L Pawłowski

Soufiane Oukach

Bernard Pateyron

Pawłowski Lech
email: lech.pawlowski@unilim.fr

B Oukach

L Pateyron

Pawłowski

Physical and chemical phenomena occurring between solid ceramics and liquid metals and alloys at laser and plasma composite coatings formation: A review

Keywords: Metal matrix composite, coatings build-up, plasma transferred arc, laser cladding, hardfacing, wetting of solid ceramics by liquid metal -zirconium Exponents

The review describes the physical and chemical phenomena occurring between solid ceramics used as reinforcement and liquid metals and alloys used as matrix in the composite coatings. Initially, the properties of typical matrix metals as Ni, Co, Fe and alloys as Ni-based (NiCr, NiAl, NiCrAlY,…) and Cobased (Stellites) alloys in liquid state are described. Then, the phenomena related to the diffusion of some atoms such as nitrogen or carbon in liquid metals and alloys solidification are described.

Subsequently, the phenomena at the interface between liquid metals and alloys and solid ceramics such as oxides or carbides during the coatings' formation are reviewed. Finally, the methods of composite coatings deposition using laser cladding and plasma transferred arc are described and the properties of the composite coatings related to their microstructure are discussed by taking into account the phenomena in melt-pool.

M -molar mass, g/mol P -pressure, Pa or power, W Q -deposition factor (see Eq. 9), J.s/(m.kg) or activation energy, J q -feed rate, kg/s or power density, W/m 2 R -constant of perfect gases R ≈ 8.314 J/( K. mol) r -radius, m slpm -standard liter per minute T -Temperature, K t -time, s U -speed, m/s 1 V -volume, m 3 W a -work of adhesion, J/m 2 X -fraction (see Table 9) Y -fraction (see Table 9)

Greeks letters

α -thermal expansion coefficient, K -1 γ -surface tension, J/m 2 λ -heat conductivity, W/(m.K) ∆G -Gibbs free energy, J/mol ∆Gf 0 -Gibbs free energy of formation, J/mol ∆Hf 0 -enthalpy of formation, J/mol ∆Hm -Gibbs free energy of mixing, J/mol θ -angle of contact, ° ρ -density, kg/m -3 σ -stress, MPa or surface energy, J/m 2 τ -duration of pulse, s

SL -contact between solid and liquid Introduction

The elaboration of composite materials enables obtaining interesting properties, impossible to reach in homogeneous materials. These properties are particularly important on their surfaces enhancing their usefulness and duration in service. One of the ways leading to a formation of composites is melting of material surface and injecting of a reinforcement. The methods associated with such manufacturing technology are called often hardfacing or surfacing by welding. Frequently, the molten surface is of metallic or alloy substrate and reinforcement is of such ceramics as carbides and/or oxides. The coatings technology may be categorized following the way of substrate melting, which occurs mainly by: (i) combustion flame; (ii) plasma and electric arc (plasma transferred arc, PTA); and, (iii) laser beam (laser cladding). Most of the published recently papers describe the coatings manufactured by PTA and by laser cladding and many of properties of coatings obtained with these two techniques are analyzed carefully in present review. The properties of composite metal matrix composite (MMC) coatings, called also surface metal matrix composites (SMMC), depend strongly of geometric factors such as shape of reinforcement and its distribution in the matrix [1]. The present review is focused on the metal matrix composites reinforced with ceramics powder, called particles reinforced MMC (PRMMC). The distribution of the reinforcement in the matrix depends strongly on the phenomena related to the wettability of solid reinforcement in liquid matrix and is also discussed in the review. The phenomena occur at high temperatures during the short time when the heat source melts the substrate forming a liquid bath which subsequently solidifies [2,[START_REF] Pawłowski | Dépôts Physiques[END_REF]. The review describes the substrates being applied often in hardfacing, namely metals 9 such as Ni, Co and Fe and alloys such as NiCr, NiCrAlY, stellites and stainless steel. Consequently, phase diagrams and some properties including some thermodynamic functions, surface energy, thermal expansion of selected metals and alloys are shortly reviewed. The problems related to rapid solidification with the rate ranging from 10 4 to 10 8 K/s of metals and alloys included in composites influence their microstructures [START_REF] Kurz | Fundamentals of Solidification[END_REF][START_REF] Dantzig | Solidification[END_REF]. In some solidification conditions the amorphous or dendrites including microstructure can be formed. The liquid matrix remains during a short time in contact with solid ceramics. The related phenomena are discussed starting from the law of Young-Dupré [START_REF] Dupré | Théorie Mécanique de la Chaleur, Chapitre IX[END_REF]. The described phenomena may occur with or without a chemical reaction on the interface between metallic matrix and ceramics. An important element of discussion is related to the geometry of liquid with solid interaction. Namely, in most of the cases discussed in the literature a liquid droplet is in contact with cold substrate (see Fig. 1 a). Inversely, at hardfacing, the solid particles are surrounded by liquid material as shows. The angle of wetting influences, in this case, the porosity between particle and matrix as show it Some important factors influencing the reactive and no-reactive wetting are shortly described. Finally, the techniques being presently used for hardfacing, including plasma and laser assisted ones, are described in details.

The hardfacing is accompanied by melting of metallic substrate by plasma, flame or laser.

The sources of heat, the methods of melting as well as the phenomena occurring may be found in the papers related to welding. For example, the modern methods of plasma arc welding were recently reviewed by Liu et al. [START_REF] Liu | Plasma arc welding: Process variants and its recent developments of sensing, controlling and modeling[END_REF].

The metal matrix composite (MMC) coatings may be obtained using PTA, laser cladding and thermal spraying. These composites were reviewed by Deuis et al. [START_REF] Deuis | Metal matrix composite by PTA surfacing[END_REF]. However, it is also possible to manufacture the MMC using other methods. An example is heat treatment of preplaced powder.

Consequently, Fan et al. [START_REF] Fan | An ultra-hard and thick composite coatings metallurgically bonded to Ti-6Al-4V[END_REF] preplaced the mixture of Ti-Zr-Cu-Ni alloy matrix with TiC powder reinforcement onto Ti6Al4V substrate. The mixture was subsequently submitted to vacuum heat treatment what enabled obtaining composite coatings. It must be added, that temperature of treatment was low and the substrate did not melt. Consequently, the method is different than the hardfacing associated formation of melt-pool in substrate by plasma, flame or laser.

The quality of the composite coatings produced by hardfacing depends on many factors related to the phenomena occurring at the processing. The process parameters resulting in a formation of melt pool and on interaction of liquid metal/alloy with solid ceramics are particularly important. The present review focuses on this interaction.

Properties of composite matrices of metals and alloys

The MMC are most frequently composed of metals as Al, Ni, Co, Ti, Fe and their alloys being MMC can be categorized as particulate composites reinforced with particles and fibrous composites reinforced with continuous monofilaments or short fibers (e.g. whiskers). Particulate MMC are more frequently applied while fibrous ones have only a few industrial applications. In fact, although the mechanical properties of fibrous composites, especially that reinforced with the monofilaments, are very good, their cost is generally higher than 100 €/kg. The high price results from the price of fibers and from the difficulty of their introduction into the matrix. That is why, the authors decided to focus the review on particulate MMCs.

It can be mentioned that the composites of cobalt reinforced with WC particles or that of nickel reinforced with TiC, TiN or Mo2C are used frequently for cutting and mining tools and for high temperature protection. The ceramic materials used frequently for reinforcement of composites are also SiC and Al2O3 and, to a lesser extent, ZrO2, Al2TiO5, B4C and Si3N4. The reinforcing particles may be also mixture of these different ceramics and may be characterized by their composition, size, hardness and shape (see e.g. Emanian et al. [START_REF] Emanian | The effect of powder composition on the morphology of in situ TiC composite coating deposited by Laser-Assisted Powder Deposition (LAPD)[END_REF]).

Mechanical properties of some metals and alloys

The main application of MMC is wear resistance against abrasion, erosion and friction. Indeed, the service life of wear parts coated with MMC may be tripled with regards to uncoated alloys. Comparing to aluminum alloys, MMCs may also have slightly higher (by 10 to 20 %) Young's modulus and yield strength. It is also possible to modify the coefficient of expansion of the composite by adding an appropriate quantity of reinforcement.

The ceramic particles finely dispersed in a matrix improve the mechanical properties of the MMCs by the following ways:

• reinforcement particles are breakpoints to the propagation of a cracks and slow down their speed;

• cracks cannot propagate in a straight line as in pure matrix but rather zigzag between the particles what increases the total path of propagation. Some properties of pure metals are collected in Table 1. Some properties may be improved by the use of superalloys. The superalloys, which are high performance metal alloys, have excellent mechanical strength and good creep resistance up to high temperatures (about 0.7 -0.8 x Tm), and are resistant against corrosion. Their crystal structure is typically face centered cubic. The metals used in superalloys are most often nickel, cobalt and iron and to a lesser extent, titanium and aluminum. The superalloys found their applications in aircraft engine turbines (turbojet turbines blades) and gas turbines. They are identified by their trade names, such as: Hastelloy, Inconel,

Stellite.

Table 1 Some properties of pure metals [START_REF] Rumble | CRC Handbook of Chemistry and Physics[END_REF]. The data showed in Table 2 concern the most commonly used alloy composed of nickel and 20 wt. % chromium. However, there are many other compositions of these metals for various applications. Nichrome is corrosion resistant. Because of its low cost of manufacturing, high strength, ductility, resistance to oxidation, stability at high temperatures, this alloy is widely used in electric heating elements used e. g. as hair dryers. Nickel aluminides have useful mechanical properties and high thermal conductivity at high temperatures but they may be fractured in a brittle way at ambient temperatures [START_REF] Dey | Physical metallurgy of nickel aluminides[END_REF]16]. These compounds are applied frequently in gas turbines and jet engines. IC-221M alloy includes Ni3Al and some other elements such as chromium, molybdenum, zirconium and boron [16]. The addition of boron increases the ductility of the alloy and its hardness. This strengthening occurs by effect Hall -Petch i.e. by decrease of the crystallites size which hampers the movement of dislocations and modifies the yield strength. This alloy is even stronger than well-known SAE 304 stainless steel and its strength increases from room temperature up to 800 °C [START_REF] Dey | Physical metallurgy of nickel aluminides[END_REF]16].

Nickel-based alloys

Nickel aluminides are resistant against heat and corrosion and some of their properties are collected in Table 3. Inconels retain their strength at high temperatures. This strength results from solid solution strengthening or from precipitation hardening.

2.1.1.6.

Hastelloy TM

Hastelloys belong to a family of nickel alloys superalloys including also chromium, cobalt, copper, iron, manganese, aluminum, magnesium, molybdenum, silicon, zirconium and titanium and other elements being particularly resistant to corrosion. The alloys may be also used resistant against high temperature corrosion and against wear. There is a lot of Hastelloys having different composition.

The alloys are note by the letters associated with numbers. Table 4 shows the composition of some Hastelloys. CoMoCrSi alloys, known also as Tribaloy TM , combine wear and corrosion resistance with mechanical strength. The alloys include very hard intermetallic phases known as Laves phases [START_REF] Stein | Structure and stability of Laves phases. Part I. Critical assessment of factors controlling Laves phase stability[END_REF].

T-800 Tribaloy alloy includes about 50 % of these hard phases in soft cobalt matrix. This alloy is useful in contact with a hard surface where lubrication is difficult to apply. However, the alloy is brittle and has low resistance against crack initiation and propagation. This is particularly important in processing associated with high thermal stresses generation such as e.g. laser cladding [22]. A reduction of these hard phases content may be realized by addition of Ni done in T-900 alloy which is more ductile than T-800 alloy having however lower hardness and wear resistance.

Titanium alloys

Titanium alloys are very light and have high tensile strength and toughness. Moreover, they resist well against corrosion thanks to the passivation layer on their surface and against high temperature. A major drawback is the cost of raw materials and of their processing what limits their application to selected fields such as e.g. military or aviation industry [START_REF] Boyer | Attributes, characteristics, and applications of titanium and its alloys[END_REF]. Titanium and its alloys include e.g. [START_REF]Catalog of society ACNIS Int[END_REF]:

• T40, which is nearly pure titanium with a small addition of iron and oxygen used in aeronautic industry having density of 4510 kg/m 3 and tensile strength of 550 MPa;

• Ti-6Al-7Nb developed recently to replace a well-known alloy Ti-6Al-4V for medical applications includes titanium alloyed with 6% aluminum and 7 % niobium and has a density of 4520 kg/m 3 and tensile strength as high as 900 MPa.

Iron-based superalloys

The iron-based superalloys, which are less expensive than that cobalt-or nickel-based can be categorized in a following way [START_REF]Iron-based superalloys[END_REF]: (i) alloys strengthened by a martensitic type of transformation;

(ii) austenitic alloys strengthened by a sequence of hot and cold working; and, (iii) austenitic alloys strengthened by precipitation hardening. Generally, the martensitic types of alloys are used at temperatures below 800 K and the austenitic types above this temperature.

15

Iron-based superalloys are resistant against corrosion and wear. The latter increases with carbon content. The alloys 611, 612, and 613 are used against wear resistance. The martensitic steels are difficult to weld and should be annealed or tempered prior to welding.

Thermodynamic properties

The reviewed thermodynamic properties of liquid alloys concern mainly: (i) Gibbs free energy; (ii) surface energy; and, (iii) thermal expansion. The theoretical models will be used if the experimental measurements of properties of liquid alloys are not available.

Gibbs free energy

Gibbs free energy, ∆G, is also known as free enthalpy is a maximum energy which may be obtained from a system at constant temperature and pressure. The reacting system has a natural tendency to reach minimum Gibbs free energy. It provides information about atomic bonding strength and about stability of the alloys. The Gibbs free energy, ΔG, is negative for spontaneous processes, being positive for non-spontaneous ones. The following models can be used to study the behavior of liquid alloys:

• Pseudo-potential model [START_REF] Harrison | Pseudo Potential theory of Metals[END_REF][START_REF] Heine | Solid State Physics[END_REF] which can be generated for a chemical element, using different methods. This pseudo-potential can then be specifically used for a given system or for a group of systems in order to describe their physical properties.

• Hard sphere model [START_REF] Theile | Equation of state for hard spheres[END_REF][START_REF] Libowitz | Exact solution of generalized Percus-Yevick equation for a mixture of hard spheres[END_REF][START_REF] Faber | Introduction to the Theory of Liquid Metals[END_REF][START_REF] Simoji | Liquid Metals[END_REF] is frequently used to describe particles of fluids and solids in a statistical way. The spheres are submitted to strong repulsion that at very close distances.

The hard spheres model is used in analytical studies and in numerical simulations of molecules movement.

• Conformal solution model [START_REF] Longuet-Higgins | The statistical thermodynamics of multicomponent systems[END_REF][START_REF] Shukla | Conformal solutions: which model for which application? Fluid Phases Equilibria[END_REF] is used when two mixed molecules are not very different and when full information of pure components is available. The model consists of use one component as a perturbation of a reference system.

• Quasi-Chemical Approximation (QCA), developed by Bhatia and Singh [START_REF] Bhatia | Thermodynamic properties of compound forming molten alloys in a weak interaction approximation[END_REF][START_REF] Bhatia | A quasi-lattice theory for compound forming molten alloys[END_REF], is applied to describe the thermodynamic properties of a compound forming alloys.

By using method QCA, the thermodynamics of mixing in liquid state of frequently used alloys, namely Co-Cr, Cr-Ni and Co-Ni has been analyzed [START_REF] Costa | Thermodynamic and surface properties of liquid Co-Cr-Ni alloys[END_REF]. The normalized Gibbs free energy of mixing ΔGM/RT for the alloys liquid system, calculated for T = 1873 K is depicted in Fig. For the Co-Fe liquid alloy, the minimum value of normalized free energy of mixing was calculated to be ΔGM/RT = -0.63 what was in good agreement with experiment results being equal to ΔGM/RT = -0.61 [37]. The energy for Fe-Si alloys in molten state at 1873 K, given by theory and by experiment methods, analyzed by Adhikari et al. [START_REF] Adhikari | Energy Disorder in Liquid Fe-Si Alloy[END_REF] is shown in Fig. 4. The minimum value of this energy is equal to -2.31 is reached for the concentration of CFe = 0.55. The calculation of free energy of mixing shows that Fe-Si is a strongly interacting system in liquid state. Thermodynamics of MMCs can be studied using Ellingham diagrams. The diagrams are used to predict equilibrium temperatures for metals and oxygen and, similarly, for metal and carbon or metal and nitrogen. The Ellingham diagrams represent graphically the standard free enthalpy of oxidation, ΔG, in function of temperature. The feasibility of a reaction depends on the sign of ΔG and more negative value indicates more favorable thermodynamic conditions for metal reaction with oxygen, nitrogen or carbon.

An interesting MMC is iron reinforced with titanium carbide. Fig. 5 shows a phase diagram of Fe-Ti-C system. It can be observed that at the temperature higher than T > 1400 °C, there a solid phase of TiC coexists with liquid. Thermodynamics of Fe-Ti-C system was studied e.g. by Jonsson [START_REF] Jonsson | Assessment of the Fe-Ti-C system, calculation of the Fe-Ti-N system and prediction of the solubility limit of Ti(C,N) in liquid Fe[END_REF]. The possible reactions in the Fe-Ti-V-C system between Ti and C, V with C, Fe with -Ti and Fe with C associated with standard free energy changes are shown in Table 5 Table 5 Main chemical reaction in the Fe-Ti-V-C system after Wang et al. [START_REF] Wang | Microstructure of Fe-based alloy hardfacing coating reinforced by TiC-VC particles[END_REF]. Reproduced with permission.

The data from Table 5 enabled to create the Ellingham diagram for the system Fe-Ti-V-C (see Fig. 6). The values of Gibbs free enthalpy are negative at high temperature occurring e.g. at arc or laser cladding processes. The diagram indicates that TiC and VC are stable carbides.

(Fig. 6) Fig. 6 Ellingham diagram for system Fe-Ti-V-C created using data from Table 5.

The liquidus of a ternary phase diagram of Fe-Ti-C system is showed in Fig.

Surface energy

The properties of final coatings obtained by hardfacing are closely related to the properties of liquid metals (alloys) and to the phenomena occurring at processing at the interface between these liquids and solid reinforcements. The surface energy of liquids is an important thermodynamic parameter which can be found directly from the Gibbs energy. The surface tension (γ) of some pure metals are presented in the Table 6.

Table 6

Surface tension of some pure metals at the melting point [START_REF] Brandes | Metals Reference Book[END_REF].

The surface tensions of molten Ni-(Cr, Co, W) binary alloys were found experimentally vs.

temperatures in the range of 1500 -1600 °C are represented in the Fig. 8 (Fig. 8)

Reproduced with permission.

The surface tension of these molten alloys decreases with increasing temperature. Feng et al.

[42] measured surface tension in Ni with Cr, Co, and W binary alloys. The authors found out that, under controlled (Ar+ 3 vol. % H2) atmosphere, the elements with lower surface tension separate rather on the surface of molten alloy contrary to the elements with higher surface tension, which separate rather inside it. Consequently, Cr separates onto the liquid surface and Co and W -inside the alloys. The melting under uncontrolled atmosphere may lead to adsorption of oxygen what leads to decrease of surface energy [2]. It should be added that it is difficult to determine experimentally the surface tension of liquid metals and alloys and that the theoretical models are frequently used to estimate this parameter.

Volumetric thermal expansion

Volumetric thermal expansion describes the increase of liquids' volume with temperature.

At a constant pressure, the volumetric thermal expansion coefficient can be defined as:

= ( )

Eq. 1

Generally, the coefficient increases with temperature. Reproduced with permission.

Diffusion in liquid phase

Diffusion is the movement of molecules or atoms from a region of high concentration to the one of low concentration. It is driven by the concentration gradients. The study of diffusion processes in liquids helps to understand nucleation and crystal growth [START_REF] Hillert | Phase Equilibria, Phase Diagrams and Phase Transformations[END_REF]. Diffusion coefficient is an important parameter characterizing the diffusion. The diffusion depends on temperature as shows it the Arrhenius relation (Eq.2). This equation was used by e.g. Ejima and Yamamura [START_REF] Ejima | Impurity diffusion in liquid aluminum and copper[END_REF] to describe diffusion of impurities in liquid Al and Cu. Their experiments were carried out at temperatures being 200 K above the melting point temperature of the metals.

D=D0 exp(-Q/kT) Eq. 2

Diffusion of carbon

Carbon atoms diffuse easily into metals such as Fe, Ni, and Mo. The diffusivity of carbon in austenite was first determined by Smith [START_REF] Smith | The diffusivity of carbon in iron by steady-state method[END_REF] using the steady-state method. The coefficients of carbon diffusion in a wide range of concentration were determined by measuring the flux and carbon concentration profiles in many studies [START_REF] Bose | Diffusion coefficient of carbon in Fe-Ni austenite in the temperature range 950-1100 degree C[END_REF][START_REF] Roy | Diffusivity of carbon in austenitic Fe-Si-C alloys[END_REF]. It was shown the carbon diffusion coefficient is not significantly influenced by the small quantities alloying elements, such as Cr or Si [START_REF] Wells | Rate of diffusion of carbon in austenite in plain carbon[END_REF].

The temperature dependence of the diffusion coefficient of carbon in α-Fe and in austenite is given in Table 7 [ [START_REF] Dahlke | Die Auflösung von Kohlenstoff in flüssigem Eisen[END_REF][START_REF] Batz | Diffusion coefficient of carbon in austenite[END_REF] and in Co [START_REF] Morgan | Solution in liquid iron, Part 3: -Diffusion of Cobalt and carbon[END_REF]. The diffusion coefficient of carbon in liquid iron at 1 823 K is ranging from 6.7 to 7.9 x 10 -9 m 2 /s depending on initial carbon content in iron [START_REF] Batz | Diffusion coefficient of carbon in austenite[END_REF]. It must be underlined the poor affinity of C to Ni leads leading to a gradient of carbon concentration in Ni-alloys [START_REF] Bose | Diffusion coefficient of carbon in Fe-Ni austenite in the temperature range 950-1100 degree C[END_REF][START_REF] Wells | Rate of diffusion of carbon in austenite in plain carbon[END_REF].

Table 7 Carbon diffusion coefficient in iron and austenite [START_REF] Dahlke | Die Auflösung von Kohlenstoff in flüssigem Eisen[END_REF][START_REF] Batz | Diffusion coefficient of carbon in austenite[END_REF].

Diffusion of nitrogen

The studies of the diffusion of nitrogen in liquid iron and liquid iron-base alloys has been reported in many papers. The diffusivity of nitrogen in liquid iron having low concentration of carbon was determined using such experimental methods as [START_REF] Nabeel | Diffusion of elemental additives during sintering[END_REF][START_REF] Villegas | The diffusion of nitrogen in liquid iron alloys at 1600° C[END_REF][START_REF] Schwerdtfeger | Diffusion of oxygen and nitrogen in liquid iron[END_REF][START_REF] Inouye | On the measurements of diffusion coefficients of nitrogen in the liquid Fe[END_REF][START_REF] Kunze | Effect of the elements chromium, manganese, cobalt, nickel, molybdenum and tungsten on the diffusion of nitrogen in liquid iron alloys[END_REF]:

• unsteady state gas-liquid metal cell technique;

• quenching technique at temperature of 1873 K;

• capillary reservoir method at temperatures 1823 K to 1953 K; 20

• steady state technique at the temperatures ranging between 1823 K and 1973 K.

Lee and Parlee [START_REF] Lee | The Diffusion of Nitrogen in Liquid Iron and Iron Alloys[END_REF][START_REF] Lee | The diffusion of nitrogen in liquid iron and iron alloys[END_REF] measured the absorption of nitrogen in Fe-containing liquid systems at the temperature of 1873 K under pressure of nitrogen of 10 5 Pa. The authors studied the effect of alloying elements on diffusion coefficient. It was found that the nitrogen diffusivity increases significantly with additions (above 10 wt. %) of such elements as of Si, Al, Co, Ni, W and Sn. The additions of Mn results also in an increase of nitrogen diffusivity of nitrogen but to a less extent [START_REF] Villegas | The diffusion of nitrogen in liquid iron alloys at 1600° C[END_REF].

On the contrary, the additions of V and Nb result in decrease the nitrogen diffusivity. No effects on the diffusion were observed by addition of Cr and Mo.

The rates of nitrogen absorption in the Fe-Ni and Fe-Co liquid alloys were studied by Benner and Parlee [START_REF] Benner | The rates of absorption of nitrogen in the stagnant liquid Fe-Co and Fe-Ni alloy systems at 1600°C[END_REF]. Kojima et al. [START_REF] Kojima | The solubilities and diffusion coefficients of nitrogen in the liquid Iron-Nickel and Iron-Cobalt alloys at 1600°C[END_REF] determined diffusion coefficients of Fe-alloys with Ni and Co at 1600°C. Some literatures values of diffusion coefficients of N in liquid Fe and in low carbon Fe-alloys are collected in Table 8. The values of nitrogen diffusion coefficients in the iron alloyed with different metals was studied by Villegas [START_REF] Villegas | The diffusion of nitrogen in liquid iron alloys at 1600° C[END_REF] and is shown in Table 9.

Table 8 Diffusion coefficients of N in liquid Fe and low carbon Fe-alloys [START_REF] Villegas | The diffusion of nitrogen in liquid iron alloys at 1600° C[END_REF][START_REF] Inouye | On the measurements of diffusion coefficients of nitrogen in the liquid Fe[END_REF][START_REF] Kunze | Effect of the elements chromium, manganese, cobalt, nickel, molybdenum and tungsten on the diffusion of nitrogen in liquid iron alloys[END_REF][START_REF] Walbrühl | Diffusion in the liquid Co binder of cemented carbides: Ab initio molecular dynamics and DICTRA simulations[END_REF][START_REF] Bester | [END_REF][67] Table 9 Experimental values of diffusion coefficient of N in the alloys including iron with other metals noted as X and Y at 1600 °C. The content of other metals is 2.5% X and 2.5% Y [START_REF] Villegas | The diffusion of nitrogen in liquid iron alloys at 1600° C[END_REF].

Diffusion of oxygen

Saiz et al. [68] used scanning electron microscopy (SEM) and atomic force microscopy (AFM)

to observe the phenomena at the interface between liquid metals (Ni, Cu, Au, Al) and polycrystalline alumina including the diffusion of oxygen. This diffusion in liquid iron was measured experimentally under the pressures ranging between 3 and 18 GPa at the temperature ranging from 1973-2643 K [START_REF] Posner | Experimental determination of oxygen diffusion in liquid iron at high pressure[END_REF]. The diffusion coefficient was in the range from 6 × 10 -9 to 2 × 10 -8 m 2 s -1 and activation enthalpy was lower than 100 kJ mol -1 . The results obtained by Otsuka and Kozuka [START_REF] Otsuka | The diffusivities of oxygen in liquid Nickel and Liquid Iron determined by electrochemical measurements[END_REF], who found the oxygen diffusivities in liquid nickel and iron by using an electrochemical method are shown in Table 10.

Table 10

Diffusivity of oxygen in liquid nickel and iron [START_REF] Otsuka | The diffusivities of oxygen in liquid Nickel and Liquid Iron determined by electrochemical measurements[END_REF]. 21

Surface tension of metals in liquid phase

The liquid metals and alloys occurring at the processes of hardfacing can be characterized by surface tension. This parameters at the melting point are collected in Table 11 Table 11 Surface tension of metals at melting point [START_REF] Lu | Surface tension and its temperature coefficient for liquid metal[END_REF].

Physical properties of oxides and carbides used for composites reinforcements

Some properties important for composite reinforcements, such as Young modulus, hardness, melting temperature, standard enthalpy of formation for oxides are collected in Table 12. The described oxides are used as reinforcement include alumina, zirconia, yttria, and ceria. The properties of carbides of tungsten, titanium, chromium, boron, vanadium, and molybdenum are shown in Table 13.

Table 12

Physical properties of typical oxides [START_REF] Rumble | CRC Handbook of Chemistry and Physics[END_REF] Table 13 Physical properties of typical carbides [START_REF] Rumble | CRC Handbook of Chemistry and Physics[END_REF]

Interface between ceramics and liquid metals and alloys

The principal phenomena occurring in contact between ceramic reinforcement and liquid metal (alloy) matrix are shortly described. The phenomena include mainly the different aspects of wetting.

Fundamentals of wetting

The wetting phenomena description presented in the section is very elementary. More careful description of wetting at high temperatures may be found in many studies synthesized by

Estathopoulos et al. [2].

Non-reactive wetting

The fundamental energy balance of liquid, solid and vapor phase can be represented graphically as a liquid droplet being in contact with surrounding vapors and with a solid surface (see Fig. 12). The contact area between solid and liquid is supposed to not include the reacting species.

The essential parameter of contact is the angle of wetting, Θ. The wetting can be categorized in a 22 simplified way using this angle as [2]: (i) perfect wetting for Θ= 0°; (ii) wetting for 0°< Θ< 90°; and, (iii) no wetting for 90≤ Θ≤180°. Oxide ceramics have electronic structures very different from that of metals [START_REF] Dezellus | Fundamental issues of reactive wetting by liquid metals[END_REF][START_REF] Nicholas | Ceramic-Metal Interfaces in Surfaces and Interfaces of Ceramic Materials[END_REF].

Electrons are free in metals while in oxide ceramics they are ion-bound and localized in the crystal lattice. Differences in electronic structures appear at the interface between ceramic and metal. Their thermodynamic expression is Gibbs free energy which modification resulting from a contact between two different materials is given by following equation [START_REF] Howe | Bonding, Structure and properties of metal/ceramic Interfaces -Part I chemical bonding, chemical reaction and interfacial structure[END_REF][START_REF] Arroyave | Thermodynamics and Kinetics of Ceramic/Metal Interfacial Interaction[END_REF]:

= + - + + Eq. 3
Two terms of this equation should be explained. The free enthalpy of plastic deformation, ΔGpd, appears in a case of a collapse of liquid droplet with a solid substrate and the enthalpy of chemical reaction ΔGch is at its minimum at thermodynamic equilibrium [START_REF] Dezellus | Fundamental issues of reactive wetting by liquid metals[END_REF]. In the case of hardfacing processes there is no plastic mechanical deformation. For discussed case of non-reactive wetting, the Gibbs free energy ΔGf Int is equal to the surface adhesion work, Wa. The latter the sum of the surface energies between solid, liquid and vapor phase as shows it the well-known equation:

= + - Eq. 4
The equation can be also re-formulated by taking the angle of wetting, Θ (see Fig. 12) into account as, well-known, Young-Dupré law [2]:

= -= Eq. 5
Young's-Dupré law says that the contact angle between the liquid droplet and the solid substrate results from the equilibrium between the surface energies of liquid and solid phases (σSV -σSL) and from the cohesion force of the liquid σLV. Liquid metals have high cohesion forces and if the surface energy between liquid and solid phase is also high, cosθ may be close to unity. The Young-Dupré's law can then be re-written as (see Dezellus and Estathopoulos [START_REF] Dezellus | Fundamental issues of reactive wetting by liquid metals[END_REF]):

= + - = ( + ) Eq. 6 23
Lawrence [START_REF] Lawrence | Wetting and bonding characteristics of selected liquid-metals with a high power diode laser treated alumina bioceramic[END_REF] indicates that the work of adhesion Wa can be also expressed as the sum of the contributions of interfacial interactions between the two phases:

= "# + $ + "#
Eq. 7

Wneq represents the contributions to the energy of adhesion resulting from chemical reactions taking place at the metal-ceramic interface and Wcheq is the cohesive energy between two phases in contact resulting from the establishing of a chemical equilibrium. Finally, WVDW represents the energy resulting from van der Waals forces.

Wetting between metals or alloys and carbides

The analysis of Li [START_REF] Li | 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[END_REF] showed that the adhesion energy of non-reactive liquid metals to metal carbides is a function of the concentration of valence electrons in both metal and carbide.

Consequently, this adhesion energy of different metals to TiC increases linearly with the increase of the electron density on the boundary of the Wigner-Seitz cell1 of metals in contact. Li's approach shows that the interactions between metals and carbides is similar to that between the metals because of the overlap of the valence electrons at the interface. Another paper of Li [START_REF] Li | Wetting and interfacial bonding of metals with ion covalent oxides[END_REF] generalizes his analysis for the case of contact between liquid metals and ion-covalent solids. Table 14 shows a good wetting (θ << 90°) by non-reactive liquid metals in contact with metals, semiconductors and ceramics with metallic behavior.

Table 14 Wetting by non-reactive liquid metals (after Dezellus and Eustathopoulos [START_REF] Dezellus | The role of van der Waals interactions on wetting and adhesion in metal/carbon systems[END_REF])

Similar behavior has the contact between liquid metals and the semiconductors such as SiC [START_REF] Rado | Bonding and wetting in non-reactive metal/SiC systems: weak or strong interfaces?[END_REF]. This results from that fact that the semiconductors behave as metals at their surface. Liquid metals wet well the metal carbides, nitrides and borides because metallic character bonding of these materials [START_REF] Dezellus | Wettability of Ti3SiC2 by Ag-Cu and Ag-Cu-Ti melts[END_REF][START_REF] Voytovych | Reactive vs nonreactive wetting of ZrB2 by azeotropic Au-Ni[END_REF]. The solids which are not well wetted by the liquid metals are: (i) carbon; (ii) ioncovalent oxides; and, (iii) the covalent ceramics which have a large electronic gap, such as BN or AlN [83][START_REF] Naidich | The Wettability of Solids by Liquid Metals[END_REF]. More examples are shown in Table 14. 24

Wetting between metals or alloys and oxides

The liquid metals and alloys do not wet well oxide ceramics. It must be also underlined that ceramics such as SiC and Si3N4, and a lot of solid metals such as e.g. stainless steels, superalloys, and alloys containing Al are frequently oxidized on their surface. The oxidation layer modifies their wetting behavior [START_REF] Rado | The role of surface chemistry on spreading kinetics of molten silicides on silicon carbide[END_REF][START_REF] Protsenko | Wetting of Fe-7.5Cr steel by molten Pb and Pb-17Li[END_REF].

Reactive wetting

Saiz et al. [START_REF] Saiz | Atomic dynamics and Marangoni films during liquid-metal spreading[END_REF] suggested that the reactive wetting results from adsorption at the initial liquidsolid interface of a reactive alloying element while the kinetics of the spreading would be governed by the migration of a ridge formed at the solid-liquid-vapor line. This hypothesis was not confirmed experimentally [START_REF] Eustathopoulos | Progress in understanding and modeling reactive wetting of metals on ceramics[END_REF]. A model of interfacial reaction resulting in a formation of an intermediate layer was proposed by Landry and Eustathopoulos [START_REF] Landry | Dynamics of wetting in reactive metal/ceramic systems: linear spreading[END_REF].

Dissolutive wetting

Dissolutive wetting occurs when a dissolution of solid in liquid takes place. The dissolution is accompanied by formation of an interface having dendritic microstructure [START_REF] Eustathopoulos | Progress in understanding and modeling reactive wetting of metals on ceramics[END_REF][START_REF] Landry | Dynamics of wetting in reactive metal/ceramic systems: linear spreading[END_REF]. It occurs frequently at solidification of metals [START_REF] Mechighel | Document Study of macro-segregation defects formation caused by double diffusive convective flow during solidification of a binary alloy[END_REF][START_REF] Mechighel | Numerical simulation of three dimensional low Prandtl liquid flow in a parallelepiped cavity under an external magnetic field[END_REF]. The dissolutive wetting was reported to occur in contact of Ni/C [START_REF] Landry | Dynamics of wetting in reactive metal/ceramic systems: linear spreading[END_REF], Ni/HfB2 [START_REF] Passerone | Wetting and interfacial phenomena in Ni-HfB2 systems[END_REF] and AuNi/ZrB2 [START_REF] Voytovych | Reactive vs nonreactive wetting of ZrB2 by azeotropic Au-Ni[END_REF].

Local reaction at contact

The chemical reaction at contact between liquid and solid may result in formation of compounds which may constitute the wetting barriers. For example, liquid Au does not wet TiC, the contact angle is equal to θ =130° being the same as that of gold on the carbon substrate [START_REF] Frage | Wetting of TiC by non-reactive liquid metals[END_REF]. This results from small solubility of carbon in gold which precipitates without any reaction. To improve this solubility a small addition of nickel is useful. Consequently, adding of 3% to 7% nickel to gold, enabled obtaining contact angles in the range of 60 ° < θ < 80 °.

25

Similarly, in the liquid Ag /SiC system the dissolution of silicon in silver causes the precipitation at the interface of graphite which is not wetted by Ag. With the addition of Si to Ag, the carbon precipitation is suppressed, and good wetting was observed [START_REF] Kalogeropoulou | Mechanisms of reactive wetting: the wetting to non-wetting case[END_REF]. Similarly, a CuSi alloy did not wet an oxidized (in form of a thin silica layer) SiC substrate. However, the reaction between silicon and silica resulted in formation of the volatile SiO. The latter removed the oxide layer what resulted in a good wetting [START_REF] Dezellus | Spreading of Cu-Si alloys on oxidized SiC in vacuum: experimental results and modelling[END_REF].

Examples of wetting between metals or alloys and oxides

Generally, the metals are covered with a few nanometers thin layer of metal oxide formed in contact with the air at room temperature. The oxides are not well wetted by the liquid metals [START_REF] Protsenko | Wetting of Fe-7.5Cr steel by molten Pb and Pb-17Li[END_REF][START_REF] Protsenko | The role of intermetallics in wetting in metallic systems[END_REF]. Consequently, in order to improve the wettability, it is necessary to find for reactions enabling formation of intermetallic film which may replace the oxide layer. Zhou and De Hosson [START_REF] Zhou | Reactive wetting of liquid metals on ceramic substrates[END_REF] measured contact angles of contact between liquid Al and solid SiO2 and of liquid Ti with solid Al2O3.

The authors found out that the change of ceramic substrate volume at reactive wetting may be significant. It was observed at Al liquid contacting solid SiO2 in which the reaction following reaction takes place:

% &' ( + )*+ = (*+ ( ' % + % & Eq. 8
The volume of ceramic substrate initially decreased because of formation of Al2O3 (see Eq. 8).

On the other hand, the wettability increased after reaction. Similar effect was observed at the contact between liquid Ti and solid Al2O3 substrate. A dense layer of titanium-aluminum mixed oxide was formed at the solid-liquid interface what improved the wetting.

Modern methods of hardfacing

The methods of coatings manufacturing by hardfacing may be also called bulk coatings because of great quantity of material deposited [START_REF] Pawłowski | Dépôts Physiques[END_REF]. The well-known examples of bulk coatings manufacturing are painting or printing. A group of bulk coatings discussed in this review is characterized by a local melting of a substrate and by the introduction into the melt-pool of material contributing in coating formation in the form of a powder or wire. In a case of a composite coating deposition, the introduced feedstock may be:

• mixture of metal/alloy with ceramic in a form of powder or wire which form a composite;

• ceramic powder forming a composite with a metal into a molten pool of substrate.

Another possibility is the use of a composite wire containing the mixture of metal/alloys and ceramics being an electrode which is molten by arc at processing. The arc is also melting the coated substrate and the molten droplets of composite form a coating welded to a substrate (see Fig. 13).

Such a coating technique is known as arc welding [100].

Reproduced by permission

Finally, the powders may be pre-placed as a coating before the heat treatment. This method is well adapted to a laser heat treatment and was used to obtain MMC coating e.g. in the studies [101-103]. The plasma and flame heat treatment are less appropriate being associated with gas movement which may displace pre-deposited powder. The displacement can be avoided by gluing of pre-placed powders with an organic binder to the substrate e.g. with epoxy resin. However, the use of organic binder may increase the electrical conductivity of pre-placed powder which should be low in the PTA process.

The formation of melt-pool in a substrate can be realized using:

• combustion flame;

• arc and plasma;

• laser.

Since the interface between the substrate and the deposit results from the dilution of a liquid phases of substrate with that of coating (Fig. 14), this family of coatings is often called deposits by welding. The dilution, defined in Fig. 14, is an important parameter of such deposition process. In general, one seeks to obtain deposits with a dilution of a few percent. This is however difficult to reach, and the dilution values are generally in the range from 10 to 40% [104]. The technique in which the substrate is melted by the oxyacetylene combustion flame is least efficient 2 because of low melting capacity of a substrate by the flame. The resulting dilution is rather small. Better coatings' efficiency can be achieved by applying an electrical arc between the substrate and a non-consumable tungsten electrode (TIG process) or a consumable electrode (MIG process).

These techniques are described elsewhere [START_REF] Liu | Plasma arc welding: Process variants and its recent developments of sensing, controlling and modeling[END_REF]104]. Plasma may be used for the non-transferred arc melting of a substrate in a process called plasma cladding described by e.g. • particles dispersed composite layer is formed in fusion zone (Fig. 15a);

• compound layer is formed in upper part of fusion zone (Fig. 15b);

• composite layer is not formed (Fig. 15c).

(Fig. 15)

Fig

Plasma Transferred Arc (PTA)

The principle of PTA coatings is shown in Fig. 16. The "pilot" arc is initiated between the cathode of thoriated tungsten and copper anode, cooled by water. This arc heats the plasma gas which is typically argon. Then, the torch is approached to the substrate and the transferred arc is ignited between the cathode and the anode-substrate. This arc melts locally the substrate. The powder is introduced into the melt-pool to create the deposit. The pool is protected against the influence of ambient atmosphere by an inert gas such as argon [107].

(Fig. 16) Fig. 16 -Diagram of PTA processes: 1, plasma gas; 2, injection of powder with a carrier gas; 3, protective gas; 4, cathode; 5, anode; 6, substrate.

The MMC can be formed with the use of powder mixture or using separate injectors of powder of matrix and powder of ceramic reinforcement. In the latter, the powders can be fed by • torch (pilot arc current, transferred arc current, plasma gas flow rate, shielding gas flow rate);

• powder (chemistry, granulometry, particles velocity resulting from carrier gas flow rate);

• torch position with respect to the substrate (oscillation, stand-off, overlapping of the following deposition paths).

The PTA process can be also categorized in function of deposition rate in the following groups

[104]:

• micro plasma transferred arc (MPTA) with low powder feed rate, low dilution and coatings thickness up to 1.5 mm;

• standard PTA described in present paragraph;

• high power plasma transferred arc characterized by a very high deposition rate ranging from 200 to 250 g/min.

The typical industrial torch is powered electrically with 3 to 10 kW and the gas flow rates are relatively low [START_REF] Pawłowski | Dépôts Physiques[END_REF]. An example of flow rates used to spray NiCrAlY -YSZ cermets is: (i) Ar plasma gas of 1.4 slpm; (ii) Ar+ H2 shielding gas of 14 slpm; and, (iii) carrier gas of 3.5 slpm. The dilution of a coating depends on the ratio between the pilot arc current and the transferred arc current. A small transferred arc current results in a small dilution and a large pilot arc current ensures good heating of the particles before contact with the substrate. An example for deposition of NiAl alloy the pilot arc current of 45 A and the transferred arc of 80 A [110]. The powder applied in the PTA process has the particle sizes ranging typically from 40 to 150 μm. The particle sizes can be much more dispersed than that used in the thermal spraying processes. This results from a double mechanism of particles melting in PTA, including: (i) convection in pilot arc plasma; and, (ii) conduction in the melt pool created by the transferred arc. The convection melting in the plasma jet is much less important and mainly melting by conduction counts. The powder feed rates vary between a few tenths and a few 29 hundreds of g/min. The torch is subjected to two movements relative to the substrate: (i) translation (scan speed is typically equal to a few cm/min); and, ii) oscillations with an amplitude of about ten mm and its frequency about 40 to 100 mn -1 [109-110]. The stand-off between torch and substrate is as small as 6 to 8 cm [108 -111] to keep the transferred arc ignited. Some processing parameters influencing the coatings quality may be reduced to one parameter. Consequently, Demian et al.

[109] proposed a factor of deposition, Q, depending on electric power delivered to arc, P, torch scan speed, U, and powder feed rate, q. The factor is defined as: , = -# Eq. 9

The PTA coatings are formed in a few passes of a torch (see Fig. 17) and it is often necessary to rectify them before service.

(Fig. 17)

Fig. 17 Coating deposition by plasma cladding with a torch produced by Saint Gobain Coating

Solution, Avignon, France (presented with the permission).

Laser assisted methods

The laser deposits can be obtained in two processes called: (i) one-step laser deposition (1SLD); and (ii) two-steps laser deposition (2SLD). The 1SLD process, similarly to PTA, consists of melting the substrate by a laser and injecting powder into a molten pool. Another possibility is to make a predeposit with another coatings' deposition technique (typically thermal spraying) and, later on, to perform a laser treatment. This technique can be called a two-steps laser deposition (2SLD). These two techniques can be further differentiated into the following methods (see also Fig. 18):

• cladding, in which the deposits are chemically different from the substrate;

• laser surface alloying (LSA), in which the materials of the deposit and the substrate form an alloy at processing;

• hard phase dispersion, in which solid particles of a reinforcement are injected into the pool and remain solid.

Another emerging method is called laser prototyping and consists of injecting of small quantity of powder to be melted into a melt pool created by laser beam. The laser prototyping is a part of additive manufacturing method and to create the 3D objects from fine powder.

30

(Fig. 18) Fig. 18 -The laser assisted coatings processes: cladding, alloying and hard phase dispersion.

The laser deposits are mainly made using four types of lasers: CO2, Nd: YAG, diode laser, and fiber laser. The diode and fiber lasers applications grow rapidly in hardfacing industry. The main properties of these lasers are collected in Table 15.

Table 15 Selected characteristics of industrial lasers applied in laser assisted deposition coatings methods

[112-115].
The most important parameter of laser processing is power density, defined, for a continuous wave laser, as:

# = * Eq. 10
The power density for a pulsed laser is defined as:

# = . */
Eq.11

Each type of laser treatment requires a different power density. Generally, to melt the solid material, the power density should be in the range 1-10 3 W/cm 2 [116].

Cermet coatings obtained by hardfacing

The cermet coatings obtained by flame, plasma, as well as, by laser assisted methods are described in the following chapter starting from feedstock and from the process parameters used for processing. Subsequently, it follows a short overview of cermets, categorized by type of ceramic reinforcement and a description of their properties.

Feedstock used in processing

The feedstock used in cermet cladding using flame, plasma and laser assisted methods is similar and is described in one chapter. The powders are used most frequently as the feedstock. The cermet powders can be:

31

• made of metal/alloy and ceramics mixed before processing or delivered using two different powder feeders and are separately injected in the molten pool;

• manufactured as cladded powders, having thin metallic layer around ceramic particle, or as composite ones i.e. with metal/alloy particles mixed with the ceramic ones.

Sometimes, rods or fibers are used as a feedstock. In this case, ceramics and metal/alloy powders are sintered initially to a form of rod or wire.

The size of metal/alloy and carbides powders being mixed or separately delivered was discussed by Deuis et al. [START_REF] Deuis | Metal matrix composite by PTA surfacing[END_REF]. The authors underlined the following restrictions concerning the particles used in PTA surfacing:

• size of the matrix particles should be in the range 50-150 µm to avoid the feeding problems and the reinforcement particles should be rather smaller, say 5-20 µm, to achieve better coating strength by dispersion-hardening mechanism;

• morphology of reinforcement particles should be rather spherical or shaped in an angular way and the morphologies of whiskers and fibers are to be avoided because of bad flowability;

• density of reinforcement particles should have similar density to that of the melt pool in order to avoid particles falling to the bottom of the melt pool.

The typical powders and wires used in metallic matrix composited are shown in Table 16.

Table 16 Cermet powders and wires used for plasma/ flame and laser cladding after [117][118][119][120][121] The metallic matrices are often the Ni-based and Co-based alloys and ceramic reinforcements are oxides, carbides or cermets (see Table 16). The use of cermet reinforcement results from the recycling of powders and the size of cermet powder is much greater than the other reinforcement powders. Generally, the sizes of matrix powders are generally greater than that of reinforcement. The process parameters, such as feeding rate, influenced chemical composition and laser power energy influenced the melt-pool temperature. TiC morphology were influenced by chemical composition of used feedstock and by the temperature of particles. The chemical composition of the pool including solid TiC particles is shown in Fig. 19. The free carbon atoms did enter in reaction, described by reaction shown Eq. 12, with Ti being present in the pool because of melting Ti6Al4V alloy substrate.

Phenomena in melt-pool

The intensive interactions between molten alloys or metals and ceramic reinforcement take place in melt-pool during very short time. That is why; a careful description of physical and chemical phenomena occurring in melt pool is necessary. The melt-pool may be formed by: (i) electric arc heating; (ii) convective heating of plasma, flame; or, (iii) radiative heating of laser.

Physical phenomena

To simplify the description, one can imagine a liquid with cold surface and hot bottom part.

The convection movement, known as Rayleigh -Bénard convection, will take place in such a liquid.

The mechanism this movement was discussed by Kadanoff [129].

As the molten fluid has a free surface, the fluctuation of the temperature of the surface resulting from the colder fluid arriving from the bottom part and from the evaporation at the surface influences the surface tension. The gradients of surface tension create the forces moving the fluid and deforming its surface (see Fig. 22). This effect is called also Bénard -Marangoni convection being a form of Rayleigh-Bénard convection for melted liquid with free surface. The formation of melt-pool by plasma or laser and its solidification, resulting from the heat source movement, occurs in a very short period. The modeling of 2SLD process including CO2 laser heating of FeCr-TiC cermet pre-deposited by plasma spraying made by Pawłowski and Smurov [127] shows the heating and cooling rates of melt-pool being equal to about 10 4 K/s (see Fig. 23).

(Fig. 23) Cladding with plasma or laser may be associated with injection of powder in a coaxial way, i.e. The shape of melt-pool is hemispherical, and it becomes greater and more conical with increasing thermal energy input and/or with lower scan speed. This is well visualized for stationary fiber laser interactions with stainless steel AISI 304 when laser power increases (see Fig. 26).

Fig
(Fig. 26)

35

The cross-section of melt-pool visible in Fig. 26 enables estimation of its volume on a few mm3 . This is the volume to which are injected the ceramic particles being the reinforcement of MMC. On the other hand, the particles injected to the melt-pool have a size ranging from a few tenths of µm up to a few hundreds of µm (see Table 16).

The optimal composite coatings have the reinforcement particles distributed evenly. An example of such distribution in laser deposited composite with WC+W2C reinforcement and Inconel 525 alloy matrix is shown in Fig. 27.

(Fig. 27)

Fig

Chemical phenomena

The atoms available in the melt-pool and reacting with the other atoms may come from liquid metal/alloy matrix and/or from solid reinforcement. The metal atoms have temperature of the melt and their mobility is high. The atoms of carbon or oxygen enter to melt pool from the particles of ceramic reinforcement having higher melting point. Consequently, they diffuse initially through the lattice of solid carbides and oxides before entering to the pool. This diffusion is confirmed by the evacuation of carbon and titanium from the TiC sites. The dissolution of ceramic grains started at their sharp edges which were transformed to take more spherical shapes. Diffusion of Al2O3 was more intensive than that of TiC. The reaction of atoms leaving solid ceramic particle with that being present in the melt pool occurred near to particles' surfaces. For example, the carbon atoms leaving WC particle reacted with Ti in melt-pool forming TiC compound as shows it Fig. 32.

(Fig. 32) • carbides such as initial WC and newly formed W2C, Cr3C2, Cr23C6 and NiCx;

• borides such as Cr5B3 and W2B5.

The compounds generated in the melt-pool can be detected using X-ray diffraction of MMC coatings.

Their composition may be predicted by considering the possible reactions to occur in the pool by considering the following factors [137]:

• available atoms coming from: molten matrix; dissolution of reinforcement; and, dilution of the substrate;

• diffusion resulting from un-homogeneous distribution of the atoms in the melt-pool;

• Gibbs free energy analysis indicating whether a reaction can take place.

Flame and plasma assisted methods

The microstructures described in the following sections are quite similar for plasma/flame and laser assisted cladded cermets. Some differences result from the size of melt-pool generated by plasma/flame which is greater than that of laser generated. Consequently, the heat flux and the temperature gradients are greater at laser cladding. Reproduced with permission.

Properties of coatings

The cermet coatings cladded with the help of plasma and flame are mainly applied against different form of wear (adhesive, abrasive, erosive). The properties related to these applications are mainly mechanical ones, namely hardness, modulus of elasticity, and wear resistance. These properties are synthesized in Table 17. The hardness and Young modulus of reinforcement is generally greater than that of matrix (see e.g. lines 1 and 6 of the Table 17).

Table 17 Mechanical properties of plasma/flame cladded cermets [108,120,[141][142][143][144][145] This renders the entire composite coating harder and stronger. The improvement of the wear resistance of composites may be explained by the resistance of strong and hard reinforcement against third body wearing the surface. A comparison of wear resistances of a zone without 40 reinforcement with a zone reinforced with B4C particles, described in line 3 of Table 17, is shown in Wear resistance of composites depends also on the content of reinforcement and on the size of its particles. As shows it Fig. 37, the wear resistance of coating increased with the content of WC reinforcement up to 45 wt. % in the arc welded composite using wires including steel as matrix and WC as reinforcement. The size of the reinforcement grains of 135 µm was optimal to reach the greatest wear resistance.

(Fig. 37) Some of the composites obtained using PTA technique shown in Table 17 were also tested for their corrosion resistance at high temperature of 973 K [143]. The composite NiCrBSi+40 wt. % Cr2C3 (see line 2 of Table 17) was found to be useful against oxidation and action of phosphate ions.

NiCrBSi+(TiC+20 wt. % NiMo) composite coating described in line 1 of Table 17 resisted against oxidation. The detailed sketch describing corrosion resistance of different cermets is shown in Fig. 38.

(Fig. 38) Reproduced with permission.

Laser assisted methods

The coatings deposited using laser are, generally not very different of that, deposited using plasma and flame. However, the laser assisted methods enable better focusing of energy on the samples' surfaces. Consequently, the microstructure of coatings depends strongly on laser power.

For the same laser power, the microstructure and properties would depend strongly on the content of the reinforcement.

Microstructure of coatings

The influence of laser power on the microstructure of laser cladded composite with NiFeCrSiB matrix reinforced by 20 wt. % of WC was tested by Ma et al. [138]. The authors observed that the initial size of WC reinforcement decreased from 100 µm in initial powder to 60 µm in the coating while using 3.6 kW of laser power (see Fig. 39 a). Around, the WC grains was formed a eutectic structure composed of the atoms from reinforcement and from matrix. The lowering the laser power down to 3.2 kW resulted in a formation of some blocky precipitates around the WC grains (Fig. 39 b).

Finally, at the power of 2.4 kW the WC grains were only slightly dissolved (Fig. 39 c).

(Fig. 39) 18. The choice of laser cladding parameters influences the mechanical properties. To take an example, the use reinforcement did improve only slightly the hardness of cermet with NiCrBSi matrix (see line 4 of Table 18) for the content of 20 and 30 vol. % of WC. The hardness for the content of 10 vol. % WC was even smaller than that of the matrix. This resulted from the modification of microstructure shown in Fig. 40. Quite similar effect can be observed for the modulus of elasticity.

For example, the use of 20 wt. % Cr2C3 reinforcement (line 5 of Table 18) increased the modulus of Inconel 625 matrix of the composite of less than 15 %.

The use of oxides reinforcement may improve the mechanical properties of cermets when the nano-sized particles were applied.

5 PRMMC-

 5 Particle reinforced metal matrix composite PTA -Plasma transferred arc QCA -Quasi-Chemical Approximation QSM -Quasi-regular solution model RT -Room temperature SEM -Scanning electronic microscope slpm -Standard liter per hour SMMC -Surface metal matrix composite TCP -Tricalcium phosphate, Ca3(PO4)2 TEM -Transmission electron microscope TIG -Tungsten inert gas TTCP -Tetracalcium phosphate, Ca4P2O9 XRD -X-ray diffraction YAG -Yttrium aluminum garnet YSZ -Yttria stabilized zirconia Symbols A -surface, m 2 C -concentration, 1/m 3 c -constant d -diameter, m D -diffusion coefficient, m 2 /s E -Energy, J or Young modulus, GPa H -Enthalpy, J/kg HB -Brinell hardness 6 HV -Vickers hardness HV30 -Vickers hardness under load of 30 kgf HRC -Rockwell hardness k -Boltzmann's constant, k ≈1.38 × 10 -23 J/ K ky -strengthening coefficient, MPa.m 0.5

FigFig. 1

 1 Fig. 1 Geometry of liquid droplet spread out on flat solid substrate (a) and of a solid particle being surrounded by a liquid (b).

Fig. 2

 2 Fig. 2 Micrographic structure of typical MMC (self-fluxing alloy reinforced with tungsten carbide) available commercially as MetcoClad 52052 TM . Reproduced with permission of Oerlikon Metco.

  Physical and chemical phenomena occurring between solid ceramics and liquid metals and alloys at laser and plasma composite coatings formation: A review, S. Oukach, B. Pateyron and L. Pawłowski 11

  Nickel-based superalloys, such as Ni-Al-Cr, are used in high-temperature applications requiring high hot corrosion resistance. The examples are power-generation turbines and aircraft engines. The ductility of the Ni-based alloy is improved by adding Cr. Similarly, the addition of a few wt. % of Cr (up to 8) to the Ni3Al improves the tensile strength of the alloy. On the other hand, Co and Co-Ni based alloys with high Cr content are particularly efficient against hot corrosion. An addition of a small amount of Y, Si and Hf improves stability of alloys and the addition of Ta or Re -their oxidation resistance [12, 13]. 12 2.1.1.1. Nichrome

3 .(Fig. 3 )Fig. 3

 333 Fig. 3 Concentration dependence of normalized Gibbs energy for mixing, ∆Gm/RT, for liquid Co-Cr, Cr-Ni and Co-Ni alloys at T = 1873 K [36].

Fig. 4 .

 4 Fig. 4. Concentration dependence of normalized Gibbs energy for mixing, ∆Gm/RT, for liquid Fe-Si at temperature of 1873K (-) theory and (○) experimental points [38]. Reproduced with permission.

(Fig. 5 )Fig. 5

 55 Fig. 5 Phase diagram of the system Fe-Ti-C from Emanian et al. [10]. Reproduced with permission.

(Fig. 7 )Fig. 7

 77 Fig. 7 Liquidus section of Fe-Ti-C diagram with isotherms [39]. Reproduced with permission.

Fig. 8 .

 8 Fig. 8. Surface tension of molten Ni with Cr, Co, and W binary alloys in function of temperature [42].

Fig. 9 (Fig. 9 )Fig. 9 (Fig. 10 )Fig. 10 (Fig. 11 )Fig. 11

 99910101111 Fig. 9 Volumetric thermal expansion coefficient of Ni [43]. Reproduced with permission. (Fig. 10)

Fig. 12 Fig. 12

 1212 Fig. 12

Fig. 13 Fig. 13

 1313 Fig.[START_REF] Wei | Interdiffusion within the β-phase region of the Ni-Co-Cr-Al quaternary system[END_REF]

Fig. 14 Fig. 14 .

 1414 Fig.14

  Fig. 15 Possible morphologies of MMC coatings obtained by hardfacing, see description in the text (inspired by [8]).

  two powder feeders described by Zikin et al. [108]. The quality of coatings obtained by PTA depends mainly on the following elements of coating's processes after Demian et al. [109]:

32 &

 32 Another possibility, shown by, is a formation of the reinforcement at coating process. These authors injected into a melt-pool formed by fiber laser, the mixture of powders having size about 40 µm: iron, titanium and graphite. The processing, called laser assisted powders deposition (LAPD), enabled formation of TiC reinforcement having size of a few micrometers and shape depending on deposition parameters by following reaction:

Fig. 19 Fig. 19

 1919 Fig. 19

Fig. 20 (Fig. 21 )Fig. 21 -

 202121 Fig. 20 External layers of cladded powder particle obtained using different technologies [112].

34 (Fig. 22 )Fig. 22 -

 342222 Fig. 22 -Movements of liquid in a melt-pool with a cold free surface

. 23 -

 23 Fig. 23 -Evolution in time of spot center temperature at laser heating and cooling of FeCr-TiC plasma sprayed cermet coatings for different laser scan speeds [127].

(Fig. 24 )Fig. 24 -Fig. 25 -

 242425 Fig. 24 -Schema of coaxial powder injection in laser cladding process [131]. Reproduced with permission.

Fig. 26 -

 26 Fig. 26 -The simulated and experimental melt-pools cross sections generated by a fiber laser in AISI 304 stainless steel for laser power of 500 W during 1 s a) and of 750 W acting during 0.6 s. b) [132]. Reproduced with permission.

. 27 -(Fig. 28 )Fig. 28 -(Fig. 29 )Fig. 29 -(Fig. 30 )Fig. 30 -

 27282829293030 Fig. 27 -SEM micrograph (back-scattered electrons) showing cross-sections of laser cladded MMC with WC+W2C reinforcement having mean size of 125 µm and Inconel 625 alloy matrix obtained using different laser energy density and constant feedstock feed rates [121]. Reproduced with permission.

(Fig. 31 )Fig. 31 - 3 -

 31313 Fig. 31 -Evolution of reinforcement particles sizes preplaced on the steel substrate (a), entering in melt-pool (b), cooled after laser source leaved the site (c), and solidifying (d). The symbols correspond to: 1 -Al2O3 surrounded by Ti-rich alloy; 2 -Ti rich big ceramic grain; and 3 -Ti -rich small ceramic grain [136]. Reproduced by permission.

Fig. 32 -

 32 Fig. 32 -SEM micrograph of the reaction zone between the WC reinforcement and Ti atoms produced at laser cladding [126]. Reproduced with permission.

6. 3 (Fig. 33 )Fig. 33 -(Fig. 34 )Fig. 34 -(Fig. 35 )Fig. 35 -

 3333334343535 Fig. 33-SEM micrograph and EDS elemental maps microanalyses of MMC formed by NiCrAlY + 20 wt. % of 13YSZ showing an agglomerated island of oxides around a metal particle [109].

Fig. 36 .(Fig. 36 )Fig. 36 -

 363636 Fig. 36.

Fig. 37 -

 37 Fig. 37 -The influence of content of WC reinforcement a) and of size of WC grains on wear resistance, measured using ASTM G65 test method 4 of composite coatings having matrix of different steels [100] (reproduced with permission).

Fig. 38 -

 38 Fig. 38 -Corrosion resistance at 973 K of PTA cermets with NiCrBSi matrix and Cr2C3 and TiC (with NiMo) reinforcement against different corroding and oxidizing media after Rojacz et al. [146].

Fig. 39 (Fig. 40 )Fig. 40 -

 394040 Fig. 39 Optical microscope micrographs showing influence of fiber laser power at constant laser scan velocity of 3 mm/s on the microstructure of composite NiFeCrSiB + 20 wt. % WC obtained using laser power of: 3.6 kW a); 3.2 kW b); and 2.4 kW c) [138]. Reproduced with permission.

FiguresFig. 1

 1 Figures

Fig. 2

 2 Fig. 2

Fig. 4 CFig. 5

 45 Fig.3

  Fig.6

Fig. 8

 8 Fig. 8

Fig. 9 α

 9 Fig. 9

Fig. 10 α

 10 Fig. 10

Fig. 13

 13 Fig. 13

  Fig.14

  Fig. 18

Fig. 20

 20 Fig.20

Fig. 21

 21 Fig. 21

  Fig. 22

Fig. 24

 24 Fig.24

  Fig. 25

Fig. 27

 27 Fig. 27

Fig. 28

 28 Fig. 28

Fig. 29 Islands

 29 Fig.29

Fig. 31

 31 Fig. 31

Fig. 32

 32 Fig. 32

Fig. 33Error !

 33Error Fig. 33Error! Reference source not found.

Fig. 34

 34 Fig.34

Fig. 35

 35 Fig.35

Fig. 36

 36 Fig.36

Fig. 37

 37 Fig.37

Fig. 38

 38 Fig.38

Fig. 39

 39 Fig.39

Fig. 40

 40 Fig.40

Table 3 Properties

 3

		of nickel aluminides [16]
	2.1.1.3.	MCrAlY
	MCrAlY alloys (where M is metal as Co, Fe, Ni or Co/Ni) are widely used as corrosion resistant

materials. A well-known application is a bond-coating for use with zirconia top-coating in thermal barrier coatings. The high temperature corrosion resistance of MCrAlY results from the formation of oxides on alloys surface. The protective role of Cr and Al oxides in MCrAlY alloys is promoted by the 13 presence of Y. The oxidation behavior of MCrAlY alloys with different content of aluminum was discussed by e.g. Brandl et al. [17]. TM Inconels are the alloys belonging to austenitic nickel-chromium-based superalloys [18]. The alloys resist against corrosion and oxidation because of formation of stable passive oxide layer on their surface. The alloys, including e.g. Inconel 600, Inconel 617, Inconel 626 or Inconel 690 have slightly different chemical composition including mainly nickel and chromium as a second element.

Table 4

 4 Chemical composition of some Hastelloys[19].

	2.1.2. Cobalt alloys
	2.1.2.1.	Stellite TM
	Stellites belong to a family of cobalt-chromium alloys. Their chemical composition includes
	also some amount of tungsten, molybdenum, and of carbon. The alloys are resistant against wear
	and e.g. Stellite 100 is used frequently for manufacturing of cutting tools [20]. The stellites may be

  Guozhi et al. [105]. More frequently, plasma is used as with transferred arc (the anode being a substrate), being a very efficient way of melting the substrate surface. The dilution depends on the operational parameters.The statistical study carried out byBalasubramanian et al. [106] for PTA technique enabled to find out that the dilution depends mainly on: (i) transferred arc current; (ii) travel speed; (iii) powder feed rate; (iv) oscillation frequency, and; (v) distance between torch and substrate. The greatest influence has travel speed and the lowest one -the powder feed rate. The composite coating formed on the top of dilution zone may have one of three possible morphologies, described for carbides reinforcement MMC deposited onto aluminum substrate, by Deuis et al.[START_REF] Deuis | Metal matrix composite by PTA surfacing[END_REF] and shown in Fig.15:

Table 18

 18 Mechanical properties of laser cladded cermets[120, 134,[147][148][149][START_REF] Luo | Effect of NiCrBSi content on microstructural evolution, cracking susceptibility and wear behaviors of laser cladding WC/Ni-NiCrBSi composite coatings[END_REF]

  Duan et al. [126] did show the hardness of composites of

	FeCrMo steel with 8 wt. % of nano-Al2O3 treated by CO2 laser to be about HV0.5=630 and their elastic
	modulus to be about 164 GPa. The use of nano-YSZ reinforced Ni matrix obtained by preplacing
	powder and by CO2 laser treatment, enabled to o Xiong et al. [128] obtaining microhardness HV0.2
	ranging from 1280 to 1440.
	The nitride reinforcement, TiN, was used with 90 wt. % matrix of CoCrNiFeBSi self-fluxing
	alloy to obtain composite coatings with help of CO2 cw laser. The composites had the microhardness
	of HV0.2 about 1200 measured Weng et al. [137].

Bibliography 1. M.F. Ashby and D.R.H. Jones, Engineering Materials 2: An Introduction to Microstructures, Processing, and Design, Dunod, Paris, France, 1991 (in French).

Table 1

 1 Some properties of metals[START_REF] Rumble | CRC Handbook of Chemistry and Physics[END_REF]

	Table 2 Properties of NiCr (Ni + 20 wt. % Cr) in standard conditions [14]
	Property	Value
	Elasticity (Young) modulus, E, GPa 220
	Density, ρ, kg/m 3	8400
	Melting point, Tm, K	1 673
	Specific heat, cp, J/(kg.K)	450
	Thermal conductivity, λ, W/(m.K)	11.3
	Thermal expansion, α, K -1	14 × 10 -6

Table 4

 4 Chemical compositions of some Hastelloys [19].

	Alloy			Composition in wt. % (symbol * means maximum)
		Co	Cr Mo	W	Fe	Si	Mn	C	Ni	Others
	B-2	1*	1* 28	-	2*	0.1* 1*	0.01* Up	to	-
									100 %
	B-3	3*	1.5 28.5 3*	1.5	0.1* 3*	0.01* 65 %	Al-0.5*, Ti-0.2*
	C-4	2*	16 16	-	3*	0.08* 1*	0.01* Up	to	Ti-0.7*
									100 %
	C-2000	2*	23 16	-	3*	0.08* -	0.01* Up	to	Cu-1.6
									100 %
	C-22	2.5* 22 13	3	3	0.08* 0.5* 0.01* Up	to	V-0.35*
									100 %
	C-276	2.5* 16 16	4	5	0.08* 1*	0.01* Up	to	V-0.35*
									100 %

Table 5

 5 Main chemical reaction in system Fe-Ti-C after Wang et al.[START_REF] Wang | Microstructure of Fe-based alloy hardfacing coating reinforced by TiC-VC particles[END_REF].

	System and possible reactions	Ti-C Ti+C→TiC	V-C V+C→VC	3Fe+C→Fe3 C	Fe-C	2Fe+C→	Fe2C	Fe-Ti
				25 920-23T
				(298 K<T<463 K)	19 860-10T
	Standard free enthalpy of reaction ∆Gf 0 (J/mol)	-186606+13.2T -1020904 -9.581T	26 670-25T (463 K<T<l 115 K)	(298 K<T<1 115 K) 18 420-103	-53 300+53. 7T (298 K<T<2 000 K)
				10 340-10T	(1 155 K<T<1 808 K>
				(1 155 K<T<1 808 K)

Table 6

 6 Surface tension of some metals at the melting point[START_REF] Brandes | Metals Reference Book[END_REF]

		Melting point
			Surface tension
	Pure metal	temperature	γ, J/m 2
		Tm, K
	Ni	1728	1.778
	Cr	2180	1.672
	Co	1768	1.873
	Al	933.5	0.914
	Fe	1806	1.872
	Si	1684	0.865
	Zn	693	0.782

Table 7 -

 7 Carbon diffusion coefficient in iron and austenite[START_REF] Dahlke | Die Auflösung von Kohlenstoff in flüssigem Eisen[END_REF][START_REF] Batz | Diffusion coefficient of carbon in austenite[END_REF]

		Metal	D0 m 2 .s -1	Q, J.mole -1
	D=D0 exp(-Q/RT), m 2 .s -1	α-Fe	25.10 -6	144000
		Austenite	20.10 -6	83996

Table 8

 8 Diffusion coefficients of N in liquid Fe and low carbon Fe-alloys[START_REF] Villegas | The diffusion of nitrogen in liquid iron alloys at 1600° C[END_REF][START_REF] Inouye | On the measurements of diffusion coefficients of nitrogen in the liquid Fe[END_REF][START_REF] Kunze | Effect of the elements chromium, manganese, cobalt, nickel, molybdenum and tungsten on the diffusion of nitrogen in liquid iron alloys[END_REF][START_REF] Walbrühl | Diffusion in the liquid Co binder of cemented carbides: Ab initio molecular dynamics and DICTRA simulations[END_REF][START_REF] Bester | [END_REF][67]

	System	Temperature T(K)			Coefficient of diffusivity D, 10 -9 m²/s
	N in liquid	1873	4.12	9.2	8.87
	Fe and in low		5.6
	carbon alloys	1600	(with very low carbon	5.5	9.2	14.89	3.7	4.41
			alloys)

Table 9

 9 Experimental values of diffusion coefficient of N in the alloys including iron with other metals noted as X and Y at 1873 K. The content of other metals is 2.5% X and 2.5% Y[START_REF] Villegas | The diffusion of nitrogen in liquid iron alloys at 1600° C[END_REF].

	X-Y	Ni-V	Co-V	Ni-Co	Ni-Cr	Co-Cr	Cr-V
	Coefficient of
	diffusivity	4.93	5.34	21.43	7.76	8.87	2.42
	D,10 -9 m²/s
	X-Y	Cr-Si	Cr-Mo	Mn-Co	Mn-Ni	Mn-Cr	Mn-V
	Coefficient of
	diffusivity	7.75	3.0	11.81	10.31	4.63	2.32
	D, 10 -9 m²/s

Table 10

 10 Diffusivity of oxygen in liquid nickel and iron [70] D < 55x 10 -8 m 2 s -1Table11Surface tension of metals at melting point[START_REF] Lu | Surface tension and its temperature coefficient for liquid metal[END_REF].

	in liquid Ni	T= 1773 K	49x10 -8 < D < 81x10 -8 m 2 s -1
	in liquid Fe	T=1823 K	25x10 -8 <

Table 12 -

 12 Physical properties of oxides[START_REF] Rumble | CRC Handbook of Chemistry and Physics[END_REF]

					Al2O3	ZrO2	Y2O3	CeO2
	Molar mass	101.96	123.218	225.81	172.115
	M, g/mol
	Density			3987	5680	5010	7215
	ρ, kg/m 3
	Melting		2345	2988	2698	2670
	temperature
	Tm, K
	Boiling			3250	4570	4570	3770
	temperature
	Tev, K
	Specific	heat,	78.83	56.21	102.51	61.52
	J/(mol.K)
	Standard		-1675.7	-1080	-1905	--1088.7
	enthalpy	of
	formation
	∆Hf 0 , kJ/mol
					Table 13 Physical properties of typical carbides [11]
		WC		TiC	Cr3C2	B4C	VC (VC0.88)	MoC and Mo2C
	Molar mass		195.85	59.89	180.09	55.26	62.95	107.961 (MoC)
	M, g/mol							203.911 (Mo2C)
	Density		15630	4930	6680	2520	5577	8900
	ρ, kg/m 3
	Melting		3058	3430	2168	3036	3080	2960
	temperature
	Tm, K
	Boiling		6270	5090	4070	3770	4171
	temperature							-
	Tev, K
	Thermal		110	-	-	-	-	-
	conductivity
	λ, W/(m.K)
	Specific heat,	39.8	34.0	99.21	52.46	32.31	37.601 (MoC)
	J/(mol.K)							59.014 (Mo2C)
	Standard free	-40.584	-183.7	-85.349	-62.68	-101.7
	enthalpy	of						-284.510 (MoC)
	formation							-531.276 (Mo2C)
	∆Hf 0 [kJ/mole]
	Elasticity	530-700	400	-	460	380
	(Young)							-
	modulus

Table 14

 14 Wetting by non-reactive liquid metals (after Dezellus and Eustathopoulos[START_REF] Dezellus | The role of van der Waals interactions on wetting and adhesion in metal/carbon systems[END_REF])

	Kind of solid		Contact angle	Examples of contact angles
				θ
	Solid metals				Pb/Fe -40°
					AgCu/Stainless Steel -10°-60°
	Semiconductors Ceramics with	a	θ << 90°	Sn/Ge -40° AgCu/Ti3SiC2 -10°
	partially	metallic		Au/ZrB2 -25 °
	behavior
	Carbon materials			Au/C -119°-130°
	Iono-covalent oxides			Cu/Al2O3, Cu/SiO2 -120°-130°
				θ >> 90°
	Covalent ceramics			Al/AlN -134°-138°
					Au/BN -1356°-150°

Table 15 -

 15 Selected characteristics of industrial lasers applied in laser assisted deposition coatings

			methods [112-115]
	Parameter			Laser type
		CO2	Nd doped	Diode laser	Fibre laser
			YAG
	Wavelength,	10.6	1.06	0.82-1.07	0.4 -2.8 (most frequent 1.05 for
	µm				Ytterbium doped fibre)
	Excitation	Gas discharge Flash or arc	Electric	Optical pumping of diode 's light
	technique		lamp	excitatio
				n
				(electron
				s passing
				band
				gap)
	Pulsed/cw	Both	Both	Both	Both
	Maximum	100	15	3	20
	average
	power, kW
	Beam quality	Very high	Low	Low	Very high
	Efficiency, %	5-10	2-5	Up to 70	Optical-to-optical efficiency up to
					70% and total efficiency up to
					35%

Table 16

 16 Cermet powders and wires used for plasma/ flame and laser cladding[117][118][119][120][121]

	N	Substrate

Table 17

 17 Mechanical properties of plasma/flame cladded cermets[108, 120,

	No	Cermet composition (reinforcement + matrix	Process of cladding			Properties	Reference
			wt. %)
		Reinforcement	Matrix		Hardness		Elasticity	Wear resistance
							modulus
	1	TiC+20 NiMo	NiCrBSi	PTA	Matrix about 2 GPa	Matrix about	Zikin et al.
					Carbide about 34 GP	230 GPa	[108]
							Carbide about
							390 GPa
	2	Cr3C2	60 NiCrBSi	PTA	HV10=680 at RT and		Impact-abrasive volumetric	Chang et al.
					HV10=300 at 973 K		wear 12 mm 3 at RT and 18	[120]
								mm 3 at 973 K
	3	B4C	80 (Fe+12 Cr+1 B+ 1	Injection of powders into plasma				Pin-on-disk test 0.05 mg/(mN)	Lyu et al.
			Si)	formed melt pool				depending on B4C injection	[141]
								geometry (see Fig. 36)
	4	TiC	47 Fe	Reactive plasma cladding of pre-	HV0.2 in the range		Ball-on-disk wear test about	Liu et al.
				prepared powder	1350 to 1900			0.01 mm 3 volume worn	[142]
	5		40 vol. % γ-(Fe,Ni)	PTA	HV0.5 above 1600			Ball-on-disk fretting wear test	Chen et al.
								about 0.22 mm 3 volume worn	[143]
	6	WC	40 vol. % CuNiMn	Flame spraying of WC and	HV0.2 of matrix 125		3-body abrasion test with
				CuNiMn particles including wire	and	of		silica sand show volume loss
					reinforcement 2440		of 100 mm 3 after sliding
								distance of 800 m

The Wigner-Seitz mesh is an elemental mesh. The Wigner-Seitz mesh corresponds to the first Brillouin zone in the reciprocal space

The authors wrote 280 mesh what was probably an error and the real value was 230 mesh corresponding to

Standard test method for Measuring Abrasion Using the Dry Sand/Rubber Wheel Apparatus, G 65-04 (1 November 2004)