**4. Equilibrium states in M-F-H systems**

408 Thermodynamics – Interaction Studies – Solids, Liquids and Gases

H2 0,0 130,4 32,02 -7,36 0,58 1,34 [10, 26] H 217,8 114,5 20,77 0,0 0,0 0,0 [10, 26] F2 0,0 202,5 26,42 22,36 -1,25 -0,63 [10, 26] F 79,4 158,5 25,08 -7,86 0,42 -0,33 [10, 26] HF -270,4 173,5 30,01 -3,47 3,47 -0,25 [10, 26] WF6 -1719,9 357,2 117,46 83,60 -5,02 -16,93 [10, 21, 26] WF5 -1292,0 342,8 114,95 54,76 -3,26 -14,13 [12, 21] WF4 -928,0 329,8 80,67 56,85 -3,43 -7,98 [12, 21] WF3 -506,6 313,9 65,63 36,28 -2,21 -7,57 [12, 21] WF2 -86,1 285,5 53,92 26,41 -1,59 -3,85 [12, 21] WF 384,6 250,4 30,72 13,92 -0,79 -1,55 [12, 14] W2F8 -2042,4 414,5 166,36 112,86 -6,81 -22,40 [7, 27] W2F10 -2829,4 497,0 202,31 142,12 -8,61 -28,34 [7, 27] W3F15 -4244,0 631,2 295,00 247,94 -15,29 -42,39 [7, 15] HWF5 -1383,9 352,2 98,65 103,25 -5,60 -15,01 [27]

Temperature dependencies of equilibrium compositions in the M-F systems (M = V, Nb, Ta, Mo, W, Re) are presented at the Fig.1. The data represent the thermodynamic stability of the refractory metal fluorides with different valencies both monomer and polymer states depending on the place of the metal in the Periodic table. The gas phase composition depends on both the heat of the fluoride formation and the vaporation heat of the fluorides. The thermodynamic analysis of M-F systems shows that the highest fluorides of the metals are stable at temperatures up to 2000 K. The exceptions contain the fluorides VF5, MoF6, ReF6 that decompose slightly at the high temperature range and their thermal stability

The gas low-valent fluoride concentrations, which depend upon the metal place in the periodic system, rise with the increase of atomic number within each group and decrease with the increase of atomic number within each period. Thus tantalum fluorides are most strongly bonded halids and vanadium fluorides are most unstable among considered fluorides. It is nesessary to note that partial pressures of low valent fluorides in Re-F system are close to each other but low valent fluorides in Ta-F system have very different

Nevertheless the vaporation temperature of fluorides varies depending upon the metal place in the periodic system in opposite direction than the gas low-valent fluorides concentration. The most refractory fluorides are VF2 and VF3 (above 1500 K), the low-valent fluorides of Nb and Mo possess the mean vaporation temperature (900-1100 K). Th low-

Ср = α + βT + γT2 + δT-2, J/mol·K References

α 103 β 105 γ 10-5 δ

Komponents ∆Ноf 298, kJ/mol

So298, J/mol·K

Table 3. Standart thermochemical constants of W-F-H components.

increase according to the following order: VF5 > MoF6 > ReF6 .

**3. Equilibrium states in M-F systems** 

concentrations.

The equilibrium analysis of the metal-fluorine-hydrogen (M-F-H) systems for the temperature range 400-2000 K, total pressure of 1.3×105 Pa and 2 kPa and for fluoride to hydrogen ratio from 1:3 to 1:100 have been calculated using a special procedure based on the search of entropy extremum for the polycomponent mixture [7, 31]. All experimental and calculated thermochemical constants of the fluorides and the characteristics of the fluoride phase transitions were involved into the data set. The equilibrium compositions of M-F-H systems (M=V, Nb, Ta, Mo, W, Re) for the optimal total pressure and the optimal reagent ratio are presented at the Fig.2.

The comparison of the results presented at the Fig. 1 and Fig.2 shows that the addition of hydrogen to VB metal pentafluorides decrease concentrations of the highest fluorides in monomer and polymer states (except of V2F6) and rise the concentration of lower-valent fluorides. The large difference is observed for V-F-H system and small difference - for Ta-F-H system.

The hydrogen addition to tungsten, molibdenium and rhenium hexafluorides leads to the decrease of MFx concentration, 7 ≤ x ≥ 3, and to a small increase of di- and monoflouorides concentration.

The source of VB group metals formed from M-F-H systems are highest fluorides and polymers. The VI group metals are the product of hexa-, penta- and terafluoride decomposition, but all known rhenium fluorides produce the metallic deposit. The variation of the external conditions (total pressure and fluoride to hydrogen ratio) influence on the gas phase composition according to the law of mass action and Le Chatelier principle.

Fig. 3 presents the equilibrium yield of solid metallic deposit from the mixtures of their fluorides with hydrogen as a function of the temperature. It is shown that metallic Re, Mo, W may be deposited from M-F-H system at temperatures above 300 K. Yields of Nb and Ta were varied in the temperature range from 800 K to 1300 K. Metallic V may be not deposited from M-F-H system until 1700 K due to the high sublimation temperature of VF2 and VF3. It was established that the moving force (supersaturation) of the metal crystallization in M-F-H system increase in the order for following metals: Re, Mo, W, Nb, Ta, V. These thermodynamic results are in agreement with experimental data reviewed in [7, 32, 33].

Thermodynamic Aspects of CVD Crystallization of Refractory Metals and Their Alloys 411

Fig. 2. Equilibrium gaseous composition in M-F-H systems at total pressure of 2 kPa and

hydrogen to highest fluoride initial ratio of 10 [31].

Fig. 1. Equilibrium gaseous composition in M-F systems at total pressure of 2 kPa [7].

Fig. 1. Equilibrium gaseous composition in M-F systems at total pressure of 2 kPa [7].

Fig. 2. Equilibrium gaseous composition in M-F-H systems at total pressure of 2 kPa and hydrogen to highest fluoride initial ratio of 10 [31].

Thermodynamic Aspects of CVD Crystallization of Refractory Metals and Their Alloys 413

from (100) tungsten surface and sublimation energy of pure metal. These values are presented in the table 4 in terms of polynomial's coefficients, which were estimated in the case of the infinite dilute solution. The peculiarity of the detail calculation of polynomial's coefficients is discussed in [7]. The data predict that the co- crystallization of tungsten with Nb, V, Mo, Re will be performed more easily than the crystallization of pure tungsten. The crystallization of W-Ta alloys has the reverse tendency. Certainly the synergetic effects will

> h1, i kJ/mol

1 W 0 0 0 0 1,0000-0,9375 Ta 36,4±10,9 36,4 -0,00042 72,7 0,0000-0,0625 2 W 0 0 0 0 1,0000-0,9375 Nb -225,7±50,2 -225,7 -0,00025 -451,4 0,0000-0,0625 3 W 0 0 0 0 1,0000-0,9375 V -434,7±50,2 -434,7 -0,00017 -1304,2 0,0000-0,0625 4 W 0 0 0 0 1,0000-0,9375 Mo -467,7±10,9 -467,7 -0,00117 -935,5 0,0000-0,0625 5 W 0 0 0 0 1,0000-0,9375 Re -220,3±10,9 -220,3 -0,00058 -440,5 0,0000-0,0625

Table 4. Excess partial "enthalpy of mixing" atoms for crystallization of W-M binary solid solution and hi polynomial's coefficients for xi = 0 – 0.0625 and T = 298 – 2500 K [7, 31].

Therefore the thermodynamic calculation for gas and solid composition of W-M-F-H

The temperature influence on the conversion of VB group metal fluorides and their addition to the tungsten hexafluoride – hydrogen mixture is presented at the Fig.5 a,b,c. If the metal interaction in the solid phase is not taken into account, the vanadium pentafluoride is reduced by hydrogen only to lower-valent fluorides. It should be noted that metallic vanadium can be deposited at temperatures above 1700 K. Equilibrium fraction of NbF5

The thermodynamic consideration of ideal solid solution shows that tungsten-vanadium alloys may deposit at the high temperature range (T ≥ 1400 K) and metallic vanadium is deposited in mixture with lower-valent fluorides of vanadium (Fig. 5 a, curves 2). The beginnings of formation of W-Nb and W-Ta ideal solid solutions are shifted to lower

conversion achieves 50% at 1400 K, and of TaF5 – at 1600 K (Fig. 5 a,b,c, curves 1).

temperature by about 100 K (Fig. 5 b,c, curves 2) in comparison with the case (1).

h2, i kJ/mol h3, i

kJ/mol xi

influence on the composition of gas and solid phases.

<sup>m</sup>◌ּ 298 К xi = 0

systems were carried out for following cases:

2. for the formation of ideal solid solution

1. without the mutual interaction of solid components;

3. for the interaction of binary solution components on the surface.

№ <sup>М</sup> <sup>∆</sup>H0

Fig. 3. Yield of metals (V, Nb, Ta, Mo, W, Re) from the equilibrium mixtures of their fluorides with hydrogen (1:10) as a function of the temperature [31].

### **5. Equilibrium composition of solid deposit in W-M-F-H systems**

A thermodynamics of alloy co-deposition is often considered as a heterogeneous equilibrium of gas and solid phases, in which solid components are not bonded chemically or form the solid solution. The calculation of the solid solution composition requires the knowledge of the entropy and enthalpy of the components mixing. The entropy of mixing is easily calculated but the enthalpy of mixing is usually determined by the experimental procedure. For tungsten alloys, these parameters are estimated only theoretically [34]. A partial enthalpy of mixing can be approximated as the following:

$$
\Delta \mathbf{H}\_{\rm m} = (\mathbf{h}\_{\rm l,i} + \mathbf{h}\_{\rm 2,i} \, \mathbf{T} + \mathbf{h}\_{\rm 3,i} \, \mathbf{x}\_{\rm i}) \times (1 - \mathbf{x}\_{\rm i}) \, ^2 \mathbf{y}\_{\rm j}
$$

where h1,i , h2,i , h3,i – polynomial's coefficients, T – temperature, xi - mole fraction of solution component.

The surface properties of tungsten are sharply different from the bulk properties due to strongest chemical interatomic bonds. Therefore, there is an expedience to include the crystallization stage in the thermodynamic consideration, because the crystallization stage controls the tungsten growth in a large interval of deposition conditions. To determine the enthalpy of mixing of surface atoms we use the results of the desorption of transition metals on (100) tungsten plane presented at the Fig. 4. [35]. The crystallization energy can be determined as the difference between the molar enthalpy of the transition metal sublimation

Fig. 3. Yield of metals (V, Nb, Ta, Mo, W, Re) from the equilibrium mixtures of their

A thermodynamics of alloy co-deposition is often considered as a heterogeneous equilibrium of gas and solid phases, in which solid components are not bonded chemically or form the solid solution. The calculation of the solid solution composition requires the knowledge of the entropy and enthalpy of the components mixing. The entropy of mixing is easily calculated but the enthalpy of mixing is usually determined by the experimental procedure. For tungsten alloys, these parameters are estimated only theoretically [34]. A

Δ Н m = (h1,i + h2,i T + h3,i xi) × (1 - xi ) 2 , where h1,i , h2,i , h3,i – polynomial's coefficients, T – temperature, xi - mole fraction of solution

The surface properties of tungsten are sharply different from the bulk properties due to strongest chemical interatomic bonds. Therefore, there is an expedience to include the crystallization stage in the thermodynamic consideration, because the crystallization stage controls the tungsten growth in a large interval of deposition conditions. To determine the enthalpy of mixing of surface atoms we use the results of the desorption of transition metals on (100) tungsten plane presented at the Fig. 4. [35]. The crystallization energy can be determined as the difference between the molar enthalpy of the transition metal sublimation

**5. Equilibrium composition of solid deposit in W-M-F-H systems** 

fluorides with hydrogen (1:10) as a function of the temperature [31].

partial enthalpy of mixing can be approximated as the following:

component.

from (100) tungsten surface and sublimation energy of pure metal. These values are presented in the table 4 in terms of polynomial's coefficients, which were estimated in the case of the infinite dilute solution. The peculiarity of the detail calculation of polynomial's coefficients is discussed in [7]. The data predict that the co- crystallization of tungsten with Nb, V, Mo, Re will be performed more easily than the crystallization of pure tungsten. The crystallization of W-Ta alloys has the reverse tendency. Certainly the synergetic effects will influence on the composition of gas and solid phases.


Table 4. Excess partial "enthalpy of mixing" atoms for crystallization of W-M binary solid solution and hi polynomial's coefficients for xi = 0 – 0.0625 and T = 298 – 2500 K [7, 31].

Therefore the thermodynamic calculation for gas and solid composition of W-M-F-H systems were carried out for following cases:


The temperature influence on the conversion of VB group metal fluorides and their addition to the tungsten hexafluoride – hydrogen mixture is presented at the Fig.5 a,b,c. If the metal interaction in the solid phase is not taken into account, the vanadium pentafluoride is reduced by hydrogen only to lower-valent fluorides. It should be noted that metallic vanadium can be deposited at temperatures above 1700 K. Equilibrium fraction of NbF5 conversion achieves 50% at 1400 K, and of TaF5 – at 1600 K (Fig. 5 a,b,c, curves 1).

The thermodynamic consideration of ideal solid solution shows that tungsten-vanadium alloys may deposit at the high temperature range (T ≥ 1400 K) and metallic vanadium is deposited in mixture with lower-valent fluorides of vanadium (Fig. 5 a, curves 2). The beginnings of formation of W-Nb and W-Ta ideal solid solutions are shifted to lower temperature by about 100 K (Fig. 5 b,c, curves 2) in comparison with the case (1).

Thermodynamic Aspects of CVD Crystallization of Refractory Metals and Their Alloys 415

Fig. 5. Equilibrium yield of VB metals during crystallization with tungsten at initial ratio

Fig. 6. Temperature influence on equilibrium yield of tungsten in W-Re-F-H (1) and W-F-H (2) systems at total pressure of 2 kPa and gaseous composition of (WF6+6% ReF6) : H2 = 10 Taking into account the interaction of component of alloys during crystallization, the formation of W-V and W-Nb alloys possibly takes place at the temperatures above 300 K

WF6:MF5:H2=10, total pressure of 2 kPa calculated for following cases:

3. for the interaction of binary solution components on the surface.

1. without the mutual interaction of solid components;

2. for the formation of ideal solid solution

b) Nb c) Ta

a) V k\*VF2 k\*VF3

Fig. 4. Partial molar enthalpy of 4d и 5d atoms sublimation *( sH )* from tungsten plane (100) and atomization energy *(Ω)* of transition metals in dependence on their place in periodic table [35]

Fig. 5. Equilibrium yield of VB metals during crystallization with tungsten at initial ratio

WF6:MF5:H2=10, total pressure of 2 kPa calculated for following cases:


414 Thermodynamics – Interaction Studies – Solids, Liquids and Gases

Fig. 4. Partial molar enthalpy of 4d и 5d atoms sublimation *( sH )* from tungsten plane (100) and atomization energy *(Ω)* of transition metals in dependence on their place in

periodic table [35]

3. for the interaction of binary solution components on the surface.

Fig. 6. Temperature influence on equilibrium yield of tungsten in W-Re-F-H (1) and W-F-H (2) systems at total pressure of 2 kPa and gaseous composition of (WF6+6% ReF6) : H2 = 10

Taking into account the interaction of component of alloys during crystallization, the formation of W-V and W-Nb alloys possibly takes place at the temperatures above 300 K

Thermodynamic Aspects of CVD Crystallization of Refractory Metals and Their Alloys 417

wear of movable units, and erosion of immobile parts of drilling bits operating underground take special significance because their replacement is very expensive. The carbide coatings can be deposited inside cylinders and on the outer surfaces of components of rotary or piston oil pumps. Numerous units in the oil and gas equipment, for example, block bearings, solution-supplying channels in drilling bits, backings directing the sludge flow,

Another application in this field is the coating of metal–metal gaskets in the high- and ultrahigh-pressure stop and control valves. In addition to intense corrosion, abrasion and erosion wear, the working surfaces of ball cocks and dampers are subject of seizing under high pressure; W–C-coatings prevent the seizure. An important advantage of the carbide coatings is their accessibility for the quality of surface polishing, due to the initial smooth morphology. The examples mentioned above relate not only to oil and gas but also to chemical industry. The W–C-coatings are promising for working in contact with hydrogensulfide-rich oil, acids, molten metals, as well as chemically aggressive gases. Due to their high wear and corrosion resistance, these coatings can be use instead of hard chromium. The abrasion mass extrusion and the metal shape draft require expensive extrusion tools; the product price depends on the working surface quality and life time. The extrusion tools must often have sophisticated shape inappropriate for coating with PVD or PACVD methods. Therefore, W–C-coating prepared by a thermal CVD-method is promising in strengthening these tools. Strengthening of spinneret for drawing wires or complicated section of steel, copper, matrices for aluminum extrusion, ceramic honeycomb structures for the porous substrate of catalytic carriers may give the same effect. Also, very perspective is the deposition of strengthening coatings onto components of equipment for the pressing of powdered abrasion materials. One may also mention the strengthening of knife blade used

In addition to the surface strengthening, the W–C-coatings can function as high-temperature glue for mounting diamond particles in a matrix when preparing diamond tools or diamond cakes (conglomerates) in drilling bits [39]. The above-given examples demonstrate the variety of applications for tungsten, its alloys and carbides in mechanical engineering,

1. A number of unknown thermochemical constants of refractory metal fluorides were

2. The systematic investigation of equilibrium states in the M-F, M-F-H (M = V, Nb, Ta, Mo, W, Re) systems was carried out. It was demostrated that the equiblibrium concentrations of highest fluorides in the M-F systems are determined by the place of metal in the periodic table. They rise with the increase of atomic number within each group and decrease with the increase of atomic number within each period. The low valent fluoride concentrations have the opposite tendency. It was shown that the equilibrium yield of Re, Mo, W deposition from the M-F-H systems achieve 100% at room temperature, equilibrium yield of Nb, Ta and V deposition - at temperatures

3. The solid compositions of the W-M-F-H systems were calculated by taking into account the formation of ideal, nonideal solid solution, the mechanical mixture of solid

etc. require the strengthening of their working surfaces.

for cutting paper, cardboard, leather, polyethylene, wood, etc [38].

chemical, gas and oil industry, metallurgy, and microelectronics.

calculated and collected in this chapter.

above 1300 K, 1600 K and 1700 K, respectively.

**7. Conclusion** 

(Fig. 5 a,b, curves 3). Temperature boundary shown at the Fig. 5 is shifted in reverse direction for the W-Ta system (Fig. 5 c, curves 3). It should be noted, that the calculation results performed for cases (2) and (3) (for ideal and nonideal solid solution) for the W-Ta system are almost identical due to the small enthalpy of mixing [35].

The influence of rhenium and molibdenium on the equilibrium yield of tungsten in the M-W-F-H systems is observed for W-Re and W-Mo alloys deposition. The ReF6 addition to the gas mixture with WF6 increase insignificantly the yield of tungsten in spite of strong atom interaction during the crystallization according to thermodynamic calculations (Fig. 6). This effect is still smaller for the case of W-Mo co-deposition. However equilibrium yield of metals for their co-deposition with tungsten and the energy of the interaction of metallic components during the crystallization have the common tendency. The knowledge of refined data of process energies will allow us to obtain a more realistic situation.
