SURFACE PHASES OF SILVER AND TIN
IN CRYSTALLINE AND LIQUID COPPER-BASED ALLOYS
G.P. Vyatkin, T.P. Privalova, T.O. Alekseeva,
A.E. Chudakov, S.I. Morozov, A.V. Gusev
Southern Ural State University, Lenin str, 76, Chelyabinsk, Russia, 454080
There is a strong surface segregation of Ag and Sn atoms in Cu-Ag and Cu-Sn
alloys. Surface segregation changes physical and chemical properties of these alloy
surfaces. Enrichment of the surface in these alloys is found by means of spectroscopic
experiments and computer simulation, but in a solid state and for low Ag and Sn bulk
concentration only. Our spectroscopic and computer experiments confirm these
results and show that surface segregation exists in a liquid state too. Moreover, this
effect can be found up to about 15 at.% of Ag and Sn in bulk. Our experimental
method is temperature-programmed desorption (TPD); computer simulation is based
on Monte Carlo method with Embedded-Atom Method (EAM).
INTRODUCTION
It was found many years ago there is significant surface segregation of Sn and
Ag atoms in copper based alloys. This phenomenon is studied by means different
experimental methods during the past few years (1). Now the theoretical study of this
problem is growing extensively, for Cu–Ag solid alloys especially. The theoretical
investigations in this area are often provided by means mean-field calculations (2) or
approaches based on density functional theory, e.g. Embedded Atom Method (EAM)
(3). We used the Temperature-Programmed Desorption method (TPD) (4) as the main
experimental method and EAM in conjunction with Monte Carlo modeling as a
simulation method (5). These two methods are appropriate both for solid and liquid
alloys under consideration. Moreover, they give comparable results on structure and
surface stuff.
EXPERIMENTAL
The measurements were executed on equipment, which is created on the basis
of a magnetic mass spectrometer (4). The alloys are prepared from pure metals, such
as oxygen-free copper (99,98 %), silver (99,99 %), tin (99,99 %) by melting in
atmosphere of helium during 10 min at 1500K and with a annealing within 2 hours at
1100K. Investigated metal was placed in the holder of tungsten. The cleaning of an
investigated surface from impurities and molecules, which one are adsorbed from a
gas phase, was made by desorption in repeated heatings with melting of metal.
Experiments were provided in conditions of vacuum 10-5Pa at partial pressure of
oxygen less than 10-7Pa. Intensity of desorption flux I at continuous heating and
consequent cooling with constant speed (from 5 up to 20Kps) in temperature range
from 400 up to 1500K was registered for following spectral lines of masses: 53,5 and
54,5 (Ag ++), 107 and 109 (Ag), 63 and 65 (Cu), 118 and 119 (Sn).
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The parameters of desorption of atoms Ag, Sn and Cu were instituted from
experimental TPD-spectra of these fractions, which can be described by next
equation:
I = T -1/2 N x Cexp(-E / kT),
where I is the flux of desorption of fragments;  is the equipment coefficient;
Т is the temperature of metal; N is the surface concentration or number of fractions
per a unit area; x is the order of desorption (х=1); С is the exponential factor; Е is the
activation energy of desorption; k is constant Boltzmann’s constant.
Value of desorption activation energy of Ag, Sn and Cu atoms is instituted on
linear lease of ln(I T 1/2) – 1/T dependence. Method, which one is basis on the first
equation, are used for definition of surface concentrations. This method are used a
measurement of relative variations of flux of desorption of each component of alloy at
phase change of melting (or crystallization) from TPD-spectra:
а1=I1liq/I1sol; а2=I2liq/I2sol .
COMPUTER SIMULATION
Our computer simulation is based on Monte Carlo modeling in conjunction
with EAM (3). The transition probability for atomic structure changes is evaluated
from total energy. The total energy is a sum over all individual contributions:
1
E   Fi  i     ij Rij ,
2
i
i j  i
st
where the 1 term is embedding energy, or energy to embed atom i into the electron
density , the 2nd term is short-range electrostatic pair potential. Electron density i is
approximated by the superposition of atomic densities.
Computer simulation which is based on Monte Carlo modeling of (N,V,T)
ensemble in conjunction with EAM allows to explore different metal properties. For
alloys it is possible to evaluate the surface segregation degree, the microscopic surface
structure and concentration profile. In order to provide such simulation it is enough to
fit a few elastic and vacation properties of pure metals, and to get a set of parameters
for description of these elements in EAM. These parameters are appropriate both for
pure metals and alloys.
In order to verify the evaluated parameters and to check the program complex,
the surface relaxation and surface energy of silver and copper were calculated:
=(Е–NЕsub)/S,
were E is the energy of ensemble with surface S, and this energy is evaluated
according to EAM, and NЕsub is the energy of the same number of N atoms in bulk.
These properties simulation shows good results, which are similar to
experimental ones (Table 1).
 
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Table 1
Structural and energy properties of pure surfaces
(Monte Carlo with EAM and experimental)
Surface relaxation, 10-9 m
Surface energy, arb.u.
Metal
Cu
Ag
EAM, (111)
1240200
675120
Experimental
1790
1240
EAM, (111)
–5,02,0
–6,02,0
Experimental
–2,6
–3,8
The next step of parameters’ verification was simulation of pure silver and
copper melting. The atom distribution analysis in solid and liquid state shows the
presence of melting phase transition in slab under simulation. Also good agreement
with experiment was found for melting thermal effect calculations.
RESULTS AND DISCUSSION
TPD experiments with Cu1-xAgx (x=0.005 .. 0.13) alloys
During the heating and cooling of polycrystalline alloys Cu1-xAgx (x=0.005 ..
0.13) TPD experiment shows stimulating of surface segregation and desorption of
silver. This is confirmed by a sharp increase of desorption rate during crystallization
and melting. This increase is due to intensive segregation of silver. Evaluation of
silver surface concentration from TPD spectra shows that it is 6010 at.% in solid
polycrystalline state and it is 23–35 at.% in liquid state.
Surface concentration of silver atoms in liquid and solid state for different
temperature ranges are listed in Table 2.
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Table 2
Surface concentration of silver in Cu–Ag alloys
Ag bulk
concentration,
at.%
Parameters
a1=(Isol/Iliq)Cu
a2=(Isol/Iliq)Ag
Surface concentration of Ag, at. %, and
corresponding temperature ranges
Liquid state
Crystalline state
0,3
a1=0,470,05
a2=2,320,10
1350…1450 К
245
970…1100 К
6010
0,86
a1=0,690,02
a2=1,560,05
1370…1420 К
305
950…1100 К
497
1,3
a1=0,510,03
a2=1,960,07
1370…1450 К
285
1060…1100 К
615
3,0
a1=0,510,08
a2=2,720,15
1300…1350 К
187
900…1050 К
5513
3,6
a1=0,570,05
a2=1,710,05
1350…1450 К
325
950…1050 К
599
12,8
a1=0,560,02
a2=1,680,12
1250…1280 К
338
850…1000 К
6010
Considering these experimental data with respect to width of each temperature
range, the increase of silver bulk concentration finally gives an increase of surface
concentration in a liquid state, and a decrease of surface concentration in a solid state.
Simulations of Cu1-xAgx alloys
In a liquid alloy the increase of silver bulk concentration during simulation
also gives an increase of surface concentration of silver atoms, and the decrease of
surface concentration in a solid state too. Of course, values obtained during simulation
differ from experimental ones but ranges of calculated surface concentration and the
measured one are overriding for each bulk concentration values. The surface
concentration of silver is higher than the bulk one both for solid and for liquid state.
Possibly, the reason of such surface segregation is the size mismatch between Ag and
Cu atoms, which doesn’t depend on the temperature and structure. Also there is a
dependence of surface concentration on surface index. In Cu–3 at.% Ag alloy surface
concentration is 11 at.% on (110)Cu, 25 at.% on (100)Cu, 60 at.% on (111)Cu. If to
remember that (111) fcc surface has the minimal surface energy, it is good agreement
with TPD experiment (see table 2).
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In the second atomic layer concentration of silver atoms is less about 10 times than in
the surface layer. The third layer contains approximately the same quantity of silver
atoms as any bulk layer. Thus, it is possible to approve, that in computing experiment
the monotonous structure of concentration is observed. An exit of separate atoms of
silver in ad layer also is take place in simulation.
It is observed the change of silver contents in volume on 300 % corresponds
the change on 10 % in a surface only. It can be explained by the segregation of silver
occurs due to formation of specific surface phases. In a surface of a crystal (111) Cu
(Ag) silver and copper join in separate surface phases; the Ag atoms are forming
p(1х1) structures, the placement of separate Ag atoms in ad layer above a surface
monolayer also is observed. In liquid alloy the surface consists of copper atoms
mainly, It is smoother, without precisely expressed ad layer. The significant part of
Ag atoms stays separately from other silver atoms, i.e. in an environment of atoms
Cu. In a solid state there are several surface phases, which correspond to different
indexes of monocrystal. In the liquid state surface structure p(1x1)Ag is preferable.
Also this structure exists on (111)Cu surface of monocrystal. If to compare the surface
concentrations of silver in (100), (110), (111) copper surface, then it is possible to
look following law: than more densely packing of a surface, then segregation degree
of Ag is more. By the way, the structure of a surface liquid Cu has appeared very
similar to a side (111)Cu according to our simulation .
In copper monocrystals with low silver contents the analysis of concentration
shows that the gradient of concentration of silver atoms practically disappears since
the 3rd layer. This allows to consider layers below as a volume layers. In more
concentrated solutions the volumetric stratification on phases enriched with silver and
copper is observed. In the liquid alloy (fig. 1) the top monolayer contains almost all
Ag atoms of slab. After that sharp jump silver enrichment is absent almost.
Fig. 1. Concentration profile of liquid Cu–3 at.% Sn alloy
T=1500 K; Sn is black; Cu is white
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TPD experiments with alloys Cu1-xSnx (x=0.005.. 0.17)
In alloys Cu1-xSnx (x=0.005.. 0.17) the experiment hold by TPD method gives
that nature of segregation of tin is about the same as segregation of silver in a system
Cu–Ag with the small differences. The surface monolayer contains approximately
twice less quantity of 2nd component than in previous system both in solid and in
liquid state. Then the computer simulation demonstrates that in second, third and even
in the fourth layers there is a large surplus of Sn atoms respectively to bulk, i.e. the
segregation encompasses several layers. Moreover, the ad-layers replacement of tin in
a surface is confirmed by experimental values of an activation energy of desorption
Sn, which are close to a dissociation energy of dimers Sn2.
Simulation of alloys Cu1-xSnx
Results of surface modeling of alloys Cu-Sn of different composition (from 0.5
up to 17 at. % Sn) in solid and liquid states demonstrate a high scale of surface
segregation of tin. The coverage of a surface by atoms Sn in solid state reaches about
half of monolayer. For melts the surface concentration Sn is less, but if a bulk
concentration of tin increases then a surface concentration increase too. Formation of
phases on the basis of an edge (111)Cu, and (100)Cu is equally favorite for a
monocrystals. The obtained concentration values are in the quantitative agreement
with accounts of a surface concentration of tin in alloys of the same compositions
executed on the basis of dates TPD-experiment.
Computer simulation gives the snapshots of alloy surface. It makes possible to
indicate structures, which are specific for different indexes of a surface: for example,
р(1х2)Sn structure for an edge (111)Cu and for liquid surface, and phase with (2х2)
Sn structure for less packed edge (100) Cu.
In a surface (100)Cu the structure c(2х2)Sn is the most stable. In a surface
(111)Cu, as well as in liquid state, the structure р(1х2)Sn is the most stable. These
surface structures are approximately equivalent on the formation energy and their
combination is possible. In surface layer it is possible to find the chains from Sn
atoms, which are placed in one layer with atoms of copper. Their existence can be
explained by following. In a weak solution the Sn atoms substitute atoms of copper,
but the formation of two- or three-dimensional fields from atoms of tin appears
energetically unprofitable because positive cores are repulsing and these cores would
appear too close in solid area. The realization of zigzag line-ups in Cu–Sn alloys
allows to reach a maximum of electron density in the location of each of atoms of tin,
and consequently, minimum of the contribution from energy of attraction between
atom core and electron density in this point.
The small tendency to oscillating allocation of concentration of tin is revealed
during analysis of concentration profiles. It is visible from tab.3 for two melts and
from a fig.2 and tab.3 for two mono-crystalline compositions. The formation in the
bulk of structure, which is similar to -phase, is appropriate to all compositions, that
corresponds to the phase diagram of a system. The typical scale of oscillations is 3-4
layers.
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Table 3
Tin concentrations over the layers in Cu–Sn alloys
Layer No.
1
2
3
4
5
6
Monocrystalline Cu–15 % Sn,
T=500 K
(100)Cu
(111)Cu
48.3
55.2
52.2
27.9
30.7
25.0
34.4
31.2
12.2
14.1
12.2
14.2
Liquid Cu–Sn, T=1500 K
Cu–2 % Sn
5.6
3.1
15.8
2.8
2.5
2.5
Cu–11 % Sn
33.2
32.0
26.0
32.5
11.3
11.1
Fig. 2. Concentration profile of liquid Cu–0.5 at.% Sn alloy
T=1500 K; Sn is black; Cu is white
In alloys Cu1-xSnx (x>0.01) comparison of the 1st and 2nd layer structures,
which were the result of computer simulation, confirms the idea about two-layer
character of tin segregation in a crystalline state. This idea was found on experimental
activation energy values. Also here is a correlation between Sn–Sn chains along the
surface and Sn–Sn links in the first two layers.
CONCLUSION
There is a strong silver and tin surface segregation in copper-based alloys, at
least if bulk concentration is less than 17 at.% and temperature is less than 1500 K.
TPD experiments allowed to define surface concentrations of segregating atoms and
their desorption activation energy values. The conclusion about surrounding atoms
may be done on the base of these energies. Computer simulation confirms these
predictions. More important for understanding, simulation shows a full structure of a
slab of atoms. There was found a lot of similar things about tin and silver
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segregation. First, the surface concentration can be much more than the bulk one
even in a liquid state. Second, differences between surface and bulk concentration are
less for liquid alloys than for solid. Third, concentration profile achieves bulk values
quickly. Fourth, segregating atoms are more than Cu atoms. Fifth, usually,
segregating atoms are not isolated mutually. They group in surface phases.
At the same time, there is set of differences between tin and silver segregation.
First, the values of segregation degree and their dependence on temperature. Second,
the structure of the 1st layer. It is two-dimensional in Cu–Ag alloys and it is chain-like
in Cu–Sn alloys. Third, concentration profile is monotonic in Cu–Ag alloys and it is
oscillating in Cu–Sn alloys. Fourth, presence or absence of atoms or groups of atoms
above first layer in crystalline state.
It seems the most important factor which influents on character of segregation
is electron structure. It is more important than lattice constant or sizes of atoms. EAM
allows to account it approximately. But it is enough to achieve a lot of data, which
correspond to experimental results. More accuracy in description of electron structure
and additional experiments with ternary alloys Cu–Ag–Sn which are in progress can
give new useful information in segregation processes in Cu-based alloys.
ACNOWLEGEMENTS
This work was supported by the Russian Ministry of Education (grant on
researches in the metallurgy, 1997–2000)
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