**2. Estimation of thermochemical constants**

The accuracy of thermodynamic analysis depends on the completeness and reliability of thermochemical data. Unfortunately, a limited number of the transition metal fluorides have been characterized thermochemically or have been studied by a spectroscopic technique. The experimental data were completed with the evaluated thermochemical constants for fluorides in different valent and structural states. The calculated data were obtained by the interpolation procedure based on the periodic law. The interpolation was performed on properties of a number of the compounds that represent the electron-nuclei analogies [6]. The unknown enthalpy of the fluorides formation was calculating via energy of halids

atomization as following:

$$
\Delta\text{ (MX}\_{\text{n}}\text{)} = \Delta\text{ }\text{H (M}\_{\text{at}}\text{)} + \text{n }\Delta\text{ }\text{H (X}\_{\text{at}}\text{)}\text{ - }\Delta\text{ }\text{H (MX}\_{\text{n}}\text{)}\text{}\tag{1}
$$

Thermodynamic Aspects of CVD Crystallization of Refractory Metals and Their Alloys 405

№ Substance Δ<sup>f</sup> Но298 (g) Δ<sup>f</sup> Но (s) Δs H<sup>о</sup><sup>298</sup> 1 V 514,1±4,2 [10] 0 514,1±4,2

2 VF 2,5±63 [11] - - 3 VF2 ≤-514±28 [7] ≤-899±28 [7] 385±28 4 VF3 -878,0±48,1 [12] -1263,1±48,1 [7] 385,1 5 VF4 ≤-1241±8 [7] -1412,1 [10] 169,1±8,0

6 VF5 ≤-1429,7±5,0 [11] - - 7 V2F6 -1963,4±48,0 [13] - - 8 V2F8 -2746,7±20,9 [14] - -

2 NbF 228±25 [7] - - 3 NbF2 ≤-226±21 [7] - - 4 NbF3 ≤-754±16 [7] - - 5 NbF4 -1257±22 [7] -1506±21 [7] 249±22 6 NbF5 -1711,7±6,3 [12] -1813,8±0,6 [10] 102,1±6,9

7 Nb3F15 -5342,0±4,6 [15] - -

2 TaF 289,3±12,5 [16] - 3 TaF2 -287,2±12,5 [16] - 4 TaF3 -810,9±12,5 [16] - 5 TaF4 -1275,7±12,5 [16] -

7 Ta3F15 -5611,2±5,4 [15]

2 WF ≤385 [21] - 3 WF2 -86,2±13,4 [21] - 4 WF3 -507,1±11,7 [21] -

7 WF6 -1721,5±0,7 [10] -

1 Nb 721,9±4,2 [10] - 721,9±4,2

1 Ta 785,4±4,2 [10] 0 785,4±4,2

6 TaF5 -1774,8±12,5 [16] -1901,8±0,8 [10] 127±13,3

1 Mo 655,8±3,4 [7] 0 655,8±3,4

4 MoF3 -591,5±14,6 [17] -909,6±19,7 [18] 318,1±34,3 5 MoF4 -953,0±16,3 [17] -1149,0±14,6 [18] 196,0±30,9 6 MoF5 -1240,2±35,9 [17] -1394,4±4,6 [19] 154,2±40,5

1 W 856,1±4,2 [10] 0 856,1±4,2

5 WF4 -928,8±10,5 [21] -1206,2±7,5 [18] 277,4±13 6 WF5 -1293,3±8,4 [21] -1446,8±8,4 [10] 153,5±16,8

2 MoF 271,7±9,2 [17] - - 3 MoF2 -168,0±12,1 [17] - -

7 MoF6 -1556,2±0,8 [10] - - 8 Mo3F15 -4091,0±9,6 [20] - -

The atomization energies of isovalent fluorides, chlorides and oxides of 4, 5, 6 period metals were disscused in [7]. It can be emphasised that the chlorides and oxides are studied well by experimental way. These curves are calling as "two-hilled"curves. Quantum-mechanical interpretation of these dependences can be found in [8, 9].

$$\text{Q} \quad \text{(MX}\_{\text{n}}\text{)}=\quad \text{q}(Z\_{\text{m}}),\tag{2}$$

$$
\Delta Z\_{\mathfrak{m}} \,\Omega \text{ (MF}\_{\mathfrak{n}}\text{) / } \Delta Z\_{\mathfrak{m}} \,\Omega \text{ (MF}\_{\mathfrak{s}}\text{) = } \text{q}\,(Z\_{\mathfrak{m}} \text{ } \mathfrak{n}),\tag{3}
$$

$$
\Delta \mathfrak{n}\_{\mathfrak{m}} \mathfrak{Q} \text{ (MF}\_{\mathfrak{n}}\text{) / } \Delta \mathbb{Z}\_{\mathfrak{m}} \mathfrak{Q} \text{ (MCl}\_{\mathfrak{n}}\text{) = } \mathfrak{q} (Z\_{\mathfrak{m}\vee} \mathfrak{n}) . \tag{4}$$

$$\text{\textbullet (MF}\_{\text{n}}\text{) / }\text{\textbullet (MCl}\_{\text{n}}\text{) = \text{q} (Z\_{\text{m}}\text{ n}),\tag{5}$$

$$
\Omega \text{ (MF}\_{\text{n}}\text{)}\;/\ \Omega \text{ (MO}\_{\text{n}/2}\text{)}=\text{q}(Z\_{\text{m}}\text{ n}),\tag{6}
$$

$$\left[\Omega\left\{\mathbf{M}\left(\mathbf{Z}\_{\mathrm{m}}\right)\mathbf{F}\_{\mathrm{n}}\right\}/\mathfrak{Q}\left[\mathbf{M}\left(\mathbf{Z}\_{\mathrm{m}}+\mathfrak{Z}\right)\mathbf{F}\_{\mathrm{n}}\right]=\mathfrak{q}(\mathbf{Z}\_{\mathrm{m}}\,\mathbf{n}),\text{ where }\mathbf{Z}\_{\mathrm{m}}=\mathfrak{P}9\text{-}48\tag{7}$$

$$\mathbf{Q} \cdot (\mathbf{M} \mathbf{X}\_{\mathbf{n}}) = \ \mathbf{q}(Z\_{\mathbf{x}}) = \mathbf{A}\_{\mathbf{n}} \ \mathbf{u}(Z\_{\mathbf{x}}) + \mathbf{B}\_{\mathbf{n}} \ \ \mathbf{X} = \mathbf{F}\_{\prime} \ \mathbf{C} \mathbf{l} \ \ \mathbf{B} \mathbf{r} \ \mathbf{I} \tag{8}$$

Ω (МFn) = φ( n ) = ψ [ Ω (МCln) ] : Ω (МFn) = C Ω (МCln) +D (9)

E (МFn) = φ( n ) = ψ [ D (МFn) ] : E (МFn) = L Ω (МFn) + N, (10)

where An, Bn, C, D, L, N –const.

These sequences are the dependencies of energies of halids atomization (2, 8-10), one of ratio of loss of energies of fluoride and chloride atomization (3, 4) from atom number of metal Zm (2-7), from halid Zx (8) and from valent state n (3-7, 9, 10).

All sequences were analyzied in order to determine the probable regions for interpolation by linear function. For example, the estimation of unknown atomization energies can be performed by the use of the sequence (2) within following region:

Ω (МF) where Zm, corresponds to (III-IV-V) and (VI-VII-VIII-I) groups;

Ω (МF2) where Zm, corresponds to (V-VI) and (VI-VII-VIII) groups;

Ω (МFn, n≥3) where Zm, corresponds to (V-VI-VII) groups.

The sublimation heat Δs Н (МXn) and enthropy S (МXn) were analyzied:

$$
\Delta\_\star \text{ H (MX}\_\text{n}\text{) } = \text{q}(Z\_{\text{m}\nu} Z\_{\text{x}\nu} \text{ n})\,,\tag{11}
$$

$$\mathbf{S}\left(\mathbf{M}\mathbf{X}\_{\mathbf{n}}\right) = \mathbf{q}\left(Z\_{\mathbf{m}\nu}Z\_{\mathbf{x}}\mathbf{n}\right). \tag{12}$$

All calculated thermochemical constants together with most reliable literature data are collected in tables 1, 2. The accuracy of the estimation data is ± 30 kJ/mol for atomization energy and ± 4 J/mol K for atomization enthropy. The accurate thermochemical data of W-F-H components are collected in the table 3, due to their importance for this analysis.

The literature review shows that the formation enthalpy is determined for several fluorides enough reliable which are taken as milestone points. Among them are AlF3, UF4, UF5, ScF3, CrF2, MnF2, TiF4, FeF3 and other [28, 29]. Table 1 contains also the thermochemical constants for polymer fluorides. Most reliable thermochemical data among the fluoride associations were obtained for Al2F6 , Fe2F8 , Cr2F4. The thermochemical data for tungsten fuorides are collected in table 2 because of the special importance for this investigation. Of course these data will be more full and reliable in the progress of fluoride chemistry.

The atomization energies of isovalent fluorides, chlorides and oxides of 4, 5, 6 period metals were disscused in [7]. It can be emphasised that the chlorides and oxides are studied well by experimental way. These curves are calling as "two-hilled"curves. Quantum-mechanical

Ω (МFn) / Ω (МCln) = φ( Zm, n), (5)

These sequences are the dependencies of energies of halids atomization (2, 8-10), one of ratio of loss of energies of fluoride and chloride atomization (3, 4) from atom number of

All sequences were analyzied in order to determine the probable regions for interpolation by linear function. For example, the estimation of unknown atomization energies can be

All calculated thermochemical constants together with most reliable literature data are collected in tables 1, 2. The accuracy of the estimation data is ± 30 kJ/mol for atomization energy and ± 4 J/mol K for atomization enthropy. The accurate thermochemical data of W-F-H components are collected in the table 3, due to their importance for this analysis.

The literature review shows that the formation enthalpy is determined for several fluorides enough reliable which are taken as milestone points. Among them are AlF3, UF4, UF5, ScF3, CrF2, MnF2, TiF4, FeF3 and other [28, 29]. Table 1 contains also the thermochemical constants for polymer fluorides. Most reliable thermochemical data among the fluoride associations were obtained for Al2F6 , Fe2F8 , Cr2F4. The thermochemical data for tungsten fuorides are collected in table 2 because of the special importance for this investigation. Of course these

metal Zm (2-7), from halid Zx (8) and from valent state n (3-7, 9, 10).

performed by the use of the sequence (2) within following region: Ω (МF) where Zm, corresponds to (III-IV-V) and (VI-VII-VIII-I) groups; Ω (МF2) where Zm, corresponds to (V-VI) and (VI-VII-VIII) groups;

The sublimation heat Δs Н (МXn) and enthropy S (МXn) were analyzied:

data will be more full and reliable in the progress of fluoride chemistry.

Ω (МFn, n≥3) where Zm, corresponds to (V-VI-VII) groups.

Ω [ M (Zm) Fn] / Ω [ M (Zm + 32) Fn] = φ( Zm, n), where Zm = 39-48 (7)

Ω (МFn) = φ( n ) = ψ [ Ω (МCln) ] : Ω (МFn) = C Ω (МCln) +D (9)

E (МFn) = φ( n ) = ψ [ D (МFn) ] : E (МFn) = L Ω (МFn) + N, (10)

Ω (МХn) = φ( Zx ) = An ψ( Zx ) + Bn, X = F, Cl, Br, I, (8)

Ω (МХn) = φ( Zm ), (2)

ΔZm Ω (МFn) / ΔZm Ω (МFs) = φ( Zm, n), (3)

Δnm Ω (МFn) / ΔZm Ω (МCln) = φ( Zm, n), (4)

Ω (МFn) / Ω (МOn/2) = φ( Zm, n), (6)

Δs Н (МXn) = φ( Zm, Zx, n), , (11)

S (МXn) = φ( Zm, Zx, n). (12)

interpretation of these dependences can be found in [8, 9].

where An, Bn, C, D, L, N –const.


Thermodynamic Aspects of CVD Crystallization of Refractory Metals and Their Alloys 407

№ Substance Sо298 (g) Sо298 (s)

6 TaF5 332,7 [12] 169,7±16,7 [10]

1 Mo 181,663±0,029 [10] 28,59±0,21 [10] 2 MoF 243,53 [12] - 3 MoF2 275,9 [12] - 4 MoF3 301,3 [12] 93±12 [7] 5 MoF4 319,3 [12] 100±12 [7] 6 MoF5 327,7±1,7 [10] 125±12 [10] 7 MoF6 350,3±1,2 [10] - 8 Mo3F15 580,6±16,7 [20] - 1 W 173,675±0,029 [10] 32,65±0,33 [10]

5 WF4 330,1 [12] 103,3±8,4 [10] 6 WF5 343,1 [12] 146±13 [10]

1 Re 188,643±0,029 [10] 36,49±0,33 [10] 2 ReF 251±4 [7] - 3 ReF2 285±4 [7] - 4 ReF3 308,8 [12] - 5 ReF4 333,9±6,3 [10] 146,4±8,4 [10] 6 ReF5 337,6±6,3 [10] 175,7±8,4 [10] 7 ReF6 363,6±2,1 [10] - 8 ReF7 360 [22] -

3 TaF2 290,9 [12] - 4 TaF3 308,1 [12] - 5 TaF4 336,1 [12] -

7 Ta3F15 720,6±14,6 [15] -

2 WF 250,6±4,2 [10] - 3 WF2 285,8 [12] - 4 WF3 314,2 [12] -

7 WF6 353,5±1,3 [10] - 8 W3F15 631±12 [15] -

1 F 158,489±0,021 [10] - 2 F2 202,52±0,25 [10] - 1 H 114,494±0,021 [10] - 2 H2 130,395±0,021 [10] - 1 HF 173,512±0,033 [10] -

Table 2. Entropy data Sо298 (J/К mol) of system M-F-H components in gas (g) and solid (s)

9 Re 2F8 497±17 [23] 10 Re 3F15 736±17 [24]

states.


Table 1. Enthalpy of forming Δf Н (kJ/mol) and sublimation Δs H (kJ/mol) of system M-F-H components in gas (g) and solid (s) states.


№ Substance Δ<sup>f</sup> Но298 (g) Δ<sup>f</sup> Но (s) Δs H<sup>о</sup><sup>298</sup>

1 Re 775,0±6,3 [10] 0 775,0±6,3

5 ReF4 -733±33 [7] -995±33 [7] 263±26 6 ReF5 -962±29 [7] -1142±18 [7] 180±29

8 ReF7 -1410±11 [22] -1450,5±10,9 [22] 40,5±21,9

Table 1. Enthalpy of forming Δf Н (kJ/mol) and sublimation Δs H (kJ/mol) of system M-F-

№ Substance Sо298 (g) Sо298 (s) 1 V 182,010±0,033 [10] 28,88±0,33 [10]

3 VF2 254,4 [12] 76,220 [25] 4 VF3 283,05 [12] 96,99 [10] 5 VF4 305±4 [7] 126,13 [10]

1 Nb 186,000±0,033 [10] 36,53±0,21 [10]

5 NbF4 325,5 [12] 100±4 [10] 6 NbF5 323,8 [12] 157,3±2,1 [10]

1 Ta 184,927±0,033 [10] 41,47±0,17 [10]

2 VF 230±4 [10] -

6 VF5 331,0±2,9 [10] - 7 V2F6 397,0±17 [13] - 8 V2F8 456±17 [14] -

2 NbF 241,4 [12] - 3 NbF2 281,6 [12] - 4 NbF3 296,2 [12] -

7 Nb3F15 683,0±16,7 [15] -

2 TaF 240,8 [12] -

1 F 79,43±1,05 [10] - - 2 F2 0 - - 1 H 217,77±0,02 [10] - - 2 H2 0 - - 1 HF -270,4±1,2 [10] - -

8 W3F15 -4244,0±8,4 [15] -

2 ReF 343±60 [7] - 3 ReF2 -116±46 [7] - 4 ReF3 -354±36 [7] -

7 ReF6 -1353,5±12,6 [10] -

9 Re2F8 -1854,2±33,4 [23] 10 Re3F15 -3337,7±17,6 [24]

H components in gas (g) and solid (s) states.


Table 2. Entropy data Sо298 (J/К mol) of system M-F-H components in gas (g) and solid (s) states.

Thermodynamic Aspects of CVD Crystallization of Refractory Metals and Their Alloys 409

valent fluorides of tantalum, tungsten, rhenium have the lowest vaporation temperature

The peculiarity of the fluorides is the possibility of their polymerization. It is known that dimers or threemers are observed in gas state but tetramer clasters of Nb, Ta, Mo, W fluorides and chains of V, Re fluoride polymers are forming in solid state [30]. For example, fluorides W2F8, W2F10 and Mo2F6, Mo2F8, Mo2F10 exist in W-F and Mo-F system, correspondingly. The main structural state of Nb, Ta, Mo, W, Re fluoride polymers are threemers but vanadium pentafluoride does form polymer state. M3F15 polymers are forming by the single M-F-M bonds but the fluoride dimers have double fluorine bridge bonds. The exception are dimer molecules V2F6, V2F8, Re2F8 with the M-M bonds. All

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

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-

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

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

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

(500-550 K).

H system.

concentration.

Chatelier principle.

[7, 32, 33].

polymer states are presented in tables 1-3.

reagent ratio are presented at the Fig.2.

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


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