Adhesion Phenomenon of Liquid Metals

*Hadef Zakaria and Kamli Kenza*

#### **Abstract**

In this chapter, we study an interfacial phenomenon between liquid metals and ceramic substrates. Therefore, investigation of these phenomena is of great importance not only in technological applications but also in fundamental understanding of physical behavior of the adhesion between two different materials as far as their electrical structures and physiochemical properties are concerned. Moreover, adhesion energy is interpreted thermodynamically by the interfacial interactions and the nature of bonding between liquid metal and ceramic material. The adhesion energy in metal/ceramic systems is determined by using an electro-acoustical model based on the propagation of the acoustic wave in the interface and strongly depends on the electric properties of combination.

**Keywords:** Liquid metal, Ceramics, Adhesion, Interfaces, Gap energy, Acoustic parameters

#### **1. Introduction**

Metalized ceramics by liquid metal have a crucial uses in several modern technological applications such as solar cell [1–4] electrical devices [5–7] and Micro Electro Mechanical Systems (MEMS) [8–10]. Recently, these systems are used as the conductive wiring of microelectronic circuits; there has been considerable interest in the characterization of the structure and properties of liquid metal/ ceramic interface [11].

However, the coating of ceramic surfaces can affect most of the properties of the interface. Therefore, the investigation of interfacial phenomena between metals and ceramic substrates is of great importance not only in technological applications but also in fundamental understanding of physical behavior of the adhesion between two different materials as far as their electrical structures and physiochemical properties are concerned. In fact, at the interface of a metal/ceramic system, adhesion occurs when the atoms or molecules of the two contacting surfaces approach each other so closely that attractive forces between approaching atoms (or molecules) bond them together. The strength of the bond depends on the size of the atoms, the distance between them, and the presence or absence of contaminant matter on the surface [1]. Hence, the strength or wea1kness of bonds is the key factor to determine the interface stability: good adhesion, welded adhesion, perfect bonding, weak bonding smooth interface, etc. The metal/ceramic contact is characterized by the adhesion energy, *Wad*, which is the work per unit area of the interface needed to separate reversibly a metal/ceramic interface [2]. This physicochemical

parameter is given by Young-Dupré equation relating surface tension of molten metal above melting temperature, *γLV*, and measured equilibrium contact angle *θ* formed between deposited liquid metal and its ceramic substrate [12]:

$$W\_{ad} = \chi\_{LV} \left( 1 + \cos \theta \right) \tag{1}$$

are most often hard, rigid and plastically deformable. It should be noted that a large number of metals have a very high melting point, since they have relatively weak mechanical properties and are most often characterized by a wettability, a low thermal and electrical conductivity (as in the case of copper and gold). Therefore, the use of metals in metallized ceramic structures requires a fusion process in order to liquefy or melt these metals. For this, the role of metallization is to make the

Several liquid metals parameters used in this investigation are listed in **Table 1**; sound velocities at melting temperatures are tabulated by Blairs [16], surface tension values are proposed by Keene [17], Liquid densities are taken by Crawley [18] and by Blairs [16]. Whiles the elastic constants, solid densities and Rayleigh velocity

**)** *Tf* **(K)** *E* **(GPa***) ρsm* **(Kg/m<sup>3</sup>**

**)** *VRM* **(m/s)**

**)** *Plm* **(Kg/m<sup>3</sup>**

ceramic wettable by the liquid metal.

*Adhesion Phenomenon of Liquid Metals DOI: http://dx.doi.org/10.5772/intechopen.97419*

are obtained from Briggs [19].

**Metal** *c* **(m/s)** *γLV* **(mJ/m<sup>2</sup>**

**35**

Adhesion energy represent in generally the sum of all interfacial interactions between two surfaces [13]:

$$\mathcal{W}\_{ad} = \mathcal{W}\_{non-equilibrium} + \mathcal{W}\_{equil} \tag{2}$$

*Wnon-equil* and *Wequil* represents non-equilibrium and equilibrium contributions respectively of interfacial interactions. The first term does not exist in the absence of chemical reactions, and the second term corresponds to non-reactive metals/ ceramic systems [13], this later expressed by:

$$\mathcal{W}\_{equil} = \mathcal{W}\_{VDW} + \mathcal{W}\_{chem-equil} \tag{3}$$

*WVDW* is van der Waals interaction and *Wchem-equil* is chemical equilibrium interactions accompanied by formation of these chemical bonds between two contact phases. It is imported to note that these interfacial bonds rested without rupture contrary in non-equilibrium systems [13].Van der Waals energy in metal/ceramic systems estimate the can be numerically estimated by considering the dispersion interaction between a pair of atoms:

$$\mathcal{W}\_{\rm VDW} = n \frac{3a\_{\rm Ma}a\_{\rm C}}{2\mathcal{R}^6} \left[ \frac{I\_{\rm M}I\_{\rm C}}{I\_{\rm M} + I\_{\rm C}} \right] \tag{4}$$

*α<sup>M</sup>* and *α<sup>C</sup>* are the polarizability volume of metal and ceramic; *IM* and *IC* the first ionization potential of metal atom and ceramic atom respectively. *R* is the distance between centers of the interacting atom.

At the interface zone, the surface acoustic wave (SAW) propagation which depends on elastic properties of solid substrates is greatly affected: the response would be different depending on the weakness or strength of bonds due to impedance mismatching [14]. Hence, in this context, we investigate the dependences of adhesion energy on acoustic parameters, in particular SAW velocities, for many metal/ceramic systems.

The objective of the electro-acoustic model [15] is the investigation of interfacial adhesion in liquid metal/ceramic systems subjected to non-reactive wetting in order to eliminate the non-equilibrium contribution Wnon-equil of adhesion work during a chemical reaction at the interface. A wide range of non-reactive liquid metals were used in this proposed model.

#### **2. Choice of liquid metals**

At the room temperature, most metals have a crystalline phase; the most widely used are iron, aluminum and copper. They are often present in oxide form (sodium oxide, magnesium oxide … ), some metals are present in the non-oxidized state (precious metals: platinum, gold) or in the form of alloys. Metal alloys are in general the combination of two or more metals as in the case of brasses (alloys of copper and zinc); but they can also contain non-metallic elements (i.e. iron-carbon alloy). Metals and their alloys are usually very good conductors of heat and electricity; they

#### *Adhesion Phenomenon of Liquid Metals DOI: http://dx.doi.org/10.5772/intechopen.97419*

parameter is given by Young-Dupré equation relating surface tension of molten metal above melting temperature, *γLV*, and measured equilibrium contact angle *θ*

Adhesion energy represent in generally the sum of all interfacial interactions

*Wnon-equil* and *Wequil* represents non-equilibrium and equilibrium contributions respectively of interfacial interactions. The first term does not exist in the absence of chemical reactions, and the second term corresponds to non-reactive metals/

*WVDW* is van der Waals interaction and *Wchem-equil* is chemical equilibrium interactions accompanied by formation of these chemical bonds between two contact phases. It is imported to note that these interfacial bonds rested without rupture contrary in non-equilibrium systems [13].Van der Waals energy in metal/ceramic systems estimate the can be numerically estimated by considering the dispersion

> 3*αMα<sup>C</sup>* 2*R*<sup>6</sup>

*α<sup>M</sup>* and *α<sup>C</sup>* are the polarizability volume of metal and ceramic; *IM* and *IC* the first ionization potential of metal atom and ceramic atom respectively. *R* is the distance

The objective of the electro-acoustic model [15] is the investigation of interfacial adhesion in liquid metal/ceramic systems subjected to non-reactive wetting in order to eliminate the non-equilibrium contribution Wnon-equil of adhesion work during a chemical reaction at the interface. A wide range of non-reactive liquid metals were

At the room temperature, most metals have a crystalline phase; the most widely used are iron, aluminum and copper. They are often present in oxide form (sodium oxide, magnesium oxide … ), some metals are present in the non-oxidized state (precious metals: platinum, gold) or in the form of alloys. Metal alloys are in general the combination of two or more metals as in the case of brasses (alloys of copper and zinc); but they can also contain non-metallic elements (i.e. iron-carbon alloy). Metals and their alloys are usually very good conductors of heat and electricity; they

At the interface zone, the surface acoustic wave (SAW) propagation which depends on elastic properties of solid substrates is greatly affected: the response would be different depending on the weakness or strength of bonds due to impedance mismatching [14]. Hence, in this context, we investigate the dependences of adhesion energy on acoustic parameters, in particular SAW velocities, for many

*WVDW* ¼ *n*

*Wad* ¼ *γLV* ð Þ 1 þ *cosθ* (1)

*Wad* ¼ *Wnon*�*equil* þ *Wequil* (2)

*Wequil* ¼ *WVDW* þ *Wchem*�*equil* (3)

*IMIC IM* þ *IC* 

(4)

formed between deposited liquid metal and its ceramic substrate [12]:

between two surfaces [13]:

*Liquid Metals*

ceramic systems [13], this later expressed by:

interaction between a pair of atoms:

between centers of the interacting atom.

metal/ceramic systems.

used in this proposed model.

**2. Choice of liquid metals**

**34**

are most often hard, rigid and plastically deformable. It should be noted that a large number of metals have a very high melting point, since they have relatively weak mechanical properties and are most often characterized by a wettability, a low thermal and electrical conductivity (as in the case of copper and gold). Therefore, the use of metals in metallized ceramic structures requires a fusion process in order to liquefy or melt these metals. For this, the role of metallization is to make the ceramic wettable by the liquid metal.

Several liquid metals parameters used in this investigation are listed in **Table 1**; sound velocities at melting temperatures are tabulated by Blairs [16], surface tension values are proposed by Keene [17], Liquid densities are taken by Crawley [18] and by Blairs [16]. Whiles the elastic constants, solid densities and Rayleigh velocity are obtained from Briggs [19].



acoustic velocities, *VR*, of these metals at solid state by SAM technique. The variation of *VR*-values as function of *c* was made; it shows a linear increase of *VR* with *c* increasing. Simple fitting was made and resulted in a well-defined linear correlation

between the quantities, as can be seen in **Figure 1**.

*Adhesion Phenomenon of Liquid Metals DOI: http://dx.doi.org/10.5772/intechopen.97419*

*Correlation between liquid and solid densities of metals [20].*

*Correlation between Young's moduli and surface tension of liquid metals [20].*

**Figure 2.**

**Figure 3.**

**37**

#### **Table 1.**

*Experimental sound velocities,* c*, surface tensions,* σm*, densities,* ρlm *of different liquid metals at the melting temperature, elastic moduli,* E*, solid density,* ρsm*, and calculated Rayleigh velocities,* VR *of these metals at solid state.*

#### **3. Relationship between the properties of metals in solid and liquid states**

Analytical study has been proposed to express the relation between experimental sound velocities of liquid metals at the melting temperature, *c*, and determinate

**Figure 1.**

*Correlation between experimental sound velocities of liquid metals and Rayleigh velocities of these metals in solid state [20].*

acoustic velocities, *VR*, of these metals at solid state by SAM technique. The variation of *VR*-values as function of *c* was made; it shows a linear increase of *VR* with *c* increasing. Simple fitting was made and resulted in a well-defined linear correlation between the quantities, as can be seen in **Figure 1**.

**Figure 2.** *Correlation between liquid and solid densities of metals [20].*

**Figure 3.** *Correlation between Young's moduli and surface tension of liquid metals [20].*

**3. Relationship between the properties of metals in solid and liquid**

*Experimental sound velocities,* c*, surface tensions,* σm*, densities,* ρlm *of different liquid metals at the melting temperature, elastic moduli,* E*, solid density,* ρsm*, and calculated Rayleigh velocities,* VR *of these*

Analytical study has been proposed to express the relation between experimental sound velocities of liquid metals at the melting temperature, *c*, and determinate

*Correlation between experimental sound velocities of liquid metals and Rayleigh velocities of these metals in*

**states**

**Figure 1.**

**36**

*solid state [20].*

*metals at solid state.*

**Table 1.**

**Metal** *c* **(m/s)** *γLV* **(mJ/m<sup>2</sup>**

*Liquid Metals*

**)** *Plm* **(Kg/m<sup>3</sup>**

Nb 3385 1757 7830 2740 105 8570 2406 Pb 1821 471 10587 601 16 1146 2118 Pd 2657 1482 10495 1825 117 12023 742 Hf 2559 1517 11550 2500 78 13310 1789 Nd 2212 685 6890 1289 41 6800 1503 Sm 1670 431 7420 1345 50 7353 1411 Eu 1568 264 5130 1090 18 5244 1301 Gd 2041 664 7790 1585 55 7901 1083 Tb 2014 669 8050 1630 56 8219 1537 Dy 1941 648 8370 1682 61 8551 1525 Ho 1919 650 8580 1743 65 8795 1561 Er 1867 637 8860 1795 70 9066 1592 Lu 2176 940 9750 1936 69 9841 1426

**)** *Tf* **(K)** *E* **(GPa***) ρsm* **(Kg/m<sup>3</sup>**

**)** *VRM* **(m/s)**

Relationship between these parameters can be quantified by the following equation:

$$V\_R = 0.674 \text{ c} \tag{5}$$

One can see also a clear tendency between the liquid metals densities, *ρlm*, with that of these metals at solid state, *ρsm*, as can be seen in **Figure 2**.

The relationship that expresses this tendency can take the following form:

$$
\rho\_{sm} = \text{1.088 } \rho\_{lm} \tag{6}
$$

A close comparative between one of very important properties of liquid metal, which is the surface tension, σm, and Young's moduli, E, values shows a linier dependence between these parameters, as can be seen in **Figure 3**.

To quantify the relationship between elastic moduli and surface tension, a simple plot was made; a linear correlation is defined, that it can be written as:

$$E = 0.083 \,\sigma\_m \tag{7}$$

The variations of work of adhesion on Rayleigh velocity for different ceramic substrate, VRC, in contacting with different non-reactive metals (Au, Cu, Sn, Ga and Ag) are investigated. In this study, some published data on wok of adhesion for

*Characteristics of investigated ceramic materials: energy gap,* Eg*, density,* ρ<sup>C</sup> *and Young's modulus,* EC*, and*

**)** *EC* **(GPa***) VRC* **(m/s)**

In the first time liquid gold/ceramic combinations are taken the obtained results

In order to generalize the above observations obtained with liquid Gold/ceramic

*Work of adhesion as function of calculated Rayleigh velocities of different ceramic substrates in contacting with*

different metals/ceramics systems are considered [12, 13, 22–34].

*Eg* **(eV)** *ρ<sup>C</sup>* **(kg/m<sup>3</sup>**

TiO 0.0 4950 387 3960 TiO2 3.1 4230 315 4917 Ti2O3 0.1 4468 118 4411 Y2O3 5.5 5030 176 3398 Yb2O3 1.4 9293 229 2677 ZnO 3.4 5606 125 2730 ZrO2 8.0 5600 244 3781

systems and to put into evidence the results reproducibility, several other nonreactive metals deposed in different ceramic substrates are considered, i.e.,

are illustrated in **Figure 4**.

*determined Rayleigh velocities,* VRC*.*

(Cu, Sn, Ga and Ag):

**Figure 4.**

*gold [15].*

**39**

**Ceramics Substrate**

*Adhesion Phenomenon of Liquid Metals DOI: http://dx.doi.org/10.5772/intechopen.97419*

**Table 2.**

The importance of the Eqs. (5)-(7) lies in the prediction of acoustic parameters from liquid to solid states of metals and vice versa.

#### **4. Determination of adhesion energy in liquid metal/ceramic systems**

Very recently, an electro-acoustical model [15] has been proposed to estimate and interpreted the work of adhesion of non-reactive liquid metal/ceramic substrates systems in terms of the Rayleigh velocity of acoustic wave propagation in surface of all types of corresponding ceramic substrates, VRC.

In this model, several metals are considered (Au, Cu, Sn, Ga and Ag) on a great number of ceramic substrates (AlN, Al2O3, BN, CoO, Er2O3, Ho2O3, Lu2O3, MgO, NiO, SiC, SiO2, TiC, TiO, TiO2, Ti2O3, Y2O3, Yb2O3, ZnO and Zr2O3). The characteristics of all ceramic materials: energy gap, *Eg* [21] density, *ρC*, Young's modulus, *EC*, and Rayleigh velocities [19] are listed in **Table 2**.


#### *Adhesion Phenomenon of Liquid Metals DOI: http://dx.doi.org/10.5772/intechopen.97419*


#### **Table 2.**

Relationship between these parameters can be quantified by the following

One can see also a clear tendency between the liquid metals densities, *ρlm*, with

A close comparative between one of very important properties of liquid metal,

To quantify the relationship between elastic moduli and surface tension, a sim-

The importance of the Eqs. (5)-(7) lies in the prediction of acoustic parameters

**4. Determination of adhesion energy in liquid metal/ceramic systems**

Very recently, an electro-acoustical model [15] has been proposed to estimate and interpreted the work of adhesion of non-reactive liquid metal/ceramic substrates systems in terms of the Rayleigh velocity of acoustic wave propagation in

In this model, several metals are considered (Au, Cu, Sn, Ga and Ag) on a great number of ceramic substrates (AlN, Al2O3, BN, CoO, Er2O3, Ho2O3, Lu2O3, MgO, NiO, SiC, SiO2, TiC, TiO, TiO2, Ti2O3, Y2O3, Yb2O3, ZnO and Zr2O3). The characteristics of all ceramic materials: energy gap, *Eg* [21] density, *ρC*, Young's modulus,

The relationship that expresses this tendency can take the following form:

which is the surface tension, σm, and Young's moduli, E, values shows a linier

ple plot was made; a linear correlation is defined, that it can be written as:

that of these metals at solid state, *ρsm*, as can be seen in **Figure 2**.

dependence between these parameters, as can be seen in **Figure 3**.

from liquid to solid states of metals and vice versa.

surface of all types of corresponding ceramic substrates, VRC.

*Eg* **(eV)** *ρ<sup>C</sup>* **(kg/m<sup>3</sup>**

AlN 5.6 3260 318 5616 Al2O3 7.1 3980 330 5650 BN 8.1 3487 34 1834 CoO 0.5 9423 281 2871 Er2O3 3.2 8651 179 2633 Ho2O3 3.9 8414 175 2639 Lu2O3 4.0 9423 204 2691 MgO 7.3 3580 310 5297 NiO 2.5 6670 420 6205 SiC 3.3 3210 393 6714 SiO2 7.9 2600 75 3678 TiC 0.3 4940 400 5370

*EC*, and Rayleigh velocities [19] are listed in **Table 2**.

**Ceramics Substrate**

**38**

*VR* ¼ 0*:*674 *c* (5)

*ρsm* ¼ *1:088 ρlm* (6)

*E* ¼ *0:083 σ<sup>m</sup>* (7)

**)** *EC* **(GPa***) VRC* **(m/s)**

equation:

*Liquid Metals*

*Characteristics of investigated ceramic materials: energy gap,* Eg*, density,* ρ<sup>C</sup> *and Young's modulus,* EC*, and determined Rayleigh velocities,* VRC*.*

The variations of work of adhesion on Rayleigh velocity for different ceramic substrate, VRC, in contacting with different non-reactive metals (Au, Cu, Sn, Ga and Ag) are investigated. In this study, some published data on wok of adhesion for different metals/ceramics systems are considered [12, 13, 22–34].

In the first time liquid gold/ceramic combinations are taken the obtained results are illustrated in **Figure 4**.

In order to generalize the above observations obtained with liquid Gold/ceramic systems and to put into evidence the results reproducibility, several other nonreactive metals deposed in different ceramic substrates are considered, i.e., (Cu, Sn, Ga and Ag):

**Figure 4.** *Work of adhesion as function of calculated Rayleigh velocities of different ceramic substrates in contacting with gold [15].*

#### *Liquid Metals*

The obtained results are illustrated in **Figure 5** in terms of work of adhesion as a function of ceramic Rayleigh velocities in contacting with several non-reactive metals. All the curves show the same behavior: the work of adhesion increases linearly with increasing VRC. However, two sets of linear dependences are distinguished that are regrouped according to the band gap energy of the ceramic substrate, as discussed below.

The dependence of Wad on VRC (Au) is quantified via curve fitting, (lines in **Figures 4** and **5**). We distinguish two parallel dependences for gold/ceramic substrate systems: for higher energy values (upper curve) the linear variation is found to be of the form:

$$W\_{ad}(Au) = 0.07V\_{RC} + 553\tag{8}$$

where the subscript, (Me), represents any given investigated nonreactive liquid metal (Ag, Au, Cu, Ga and Sn), C and Ć are characteristic constants for each metal/

The similar dependence (with the same slope equal to 0.07VRC) is indicative of the existence of the same mechanism responsible for this behavior. However the existence of two parallel dependences for every system is due to the energy band structure of the ceramic materials in particular the energy gap (**Table 1**). A close analysis of **Figure 5** and the Eg column clearly shows that the upper set of curves corresponds to solid ceramic materials with small energy gaps (Eg ≤ 3 eV), whereas the lower ensemble of curves represents ceramic materials with large energy gaps

In fact, solid materials with small band gaps behave as conductors (Eg ! 0) or semiconductors (Eg ≤ 3 eV). In this case, it was reported [35] that the high adhesion energy values of same metal/ceramic systems are associated with high electron density of metals and low band gap energy of solids ceramics. The interfacial adhesion between a metal and a ceramic crystal is assured by the electron transfer [12], it is interesting to define an interfacial propriety represents the minimum energy needed for appearance of a limit number of interfacial bonds responsible for generating of the adhesion between the metal and the ceramic, this energy is caused by Van der Waals interaction, WVDW. The intensity of the electron transfer at small band gap solid ceramic is increased because of its wealth by the free charges inside

For large band gaps, there will be practically a small number of free charges inside in the ceramic crystal. As a result, the chemical equilibrium contribution Wchem-equil, to the adhesion energy is negligible. Consequently, the adhesion energy is approximately resulted by from the Van der Waals interaction [12]. The Van der Waals contribution of adhesion energy rested constant and proportional with Rayleigh velocity of ceramic materials whether it is the band gap

The determinate WVDW energy values for different metal/ceramic systems depend directly on the choice of various parameters appearing in Eq. (3). For example, Mc Donald and Eberhart [36] calculated WVDW values equal to

<sup>500</sup> � 150 mJ/m<sup>2</sup> for different metal/alumina systems, that in our model and for the

found WVDW values of 350 150 mJ/m<sup>2</sup> for metal/oxide ceramic systems, this

Ag 991 14 Au 533 76 Cu 1309 228 Ga 863 78 Sn 602 37

*WVDW* ¼ 0*:*07 *VRC* (12)

**)** *Ć* **(mJ/m2**

. While Naidich [13]

**)**

and the chemical equilibrium contribution Wchem-equil taking place.

energy, for the first time it is determined exactly as follows:

same system we have found WVDW values equal to 396 mJ/m<sup>2</sup>

**Metals** *C* **(mJ/m2**

*C and Ć values of different liquid metal/ceramic system.*

The exact corresponding values of characteristic constants C (for small gap ceramic materials) and Ć (for large gap ceramic materials) of several liquid metal/

ceramic combination.

(Eg > 3 eV).

**Table 3.**

**41**

ceramic systems are giving in the **Table 3**.

*Adhesion Phenomenon of Liquid Metals DOI: http://dx.doi.org/10.5772/intechopen.97419*

Whereas, for small energy values (lower curve), the linear dependence is found to be of the form:

$$W\_{ad}(A\mu) = 0.07V\_{RC} + 76\tag{9}$$

Moreover, it should be noted that the same behavior of two parallel lines is obtained for all metal/ceramic systems. Therefore, all curves have a same slop not only for small gap materials but also for large gap ceramics; the general expression takes the form:

$$W\_{ad} \ (Me) = 0.07 \ V\_{RC} + C \tag{10}$$

$$W\_{ad} \ (Me) = 0.07 \ V\_{RC} + ^\prime C \tag{11}$$

**Figure 5.** *Work of adhesion as function of calculated Rayleigh velocities of different ceramic substrates in contacting with several metals [15].*

#### *Adhesion Phenomenon of Liquid Metals DOI: http://dx.doi.org/10.5772/intechopen.97419*

The obtained results are illustrated in **Figure 5** in terms of work of adhesion as a

function of ceramic Rayleigh velocities in contacting with several non-reactive metals. All the curves show the same behavior: the work of adhesion increases linearly with increasing VRC. However, two sets of linear dependences are distinguished that are regrouped according to the band gap energy of the ceramic sub-

The dependence of Wad on VRC (Au) is quantified via curve fitting, (lines in **Figures 4** and **5**). We distinguish two parallel dependences for gold/ceramic substrate systems: for higher energy values (upper curve) the linear variation is found

Whereas, for small energy values (lower curve), the linear dependence is found

Moreover, it should be noted that the same behavior of two parallel lines is obtained for all metal/ceramic systems. Therefore, all curves have a same slop not only for small gap materials but also for large gap ceramics; the general expression

*Work of adhesion as function of calculated Rayleigh velocities of different ceramic substrates in contacting with*

*Wad*ð Þ¼ *Au* 0*:*07*VRC* þ 553 (8)

*Wad*ð Þ¼ *Au* 0*:*07*VRC* þ 76 (9)

*Wad* ð Þ¼ *Me* 0*:*07 *VRC* þ *C* (10) *Wad* ð Þ¼ *Me* 0*:*07 *VRC* þ ́*C* (11)

strate, as discussed below.

to be of the form:

*Liquid Metals*

to be of the form:

takes the form:

**Figure 5.**

**40**

*several metals [15].*

where the subscript, (Me), represents any given investigated nonreactive liquid metal (Ag, Au, Cu, Ga and Sn), C and Ć are characteristic constants for each metal/ ceramic combination.

The exact corresponding values of characteristic constants C (for small gap ceramic materials) and Ć (for large gap ceramic materials) of several liquid metal/ ceramic systems are giving in the **Table 3**.

The similar dependence (with the same slope equal to 0.07VRC) is indicative of the existence of the same mechanism responsible for this behavior. However the existence of two parallel dependences for every system is due to the energy band structure of the ceramic materials in particular the energy gap (**Table 1**). A close analysis of **Figure 5** and the Eg column clearly shows that the upper set of curves corresponds to solid ceramic materials with small energy gaps (Eg ≤ 3 eV), whereas the lower ensemble of curves represents ceramic materials with large energy gaps (Eg > 3 eV).

In fact, solid materials with small band gaps behave as conductors (Eg ! 0) or semiconductors (Eg ≤ 3 eV). In this case, it was reported [35] that the high adhesion energy values of same metal/ceramic systems are associated with high electron density of metals and low band gap energy of solids ceramics. The interfacial adhesion between a metal and a ceramic crystal is assured by the electron transfer [12], it is interesting to define an interfacial propriety represents the minimum energy needed for appearance of a limit number of interfacial bonds responsible for generating of the adhesion between the metal and the ceramic, this energy is caused by Van der Waals interaction, WVDW. The intensity of the electron transfer at small band gap solid ceramic is increased because of its wealth by the free charges inside and the chemical equilibrium contribution Wchem-equil taking place.

For large band gaps, there will be practically a small number of free charges inside in the ceramic crystal. As a result, the chemical equilibrium contribution Wchem-equil, to the adhesion energy is negligible. Consequently, the adhesion energy is approximately resulted by from the Van der Waals interaction [12].

The Van der Waals contribution of adhesion energy rested constant and proportional with Rayleigh velocity of ceramic materials whether it is the band gap energy, for the first time it is determined exactly as follows:

$$W\_{\rm VDW} = 0.07 \,\text{V}\_{\rm RC} \tag{12}$$

The determinate WVDW energy values for different metal/ceramic systems depend directly on the choice of various parameters appearing in Eq. (3). For example, Mc Donald and Eberhart [36] calculated WVDW values equal to <sup>500</sup> � 150 mJ/m<sup>2</sup> for different metal/alumina systems, that in our model and for the same system we have found WVDW values equal to 396 mJ/m<sup>2</sup> . While Naidich [13] found WVDW values of 350 150 mJ/m<sup>2</sup> for metal/oxide ceramic systems, this


**Table 3.** *C and Ć values of different liquid metal/ceramic system.* confirms the compatibility between our proposed model and other model of WVDW estimation.

For small gap ceramic materials, the characteristic constant C of Eq. (10) represents Wchem-equil contribution, this energy is relatively important compared to WVDW energy, it represents another interfacial property responsible for putting the stability and the perfection to the interface between metal and ceramic. The good convergence in Wchem-equil values for a given metal/small gap ceramics could be explained by the fact that for (Eg < 3 eV), here will be a big density of inside in the ceramic crystal and consequently height electron transfer.

In this work, an analytical approach [20] is adopted to express the relation between experimental sound velocities of liquid metals, c, at the melting temperature and determinate Rayleigh velocity of these metals at solid state, VRM, by SAM program. Hence, VRM is expressed in terms of c, as we recently reported [20].

$$V\_{RM} = 0.674 \,\text{c} \tag{13}$$

The determinate chemical equilibrium energy, Wchem-equil of metal/small band gap ceramic system by Eq. (10) are summarized in **Table 4**.

The variations of chemical equilibrium energy on normalized Rayleigh velocity, (VRM/z) for different bulk metals in contacting with several small band gap ceramic materials are investigated, where z is number of coordination's of each metal atom. In this investigation, we consider Eq. (10) to determine Wchem-equil and some published wok on adhesion energy for different metals/ceramics systems [12, 13, 22–34]. The obtained results are presented below.

The dependence of Wchem-equil on (VRM/z) is quantified via curve fitting, (line in **Figure 6**). We distinguish dependence for liquid metal/small band gap ceramic substrate systems: the linear variation is found to be of the form:

$$W\_{chem-equil} = \ (\mathbf{1.3/z}) V\_{RM} \tag{14}$$

smaller density of inside in the ceramic crystal (practically no free charges inside) and consequently the electron transfer at metal/ceramic interfaces cannot be important [2]. As a result, the characteristic constant Ć values are negligible com-

*Chemical equilibrium energy of metal/small band gap ceramic system as function of normalized Rayleigh*

The importance of the deuced relation lies in its applicability to all investigated metal/ceramic systems. It could be extended, through familiar relations, to other acoustic parameters. Similar results for longitudinal and transverse velocities were obtained. Moreover, preliminary results for elastic constants (Young's modulus and

In this work, an interfacial phenomenon between liquid metals and ceramic substrates has been investigated. Moreover, same liquid metal characteristics (sound velocity propagation in liquid metal, liquid density and surface tension) were predicted by the metal characteristics in solid state (Rayleigh velocity, solid

*Wad* ð Þ¼ *Me* 0*:*07 *VRC* þ ð Þ 1*:*3*=z VRM* (15)

*Wad* ð Þ¼ *Me* 0*:*07 *VRC* þ *Wnegl* (16)

Therefore, the general expression of adhesion energy takes the form:

pared to WVDW energy and/or especially to Wchem-equil energy.

a. For small gap ceramic materials:

*velocities of different bulk metals [15].*

*Adhesion Phenomenon of Liquid Metals DOI: http://dx.doi.org/10.5772/intechopen.97419*

b. For large gap ceramic materials:

shear modulus) are very satisfying.

**5. Conclusions**

**43**

**Figure 6.**

So, the chemical equilibrium contribution of adhesion energy in metal/ceramic system is related directly to the Rayleigh velocity of metals.

For large gap ceramic materials, the discrepancy in Ć values for a given metal/ large gap ceramics could be explained by the fact that for (Eg > 3 eV), here will be a


#### **Table 4.**

*Determinate chemical equilibrium energy,* Wchem-equil *of metal/small band gap ceramic system and the number of coordination's of each atom of metal,* z*.*

**Figure 6.**

confirms the compatibility between our proposed model and other model of WVDW

sents Wchem-equil contribution, this energy is relatively important compared to WVDW energy, it represents another interfacial property responsible for putting the stability and the perfection to the interface between metal and ceramic. The good convergence in Wchem-equil values for a given metal/small gap ceramics could be explained by the fact that for (Eg < 3 eV), here will be a big density of inside in the

In this work, an analytical approach [20] is adopted to express the relation between experimental sound velocities of liquid metals, c, at the melting temperature and determinate Rayleigh velocity of these metals at solid state, VRM, by SAM program. Hence, VRM is expressed in terms of c, as we recently reported [20].

The determinate chemical equilibrium energy, Wchem-equil of metal/small band

The variations of chemical equilibrium energy on normalized Rayleigh velocity, (VRM/z) for different bulk metals in contacting with several small band gap ceramic materials are investigated, where z is number of coordination's of each metal atom. In this investigation, we consider Eq. (10) to determine Wchem-equil and some published wok on adhesion energy for different metals/ceramics systems [12, 13,

The dependence of Wchem-equil on (VRM/z) is quantified via curve fitting, (line in **Figure 6**). We distinguish dependence for liquid metal/small band gap ceramic

So, the chemical equilibrium contribution of adhesion energy in metal/ceramic

For large gap ceramic materials, the discrepancy in Ć values for a given metal/ large gap ceramics could be explained by the fact that for (Eg > 3 eV), here will be a

> *(mJ/m<sup>2</sup> )*

Ag 991 2 Al 1269 3 Au 553 3 Cu 1309 2 Co 1341 3 Fe 1276 3 In 723 3 Ni 1193 3 Ga 863 3 Sn 602 4

*Determinate chemical equilibrium energy,* Wchem-equil *of metal/small band gap ceramic system and the*

*VRM* ¼ 0*:*674 *c* (13)

*Wchem*�*equil* ¼ ð Þ 1*:*3*=z VRM* (14)

**Z**

ceramic crystal and consequently height electron transfer.

gap ceramic system by Eq. (10) are summarized in **Table 4**.

substrate systems: the linear variation is found to be of the form:

system is related directly to the Rayleigh velocity of metals.

**Metals** *Wchem-equil*

*number of coordination's of each atom of metal,* z*.*

22–34]. The obtained results are presented below.

For small gap ceramic materials, the characteristic constant C of Eq. (10) repre-

estimation.

*Liquid Metals*

**Table 4.**

**42**

*Chemical equilibrium energy of metal/small band gap ceramic system as function of normalized Rayleigh velocities of different bulk metals [15].*

smaller density of inside in the ceramic crystal (practically no free charges inside) and consequently the electron transfer at metal/ceramic interfaces cannot be important [2]. As a result, the characteristic constant Ć values are negligible compared to WVDW energy and/or especially to Wchem-equil energy.

Therefore, the general expression of adhesion energy takes the form:

a. For small gap ceramic materials:

$$\left(\mathcal{W}\_{ad}\left(\mathrm{Me}\right) = \mathbf{0}.07\,\,\mathcal{V}\_{\mathrm{RC}} + \left(\mathbf{1}.\mathbf{3}/\mathbf{z}\right)\,\,\mathcal{V}\_{\mathrm{RM}}\tag{15}$$

b. For large gap ceramic materials:

$$\mathcal{W}\_{ad} \ (\mathcal{M}e) = 0.07 \ V\_{\mathcal{R}\mathcal{C}} + \mathcal{W}\_{\text{neg}l} \tag{16}$$

The importance of the deuced relation lies in its applicability to all investigated metal/ceramic systems. It could be extended, through familiar relations, to other acoustic parameters. Similar results for longitudinal and transverse velocities were obtained. Moreover, preliminary results for elastic constants (Young's modulus and shear modulus) are very satisfying.

#### **5. Conclusions**

In this work, an interfacial phenomenon between liquid metals and ceramic substrates has been investigated. Moreover, same liquid metal characteristics (sound velocity propagation in liquid metal, liquid density and surface tension) were predicted by the metal characteristics in solid state (Rayleigh velocity, solid density and Young's modulus). Adhesion energy terms in metals/ceramic systems were determined by using an electro-acoustic model. It was shown that the adhesion energy increases linearly with Rayleigh velocity of ceramic substrates for all types of ceramics. Van der Waals term of adhesion energy was deduced only depends on Rayleigh velocities of ceramic. On the other hand, the chemical equilibrium term was deduced strongly depends on the energy gap of the ceramics materials: it was higher for small band gap ceramic materials and depends on Rayleigh velocities of metals, for the opposite case it was deduced negligible. These universal relations that could be extended to other acoustic parameters are applicable to all metal/ceramic combinations.

**References**

2005.01.047

optcom.2019.124437

2019.01.005

2019.06.011

121871

**45**

[3] Yan D, Phang SP, Wan YM,

[1] Gordon I, Van Gestel D, Van Nieuwenhuysen K, Carnel L,

*Adhesion Phenomenon of Liquid Metals DOI: http://dx.doi.org/10.5772/intechopen.97419*

https://doi.org/10.1016/j.tsf.

Poortmans J. Thin-film polycrystalline silicon solar cells on ceramic substrates by aluminium-induced crystallization, Thin Solid Films, 2005;487: 113-117.

[7] Bulyarskiy SV, The effect of electronphonon interaction on the format,ion of reverse currents of p-n-junctions of silicon-based power semiconductor devices, Solid-State Electronics, 2019; 160: 107624. https://doi.org/10.1016/j.

[8] Wang J, Wu L, Chen X, Zhuo W, Avoiding blister defects in low-stress hydrogenated amorphous silicon films for MEMS sensors, Sensors and

Actuators A: Physical, 2018; 276: 11-16. https://doi.org/10.1016/j.sna.2018.

Leepattarapongpan C, Srisuwan A, Jeamsaksiri W, Sooriakumar K,

[10] Almuramady N, Borodich,

microgear MEMS, Tribology International, 2018; 129: 202-213. https://doi.org/10.1016/j.triboint.

Photonic Materials, Springer Handbooks. Springer, Cham; 2017, https://doi.org/10.1007/978-3-

[12] Li JG, Chemical trends in the thermodynamic adhesion of metal/ ceramic systems, Mater. Let.. 1995; 22: 169-174. https://doi.org/10.1016/

[13] Naidich YV, The wettability of solids by liquid metals, Progr. Surf.

0167-577X(94)00244-4

2018.07.049

319-48933-9\_53

Feodor MB, Goryacheva I, Torskaya EV, Damage of functionalized self-assembly monomolecular layers applied to silicon

[11] Frear D, Packaging Materials, Eds, Springer Handbook of Electronic and

Austin A, Niemcharoena S, Fabrication of MEMS-based capacitive silicon microphone structure with staircase contour cavity using multi-film thickness mask, Microelectronic Engineering, 2019; 206: 17-24. https:// doi.org/10.1016/j.mee.2018.12.004

[9] Jantawong J, Atthi N,

sse.2019.107624

04.021

[2] Tabrizia AA, Pahlavan A. Efficiency, improvement of a silicon-based thinfilm solar cell using plasmonic silver nanoparticles and an antireflective layer, Optics Communications, 2020; 454: 124437. https://doi.org/10.1016/j.

Samundsett C, Macdonald D, Cuevas A. High efficiency n-type silicon solar cells with passivating contacts based on PECVD silicon films doped by phosphorus diffusion, Solar Energy Materials and Solar Cells, 2019;193: 80-84. https://doi.org/10.1016/j.solmat.

[4] Shao X, XiS, Li G, Liu Peng R, Li C, Chen G, ChenR. Longer hydrogenation duration for large area multi-crystalline

silicon solar cells based on highintensity infrared LEDs, Optics Communications, 2019; 450: 252-260. https://doi.org/10.1016/j.optcom.

[5] Legallais M, Thu T, Nguyen T, Cazimajou T, Mouis M, SalemB, Ternon C, Material engineering of percolating silicon nanowire networks for reliable and efficient electronic devices, Materials Chemistry and Physics, 2019;2 38: 121871, https://doi. org/10.1016/j.matchemphys.2019.

[6] Zhang X, Feng M, Zhao M, Zhang P, He C, Qi H, Han W, Guo F, Failure of silicon nitride ceramic flotation spheres at critical state of implosion, Applied Ocean Research, 2020;97: 102080 https:// doi.org/10.1016/j.apor.2020.102080

## **Author details**

Hadef Zakaria\* and Kamli Kenza Department of Physics, Faculty of Sciences, University 20 Août 1955-Skikda, Skikda, Algeria

\*Address all correspondence to: zaki-hd2013@yahoo.fr; z.hadef@univ-skikda.dz

© 2021 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

*Adhesion Phenomenon of Liquid Metals DOI: http://dx.doi.org/10.5772/intechopen.97419*

#### **References**

density and Young's modulus). Adhesion energy terms in metals/ceramic systems were determined by using an electro-acoustic model. It was shown that the adhesion energy increases linearly with Rayleigh velocity of ceramic substrates for all types of ceramics. Van der Waals term of adhesion energy was deduced only depends on Rayleigh velocities of ceramic. On the other hand, the chemical equilibrium term was deduced strongly depends on the energy gap of the ceramics materials: it was higher for small band gap ceramic materials and depends on Rayleigh velocities of metals, for the opposite case it was deduced negligible. These universal relations that could be extended to other acoustic parameters are applica-

ble to all metal/ceramic combinations.

*Liquid Metals*

**Author details**

Skikda, Algeria

**44**

Hadef Zakaria\* and Kamli Kenza

provided the original work is properly cited.

Department of Physics, Faculty of Sciences, University 20 Août 1955-Skikda,

\*Address all correspondence to: zaki-hd2013@yahoo.fr; z.hadef@univ-skikda.dz

© 2021 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

[1] Gordon I, Van Gestel D, Van Nieuwenhuysen K, Carnel L, Poortmans J. Thin-film polycrystalline silicon solar cells on ceramic substrates by aluminium-induced crystallization, Thin Solid Films, 2005;487: 113-117. https://doi.org/10.1016/j.tsf. 2005.01.047

[2] Tabrizia AA, Pahlavan A. Efficiency, improvement of a silicon-based thinfilm solar cell using plasmonic silver nanoparticles and an antireflective layer, Optics Communications, 2020; 454: 124437. https://doi.org/10.1016/j. optcom.2019.124437

[3] Yan D, Phang SP, Wan YM, Samundsett C, Macdonald D, Cuevas A. High efficiency n-type silicon solar cells with passivating contacts based on PECVD silicon films doped by phosphorus diffusion, Solar Energy Materials and Solar Cells, 2019;193: 80-84. https://doi.org/10.1016/j.solmat. 2019.01.005

[4] Shao X, XiS, Li G, Liu Peng R, Li C, Chen G, ChenR. Longer hydrogenation duration for large area multi-crystalline silicon solar cells based on highintensity infrared LEDs, Optics Communications, 2019; 450: 252-260. https://doi.org/10.1016/j.optcom. 2019.06.011

[5] Legallais M, Thu T, Nguyen T, Cazimajou T, Mouis M, SalemB, Ternon C, Material engineering of percolating silicon nanowire networks for reliable and efficient electronic devices, Materials Chemistry and Physics, 2019;2 38: 121871, https://doi. org/10.1016/j.matchemphys.2019. 121871

[6] Zhang X, Feng M, Zhao M, Zhang P, He C, Qi H, Han W, Guo F, Failure of silicon nitride ceramic flotation spheres at critical state of implosion, Applied Ocean Research, 2020;97: 102080 https:// doi.org/10.1016/j.apor.2020.102080

[7] Bulyarskiy SV, The effect of electronphonon interaction on the format,ion of reverse currents of p-n-junctions of silicon-based power semiconductor devices, Solid-State Electronics, 2019; 160: 107624. https://doi.org/10.1016/j. sse.2019.107624

[8] Wang J, Wu L, Chen X, Zhuo W, Avoiding blister defects in low-stress hydrogenated amorphous silicon films for MEMS sensors, Sensors and Actuators A: Physical, 2018; 276: 11-16. https://doi.org/10.1016/j.sna.2018. 04.021

[9] Jantawong J, Atthi N, Leepattarapongpan C, Srisuwan A, Jeamsaksiri W, Sooriakumar K, Austin A, Niemcharoena S, Fabrication of MEMS-based capacitive silicon microphone structure with staircase contour cavity using multi-film thickness mask, Microelectronic Engineering, 2019; 206: 17-24. https:// doi.org/10.1016/j.mee.2018.12.004

[10] Almuramady N, Borodich, Feodor MB, Goryacheva I, Torskaya EV, Damage of functionalized self-assembly monomolecular layers applied to silicon microgear MEMS, Tribology International, 2018; 129: 202-213. https://doi.org/10.1016/j.triboint. 2018.07.049

[11] Frear D, Packaging Materials, Eds, Springer Handbook of Electronic and Photonic Materials, Springer Handbooks. Springer, Cham; 2017, https://doi.org/10.1007/978-3- 319-48933-9\_53

[12] Li JG, Chemical trends in the thermodynamic adhesion of metal/ ceramic systems, Mater. Let.. 1995; 22: 169-174. https://doi.org/10.1016/ 0167-577X(94)00244-4

[13] Naidich YV, The wettability of solids by liquid metals, Progr. Surf. Membr. Sci., 1981; 14:353-486. http:// dx.doi.org/10.1016/B978-0-12-571814- 1.50011-7

[14] Viktorov IA, Rayleigh and Lamb Waves, Plenum Press, New York, 1967.

[15] Kamli K, Hadef Z, Gacem A, Houaidji N. Prediction of Adhesion Energy Terms in Metal/Ceramic Systems by Using Acoustic Parameters, Metallophysics and Advanced Technologies, 2020; 42(5): 717–730. https://doi.org/10.15407/mfint. 42.05.0717

[16] Blairs S, Correlation between surface tension, density, and sound velocity of liquid metals, Coll. Inter. Sci., 2006; 302: 312-314. https://doi: 10.1016/j.jcis.2006.06.025

[17] Keene BJ, Review of data for the surface tension of pure metals, Int. Mat. Rev., 1993; 38: 157-192. https://doi.org/ 10.1179/imr.1993.38.4.157

[18] Crawley AF, Densities of Liquid Metals and Alloys, Int. Met. Rev., 1974; 19: 32-48. https://doi.org/10.1179/ imtlr.1974.19.1.32

[19] Briggs GAD, Kolosov OV, Acoustic Microscopy, Oxford Univ. Press, 2nd Edition, New York, 2010. DOI:10.1093/ acprof:oso/9780199232734.001.0001

[20] Hadef Z, Doghmane A, Kamli K, Hadjoub Z, Correlation between surface tension, work of adhesion in liquid metals/ceramic systems and acoustic parameters, Progress in Physics of Metals, 2018; 19(2): 198-223. https://doi. org/10.15407/ufm.19.01.198

[21] Strehlow WH, Cook EL, Compilation of Energy Band Gaps in Elemental and Binary Compound Semiconductors and Insulators, J. Phys. Chem. Ref. Data, 1973; 2: 163-199. https://doi.org/10.1063/1.3253115

[22] Eustathopoulos N, Sobczak N, Passerone A. Nogi K. Measurement of contact angle and work of adhesion at high temperature, Mater. Sci., 2005; 40: 2271-2280. https://doi.org/10.1007/ s10853-005-1945-4

https://doi.org/10.1016/0167-577X(91)

[31] Li JG, Wetting and interfacial bonding in liquid metal/solid ceramic systems, Comp. Interf., 1993; 1: 37-53.

*Adhesion Phenomenon of Liquid Metals DOI: http://dx.doi.org/10.5772/intechopen.97419*

[32] Li JG, Hausner H, Wetting and adhesion in liquid silicon/ceramic systems,Mater. Letters, 1992; 14: 329-332. https://doi.org/10.1016/

thermodynamique dans les systèmes non-réactifs métal liquide-alumine, Chim. Phys., 1986; 83: 561-567. https:// doi.org/10.1051/jcp/1986830561

[34] Sotiropoulou D, Nikolopoulos P, Work of adhesion in ZrO2-liquid metal systems, J. Mater. Sci., 1993; 28: 356-360. https://doi.org/10.1007/

[35] Li JG, Role of electron density of liquid metals and band gap energy of solid ceramics on the work of adhesion and wettability of metal-ceramic systems, Mater. Sci. Let., 1992; 11: 903-905. https://doi.org/10.1007/

[36] Mc Donald JB, Eberhart JG. Adhesion in aluminum oxide-metal systems, Trans. AIME, 1965; 233:

https://doi.org/10.1163/ 156855493X00301

0167-577X(92)90047-N

[33] Chatain D, Rivollet I, Eustathopoulos N, Adhésion

BF00357807

BF00729089

512-517.

**47**

90133-Q

[23] Naidich YV, Zhuravlev VS, Frumina NI, Wetting of rare-earth element oxides by metallic melts, Mater. Sci., 1990; 25: 1895-1901. https://doi. org/10.1007/BF01045739

[24] Li JG, Wettability of Solid Inorganic Materials by Gold, Scripta Metall. Mater., 1994; 30: 337-342. https://doi. org/10.1016/0956-716X(94)90385-9

[25] Taranets NY, Naidich YV, Wettability of aluminum nitride by molten metals, Powder Metall. Met. Ceramics, 1996; 35: 74-78. https://doi. org/10.1007/BF01328834

[26] Liu GW, Muolo ML, Valenza F, Passerone A, Survey on wetting of SiC by molten metals, Ceram. Inter., 2010; 36: 1177-1188. https://doi.org/10.1016/j. ceramint.2010.01.001

[27] Kida M, Bahraini M, Molina JM, Weber L, Mortensen A, Hightemperature wettability of aluminum nitride during liquid metal infiltration, Mater. Sci. Eng. A, 2008; 495: 197-202. https://doi:10.1016/j.msea.2007.12.050

[28] Naidich YV, About liquid metal/ ceramic interface interaction mechanism and mode of a new intermediate compound formation, Curr. Opi. Sol. Sta. Mater. Sci., 2005: 161-166. https://doi.org/10.1016/j. cossms.2005.11.001

[29] Li JG, Wetting and Interfacial Bonding of Metals with Ionocovalent Oxides, J. Amer. Ceram. Soc., 1992; 75: 3118-3126. https://doi.org/10.1111/ j.1151-2916.1992.tb04396.x

[30] Li JG, Hausner H, Contact angle and work of adhesion isotherms of silicontin alloys on monocrystalline silicon carbide, Mater. Let,, 1991; 11: 355-357.

*Adhesion Phenomenon of Liquid Metals DOI: http://dx.doi.org/10.5772/intechopen.97419*

https://doi.org/10.1016/0167-577X(91) 90133-Q

Membr. Sci., 1981; 14:353-486. http:// dx.doi.org/10.1016/B978-0-12-571814contact angle and work of adhesion at high temperature, Mater. Sci., 2005; 40: 2271-2280. https://doi.org/10.1007/

[24] Li JG, Wettability of Solid Inorganic Materials by Gold, Scripta Metall. Mater., 1994; 30: 337-342. https://doi. org/10.1016/0956-716X(94)90385-9

[23] Naidich YV, Zhuravlev VS, Frumina NI, Wetting of rare-earth element oxides by metallic melts, Mater. Sci., 1990; 25: 1895-1901. https://doi.

org/10.1007/BF01045739

[25] Taranets NY, Naidich YV, Wettability of aluminum nitride by molten metals, Powder Metall. Met. Ceramics, 1996; 35: 74-78. https://doi.

[26] Liu GW, Muolo ML, Valenza F, Passerone A, Survey on wetting of SiC by molten metals, Ceram. Inter., 2010; 36: 1177-1188. https://doi.org/10.1016/j.

[27] Kida M, Bahraini M, Molina JM, Weber L, Mortensen A, Hightemperature wettability of aluminum nitride during liquid metal infiltration, Mater. Sci. Eng. A, 2008; 495: 197-202. https://doi:10.1016/j.msea.2007.12.050

[28] Naidich YV, About liquid metal/

[29] Li JG, Wetting and Interfacial Bonding of Metals with Ionocovalent Oxides, J. Amer. Ceram. Soc., 1992; 75: 3118-3126. https://doi.org/10.1111/

[30] Li JG, Hausner H, Contact angle and work of adhesion isotherms of silicontin alloys on monocrystalline silicon carbide, Mater. Let,, 1991; 11: 355-357.

j.1151-2916.1992.tb04396.x

ceramic interface interaction mechanism and mode of a new intermediate compound formation, Curr. Opi. Sol. Sta. Mater. Sci., 2005: 161-166. https://doi.org/10.1016/j.

cossms.2005.11.001

org/10.1007/BF01328834

ceramint.2010.01.001

s10853-005-1945-4

[14] Viktorov IA, Rayleigh and Lamb Waves, Plenum Press, New York, 1967.

[15] Kamli K, Hadef Z, Gacem A, Houaidji N. Prediction of Adhesion Energy Terms in Metal/Ceramic Systems by Using Acoustic Parameters,

Metallophysics and Advanced Technologies, 2020; 42(5): 717–730. https://doi.org/10.15407/mfint.

[16] Blairs S, Correlation between surface tension, density, and sound velocity of liquid metals, Coll. Inter. Sci., 2006; 302: 312-314. https://doi:

[17] Keene BJ, Review of data for the surface tension of pure metals, Int. Mat. Rev., 1993; 38: 157-192. https://doi.org/

[18] Crawley AF, Densities of Liquid Metals and Alloys, Int. Met. Rev., 1974; 19: 32-48. https://doi.org/10.1179/

[19] Briggs GAD, Kolosov OV, Acoustic Microscopy, Oxford Univ. Press, 2nd Edition, New York, 2010. DOI:10.1093/ acprof:oso/9780199232734.001.0001

[20] Hadef Z, Doghmane A, Kamli K, Hadjoub Z, Correlation between surface tension, work of adhesion in liquid metals/ceramic systems and acoustic parameters, Progress in Physics of Metals, 2018; 19(2): 198-223. https://doi.

org/10.15407/ufm.19.01.198

[21] Strehlow WH, Cook EL,

Compilation of Energy Band Gaps in Elemental and Binary Compound Semiconductors and Insulators, J. Phys. Chem. Ref. Data, 1973; 2: 163-199. https://doi.org/10.1063/1.3253115

[22] Eustathopoulos N, Sobczak N, Passerone A. Nogi K. Measurement of

**46**

10.1016/j.jcis.2006.06.025

10.1179/imr.1993.38.4.157

imtlr.1974.19.1.32

1.50011-7

*Liquid Metals*

42.05.0717

[31] Li JG, Wetting and interfacial bonding in liquid metal/solid ceramic systems, Comp. Interf., 1993; 1: 37-53. https://doi.org/10.1163/ 156855493X00301

[32] Li JG, Hausner H, Wetting and adhesion in liquid silicon/ceramic systems,Mater. Letters, 1992; 14: 329-332. https://doi.org/10.1016/ 0167-577X(92)90047-N

[33] Chatain D, Rivollet I, Eustathopoulos N, Adhésion thermodynamique dans les systèmes non-réactifs métal liquide-alumine, Chim. Phys., 1986; 83: 561-567. https:// doi.org/10.1051/jcp/1986830561

[34] Sotiropoulou D, Nikolopoulos P, Work of adhesion in ZrO2-liquid metal systems, J. Mater. Sci., 1993; 28: 356-360. https://doi.org/10.1007/ BF00357807

[35] Li JG, Role of electron density of liquid metals and band gap energy of solid ceramics on the work of adhesion and wettability of metal-ceramic systems, Mater. Sci. Let., 1992; 11: 903-905. https://doi.org/10.1007/ BF00729089

[36] Mc Donald JB, Eberhart JG. Adhesion in aluminum oxide-metal systems, Trans. AIME, 1965; 233: 512-517.

**49**

Section 3

Surface Modification

Section 3
