of the density of
states may be obtained from the specific heat, the magnetic susceptibility and
from UPS experiments.
3.2. The experimental quadrupole splitting
The concentration dependence of the quadrupole splitting in amorphous Fe-Zr
alloys was presented in /8/ and is shown in fig. 3. In fig. 4 we show the
splittings in a number Qf amorphous (Fe,Cu)-Zr alloys; the Fe-Zr splittings are
indicated by the dashed line. In both systems we observe a rather steep increase
of the splitting as a function of the concentration. The splitting in the Fe-Zr
alloys is more or less constant up to 60 at.% Zr. The concentration dependence
does not resemble fig. I. Within our model this steep increase is caused by a
lowering of the Fermi level d.o.s, with increasing Zr content. This is
corroborated by the Work of Matsuura et al./lO/, who observed a steep lowering
of the linear term in the specific heat at 60 at.% Zr. This causes a lowering of
the Fermi level d.o.s.; though this interpretation is not straightforward
because of the magnetic and electron-fonon interactions, which also contribute
to the specific heat. But after correcting for these effects Matsuura et al.
calculate a d.o.s, which decreases from 70 at.% Zr /i0/.
3.3. Conclusion
We conclude that the quadrupole splitting in these alloys is complicated by
the contribution of the conduction electrons, which is not simply an
amplification effect.
Since the sensitivity of the splitting to the screening length is not very
much dependent on the structural model used it is obvious that structural
information is not easily obtained from the Mossbauer quadrupole splitting.
Additional information concerning the d.o.s, is necessary.
ACKNOWLEDGEMENTS
This investigation forms part of the research program of the "Stichting
voor Fundamenteel Onderzoek der Materie" (Foundation for Fundamental Research on
Matter - FOM) and was made possible by financial support from the "Nederlandse
Organisatie voor Zuiver- Wetenschappelijk Onderzoek" (Netherlands Organization
for the Advancement of Pure Research - ZWO)
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