J Mater Sci
DOI 10.1007/s10853-012-6680-z
HTC 2012
Wetting of calcium fluoride by liquid metals
Shmuel Barzilai • Natalya Froumin •
Eugene Glickman • David Fuks • Nahum Frage
Received: 4 May 2012 / Accepted: 15 June 2012
Ó Springer Science+Business Media, LLC 2012
Abstract The results of wetting experiments for the
CaF2/Me and CaF2/Me–Ti systems (Me = Cu, Ge, Al, In,
Ga, Sn, and Au) are presented and discussed. It was found
that pure metals do not wet the CaF2 substrate, while a
small quantity of Ti added to the melt improves the wetting. The effect of Ti depends on its thermodynamic
activity in the melts. According to the thermodynamic
analysis and experimental observations, Ti dissolved in the
metals does not react with the substrate to form any new
condensed phase at the interface and its effect cannot be
attributed to the ‘‘reactive wetting’’ phenomenon. Density
functional theory (DFT) was applied to focus on the nature
of chemical bonding between the atoms in the melt and the
surface of the substrate in these systems. It was demonstrated that partly filled d-states of Ti stimulate its
adsorption onto F ions. Ab initio calculations show that Ti
may segregate to the interface, decreasing the energy of
CaF2/Me–Ti system. Based on the results of thermodynamic and DFT analyses, it is proposed that Ti segregation
at the interface may be considered as the source of the
improved wetting.
S. Barzilai
NRC-Negev, P.O. Box 9001, 84190 Beersheba, Israel
N. Froumin (&) E. Glickman D. Fuks N. Frage
Department of Material Engineering, Ben-Gurion University
of the Negev, P.O. Box 653, 84105 Beersheba, Israel
e-mail: [email protected]; [email protected]
Introduction
In general, pure non-reactive liquid metals (Cu, Ga, In,
Ag, Au, and Sn) do not wet ceramic substrates (oxides,
carbides, and nitrides). For these systems, the wetting
improvement is achieved by adding active elements, such
as Ti, Zr, or V, to the melt. It is well established that the
effect of these elements on the wetting of ceramic substrates is attributed to chemical interaction between the
melt and the substrate at the interface and the formation
of a new solid interfacial layer, which consists of the
active element and the non-metallic component (oxygen,
carbon, nitrogen, or boron) originating from the substrates
[1–8].
Alkaline earth fluorides are relatively stable compounds, and therefore may serve as appropriate materials
for containers for the storage and transportation of reactive melts in which chemical interactions between the
melt and the container must be avoided. To estimate the
thermodynamic stability of fluorides, the standard Gibbs
formation energy for various fluorides was calculated [9]
and is presented in Fig. 1. According to the reported data,
CaF2 has the largest negative Gibbs formation energy and
may be considered as the most prospective candidate for
such applications. On the other hand, the high thermodynamic stability of the alkaline earth fluorides may lead
to the lack of wetting of these compounds by liquid
metals and thus to difficulties when brazing this type of
solid to metals and ceramics.
Despite the technological importance of alkaline earth
fluorides, the number of investigations of the interfacial
interaction between fluorides and liquid metals, as well as
of the wetting behavior in these systems was limited before
we started to study these compounds about 7 years ago.
The main reported results of Naidich, Krasovsky, and
123
J Mater Sci
200
Methodology
AuF2
[kJ/mol F2 ]
0
-400
CuF2
5
6
7
8
9
10
11
12
13
15
14
16
MoF3
17
-600
E
G
H
I
J
K
L
M
O
N
Δ
-800
F
-1000
1000
1200
1400
P
Q
18
NiF2
WF4
SnF2
FeF2
InF
CrF2
GaF
R
TiF3
ZrF3
AlF
BeF2
MgF2
ScF3
ErF3
LiF
BaF2
CaF2
1600
Temperature [K]
Fig. 1 The standard Gibbs formation energy for various fluorides.
The thermodynamic data were extracted from Thermodynamic
Database SSUB3, version 3.1 [9] and normalized to 1 mol of F2
coworkers [10–18] present macroscopic observations of the
contact angle obtained by sessile drop wetting experiments
with pure liquid metals (Cu, Au, Ag, Ga, Sn, Pb, and Al)
and their alloys with active additives (Ti, Zr, Hf, V, Cr, and
Nb). The authors observed that pure metals did not wet the
fluorides over a wide temperature range, up to 1423 K [10,
11, 15], and the effect of active elements on wetting
depends on the nature of the liquid metal solvent. It was
suggested [10–18] that the improved wetting occurs due to
the interaction of Ti with the CaF2 substrate and to the
formation of titanium fluorides as a liquid phase at the
interface. The contribution of Naidich and coworkers to
understanding the processes that take place at the fluoride/
liquid metal interface is very important; however, the
proposed mechanism behind the wetting behavior in these
systems is rather problematic and cannot be accepted. It
does not explain the experimental results for the CaF2/Cu–
Ti system, and the unusual behavior observed in the CaF2/
Sn–2 at% Ti system, where non-monotonic change in the
contact angle as a function of temperature was revealed.
Moreover, these authors have tried to find a correlation
between standard Gibbs formation energy of the fluorides
and the values of contact angle in the fluoride/metal systems. This approach is too simplified and does not take into
account the thermodynamic properties of the liquid solution, whose nature and composition strongly affect the
interfacial interaction and, therefore, the wetting behavior.
In this perspective article, the results of our systematic
experimental investigation of the alkali earth fluoride/Me
systems (mostly related to the CaF2 substrate) accompanied
by classical thermodynamic and ab initio analysis performed for clarifying the nature of wetting phenomena are
presented and discussed.
123
Experimental procedures
Wetting experiments were performed by the sessile drop
method at various temperatures in a vacuum furnace (10-5
torr). The alloys (0.1–0.3 g) were prepared in situ using the
appropriate quantities of the corresponding elements. The
heating profile consisted of two steps: 10°/min up to 70 %
of the target temperature, followed by 50°/min. The contact
angles were determined from a Nikon 990 Coolpix digital
camera magnified images using ‘‘Image Pro 4’’ software.
The substrates for the sessile drop experiments were
prepared by hot isostatic pressing of CaF2 powder (0.5–8lm particle size and 99.99 % purity) at 1273 K under
100 MPa. The relative density of the substrates was
[99 %. For wetting experiments, the substrate surface was
polished down to 1 lm using a diamond paste (the measured substrate roughness (Ra) was 0.15 lm), and successively cleaned ultrasonically using acetone and ethanol.
After drop solidification, the samples were cross sectioned and polished down to 1 lm using SiC papers and
diamond paste. The interface structure and the chemical
composition of metal/ceramic interfaces and metallic drops
were characterized using X-ray diffraction (XRD) and
scanning electron microscopy (SEM) (JEOL GSM 5600)
equipped with energy dispersive spectroscopy (EDS) and
wavelength dispersive spectrometry (WDS) analyzers.
Thermodynamic considerations
Thermodynamic analysis based on the Thermo-Calc Software database [9] was performed to evaluate possible
chemical reactions at the fluoride/metal interface. Various
states of CaF2 (gas, liquid, and solid) and liquid metallic
phases were taken into account according to the reactions
presented by Eq. 1(a–f). The equilibrium constants for
these reactions were calculated using Eq. 2.
x
x
ðaÞ Me þ CaF2 ðsÞ ¼ MeFx ðs,l,gÞ þ Ca
2
2
ðbÞ Me ¼ Me(g)
ðcÞ CaF2 ðs) ¼ CaF2 ðg)
ðdÞ MeFx ðs,l) ¼ MeFx ðg)
ðeÞ CaF2 ðs) ¼ Ca þ F2 ðg)
ðfÞ Ca ¼ Ca(g)
DG0i
Ki ¼ exp :
RT
ð1Þ
ð2Þ
Here, DG0 represents the standard Gibbs energy and K is
the equilibrium constant. The underlined symbols in
Eq. 1(a, b, e, f) correspond to the components in the liquid
J Mater Sci
solution; s, l, and g denote the solid, liquid, or gaseous
phases. The subscript i corresponds to reactions a–f.
Results and discussion
Wetting behavior and interface in the CaF2/Me systems
Ab initio calculations
The experimental results on wetting kinetics in the CaF2/
Me (Me = Ga, In, Al, Ge, and Cu) systems are given in
Fig. 2 [25]. The metals that were studied can be divided
into two groups: metals with low melting temperatures (Ga
and In) and metals with relatively high melting temperatures (Al, Ge, and Cu). The values of the contact angle for
Ga and In at 1173 K as a function of the duration of contact
are shown in Fig. 2a. In these systems, the contact angles
are significantly [90° and do not change with time. At
higher temperature (1423 K), the initial contact angle is
close to 120°; for In, no change in the contact angle was
observed, while for the CaF2/Ga system the contact angle
decreases monotonically with contact duration (Fig. 2b).
These results are similar to the results reported in [10, 15].
For the second group of the metals, at 1423 K relatively
high values of initial contact angle were observed (Fig. 2c).
The contact angle for Cu and Ge does not change with
time, while the contact angle for the CaF2/Al system
decreases rapidly from 140° to 92°. This feature is well
known for Al and is attributed to the formation of a volatile
aluminum sub-oxide and deoxidation of the drop surface
during heating under vacuum at T [ 1100 K [1]. A unique
spreading behavior (monotonically increasing contact
angles with time) was detected for Ge, Cu, and Al at
T = 1523 K (Fig. 2d). No evidence of new phases or
The thermodynamic approach is useful to clarify the role
of chemical interactions in wetting phenomena. However,
it does not provide information about the nature of the
bonding at the interface on the atomic level. Such
information can be obtained from ab initio calculations
in the framework of the density functional theory (DFT)
[19, 20]. DFT is an approach that allows performing
quantum mechanical calculations of different electronic
and atomic properties of materials. It uses the input
information about the constituents (types of atoms) in the
system under consideration and may venire data on
the structure. The theory considers the total energy of the
system as a functional that depends on the density of
electrons.
DFT was applied to understand the bonding nature of
Me atoms with the CaF2 substrate. The DFT calculations
were carried out using the full potential augmented plane
waves ? local orbitals (FP APW ? lo) method as
implemented in the WIEN 2k code [21, 22]. In this code,
the core states are treated fully relativistically and the
valence states are treated using a scalar relativistic treatment. The details of our DFT calculations are reported
elsewhere [23, 24].
In
Ga
120
130
125
120
115
In
Ga
110
(a)
Contact angle, deg.
Contact angle, deg
135
110
100
90
(b)
105
80
0
10
20
30
40
50
0
10
20
30
40
Time, min
Time, min
Ge
Cu
Al
130
120
110
100
(c)
Contact angle, deg
130
140
Contact angle, deg
Fig. 2 Contact angle variation
with time in the CaF2/Me
systems at different
temperatures. a 1173 K,
b 1423 K, c 1423 K, and
d 1523 K [25]
125
Ge
Cu
Al
120
115
110
(d)
90
105
0
10
20
Time, min
30
40
0
10
20
30
40
Time, min
123
J Mater Sci
In
Ge
10 μm
CaF2
Cu
50 μm
CaF2
CaF2
50μm
Fig. 3 SEM images of the interface in the CaF2/Me systems after wetting experiments at 1423 K [25]
traces of Ca in the melts was detected by SEM/EDS
analysis in the CaF2/Me (Me = Cu, Ge, In) systems
(Fig. 3). However, in the CaF2/Al system, groove formation at the metal/ceramic interface was observed (Fig. 4b).
Within the Al drop, a detectable quantity of Ca in the form
of Ca-containing inclusions and porosity (see the arrows in
Fig. 4a) was revealed. These observations reflect the
chemical interaction between the substrate and the liquid
Al.
To verify the ability of a liquid metal to react with the
CaF2 substrate, thermodynamic calculations were performed. It was taken into account that the interaction may
lead to the formation of fluoride phases and to dissolution
of Ca in the melt (chemical reaction 1a).
According to the Gibbs phase rule, the ternary Ca–Me–F
system has two degrees of freedom. If the three phases
(solid CaF2, liquid Me–Ca solution, and gaseous phase
consisting of vapor of metals and fluorides) are in
Fig. 4 SEM image of the
interface between Al and CaF2
substrate after wetting
experiments at 1423 K. The
arrows point to the Al–Ca
inclusions (a) and AFM pattern
of the CaF2 substrate, which
was in contact with molten Al at
1273 K for 30 min (b) [25]
equilibrium, then, at each temperature, the composition of
the gaseous phase depends on the composition of the metal
solution, i.e., on the activity of Ca in the melt. Preliminary
thermodynamic analysis indicated that the partial pressures
of MeF2 and MeF3 fluorides are several orders of magnitude lower than that of the MeF, and no condensed fluoride
phases may be formed. The calculated partial pressures of
the monofluorides and the vapor pressure of Ca as a
function of temperature are shown in Fig. 5a, b for two Ca
activities in the melt. The horizontal line in these figures
corresponds to the vacuum conditions (10-8 atm) in our
experimental set-up. As is seen from Fig. 5, at any temperature and for both activities, the partial pressure of
fluorides (and as a consequence CaF2 corrosion) decreases
in the order AlF [ GaF [ InF [ GeF [ CuF. Moreover,
for a fluoride such as AlF, with a partial pressure much
higher than the pressure in the vacuum chamber, the corrosion can be accentuated by the formation of bubbles that
Area around the drop,
far from the Al drop
Al
Z 821μm
CaF 2
20μm
aCa=10-8
AlF
1E-6
GeF
1E-9
GaF
1E-12 InF
CuF
Ca
(a)
1E-15
Partial pressure, atm
Partial pressure, atm
(a)
1E-3
Area beneath the
liquid Al drop
1E-3
(b) X 63.45μm
aCa=10-4
Y 66.07μm
AlF
Ca
1E-7
1E-11
GeF
GaF
CuF
InF
(b)
1E-15
900 1000 1100 1200 1300 1400 1500
900 1000 1100 1200 1300 1400 1500
Temperature, K
Temperature, K
Fig. 5 Gaseous phase composition as a function of temperature for two values of Ca activity in the melt (a aCa = 10-8, b aCa = 10-4). The
horizontal line corresponds to the total pressure in the experimental set-up [25]
123
J Mater Sci
6
10
Neck-formation criterion
3
10
0
10
-3
10
-6
10
-9
CaF2/Sn
CaF2/Ga
CaF2/In
CaF2/Bi
NaCl/Sn
NaCl/Ga
NaCl/In
10
NaCl/Bi
are probably responsible for the pores observed in the
solidified metal. The relatively high corrosion rate of CaF2
in contact with Al at 1423 K explains the grooves formed
close to the liquid meniscus (Fig. 4b) and the lower contact
angle observed in this system. The behavior of liquid Ga at
1173 K is similar to that of low reactivity metals In, Ge,
and Cu (Fig. 2a), but at higher temperature (1423 K,
Fig. 2b) corrosion may be significant in view of the high
value of PGaF.
Unique wetting kinetics (Fig. 2d), demonstrated by the
increase of the contact angle with time (dewetting), needs
special consideration. The generally accepted explanation
of dewetting behavior is related to a liquid metal film,
which is unstable in contact with a solid substrate and
transforms to drops [26, 27]. Another mode of dewetting
was observed in the Al2O3/Al system [28–30]. In this
system, the contact angle initially decreased due to significant evaporation of the Al drop, which is strongly
‘‘pinned’’ to the substrate. At a certain moment, when the
system was far enough from the equilibrium state, the drop
‘‘jumped up’’ to achieve its equilibrium contact angle and
an apparent dewetting was observed. The dewetting in the
CaF2/Me systems may be attributed to the rates of evaporation of the metals and to the rate of sublimation of the
substrate. An apparent dewetting occurs when the Me and
the substrate have comparable vapor pressures and evaporate simultaneously. In this case, the sublimation of the
substrate occurs only from the free surface around the drop,
where a neck-shape contact between the metal and the
substrate is formed (Fig. 6), causing an apparent increase
of the contact angle as shown for Cu and Ge in Fig. 2d.
To understand the apparent dewetting phenomenon, a
model that considers the geometric characteristics of the
metal/ceramic interface and the thermophysical properties
of the metals and the substrates was proposed in [31]. It
was found that the neck-shape geometry of the interface
_
will be formed when the rate of the substrate thinning (h)
due to sublimation of the substrate is higher than the rate of
decrease of the substrate/melt contact area ( r ). According
to the model, the dominant factor that affects the shape of
_ r) for CaF2
Fig. 7 Illustration of the neck-formation criterion (ratio h/_
and NaCl in contact with various metallic melts at 1000 K
the interfacial contact in the investigated systems is the
ratio between the equilibrium vapor pressures of the substrate and of the liquid metals. The model [31] was confirmed by additional wetting experiments for four liquid
metals (Bi, In, Sn, and Ga) on two substrates (CaF2 and
NaCl) with different evaporation rates. Figure 7 exhibits
the results of calculations for 1000 K. As can be seen, the
neck-shape should appear only for the NaCl/Me systems,
where the neck-formation criterion is satisfied. This shape
should not appear in the CaF2/Me systems, where the neckformation criterion fails. Such dissimilar behavior of the
systems is attributed to the differences in the substrate
vapor pressure. The vapor pressure of NaCl at 1000 K is
10-4 atm, while for CaF2 it is 10-13 atm.
No changes at the interface were observed for the CaF2/
In system at 1000 K in accordance with the above model,
and the contact angle remains constant. At the same time,
for the NaCl/In system at this temperature, a significant
sublimation of the substrate occurs around the drop and the
formation of a neck-shape contact is definitely seen. After a
few minutes, the neck has broken down and a new one is
formed in a cyclic manner. The suggested model reflects
Fig. 6 Macroscopic view of the
Ge drops on the CaF2 substrate
at 1523 K after a 10 min,
b 20 min, and c 30 min. The
thickness of the substrate is
indicated by the arrows [25]
2mm
(a)
(b)
(c)
123
J Mater Sci
(a)
120
100
Ge-2at%Ti
80
60
Ga-2at%Ti
Sn-2at%Ti
40
Contact angle, deg
Au-2at%Ti
Au-Ti (1373K)
100
Ge-Ti (1373K )
80
Ga-Ti (1173K)
60
Sn-Ti (1173K)
40
In-2at%Ti
20
0
5
10
15
20
Time, min
the experimental observations for the NaCl/Me and CaF2/
Me systems as illustrated in Fig. 3 from Barzilai et al. [31].
For the first system, the formation of the neck-shape
interface takes place and the apparent contact angle
increases with time, while for the second, the contact angle
and the interface area do not change.
Wetting behavior and interface in the CaF2/Me–Ti
systems
Previous discussion demonstrates that evaporation of the
materials in the systems may affect the apparent contact
angle. To prevent the effect of evaporation, the experiments were carried out at relatively low temperatures,
where the evaporation of the metal and/or of the substrate
is negligible. The measured data on spreading kinetics for
Me–2 at% Ti alloys on CaF2 substrate and the concentration dependencies of the contact angle for the CaF2/Me–Ti
systems are presented in Fig. 8. Experimental results
demonstrate that the addition of 2 at% Ti to the melt
improves the wetting, and Ti-induced effect depends on the
nature of the Me (Fig. 8b). The improved wetting is more
significant for In–Ti melt; moderate decreases of the contact angle are observed for the Sn–Ti and Ga–Ti alloys,
while only limited changes occur for the Ge–Ti and Au–Ti
melts. Krasovsky and Naidich [10, 16] suggested that a
decrease in the contact angle in the CaF2/Me–Ti systems
occurs as a result of the formation of a condensed Ti–
fluoride at the interface. According to Krasovsky and
Fig. 9 Representative SEM images of the CaF2/Me–Ti interfaces
123
(b)
120
Contact angle, deg.
Fig. 8 Wetting kinetics a and
final contact angles b for
various CaF2/(Me–Ti) systems
[35]
25
30
35
In-Ti (1123K)
20
0
1
2
3
4
5
6
7
8
9
10
Ti concent. at.%
Naidich [10, 16], this condensed phase decreases the
liquid–solid interfacial energy and, therefore, decreases the
contact angle. However, no evidence of new phase formation at the interface was detected by our SEM/EDS
analysis (Fig. 9) for all the investigated systems.
To elucidate the role of Ti as an active element in the
studied systems, thermodynamic analysis and DFT calculations were carried out. To clarify the possibility of formation
of interfacial Ti–F phases in the CaF2/Me–Ti systems, let us
consider the thermodynamic aspect of the problem.
Titanium displays high affinity to fluorine and forms
various stable fluorides [32]. The most stable titanium fluoride in the 900–1473 K temperature range is TiF3, which
melts at 1473 K [9]. Let us assume for a moment that the only
reason for existence of TiF3 in gaseous phase in the experimental chamber is its formation according to the reaction
Ti þ 1:5CaF2ðsÞ ! TiF3ðgÞ þ 1:5Ca
ð3Þ
This reaction corresponds to three-phase (gas–liquid–
solid) equilibrium. In this case, the partial pressure of TiF3
depends on the temperature and on the activity of Ca in the
melt. This partial pressure as a function of temperature for
different activities of Ca in the melt was calculated (see
Fig. 10) for the CaF2/In–Ti system using the equilibrium
a1:5 P
constant of the reaction ðK ¼ CaaTiTiF3 Þ: K was derived from
the standard Gibbs energies [9] of the reaction (3). The
activity of titanium was estimated using its activity
coefficient (ðc0Ti ¼ 0:87 [33]) for dilute In–Ti solutions.
J Mater Sci
detected by XPS in [35] probably was formed during drop
solidification and cooling.
In the absence of a new compound at the interface, the
wetting improvement may occur due to the interplay
between the surface and the interfacial energies. We
assume that the surface energy of the substrate (cSV ) is
constant and Ti has only minor effect on the magnitude of
cLV [36]. According to Young’s equation, wetting
improvement may be attributed to the decrease of the
solid–liquid (SL) interfacial energy (cSV ) due to Ti segregation at the interface. To understand the specific mechanisms that lead to the improved wetting ab initio
calculations were performed
4
0.01
Pressure, atm
3
1E-6
2
1E-10
1
1E-14
1100
1200
1300
1400
Temperature, K
Ab initio calculations
Fig. 10 The partial pressure of TiF3 as a function of temperature for
the In–3.0 at.% Ti alloy at various Ca activities (aCa): 1 10-4, 2 10-8,
and 3 10-10. Curve 4 corresponds to the equilibrium partial pressure
of solid TiF3
Whereas a full evaluation requires substantial computer
resources, qualitative information can be gleaned from
modest calculations, involving a limited number of metal
atoms in a cell [37, 38]. In our calculations, the slab model
was applied to construct the supercell and to simulate the
surface of the substrate. We limit ourselves to consideration of the wetting of the (111) F-terminated CaF2 surface
and do not consider other surfaces, although the experiments were carried out on polycrystalline substrates. The
reason is that this surface has the lowest surface energy
compared with other low-index surfaces in CaF2 [39].
As a first step, the adsorption of single adsorbates was
investigated to elucidate the nature of the bonding between
the Me atoms and the CaF2 substrate. To reduce the
computational expense, we used a one-sided adsorption
model for the Me/CaF2(111) interface [40]. We considered
three atomic configurations on the F-terminated CaF2(111)
surface (Fig. 11) and used a supercell (periodic boundary
conditions) containing a nine-layer slab with three layers of
Ca, six layers of F, a vacuum separation of *10 Å
between the slabs, and one Me atom above each site, giving
a 10-atom supercell, thus simulating one monolayer (ML)
of Me on the substrate.
The formation of solid TiF3 will occur if the calculated
partial pressure for gaseous TiF3 will be higher than the
equilibrium vapor pressure for reaction
TiF3ðsÞ ¼ TiF3ðgÞ
ð4Þ
As is seen from Fig. 10, all the calculated P(T) curves
are located lower than P(T) curve for reaction (4). Thus,
solid TiF3 could not be formed at the interface and the
observed improved wetting cannot be attributed to the
formation of the solid TiF3.
The decrease of the contact angle may occur also due to
precipitation of a thin layer of Ti–In intermetallic at the
interface. It was shown in [34] that the composition of In–
Ti drops changes only slightly during wetting experiments
and corresponds to a single-phase region of the In–Ti
system. If the drop and the interface are in equilibrium (the
activities of In and Ti in liquid volume and in a nearsurface substrate liquid layer are the same), then intermetallics cannot precipitate at the interface. Thus, a region of
a few tens of nanometers thick close to the interface
Fig. 11 Configurations of the
sites on a F-terminated CaF2
(111) surface considered for Me
adsorption. i Top view and ii
three-dimensional illustration.
Sites 1, 2, and 3 correspond to
the cases simulating the Me
adsorption atop F atoms, atop
Ca atoms in the layer underlying
F atoms, and atop interstitial site
between these two atoms,
respectively [43]
1 ML of Me on CaF2(111) sites
(ii)
(i)
Site(1)
Me
Site(2)
Site(3)
1
2
3
F
Ca
123
J Mater Sci
equilibrium distance between the adsorbed atoms and the
substrate surface remains almost unchanged. The important
conclusions drawn from these calculations are: (a) all
considered Me atoms and Ti prefer to occupy the sites onto
F atoms on the surface; and (b) bonding of these atoms
with the underlying F atom is almost independent of their
atomic fraction on the surface.
The redistribution of electrons due to adsorption allows
visualization of the formation of bonds between the
adsorbed atom and the substrate. The differential electron
densities—the differences between the electron density of
the system and the sum of the electron densities of the
individual atoms—were calculated for the clean CaF2(111)
surface and for the most stable adsorption site of the CaF2/
Me system. These differential electron densities are shown
in Fig. 13. For the CaF2(111) surface, similar electron
density distributions are observed for the F atoms on the
surface and for those inside the slab (Fig. 13i). This distribution is hardly affected when 1 ML of Au atoms is
brought toward the slab (Fig. 13ii), and slightly affected
when 1 ML of Sn or In is adsorbed on the surface
(Fig. 13iii, iv). The situation is quite different for Ti, V, or
Zr. As is seen in Fig. 13v and vi, there is a considerable
difference between the electron distributions around the
surface F atoms and the ‘‘bulk’’ F atoms. The addition of 1
ML of Ti onto the substrate increases the electron densities
in the Ti–F bonds and changes the distribution near the
surface atoms of the slab. The same is found for Zr–F and
for V–F bonds. The effect of Ti coverage may be found
when Fig. 13v and vii are compared: the decrease of the
distance between the Ti atoms increases the electron density within the layer. This indicates the formation of lateral
(parallel to the substrate surface) bonds between the
adsorbed atoms when the coverage increases.
Representative calculations were also carried out for the
slab containing six layers (two layers of Ca and four layers
of F) to estimate the effect of slab thickness, and for a
larger supercell containing 0.5 ML of Me, to evaluate the
effect of lateral interactions within the Me layer. In both
the cases, only minor changes in adsorption energy were
obtained.
The effects of relaxation (displacements of the atoms
from their geometrically determined sites) are known to be
small for substrates with mostly ionic bonding [41]. The
relaxation in the calculations of the surface energies for
CaF2 was investigated in [39, 42]. It was found that for the
pure CaF2(111) surface, the shift of F atoms in the direction
normal to the surface does not exceed 0.9 % of the lattice
parameter, while for Ca atoms this shift is even smaller.
We investigated also how the relaxation influences the
adsorption energy for the case corresponding to the model
shown as site (1) in Fig. 11, for the CaF2(111)/Ti and the
CaF2(111)/In systems. For both the systems, the changes in
the adsorption energy were \1 %. Therefore, we neglected
slab relaxation in further calculations of the adsorption
energies. Figure 12 presents the computed adsorption
potential curves for CaF2(111)/1 ML Me.
All studied Me atoms interact with the substrate in a
repulsive manner, both when they are placed onto the
calcium atoms (site 2), and when they are placed onto the
valley between the calcium and the fluorine atoms (site 3).
The situation changes when Me atoms are placed onto the
fluorine atoms (site 1). Weak attraction was observed for In
and Sn and a relatively strong attraction was identified for
Ti. Comparing the results of calculations for the adsorption
of 0.5 ML when the adsorbed atoms are well separated
from each other and 1 ML when they are close to each
other, we found that the adsorption energy as well as the
1.0
0.8
0.6
0.5ML
0.6
0.4
site (2)
site (3)
0.2
0.0
-0.2
-0.4
-0.6
1.0
site (1)
site (2)
site (3)
0.4
0.2
0.0
-0.2
-0.4
-1.0
1
2
3
4
5
Adsorption Distance [A]
6
site (2)
site (3)
0.4
0.2
0.0
-0.2
-0.4
-0.6
-0.8
-0.8
CaF2(111)/In
0.5ML
0.6
-0.6
-0.8
site (1)
site (1)
0.8
Adsorption energy [eV]
0.8
site (1)
site (1)
Adsorption energy [eV]
Adsorption energy [eV]
1.0
CaF2(111)/Sn
-1.0
1
2
3
4
5
Adsorption Distance [A]
CaF2(111)/Ti
-1.0
6
1
2
3
4
5
6
Adsorption Distance [A]
Fig. 12 Adsorption energy curves for CaF2(111)/1 ML Me systems. Me = In, Sn, Ti. The adsorption energy curve for 0.5 ML is also displayed
for In and Ti. Sites 1–3 correspond to the positions of the Me atom onto the surface shown in Fig. 12 (1 eV = 1.6 9 10-22 kJ)
123
J Mater Sci
Fig. 13 Cross sections of the differential electron density distribu´
tions (in e/Å3) for i CaF2(111) slab without Me coverage, and for the
preferred configurations of CaF2(111)/Me interfaces. ii Me = Au; iii
Me = Sn; iv Me = In; v Me = Ti; vi Me = Zr; vii results for a
lower density of adsorbed atoms (0.5 ML) with Me = Ti [43]
To elucidate the nature of the bonding of the adsorbed
atoms with the substrate, calculations of Local Densities of
States (LDOS) for the electrons were performed in [43]. As
illustrated in Fig. 14, the LDOS for In, Cu, Au, and Sn
have relatively low values in the filled part of the band in
10
10
Ti
Au
Sn
Al
Cu
In
6
(i)
EF
4
2
V DOS
Zr DOS
8
Local DOS
8
Local DOS
Fig. 14 LDOS for the electrons
of the atoms adsorbed on the
CaF2(111) surface. i Au, In, Sn,
Cu, Al, and Ti; ii Zr and V. The
calculations refer to the
preferred sites for adsorption at
the equilibrium distance [43]
the vicinity of the Fermi energy (EF). A detailed analysis of
these LDOS shows that they are mainly attributed to the
p-electrons of In and Sn or to filled d-states for Cu and Au.
This is consistent with the observed low adsorption energy
(and even repulsive interaction for Au). The LDOS results
for Ti, V, and Zr are different. These atoms have a high
LDOS in the vicinity of EF, representing the formation of a
partly filled band, mainly attributed to the d-electrons. The
LDOS for these atoms are about 5–80 times higher compared with the LDOS for the other atoms (2–8 states/eV
compared with 0.1–0.4 states/eV). Thus, we may conclude
that the relatively strong adsorption of Ti on the CaF2(111)
F-terminated surface occurs due to partly filled d-states in
the metal. This means that the wetting enhancement
mechanism identified for the CaF2/(In–Ti) system [34] may
possibly be generalized to other additives (replacing Ti)
that have partly filled d-states. This conclusion is supported
by our computations for Zr and V on CaF2(111), both
containing partly filled bands occupied by d-electrons. The
adsorption energies (about 1 eV) for Zr and V are very
similar to those obtained for the CaF2(111)/Ti system. The
electron density distributions for Zr (Fig. 13vi) and V
atoms are also very similar to those obtained for Ti
(Fig. 13v).
For evaluating the lateral interactions between the
adsorbed atoms, some atomic configurations for Sn–Ti and
In–Ti solutions on the CaF2(111) surface were considered.
At this stage, the aim of the calculations was to determine
the lateral Me–Me, Me–Ti, and Ti–Ti interactions in the
field of the substrate surface. The adsorption calculations
were performed for Me atoms onto the fluorine atom,
which was found earlier (Figs. 11i, 12) to be the favorable
adsorption site. Three types of CaF2(111) surface conditions were considered: (i) clean surface, (ii) surface with
0.5 ML of Me (In or Sn) atoms already adsorbed at their
equilibrium distance from the surface, and (iii) surface with
0.5 ML of Ti atoms already adsorbed on it (see Fig. 15).
0.5 ML of Me or Ti was placed above the fluorine atom and
the total energies of the substrate/0.5 ML Me systems were
calculated for Me-surface distances in the interval 2–5 Å.
EF
(ii)
6
4
2
0.4
0.2
0.0
0.4
0.2
0.0
-1.0
-0.5
0.0
Energy, eV
0.5
1.0
-1.0
-0.5
0.0
0.5
1.0
Energy, eV
123
J Mater Sci
atoms, calculated for each surface configuration at various
distances (z) from the surface of the substrate. Eslab is the
total energy of the slab calculated for each surface condition (i, ii, or iii) without the additional 0.5 ML of Me, and
EMe refers to the total energy of the additional 0.5 ML of
Me without the slab beneath it. To obtain an accurate
interpolation, especially in the vicinity of the minimum, we
apply Morse-type function (Eq. 5) to approximate the
adsorption potential curves
h
i
0
0
U ¼ Eads e2aðzz Þ 2eaðzz Þ :
ð5Þ
(b)
(a)
Me
(Sn or In)
Ti or Me
F
Ca
Here, Eads represents the adsorption energy at the equilibrium distance z0 from the surface of the substrate, and a is a
constant related to the width of the adsorption potential
curve in the vicinity of the minimum. The parameters Eads,
z0, and a are presented in Table 1.
Different interactions are obtained for each surface
configuration and for each system (Fig. 16). Weak attraction *0.2 eV/atom is revealed when 0.5 ML of In or Sn
are coming closer to the clean surface. A stronger attraction
exists when these atoms are placed on the surface that
already contains 0.5 ML of Me. The presence of Me adatoms at the surface increases the adsorption energy of the
additionally adsorbed Me atoms to *1.4 eV/atom for the
In atom and to *2.2 eV/atom for the Sn atom. The greatest
adsorption energies were obtained for the surface configuration that already contained Ti adatoms. The presence of
Ti adatoms increases the adsorption energy of the additionally adsorbed Me atoms to *2 eV/atom for the In atom
Fig. 15 Configurations of the F-terminated CaF2(111) surfaces
considered for adsorption. a Top view of a clean (111) surface;
b three-dimensional illustration of 0.5 ML of Me (Sn or In) placed
above a substrate, which is already covered by 0.5 ML of Ti or Me.
The rectangular scheme in (a) represents the top view of the super
cell used for the adsorption calculations. The rhombus scheme
represents the top view of the slab super cell used for further DFT
calculations; the diagonal represents the plane in which the cross
sections for the electron density maps are shown in Fig. 14 [24]
The adsorption energy curves (Uads) for In and Sn for
the three types of CaF2(111) surface conditions were cal
culated according to: Uads ðzÞ ¼ Esys ðzÞ Eslab þ EMe
and are presented in Fig. 16. For these configurations,
Esys ðzÞ is the total energy of the slab with 0.5 ML of Me
Fig. 16 The adsorption energy
curves for a 0.5 ML of Sn
(a) and In (b) computed for
different distances from the slab
surface, and for different surface
conditions (i)–(iii) [24]
(a)
0
-1
Adsorption energy [eV]
Adsorption energy [eV]
-1
-2
-3
Clean surface
Surface containing 0.5ML Sn
Surface containing 0.5ML Ti
-4
2
4
6
8
Adsorption Distance [A]
123
(b)
0
-2
-3
Clean surface
Surface containing 0.5ML In
Surface containing 0.5ML Ti
-4
10
2
4
6
8
Adsorption Distance [A]
10
J Mater Sci
Table 1 Parameters that characterize the adsorption of Sn and In
atoms on CaF2(111) surface for surface conditions (i)–(iii)
CaF2(111) surface
condition
Adsorbed
Me
Interaction parameters
from Eq. 5
A (Å-1) z0
(Å)
Eads
(eV)
Clean surface
0.5 ML of Me adatoms
0.5 ML of Ti adatoms
Sn
0.23
1.12
2.47
In
0.22
1.57
2.66
Sn
2.16
0.55
1.90
In
1.42
0.54
2.80
Sn
3.67
0.70
2.62
In
2.05
0.70
2.62
Table 2 The bonding energies (eV/bond) for Me–F, Me–Me, and
Me–Ti bonds in the vicinity of the CaF2(111) surface [24]
F
In
Sn
Ti
In
0.22
Sn
0.23
0.3
–
0.46
–
0.48
0.86
and to *3.7 eV/atom for the Sn atom. Keeping in mind the
previously obtained result that the interaction of adsorbing
atoms with the underlying fluorine atoms is almost independent of the atomic fraction of adsorbed atoms (see
Fig. 13), we can ascribe the increase in the adsorption
energies obtained here to the formation of lateral bonds
between the newly adsorbed atoms with those already
existing at the interface.
The lateral Me–Ti interactions for the studied systems
may be estimated in the framework of nearest neighbor
approximation (NNA) using the calculated values presented in Table 1. The resulting Me–Me and Me–Ti bond
energies in the vicinity of the CaF2(111) surface (Table 2)
indicate that the Me–Ti attractions are stronger than the
Me–Me attractions and that the attraction of Ti–Sn
(0.86 eV) is much stronger than that of the In (0.46 eV).
These results correlate well with the thermodynamic data,
which indicate a relatively weak attraction for the In–Ti
system [33, 45] and a strong attraction for the Sn–Ti [9, 45]
system. Analogous calculations for Ti–Ti lateral bonding
energy gave a value equal to 0.75 eV/bond. Using these
bonding energies and keeping in mind that the fluorine
atomic positions at the (111) plane have the FCC-like
structure, and that they dictate the arrangement of the metal
atoms placed over the fluorine atoms, it is possible to
estimate the contribution of Ti atoms to the total energy in
two different situations (Fig. 17), namely: (a) the Ti atom
is surrounded by 12 Me atoms (inside the ‘‘thick’’ Me layer
above the substrate) and (b) the Ti atom is segregated on
the CaF2(111) surface and is surrounded by 9 Me atoms
and 1 F atom (due to the preference for metal adsorption
onto the F atoms, Fig. 12). In case (a), 12 Me–Me bonds
are replaced by 12 new Ti–Me bonds. In this case (using
the bonding energies from Table 1), each Ti atom
decreases the total energy by 4.56 eV for the Sn–Ti system
and by 1.92 eV for the In–Ti system. In case (b), 9 Me–Me
bonds are replaced by 9 new Ti–Me bonds and 1 Me–F
bond is replaced by 1 Ti–F bond, for which the bonding
energy is 0.9 eV (Fig. 12). In this case, each Ti atom
decreases the total energy by 4.09 eV for the Sn–Ti system
and by 2.12 eV for the In–Ti system. Thus, for the
CaF2(111)/Sn–Ti system, condition (a) produces a greater
energy gain compared with case (b). For the CaF2(111)/In–
Ti, the opposite situation occurs: case (b) has lower energy
and, therefore, is preferable compared with configuration
(a).
These results clearly indicate an enhanced Ti segregation at the CaF2 surface from In–Ti melt and a weaker Ti
segregation from the Sn–Ti melt. Thus, due to preferential
Ti adsorption from the liquid, even a small quantity of Ti in
liquid In may be expected to change the interface composition, and thus to decrease the interfacial energy (cSL).
In this case, according to Young’s equation, the driving
force for wetting increases, and improved wetting occurs
(Fig. 8). On the other hand, for the CaF2(111)/Sn–Ti
(a)
CaF2 substrate
(b)
CaF2 substrate
Fig. 17 Schematic illustration of two conditions of the CaF2(111) slab beneath Me–Ti atoms in a close-packed arrangement. a Ti placed
between Me atoms containing 12 Me–Ti bonds, b Ti placed at the interface containing 9 Me–Ti bonds and 1 Ti–F bond [24]
123
J Mater Sci
system, the tendency of Ti to segregate to the interface is
less pronounced, the change of the interface composition is
smaller, and thus a smaller effect on cSL is observed.
Similar conclusions were drawn in [24] by further DFT
calculations performed by placing three metallic layers
above CaF2(111), namely, 1 ML of Ti between two layers
of Me, next to the CaF2(111)surface; or 1 ML of Ti at the
interface, between the fluorine atoms of the CaF2(111)
surface and two layers of Me atoms.
The results of ab initio calculations correlate with the
partial mixing enthalpy for diluted Me–Ti alloys [24]. For
the In–Ti alloys, the partial mixing enthalpy, DHmix(Ti) is
-6.4 kJ/mol and its activity coefficient c0Ti is 0.6 [44]. The
data for Sn–Ti dilute solution DHmix(Ti) = -52.8 kJ/mol
and c0Ti ¼ 0:01 were reported in [44]. The difference in the
DHmix(Ti) values reflects the difference in the Me–Ti
bonding in the melts and may be associated with the degree
of Ti adsorption at the interface. It is clear that the inclination of Ti atoms to segregate at the interface is greater
for CaF2(111)/In–Ti systems than for the CaF2(111)/Sn–Ti
system.
This consideration may serve as a good starting point for
explanation of the differences observed for all the investigated Me–Ti alloys in the wetting experiments (Fig. 8b).
The correlation between the effect of Ti additions and the
DHmix(Ti) values for various systems is illustrated in
Fig. 18. For high negative value of DHmix(Ti), Ti dissolved
in the melt is strongly bonded to the solvent atoms, and its
adsorption and effect on the contact wetting angle are
limited. In contrast, if Ti is weakly bonded to Me (low
DHmix(Ti) values), the degree of the Ti adsorption is
greater and its effect on the cSL value, and therefore on the
wetting angle, is more significant.
2mm
In
140
Sn
Ga
Au
Ge
Au-Ti
Ge-Ti
Contact angle, °
120
100
80
60
Sn-Ti
40
20
Ga-Ti
Pure Me/CaF2
In-Ti
0
Me- 2at% Ti /CaF 2
20
40
60
-Δ HTi
80
mix
100
120
140
, kJ/mol
Fig. 18 The contact angle for pure Me melts and for Me melts
alloyed with a small addition of Ti as a function of the Ti partial
mixing enthalpy [35]
123
Adsorption energy and interface energy
In a further investigation [45], we have applied the results
of DFT calculation to the analysis of the experimentally
observed changes in wetting angle in the CaF2/In–Ti system to clarify the effect of Ti adsorption on the wetting. As
mentioned above, the comparison of adsorption energies
for In and Ti suggests preferential adsorption of Ti onto the
F atoms on the substrate surface. The decrease of the
interfacial energy DcSL between CaF2 and In–Ti melt
depends on the equilibrium surface coverage, hTi, of the
interface by Ti adatoms [46, 47]. At a given temperature
and Ti concentration, C, hTi depends on the binding energy
of Ti with the interface. Note that the binding energy is
positive and represents the corresponding adsorption
energy taken with the opposite sign. In contrast to the
situation considered above in the framework of DFT
approach, where adsorption of Ti atoms occurs from the
gas, in the wetting experiment adsorption occurs from
the condensed state, namely, the In–Ti liquid solution. In
the following, we consider an elemental act of adsorption as
the transfer of Ti atoms from the liquid drop to the position
atop the F atom of CaF2 at the SL interface, where the Ti
atom substitutes for In and the latter returns to the drop and
occupies the place of the removed Ti. Calculation of the
energy DETi of adsorption of Ti from the liquid phase to the
(111)F-terminated surface of CaF2 should take into account
the formation of the Ti–F bond instead of the In–F bond at
the SL interface, the breaking of Ti–In bonds, and forming
instead In–In bonds within the liquid drop, as well as all
other changes in the coordination and the partial energies of
the involved inter-atomic interactions, including the lateral
interaction of Ti adatoms with their Ti neighbors within the
adsorption layer. The interactions between In and Ti atoms
in the liquid solution can be estimated quite accurately in
the framework of the NNA for regular solutions (NNARS)
[48]. The calculation of interactions of Ti and In with F
atoms of the substrate surface and of the lateral interactions
In–In, Ti–Ti, and Ti–In within the adsorption layer require a
sophisticated approach because they are affected by the
potential field of the CaF2 substrate [45]. Using the obtained
DETi, the surface coverage hTi of the SL interface with Ti
adatoms and the corresponding decrease DcSL of the interfacial energy cSL caused by Ti adsorption from the liquid
solution with the given Ti content can also be estimated.
The bonds that were taken into account are: 12 bonds in the
liquid drop, 6 bonds for the lateral interaction within the
adsorption layer, 3 bonds between Ti or In atom in the
adsorption layer and in the adjacent layer of the liquid
above it, and 1 bond between the Ti or In atom and the F
atom from the substrate surface. These numbers correspond
to the simplifying assumption that the (111)-terminated
close-packed FCC-like structure simulating the liquid is
J Mater Sci
adjacent to the (111)-terminated surface of CaF2. Such an
assumption is justified by the fact that the metal atoms (both
In and Ti) occupy the positions beyond F atoms and by the
coordination of F atoms on the (111) surface of CaF2 that
corresponds to the atomic arrangement in the (111) plane of
FCC lattice.
The binding energies ETi–Ti and EIn–In for the pairs Ti–Ti
and In–In in the melts were estimated from the sublimation
energies 4.3 and 2.4 eV for Ti and In, respectively [47].
The binding energy ETi–In = 0.34 eV was calculated
within the NNARS approach according to Eq. 6
ETiIn ¼ 0:5ðETiTi þ EInIn Þ DH InTi ;
ð6Þ
where the experimental mixing enthalpy for In–Ti dilute
solution DHIn–Ti = -0.06 eV [33].
The binding energy DETi was found as DETi = ER EA, where ER is the energy of the reference state that
corresponds to the Ti atom inside the liquid solution, while
In occupies the position above the F atoms at the interface.
EA is the energy of the state that corresponds to the Ti atom
adsorbed onto the F-sites at the SL interface. The Ti adatom in this state may have from n = 0 to 6 nearest Ti
atoms. The important result given by the ab initio calculations is that DETi increases linearly with n from 0.2 eV
for n = 0 to 1.16 eV for n = 6 [44], indicating strong
lateral attraction between Ti nearest neighbors in the
adsorption layer. The maximal DETi corresponds to maximum surface coverage hTi of the SL interface with Ti adatoms and is much larger than kT & 0.1 eV at which the
wetting experiments were carried out. In further analyses
for quantitative estimation of hTi, we use the Langmuir
adsorption isotherm [46, 47].
hTi1 ¼ bC=ð1 þ bC Þ
ð7Þ
The detailed explanation of applicability of Langmuir
adsorption model for CaF2/In–Ti may be found in [44].
Here, b = exp (DETi/kT) is the interface enrichment factor.
Equation 7 shows that b = hTi/C is the ratio of the
interface coverage to the bulk concentrations C of the
solute for extremely dilute solutions when bC 1. The
interface enrichment factor in our case is about 105 and 106
for 1123 and 973 K, respectively. Large values of b
indicate that the SL interface coverage hTi approaches 1.
Thus, considerable decrease in the interfacial energy DcSL
associated with the formation of such a dense adsorption
layer should occur. The higher the binding energy DETi, the
lower the temperature, and the lower the bulk Ti
concentration corresponds to the interface adsorption
saturation C*. The concentration dependences H?(C)
and DcSL(C) presented in Fig. 19 demonstrate clearly this
tendency characteristic for the Langmuir adsorption.
Equation 7 with DETi (n = 6) = 1.16 eV yields
hTi? = 0.9988 for In ? 0.5 % Ti at 1123 K, which is
almost complete adsorption saturation. To quantify the
DcSL (DETi, T, C) dependence, we used the Shishkovsky
surface energy isotherm [46, 47]
DcSL ¼ CMAX kT lnð1 þ CbÞ;
ð8Þ
which follows from integration of the Gibbs adsorption
equation for dilute solutions with the use of Eq. 8. Parameter
UMAX in Eq. 8 is the ultimate value of the Gibbs adsorption
(excess number of solute atoms per unit area) at the SL
interface. In our case, UMAX is determined by the surface
density of the Ti adsorption sites onto F atoms. For the
F-terminated (111) surface of CaF2, UMAX = 7.7 9
1018 m-2. For T = 973 K, Eq. 8 yields DcSL = 0.88 J/m2 for
C = 0.5 9 10-2. The cSL for various Ti concentrations C at
the same temperature (973 K) were calculated in a similar way
and depicted as the dotted line ‘‘theory’’ in Fig. 19a. The
DcSL(C) dependence for T = 1123 K was calculated in the
same manner with the above DETi = 1.16 eV and only
slightly smaller UMAX = 6.2 9 1018 m-2 (Fig. 19b).
973K
(a)
Ti concentration, C, at%
Fig. 19 The equilibrium contact angle (H?) and DcSL as a function of
titanium concentration in the melt at 973 K (a) and 1123 K (b). Dotted
lines correspond to the calculation according to Eq. 7 . Solid and open
squares, solid and open triangles correspond to the experimental values
of contact angle and to the values of DcSL calculated directly from the
(b)
Ti concentration, C, at%
experimentally measured contact angles, respectively. The contact
angle data at 973 K are from Naidich [15]; the contact angle data at
1123 K are from Nizhenko and Floka [36]. All calculations of DcSL are
from Glickman et al. [45]
123
J Mater Sci
Comparison with experiments for the system CaF2/
In ? Ti was carried out on the basis of Young equation:
H1 ¼ arccos½ðcSV cSL Þ=cLV ð9Þ
It is clear from this equation that the adsorption of Ti at
LV and/or SV interfaces should inevitably lead to an
increase in the contact angle from its initial magnitude
H?0 = 130° found for pure In. In contrast to this, Fig. 19
shows the decrease of H? from 130° to (25 ± 5)° with the
growth of Ti concentration in In. We can consider two
potential explanations for this observation: (i) formation of
a compound at the SL interface or (ii) a strong decrease in
cSL caused by adsorption of Ti adatoms at the SL interface.
The first scenario is hardly acceptable in our case. The
above thermodynamic analysis, as well as SEM/EDS
observations, shows that a stable compound between Ti
and F should not form in the conditions of our experiment.
The second scenario—strong interface adsorption of Ti—
seems at the moment to be the most likely reason for the
observed wetting improvement.
This is confirmed in particular by our calculations,
which showed close to saturation Ti adsorption at the SL
interface and large reduction in the interfacial energy,
DcSL. To check if the reduction in the interfacial energy
DcSL was great enough to explain the observed reduction in
the wetting angle H? (C, T), the DcSL calculated from
Eq. 8 was compared in [44] with that found from Eq. 9. In
this comparison, we used the experimental angles H0? (T)
and H? (C, T), and assumed that alloying In with Ti does
not change the liquid–vapor (cLV) and the solid–vapor
(cSV) surface energies. This assumption means that wetting
improvement in the studied system is considered to occur
solely due to Ti adsorption at the SL interface. With this,
Eq. 9 reduces to
DcSL ¼ c0SL cSL ¼ c0LV ðcosH1 cosH01 Þ;
ð10Þ
where the subscript zero indicates the surface energies and
wetting angle related to CaF2 in contact with non-alloyed In.
Equation 10 enables estimating DcSL (C) from the known
c0LV [19] and the measured angles H0? and H?(C). Figure 19 shows excellent inverse correlation between the calculated DcSL and experimentally determined wetting angle
H? (C), as well as close agreement between the calculated
and the experimental concentration dependence of DcS (C).
The agreement is particularly convincing because the
experimental results reported in [15, 35] by two research
groups at different temperatures were excellently reproduced using the same binding energy DETi = 1.16 eV found
in our ab initio calculations. It is also important that, as
shown in [43], the maximal surface density, UMAX, for Ti
adsorption sites, which provides the best fit of the theory to
the experiments, appears to be very reasonable and falls in
the narrow range UMAX = (7 ± 0.7) 9 1018 m-2, i.e.,
123
90 ± 10 % of the surface density of the F-sites on the closepacked F-terminated (111) plane of CaF2. All this suggests
that the classical adsorption theory with the fixed binding
energy DETi given by DFT/NNARS provides a self-consistent explanation for all available data on the concentrationand temperature-dependence of the interfacial energy
cSL(C,T) and contact angles in the system CaF2/In ? Ti. The
obtained results support the hypothesis that the decrease in
the SL interfacial energy due to Ti adsorption is the major
factor in evolution of the wetting angle H? with Ti concentration in this system.
Summary
All the investigated pure metals (In, Sn, Ga, Ge, Cu, and
Au), except Al, do not wet the CaF2 substrate in high
vacuum and no evidence of new phase formation at the
interface was found. For the CaF2/Al system at 1423 K, the
contact angle was 92°, and an interfacial interaction, which
leads to the formation of volatile compounds, was detected.
At 1523 K, an increase in the contact angle of Ge, Cu, and
Al as a function of time was observed. It was suggested that
the volatile nature of the substrate was responsible for this
unique behavior. A model that allows predicting the
geometry of the interface during the experiment and the
apparent contact angle was developed and confirmed
experimentally.
Addition of Ti to liquid metals led to the wetting
improvement and its effect depends on the thermodynamic
properties of the Me–Ti liquid solutions. It was predicted
by classical thermodynamic analysis and confirmed by
interface characterizations that the reaction between Ti and
CaF2 does not lead to formation of a new condensed phase
at the interface. In order to clarify the nature of wetting in
these systems, DFT calculations were performed. The
results of these calculations and classical adsorption theory
were applied to analyze the experimental concentrationand temperature-dependence of the wetting angle in the
CaF2/In–Ti system. The results support the assumption that
the wetting improvement can be explained by Ti adsorption
at the interface.
Possible future research
Alkaline earth fluorides with high thermodynamic stability
may serve not only for the storage and transportation of
reactive melts. The monocrystals of these materials have
unique optical properties and are used as windows for optic
devices. These windows usually should be joined hermetically to the devices, and the joining becomes a crucial
aspect in their applications. Thus, further investigations of
J Mater Sci
wetting of highly stable fluorides by various liquid metals
doped with other active elements (V, Cr, etc.) have to be
continued in the directions outlined below.
Drop sucking and drop pushing [49] experimental
approach may provide in situ ‘‘opening’’ of the drop/substrate interface characterized can help to reveal either
adsorption ML, multilayers or precipitates of active element enriched compound formed at the interface.
The classical thermodynamic and ab initio analysis
should be performed for the different alkaline earth fluorides and melts in order to understand to what extend the
suggested approach may be used for the predictions of the
wetting behavior in analogous non-reactive systems.
The mechanism of metallic drops spreading on the
surface of non-reactive fluoride substrates should be clarified. We suggest to apply for spreading kinetics analysis
the ‘‘kink’’ model, which is usually applied to crystal
growth and dislocation climb, together with the energies of
interatomic interactions obtained via ab initio calculation.
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