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

� 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 wet-

ting. 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 demon-

strated 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 thermody-

namic and DFT analyses, it is proposed that Ti segregation

at the interface may be considered as the source of the

improved wetting.

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 sub-

strates 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 com-

pounds, and therefore may serve as appropriate materials

for containers for the storage and transportation of reac-

tive 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 thermo-

dynamic 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

S. Barzilai

NRC-Negev, P.O. Box 9001, 84190 Beersheba, Israel

N. Froumin (&) � E. Glickman � D. Fuks � N. FrageDepartment of Material Engineering, Ben-Gurion University

of the Negev, P.O. Box 653, 84105 Beersheba, Israel

e-mail: nfrum@bgumail.bgu.ac.il; nfrum@bgu.ac.il

123

J Mater Sci

DOI 10.1007/s10853-012-6680-z

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 sys-

tems. This approach is too simplified and does not take into

account the thermodynamic properties of the liquid solu-

tion, 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 per-

formed for clarifying the nature of wetting phenomena are

presented and discussed.

Methodology

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 contactangles 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 (0.5–8-

lm particle size and 99.99 % purity) at 1273 K under100 MPa. The relative density of the substrates was

[99 %. For wetting experiments, the substrate surface waspolished down to 1 lm using a diamond paste (the mea-sured substrate roughness (Ra) was 0.15 lm), and succes-sively cleaned ultrasonically using acetone and ethanol.

After drop solidification, the samples were cross sec-

tioned and polished down to 1 lm using SiC papers anddiamond 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 Soft-

ware 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.

ðaÞMeþ x2

CaF2ðsÞ ¼ MeFxðs,l,gÞ þx

2Ca

ðbÞMe ¼ Me(g)ðcÞCaF2ðs) ¼ CaF2ðg)ðdÞMeFxðs,l) ¼ MeFxðg)ðeÞCaF2ðs) ¼ Caþ F2ðg)ðfÞCa ¼ Ca(g)

ð1Þ

Ki ¼ exp �DG0iRT

� �: ð2Þ

Here, DG0 represents the standard Gibbs energy and K isthe equilibrium constant. The underlined symbols in

Eq. 1(a, b, e, f) correspond to the components in the liquid

1000 1200 1400 1600

-1000

-800

-600

-4000

200

5 67 8

9 1011 12

13 1415 16

17 18

E FG H

I JK L

M NO P

Q R

ZrF3

AuF2

CuF2 MoF

3

WF4NiF

2SnF

2

FeF2

InFCrF

2

AlFTiF

3

GaF

BeF2

MgF2

ScF3

LiFBaF

2CaF2

ErF3

Temperature [K]

Δ

[kJ/

mol

F2]

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

J Mater Sci

123

solution; s, l, and g denote the solid, liquid, or gaseous

phases. The subscript i corresponds to reactions a–f.

Ab initio calculations

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 treat-

ment. The details of our DFT calculations are reported

elsewhere [23, 24].

Results and discussion

Wetting behavior and interface in the CaF2/Me systems

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 tempera-

tures (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. Athigher temperature (1423 K), the initial contact angle is

close to 120�; for In, no change in the contact angle wasobserved, 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 wellknown 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 uniquespreading 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

105

110

115

120

125

130

135

In GaC

onta

ct a

ngle

, deg

Time, min

(a)80

90

100

110

120

Con

tact

ang

le, d

eg.

Time, min

In Ga

(b)

90

100

110

120

130

140

Con

tact

ang

le, d

eg

Time, min

Ge Cu Al

(c)

0 10 20 30 40 50 0 10 20 30 40

0 10 20 30 40 0 10 20 30 40105

110

115

120

125

130

GeCu Al

Con

tact

ang

le, d

eg

Time, min

(d)

Fig. 2 Contact angle variationwith time in the CaF2/Me

systems at different

temperatures. a 1173 K,b 1423 K, c 1423 K, andd 1523 K [25]

J Mater Sci

123

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 forma-

tion 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 per-

formed. 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

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 magni-

tude 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 tem-

perature 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 cor-

rosion can be accentuated by the formation of bubbles that

Ge CuIn

10μm 50μm 50μmCaF2 CaF2 CaF2

Fig. 3 SEM images of the interface in the CaF2/Me systems after wetting experiments at 1423 K [25]

CaF2

Al

20μm

Area around the drop, far from the Al drop

Area beneath the liquid Al drop

(a) (b) Y 66.07μmX 63.45μm

Z 821μm

Fig. 4 SEM image of theinterface between Al and CaF2substrate after wetting

experiments at 1423 K. The

arrows point to the Al–Cainclusions (a) and AFM patternof the CaF2 substrate, which

was in contact with molten Al at

1273 K for 30 min (b) [25]

900 1000 1100 1200 1300 1400 15001E-15

1E-12

1E-9

1E-6

1E-3

(a)

aCa=10-8

Par

tial p

ress

ure,

atm

Temperature, K

AlF

CuF

GeF

GaF

InF Ca

900 1000 1100 1200 1300 1400 15001E-15

1E-11

1E-7

1E-3

(b)

Par

tial p

ress

ure,

atm

Temperature, K

AlF

CuF

GeFGaF

InF

Ca

aCa=10-4

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]

J Mater Sci

123

are probably responsible for the pores observed in the

solidified metal. The relatively high corrosion rate of CaF2in 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 sig-

nificant 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 evapo-

ration 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 evap-

orate 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

the interfacial contact in the investigated systems is the

ratio between the equilibrium vapor pressures of the sub-

strate and of the liquid metals. The model [31] was con-

firmed 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 neck-

formation 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

(a) (b) (c)

2mm

Fig. 6 Macroscopic view of theGe drops on the CaF2 substrate

at 1523 K after a 10 min,b 20 min, and c 30 min. Thethickness of the substrate is

indicated by the arrows [25]

NaC

l/Bi

NaC

l/In

NaC

l/Ga

NaC

l/Sn

CaF

2/B

i

CaF

2/In

CaF

2/G

a

CaF

2/S

n

10-9

10-6

10-3

100

103

106

Nec

k-fo

rmat

ion

crite

rion

Fig. 7 Illustration of the neck-formation criterion (ratio _h/_r) for CaF2and NaCl in contact with various metallic melts at 1000 K

J Mater Sci

123

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 experi-

ments 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 concentra-

tion 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 con-

tact 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

Naidich [10, 16], this condensed phase decreases the

liquid–solid interfacial energy and, therefore, decreases the

contact angle. However, no evidence of new phase for-

mation 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 calcula-

tions 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 fluo-

ride 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 experi-

mental chamber is its formation according to the reaction

Tiþ 1:5CaF2ðsÞ ! TiF3ðgÞ þ 1:5Ca ð3Þ

This reaction corresponds to three-phase (gas–liquid–

solid) equilibrium. In this case, the partial pressure of TiF3depends 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

constant of the reaction ðK ¼ a1:5Ca

PTiF3aTiÞ: 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.

0 5 10 15 20 25 30 3520

40

60

80

100

120

Sn-2at%TiGa-2at%Ti

Ge-2at%Ti

Au-2at%Ti

Con

tact

ang

le, d

eg.

Time, min

In-2at%Ti

0 1 2 3 4 5 6 7 8 9 1020

40

60

80

100

120

Ge-Ti (1373K)

Au-Ti (1373K)

Ga-Ti (1173K)

Sn-Ti (1173K)

In-Ti (1123K)

Con

tact

ang

le, d

eg

Ti concent. at.%

(a) (b) Fig. 8 Wetting kinetics a andfinal contact angles b forvarious CaF2/(Me–Ti) systems

[35]

Fig. 9 Representative SEM images of the CaF2/Me–Ti interfaces

J Mater Sci

123

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 near-

surface substrate liquid layer are the same), then interme-

tallics cannot precipitate at the interface. Thus, a region of

a few tens of nanometers thick close to the interface

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) isconstant and Ti has only minor effect on the magnitude of

cLV [36]. According to Young’s equation, wettingimprovement may be attributed to the decrease of the

solid–liquid (SL) interfacial energy (cSV) due to Ti segre-gation at the interface. To understand the specific mecha-

nisms that lead to the improved wetting ab initio

calculations were performed

Ab initio calculations

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 consider-

ation of the wetting of the (111) F-terminated CaF2 surface

and do not consider other surfaces, although the experi-

ments 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 Åbetween the slabs, and one Me atom above each site, giving

a 10-atom supercell, thus simulating one monolayer (ML)

of Me on the substrate.

1100 1200 1300 14001E-14

1E-10

1E-6

0.01

Pres

sure

, atm

Temperature, K

1

2

3

4

Fig. 10 The partial pressure of TiF3 as a function of temperature forthe 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 pressureof solid TiF3

32

1

(i) (111) sites21 ML of Me on CaF

Site(1) Site(2) Site(3) Me

F Ca

(ii)Fig. 11 Configurations of thesites on a F-terminated CaF2(111) surface considered for Me

adsorption. i Top view and iithree-dimensional illustration.

Sites 1, 2, and 3 correspond tothe 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]

J Mater Sci

123

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 neglectedslab 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

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 dis-

tribution 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 den-

sity within the layer. This indicates the formation of lateral

(parallel to the substrate surface) bonds between the

adsorbed atoms when the coverage increases.

1 2 3 4 5 6-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

CaF2(111)/Sn

site (1) site (2) site (3)

Ads

orpt

ion

ener

gy [

eV]

Adsorption Distance [A]

1 2 3 4 5 6-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

site (1) site (1)0.5ML

site (2) site (3)

CaF2(111)/In

Ads

orpt

ion

ener

gy [

eV]

Adsorption Distance [A]

1 2 3 4 5 6-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

site (1) site (1)

0.5ML

site (2) site (3)

CaF2(111)/Ti

Ads

orpt

ion

ener

gy [

eV]

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 displayedfor 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)

J Mater Sci

123

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

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 com-

pared 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 condi-

tions 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.

Fig. 13 Cross sections of the differential electron density distribu-tions (in e/Å

´ 3) for i CaF2(111) slab without Me coverage, and for thepreferred configurations of CaF2(111)/Me interfaces. ii Me = Au; iiiMe = Sn; iv Me = In; v Me = Ti; vi Me = Zr; vii results for alower density of adsorbed atoms (0.5 ML) with Me = Ti [43]

0.00.20.4

2

4

6

8

10 Ti Au Sn Al Cu In

EF

Loca

l DO

S

Energy, eV-1.0 -0.5 0.0 0.5 1.0 -1.0 -0.5 0.0 0.5 1.0

0.00.20.4

2

4

6

8

10 V DOS Zr DOS

EF

Loca

l DO

S

Energy, eV

(i) (ii)Fig. 14 LDOS for the electronsof the atoms adsorbed on the

CaF2(111) surface. i Au, In, Sn,Cu, Al, and Ti; ii Zr and V. Thecalculations refer to the

preferred sites for adsorption at

the equilibrium distance [43]

J Mater Sci

123

The adsorption energy curves (Uads) for In and Sn for

the three types of CaF2(111) surface conditions were cal-

culated according to: UadsðzÞ ¼ EsysðzÞ � Eslab þ EMe� �

and are presented in Fig. 16. For these configurations,

EsysðzÞ is the total energy of the slab with 0.5 ML of Me

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 condi-

tion (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

U ¼ Eads � e�2aðz�z0Þ � 2e�aðz�z0Þ

h i: ð5Þ

Here, Eads represents the adsorption energy at the equilib-

rium 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 attrac-

tion *0.2 eV/atom is revealed when 0.5 ML of In or Snare 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 ada-

toms at the surface increases the adsorption energy of the

additionally adsorbed Me atoms to *1.4 eV/atom for theIn atom and to *2.2 eV/atom for the Sn atom. The greatestadsorption energies were obtained for the surface config-

uration that already contained Ti adatoms. The presence of

Ti adatoms increases the adsorption energy of the addi-

tionally adsorbed Me atoms to *2 eV/atom for the In atom

Ca

Me (Sn or In)

F

Ti or Me

(b)

(a)

Fig. 15 Configurations of the F-terminated CaF2(111) surfacesconsidered for adsorption. a Top view of a clean (111) surface;b three-dimensional illustration of 0.5 ML of Me (Sn or In) placedabove 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 supercell used for the adsorption calculations. The rhombus schemerepresents the top view of the slab super cell used for further DFT

calculations; the diagonal represents the plane in which the crosssections for the electron density maps are shown in Fig. 14 [24]

2 4 6 8 10

-4

-3

-2

-1

0

Adsorption Distance [A]

Ads

orpt

ion

ener

gy [

eV]

Clean surface Surface containing 0.5ML Sn Surface containing 0.5ML Ti

2 4 6 8 10

-4

-3

-2

-1

0

Adsorption Distance [A]

Ads

orpt

ion

ener

gy [

eV]

Clean surface

Surface containing 0.5ML In

Surface containing 0.5ML Ti

(a) (b)Fig. 16 The adsorption energycurves for a 0.5 ML of Sn

(a) and In (b) computed fordifferent distances from the slab

surface, and for different surface

conditions (i)–(iii) [24]

J Mater Sci

123

and to *3.7 eV/atom for the Sn atom. Keeping in mind thepreviously obtained result that the interaction of adsorbing

atoms with the underlying fluorine atoms is almost inde-

pendent 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 pre-

sented 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 segrega-

tion 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 com-

position, 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

Table 1 Parameters that characterize the adsorption of Sn and Inatoms on CaF2(111) surface for surface conditions (i)–(iii)

CaF2(111) surface

condition

Adsorbed

Me

Interaction parameters

from Eq. 5

Eads(eV)

A (Å-1) z0

(Å)

Clean surface Sn 0.23 1.12 2.47

In 0.22 1.57 2.66

0.5 ML of Me adatoms Sn 2.16 0.55 1.90

In 1.42 0.54 2.80

0.5 ML of Ti adatoms 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, andMe–Ti bonds in the vicinity of the CaF2(111) surface [24]

F In Sn Ti

In 0.22 0.3 – 0.46

Sn 0.23 – 0.48 0.86

(a) (b)

CaF2 substrate 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 placedbetween Me atoms containing 12 Me–Ti bonds, b Ti placed at the interface containing 9 Me–Ti bonds and 1 Ti–F bond [24]

J Mater Sci

123

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]. Thedata for Sn–Ti dilute solution DHmix(Ti) = -52.8 kJ/moland c0Ti ¼ 0:01 were reported in [44]. The difference in theDHmix(Ti) values reflects the difference in the Me–Tibonding in the melts and may be associated with the degree

of Ti adsorption at the interface. It is clear that the incli-

nation 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 inves-

tigated 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 inFig. 18. For high negative value of DHmix(Ti), Ti dissolvedin 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 isgreater and its effect on the cSLvalue, and therefore on thewetting angle, is more significant.

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 sys-

tem 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 meltdepends on the equilibrium surface coverage, hTi, of theinterface by Ti adatoms [46, 47]. At a given temperature

and Ti concentration, C, hTi depends on the binding energyof 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 Tiadatoms and the corresponding decrease DcSL of the inter-facial energy cSL caused by Ti adsorption from the liquidsolution 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

0 20 40 60 80 100 120 140

20

40

60

80

100

120

140

Sn-Ti

Ge-TiAu-Ti

Ga-Ti

GeAuGa

In-Ti

Sn

Pure Me/CaF2

Me- 2at% Ti /CaF2

Con

tact

ang

le, °

, kJ/mol-ΔHTimix

In

2mm

Fig. 18 The contact angle for pure Me melts and for Me meltsalloyed with a small addition of Ti as a function of the Ti partial

mixing enthalpy [35]

J Mater Sci

123

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

ETi�In ¼ 0:5 ETi�Ti þ EIn�Inð Þ � DHIn�Ti; 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 ad-

atom in this state may have from n = 0 to 6 nearest Ti

atoms. The important result given by the ab initio calcu-

lations is that DETi increases linearly with n from 0.2 eVfor 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 maxi-mum surface coverage hTi of the SL interface with Ti ad-atoms and is much larger than kT & 0.1 eV at which thewetting experiments were carried out. In further analyses

for quantitative estimation of hTi, we use the Langmuiradsorption isotherm [46, 47].

hTi1 ¼ bC= 1þ bCð 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 theinterface coverage to the bulk concentrations C of the

solute for extremely dilute solutions when bC � 1. Theinterface 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 DcSLassociated with the formation of such a dense adsorption

layer should occur. The higher the binding energy DETi, thelower 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 thistendency characteristic for the Langmuir adsorption.

Equation 7 with DETi (n = 6) = 1.16 eV yieldshTi? = 0.9988 for In ? 0.5 % Ti at 1123 K, which isalmost complete adsorption saturation. To quantify the

DcSL (DETi, T, C) dependence, we used the Shishkovskysurface energy isotherm [46, 47]

DcSL ¼ CMAXkT ln 1þ Cbð Þ; 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 surfacedensity of the Ti adsorption sites onto F atoms. For the

F-terminated (111) surface of CaF2, UMAX = 7.7 91018 m-2. For T = 973 K, Eq. 8 yields DcSL = 0.88 J/m

2 for

C = 0.5 9 10-2. The cSL for various Ti concentrations C atthe 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 thesame manner with the above DETi = 1.16 eV and onlyslightly smaller UMAX = 6.2 9 10

18 m-2 (Fig. 19b).

(a) (b)973K

Ti concentration, C, at% Ti concentration, C, at%

Fig. 19 The equilibrium contact angle (H?) and DcSL as a function oftitanium concentration in the melt at 973 K (a) and 1123 K (b). Dottedlines correspond to the calculation according to Eq. 7 . Solid and opensquares, solid and open triangles correspond to the experimental valuesof contact angle and to the values of DcSL calculated directly from the

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 arefrom Glickman et al. [45]

J Mater Sci

123

Comparison with experiments for the system CaF2/

In ? Ti was carried out on the basis of Young equation:

H1 ¼ arccos cSV � cSLð Þ=cLV½ � 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. 19shows the decrease of H? from 130� to (25 ± 5)� with thegrowth 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 energyDcSL was great enough to explain the observed reduction inthe wetting angle H? (C, T), the DcSL calculated fromEq. 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 doesnot change the liquid–vapor (cLV) and the solid–vapor(cSV) surface energies. This assumption means that wettingimprovement 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 cosH1 � cosH01ð 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 knownc0LV [19] and the measured angles H0? and H?(C). Fig-ure 19 shows excellent inverse correlation between the cal-

culated DcSL and experimentally determined wetting angleH? (C), as well as close agreement between the calculatedand 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 repro-

duced using the same binding energy DETi = 1.16 eV foundin our ab initio calculations. It is also important that, as

shown in [43], the maximal surface density, UMAX, for Tiadsorption 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.,

90 ± 10 % of the surface density of the F-sites on the close-

packed 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-consis-tent explanation for all available data on the concentration-

and temperature-dependence of the interfacial energy

cSL(C,T) and contact angles in the system CaF2/In ? Ti. Theobtained 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 con-centration 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, whichleads 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 concentration-

and 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 hermet-

ically to the devices, and the joining becomes a crucial

aspect in their applications. Thus, further investigations of

J Mater Sci

123

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/sub-

strate interface characterized can help to reveal either

adsorption ML, multilayers or precipitates of active ele-

ment enriched compound formed at the interface.

The classical thermodynamic and ab initio analysis

should be performed for the different alkaline earth fluo-

rides 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 clar-

ified. 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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http://dx.doi.org/10.1007/BF00561219http://www.wien2k.at/reg_user/textbooks/DFT_and_LAPW-2_cottenier.pdfhttp://www.wien2k.at/reg_user/textbooks/DFT_and_LAPW-2_cottenier.pdfhttp://dx.doi.org/10.1007/BF00555046

Wetting of calcium fluoride by liquid metalsAbstractIntroductionMethodologyExperimental proceduresThermodynamic considerationsAb initio calculations

Results and discussionWetting behavior and interface in the CaF2/Me systemsWetting behavior and interface in the CaF2/Me--Ti systemsAb initio calculationsAdsorption energy and interface energy

SummaryPossible future researchReferences