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Editorial board

II. évfolyam 3. szám 2001. július
Volume 2 - No  3 - July 2001

Tartalomjegyzék - Contents

Introductory paper

G.Kaptay: On the activity of the LIMOS R&D Group in the field of ‘Materials World’ [ENG] 

Interface Science

E.Bader: Wettability of Alumina by Liquid Magnesium and Liquid AZ91 Alloy [ENG] 

L.Zoltai: Prediction of wettability between liquid metals and covalent ceramics [ENG] 

A Borsik: Dynamic simulation of the movement of ceramic particles in front of moving solidification front [ENG] 

Electrochemistry

S.V.Devyatkin: Influence of different conditions of electrochemical synthesis on the structure of the deposited refractory compound coatings [ENG] 

I.Sytchev, H.Kushov: Voltammetric Investigation of the Reduction Processes of Nickel, Cobalt and Iron Ions in Chloride and Chloro-Fluride Melts [ENG] 

M.S.Yaghmaee, E.Cserta, Á.Kovács, M.Árk: Carbon Micro-Tubes Produced by Electrochemical Synthesis from Molten Salts [ENG] 

G.Kaptay: On the Possibility to Produce a MgB2 Superconductor Layer by Electrochemical Synthesis from Molten Salt [ENG] 

Chemical Thermodynamics

M.S.Yaghmaee, G.Kaptay: On the stability range of SiC in ternary liquid Al-Si-Mg alloy [ENG] 

G. Kaptay, G. Csicsovszki, M.S.Yaghmaee: Estimation of the absolute values of cohesion energies of pure metals [ENG] 

Industrial Applied Research

M.Z.Benkő: On the computer software for the LD converter at the Dunaferr Works [ENG] 

[HUN] - Magyar cikk
[ENG] - English article

 



Prediction of Wettability between Liquid Metals and Covalent Ceramics

L.Zoltai

LIMOS R&D, Department of Physical Chemistry,
Faculty of Materials and Metallurgical Engineering, University of Miskolc,
3515 Hungary, Miskolc, Egyetemvaros

 

 

Abstract
Contact angle values have been estimated by the model developed by us earlier for 48 * 6 = 288 liquid metal / covalent ceramic systems. 130 systems can be taken as ‘non-reactive’, i.e. the calculated value in this paper is expected to be an equilibrium value, being independent of contact time. In 158 systems some chemical reaction or mutual solubility in the system is expected, and so the calculated values will be valid in reality only during short contact times. The calculated contact angle values vary within a relatively small interval, ranging from 143o for the Li/B4C system to 170o for the Pd/b -SiC system. For the given liquid metal, the contact angle increases gradually in the following row: B4C à Si3N4 à b -BN à AlN à a -BN à b -SiC. The range of contact angle for one given metal decreases with the increasing average value of the contact angle. For Li, with a highest polarising effect the contact angle varies in the interval of 10o, while for Pd this interval is only 4o. The effect of temperature has been found negligible in all systems (changing in the interval between +1o and –3o while the temperature changes by 100 K). It has been concluded, that due to high surface tension of liquid metals, in absence of chemical interaction and mutual solubility between them and covalent ceramics, liquid metals never wet the surface of covalent ceramics better than 143o.

Keywords: wettability, contact angle, adhesion energy, model calculation, liquid metals, B4C,Si3N4, b -BN, AlN, a -BN, b -SiC.

 

1. Introduction

Metals and ceramics interact with each other during innumerable engineering problems and manufacturing processes such as foundry processes, composite production etc., thus the knowledge of adhesion energy and contact angle between these phases can be very useful. A relatively large experimental databank on the contact angle between liquid metals and ceramics is available now in the literature [1-5]. In addition to that, in recent years our research group have completed a large number of experiments on determination of the contact angle in different metal/ceramic systems, including measurements on a covalently bonded Si3N4 ceramic [6-7]. Based on literature data and our own measurements, a complete adhesion theory was developed by us on the liquid metal – covalent ceramic systems [8].

The goal of the present paper is to apply the model developed in [8] to calculate the contact angle values in 48 * 6 = 288 liquid metal/covalent ceramic systems. It should be noted, however, that some of the possible combinations are ‘reactive systems’, meaning that chemical reaction or mutual solubility can take place between the phases. Therefore, in reactive systems our calculated results will be only ‘initial’ values, corresponding to short contact times between the phases (see [2, 9]). In ‘non-reactive’ systems our calculated results will refer to the equilibrium contact angle values, being valid independent of the duration of contact between the two phases.

2. Short summary of the model [8]

The model is based on the London-van-der-Waals equation, as between covalent ceramics and liquid metals no other interaction can be envisioned. For the interaction of a pure metal with a multi-component ceramics AxBy, summation should be performed over the tow components of the ceramics. The final equation for the adhesion energy between the liquid metal and non-reactive covalent ceramic phase was derived as:

    (1)

    where W - adhesion energy (J/m2),

    a - polarizability (m3),

    I - first ionisation potential (J/mol),

    R - radius of atom (m),

    indexes Me, C and i refer to liquid metal, ceramics and to the ith component of the

    ceramic, respectively,

    cMe-c - the number of bonds per unit interface area (mol/m2):

    (2)

    where NAv - is the Avogadro number (6.02 1023mol-1),

    Vm - is the molar volume (m3/mol),

    f - is the correction factor, being the function of the volume- and surface occupancy

    factors.

    The contact angle can be calculated from the Young-Dupré equation:

    (3)

    where s Mel-g is the surface tension of the liquid metal (J/m2).

     

3. Selection of Physical Constants [8]

    In order to apply Eq.(1) for the estimation of the adhesion energy in the liquid metal – covalent ceramic systems, first parameters used in Eq-s. (1-3) should be defined. The molar volume of liquid metals is taken from the compilation [10]. The molar volume of ceramics is taken from [21]. The packing factor fMe for liquid metals is taken equal 1.06 [20]. For the hexagonal and cubic ceramics fc is estimated as 1.09.

    The polarizability of the atom at the surface of the liquid metal was estimated as the 1/6th part of the polarizability of the gaseous atom:

    (4)

    Data of polarizability of gaseous atoms are taken from [13-14]. As follows from [13], the polarizability of covalent gaseous molecules can be approximately calculated additively from their atomic polarizabilities. Therefore Eq.(4) will also be applied to the components of the covalent ceramic.

    The ionization potential of a metallic atom in the surface of the liquid metal can be approximately calculated as:

    (5)

    where D vHMe is the vaporization enthalpy of the liquid metal at its melting point (Tm) [17],

    R = 8.314 J/molK – the gas constant,

    IMe,g – the first ionization energies of the gas atoms are taken from [12],

    coefficient 5/6 refers to the fact that the cohesion energy of the surface atom is

    approximately the 5/6th part of the cohesion energy of the bulk atom.

    The ionization potential of different components of the ceramic should be estimated in different ways, depending on, whether they are solid or gaseous as a pure phase under standard conditions. As an example, in case of the Si3N4 ceramics, silicon is solid, while nitrogen is two-atomic gas in standard state. Therefore, for the two components of Si3N4 the ionization energies should be estimated in slightly different ways:

    (6.a)

    (6.b)

    where D sHSi is the sublimation enthalpy of Si [17],

    D fHSi3N4 is the enthalpy of formation of Si3N4 [17],

    D dHN2 is the enthalpy of dissociation of 1 mol of N2(g) into 2 moles of N(g) [17].

    The radii for liquid metals are taken from the table for atomic (metallic) radii (coordination: 12) from [18]. The radii of the components of the ceramic is estimated from the smallest distance between the components in the compound, taking into account their radii in pure state. As an example, the smallest distance between Si and N in the Si3N4 compound is 1.71 10-10 m [11]. Using the metallic radius of Si (1.34 10-10 m [18]) and orbital radius of gaseous nitrogen (0.521 10-10 m [18]), the radii of the components of the ceramics were taken as: RSi = 1.23 10-10 m, RN = 0.478 10-10 m.

    In Tables 1-2 the initial physical data are summarised for the metals and ceramics, respectively.

    Table 1. Physical parameters of metals needed for calculations

Me

Tm [ 17]

Vm at Tm[ 10]

a [ 10]

f [ 20]

a(gas) [ 13]

I(gas) [ 12]

DvH at Tm[ 17]

R[ 18]

slg at Tm[ 20]

dslg/

dT[ 20]

K

e-6, m3/mol

10-4 K-1

 

e-30, m3

kJ/mol

kJ/mol

e-10, m

mJ/m2

mJ/m2K

Li

453.69

13.4

1.9

1.06

24.3

513.3

155.3

1.55

470

-0.2

Na

370.98

24.8

2.54

1.06

23.6

495.8

104.1

1.89

190

-0.13

K

336.35

47.1

2.9

1.06

43.4

418.8

86.3

2.36

100

-0.08

Rb

312.65

57.7

3

1.06

47.3

403

78.6

2.48

86

-0.07

Cs

301.55

72.2

3.1

1.06

59.6

375.7

74.4

2.67

69

-0.06

Be

1560

5.33

0.71

1.06

5.6

899.4

309.1

1.13

1300

-0.31

Mg

922

15.3

1.6

1.06

10.6

737.7

132.6

1.6

590

-0.19

Ca

1112

29.5

1.6

1.06

23.9

589.7

159.1

1.97

370

-0.12

Sr

1050

37

1.1

1.06

27.6

549.5

146.3

2.15

300

-0.11

Ba

1002

41.4

0.81

1.06

39.7

502.8

160.9

2.21

280

-0.11

Al

933.45

11.3

1.5

1.06

6.8

577.4

314.2

1.43

950

-0.26

Ga

302.8

11.4

0.92

1.06

8.12

578.8

266.2

1.39

715

-0.088

In

429.76

16.3

0.97

1.06

9.6

558.3

238.2

1.66

565

-0.09

Tl

577

18

1.15

1.06

7.55

589.3

174.2

1.71

460

-0.1

Si

1685

11.1

1.4

1.06

5.38

786.5

393.2

1.34

830

-0.084

Ge

1210.4

13.2

0.89

1.06

6.07

762.1

339.1

1.39

610

-0.11

Sn

505.06

17

0.87

1.06

7.7

708.2

292.7

1.58

550

-0.076

Pb

600.6

19.42

1.24

1.06

6.8

715.9

188.1

1.75

455

-0.085

Sb

904

18.8

1.3

1.06

6.6

833.6

240.6

1.61

380

-0.07

Bi

544.52

20.8

1.17

1.06

7.4

703.3

196.6

1.82

385

-0.077

Cu

1358

7.94

1

1.06

6.7

745.4

316.9

1.28

1350

-0.3

Ag

1233.95

11.6

0.98

1.06

7.88

731

265.8

1.44

920

-0.24

Au

1337.58

11.3

0.835

1.06

6.14

890.1

348.2

1.44

1140

-0.23

Zn

692.65

9.94

1.5

1.06

6.3

906

120.5

1.36

820

-0.27

Cd

594

14

1.5

1.06

7.2

867.6

103.6

1.56

630

-0.2

Hg

234.29

14.65

1.77

1.06

5.4

1007

61.83

1.6

500

-0.19

La

1193

23.3

0.4

1.06

31.1

538.1

419

1.87

750

-0.1

Ti

1939

11.6

0.56

1.06

14.6

658

441.2

1.46

1600

-0.35

Zr

2125

15.4

0.54

1.06

17.9

660

579.6

1.6

1500

-0.29

Hf

2500

14.9

0.53

1.06

16.2

642

575.7

1.59

1500

-0.24

V

2175

9.5

0.6

1.06

12.4

650

457.5

1.34

1900

-0.29

Nb

2740

11.9

0.51

1.06

15.7

664

685.2

1.45

2100

-0.21

Ta

3287

12.1

0.46

1.06

13.1

761

748.3

1.46

2200

-0.19

Cr

2130

8.27

1.1

1.06

11.6

652.7

353.6

1.27

1700

-0.35

Mo

2897

10.3

0.53

1.06

12.8

685

585.9

1.39

2300

-0.32

W

3680

10.5

0.45

1.06

11.1

770

808.9

1.4

2500

-0.25

Mn

1517

9.54

1.6

1.06

9.4

717.4

246.7

1.3

1200

-0.38

Re

3453

9.96

0.44

1.06

9.7

760

706.7

1.37

2800

-0.3

Fe

1809

7.94

1.3

1.06

8.4

759.3

378

1.26

1900

-0.42

Ru

2523

9.27

-

1.06

9.6

711

614.5

1.33

2300

-0.31

Os

3300

9.46

-

1.06

8.5

840

747.5

1.35

2500

-0.25

Co

1768

7.6

1.4

1.06

7.5

760

396.6

1.25

1900

-0.4

Rh

2233

9.27

-

1.06

8.6

720

517.4

1.34

2000

-0.34

Ir

2716

9.61

-

1.06

7.6

880

625.7

1.36

2300

-0.32

Ni

1726

7.43

1.51

1.06

6.8

736.7

399.9

1.24

1800

-0.44

Pd

1825

10.14

1.17

1.06

4.8

805

348.5

1.37

1500

-0.26

Pt

2045

10.31

1.52

1.06

6.5

870

533.3

1.38

1750

-0.36

Table 2. Physical parameters of ceramics needed for calculations

Ceramics

Si3N4

b -SiC

B4C

AlN

a -BN

b -BN

Structure

hex

cub

trig

hex

hex

cub

Vm, 293 K [ 21]

e-6, m3/mol

44

12.5

21.95

12.53

10.84

7.2

b [ 21]

e-6, 1/K

8.25

14.1

13.5

15

3.3

-

a (gas, A) [ 13]

e-30,m3

5.38

5.38

3.03

6.8

3.03

3.03

a (gas, B) [ 13]

e-30,m3

1.1

1.76

1.76

1.1

1.1

1.1

Dist(A-B) [ 11]

e-10, m

1.715

2.2

1.63

1.885

1.58

1.567

R(A, met) [ 18]

e-10, m

1.34

1.34

0.91

1.43

0.91

0.91

R(B, orb) [ 18]

e-10, m

0.521

0.62

0.62

0.521

0.521

0.521

I(A, gas) [ 12]

kJ/mol

786.5

786.5

800.6

577.4

800.6

800.6

I(B, gas) [ 12]

kJ/mol

1402.3

1086.2

1086.2

1402.3

1402.3

1402.3

DsHA298K [ 17]

kJ/mol

450

450

560

329.7

560

560

DfH(AxBy)298K [ 17]

kJ/mol

-744.8

-73.22

-71.13

-317.98

-254.39

-254.39

DdH(B2)298K [ 17]

kJ/mol

945.4

0

0

945.4

945.4

945.4

Results of calculations

The results of calculations are summarized in Table 3 for 48 * 6 = 288 systems. In the first column the symbol of the metallic element, while in following six double columns the calculated values are given for the 6 different ceramics. In each double column first the calculated contact angle is given. After that, the category of this calculated result is marked by ‘eq.’ or ‘init.’. These two categories have been defined in this paper as follows:

  1. ‘eq.’: meaning that the calculated value is an equilibrium contact angle, taking place independent of the contact time in the ceramic/liquid metal system; this category was chosen, when the liquid metal has no chemical interaction (with negative standard change of Gibbs energy of reaction) with any of the components of the metal [17], and also they are not mutually soluble (or only to a smallest extent) [15, 16]. There are 130 ‘equilibrium’ values given in Table 3.

  2. ‘init.’: meaning the calculated value is just the initial contact angle, being valid within short contact times between the ceramic and the liquid metal; this category was chosen when chemical interaction [17] or significant mutual solubility [15-16] between the phases is expected, and thus the contact angle is expected to decrease with contact time. The equilibrium contact angle cannot be calculated by the equations presented in this paper. There are 158 ‘initial’ values given in Table 3.

As one can see from Table 3., the contact angle values vary within a relatively small interval, ranging from 143o for the Li/B4C system to 170o for the Pd/b -SiC system. For the given liquid metal, the contact angle increases gradually in the following row: B4C à Si3N4 à b -BN à AlN à a -BN à b -SiC. The range of contact angle for one given metal decreases with the increasing average value of the contact angle. For Li, with a highest polarising effect the contact angle varies in the interval of 10o, while for Pd this interval is only 4o.

Finally we can conclude, that due to high surface tension of liquid metals, in absence of chemical interaction and mutual solubility between them and covalent ceramics, liquid metals never wet the surface of covalent ceramics better than 143o. This conclusion is in perfect agreement with our measured data [6-7], and also with the large number of experimental data obtained by other groups [1-5]. Although, it should be mentioned that there is a significant number of papers showing contact angle as low as 120o in non-reactive liquid metal / covalent ceramic phases. We presume that those experimental data probably refer to ceramics or liquid metals of oxidised surface. As oxides have ionic character, the new type of interaction, the ion-induced-dipole interaction becomes possible, ensuring higher adhesion energy and lower contact angle in the system (see [19, 9]).

Conclusions

Contact angle values have been estimated by the model developed by us earlier for non-reactive liquid metal / covalent ceramic systems. Among the 288 systems studied, 130 systems can be taken as ‘non-reactive’, i.e. the calculated value in this paper is expected to be an equilibrium value, being independent of contact time. In 158 systems some chemical reaction or mutual solubility in the system is expected, and so the calculated values will be valid in reality only during short contact times.

The calculated contact angle values vary within a relatively small interval, ranging from 143o for the Li/B4C system to 170o for the Pd/b -SiC system. For the given liquid metal, the contact angle increases gradually in the following row: B4C à Si3N4 à b -BN à AlN à a -BN à b -SiC. The range of contact angle for one given metal decreases with the increasing average value of the contact angle. For Li, with a highest polarising effect the contact angle varies in the interval of 10o, while for Pd this interval is only 4o.

The effect of temperature has been found negligible in all systems (changing in the interval between +1o and –3o while the temperature changes by 100 K).

Finally it is concluded, that due to high surface tension of liquid metals, in absence of chemical interaction and mutual solubility between them and covalent ceramics, liquid metals never wet the surface of covalent ceramics better than 143o.

 

Table 3. Results of calculations (for the meaning of ‘eq.’ and ‘init’ see the text above)

Me

Si3N4

b -SiC

B4C

AlN

a -BN

b -BN

Q

Type

Q

Type

Q

Type

Q

Type

Q

Type

Q

Type

Li

145

Init.

153

init.

143

eq.

148

init.

148

eq.

146

eq.

Na

149

eq.

155

eq.

146

eq.

151

eq.

152

eq.

149

eq.

K

150

eq.

155

eq.

146

eq.

152

eq.

153

eq.

151

eq.

Rb

152

eq.

156

eq.

148

eq.

153

eq.

154

eq.

152

eq.

Cs

152

eq.

155

eq.

148

eq.

153

eq.

154

eq.

152

eq.

Be

153

Init.

161

init.

154

eq.

156

init.

156

eq.

154

eq.

Mg

159

Init.

164

init.

158

eq.

161

init.

161

eq.

160

eq.

Ca

159

Init.

163

init.

157

eq.

160

init.

161

eq.

159

eq.

Sr

161

Init.

164

init.

158

eq.

162

init.

162

eq.

161

eq.

Ba

158

Init.

162

init.

156

eq.

159

init.

160

eq.

158

eq.

Al

163

Init.

167

init.

162

eq.

164

init.

165

init.

163

init.

Ga

157

Init.

163

eq.

157

eq.

160

init.

160

init.

158

init.

In

162

eq.

166

eq.

161

eq.

164

eq.

164

eq.

163

eq.

Tl

164

eq.

167

eq.

163

eq.

165

eq.

166

eq.

164

eq.

Si

159

Init.

165

init.

159

init.

162

init.

162

init.

160

init.

Ge

157

init.

163

init.

157

eq.

160

init.

160

eq.

158

eq.

Sn

161

eq.

165

eq.

160

eq.

163

eq.

163

eq.

161

eq.

Pb

165

eq.

168

eq.

164

eq.

166

eq.

166

eq.

165

eq.

Sb

159

eq.

164

eq.

158

eq.

161

init.

161

eq.

160

eq.

Bi

165

eq.

168

eq.

163

eq.

166

eq.

166

eq.

165

eq.

Cu

160

Init.

165

init.

160

init.

162

init.

162

init.

161

init.

Ag

161

Init.

165

init.

160

eq.

163

init.

163

eq.

161

eq.

Au

164

Init.

168

init.

163

eq.

165

init.

165

eq.

164

eq.

Zn

159

eq.

164

eq.

158

eq.

161

init

161

eq.

159

eq.

Cd

162

eq.

166

eq.

161

eq.

163

eq.

163

eq.

162

eq.

Hg

163

eq.

167

eq.

162

eq.

164

eq.

164

eq.

163

eq.

La

159

eq.

163

init.

157

init.

160

init.

161

eq.

159

eq.

Ti

160

Init.

165

init.

160

init.

162

init.

162

init.

161

init.

Zr

162

Init.

166

init.

161

init.

163

init.

163

init.

162

init.

Hf

162

Init.

166

init.

162

init.

164

init.

164

init.

163

init.

V

159

Init.

165

init.

159

init.

162

init.

162

init.

160

init.

Nb

161

Init.

166

init.

161

init.

163

init.

163

init.

161

init.

Ta

163

Init.

167

init.

163

init.

165

init.

165

init.

163

init.

Cr

157

Init.

163

init.

157

init.

159

init.

159

init.

158

init.

Mo

162

Init.

167

init.

162

init.

164

init.

164

init.

162

init.

W

163

eq.

168

init.

163

init.

165

init.

165

init.

164

init.

Mn

157

Init.

163

init.

157

init.

159

init.

159

init.

158

init.

Re

165

Init.

169

init.

165

init.

166

eq.

166

init.

165

init.

Fe

160

Init.

165

init.

160

init.

162

init.

162

init.

161

init.

Ru

162

Init.

167

init.

162

init.

164

eq.

164

init.

163

init.

Os

164

Init.

168

init.

164

eq.

166

eq.

166

eq.

164

eq.

Co

161

Init.

166

init.

161

init.

163

init.

163

init.

161

init.

Rh

163

eq.

167

eq.

163

eq.

164

eq.

165

eq.

163

eq.

Ir

164

eq.

169

eq.

165

eq.

166

eq.

166

eq.

165

eq.

Ni

161

Init.

166

init.

161

init.

163

init.

163

init.

161

init.

Pd

166

Init.

170

init.

166

init.

168

init.

168

init.

167

init.

Pt

164

Init.

169

init.

164

init.

166

init.

166

init.

165

init.

 

 

 

References

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  14. T.M.Miller, B.Bederson: Advances in Atomic and Molecular Physics, 13 (1977) 1

  15. Alloy Phase Diagrams, ASM Handbook vol. 3. ed. by H. Baker, 1992

  16. T.B.Massalski, et al.: Binary Alloy Phase Diagrams, 2nd ed., ASM Int., Materials Park, OH., 1990

  17. I.Barin: Thermochemical Data of Pure Substances – WCH, 1993.

  18. A.I. Efimov: Properties of Inorganic Compounds (in Russian) – Khimiia, Leningrad, 1983.

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