1. Introduction

It is well known that N-rich nitride of metals might be synthesized at comparatively low temperature T under flow of gaseous NH₃ of normal pressure. In pioneering works of this line of research published in 1930, Hägg[1] reported successful synthesis of mono-nitride for Mo and W and Lehrer[2] synthesis of Fe₄N phase. Later in 1948, Jack[3] reported synthesis of Fe₂N as well as Fe₄N under flow of NH₃ gas.

Later, Katsura and collaborators[4] confirmed experimentally the validity of evidences reported by Hägg[1] demonstrating that, under flow of NH₃ gas at normal pressure, mono-nitride MoN formed at 700ºC besides sub-nitride Mo₂N but, when the processing temperature was risen by mere 25ºC to 725ºC, MoN decomposed to turn the reaction product to be consisted of Mo₂N alone. Jehn and Ettmayer[5] reported that MoN synthesis was impossible in N₂ gas environment even in autoclave that was capable of raising N₂ gas pressure p(N₂) up to 300 bar.

Katsura[6] demonstrated that, for uranium sesqui-nitride U₂N_3+x (0 < x < 1) possessing extensive range of homogeneity composition synthesized at a given T, x tended to rise with the increasing NH₃ gas flow rate (in other words, with the decreased extent α of dissociation of NH₃). Later, Katsura and collaborators[7] demonstrated that N content in the Fe₄N phase varied over the length 4 cm being dependent on the inevitable variation of the extent αof dissociation of NH₃ along the flow path (i.e. decreasing a(N) on going from the upstream side to the downstream side of NH₃ gas flow path on account of increasing α).

During the course of surface nitriding experiment for tool steel block specimen, NH₃ gas with suppressed extent α of dissociation was proved to function as hydriding medium at comparatively low T (probably lower than 300ºC) while it worked as nitriding medium with high nitrogen activity a(N) at higher T (probably higher than 400ºC)[8].

Aiming at interpreting rationally all these available evidences regarding reaction of metals with NH₃ gas with suppressed extent α of dissociation [1-8], Katsura [9] undertook thorough thermodynamic analysis to derive isothermal plots of chemical activity a(N) of N and chemical activity a(H) of H as a function of α for NH₃. According to the analysis results presented by Katsura [9], a(N) as high as 10⁴ might be gained with α = 0.2 or 10³ with α = 0.5 at T = 700ºC while enhancement for a(H) realized by the suppressed α was modest compared with that for a(N).

Later, Katsura and collaborators [10-12] systematically evaluated activity a(H) and a(X) for tri-hydride H₃X of nitrogen-family elements X (= N, P or As) and demonstrated possibility of gaining very high a(X) and modestly enhanced a(H) through suppressed dissociation for H₃X type gas molecules in general.

In the present work, similar thermodynamic analysis was made for H₂X type gas molecules (X = S or O) to evaluate isothermal plots of a(X) and a(H) as a function of α following formally the procedure developed by Katsura [9] for analysis of H₃X gas molecules in state being away from dissociation equilibrium whereas, unlike H₃X type nitrogen-family tri-hydride gas molecules, H₂X gas molecules are highly resistant against spontaneous dissociation. Both H₂S and H₂O are known as corrosive molecular species (e.g., Ref.[13]) and thence their involvement in corrosion process is briefly considered with reference to the results of the present evaluation.

2. Thermodynamic Analysis Procedure

2.1. Characteristic features of H_nX gas molecules

As demonstrated by the available facts of corrosion cases[13], metallic materials might suffer from severe degradation in atmosphere containing H₂O and H₂S. For example, corrosion damages like SSCC (sulfide stress corrosion cracking) and HE (hydrogen embrittlement) are known to be induced in geothermal power plant and deep sour petroleum well rich in H₂S as well as H₂O. Thus, H₂X gas molecules under consideration as well as H₃X gas molecules (X = N, P or As) are certainly classified as corrosive chemical media.

Figure 1. Schematic "tetrahedral" configuration of electron pairs in sp3 hybrid orbital around

Table 1. X-H bond distance and H-X-H bond angle in HnX type gas molecules under consideration (Values taken from Ref.[15,16])

As might be understood by referring to some chemistry textbook (e.g., Chapter 8 in Ref.[14]), H_nX gas molecules under consideration (n = 2 or 3) are commonly with tetrahedral configuration of sp³ electron pairs around X atom as depicted in Fig. 1. Difference between the H₃X type gas molecule with X = Vb group element and the H₂X type gas molecule with X = VIb group element is that the former is with only single lone pair of electrons while the latter is two lone pairs of electrons. The X-H bond distance and the H-X-H bond angle in these gas molecules are compared in Table 1 with reference to the JANAF Thermochemical Tables[15,16].

Two versions of the JANAF Thermochemical Tables[15,16] are cited as the thermodynamic data source herein. This is simply because that the molecular data (values for H-X-H angle and X-H interatomic distance) for H₂O are not given explicitly in the new NIST-JANAF Thermochemical Tables[16] while the provided thermodynamic parameter values for the concerned H_nX type gas molecules in ideal gas state in the new version[16] and those in the older version[15] are largely comparable to one another. In the older version of the JANAF Thermochemical Tables[15], thermodynamic parameter values for ideal gas state of H_nX gas molecules under normal pressure condition alone were provided. On the other hand, supplemental data for H₂O including those in liquid real gas states for pressures at 1 bar, 10 bar and 100 bar and those in real fluid states at 500 bar and 5000 bar are cited additionally in the new version[16].

It is noticed in Table 1 that the H-N-H bond angle in NH₃ molecule is slightly broader than the H-O-H bond angle in H₂O while the interatomic distance between N and H in NH₃ is longer than that between O and H in H₂O. The former aspect is explainable on the basis of knowledge that lone pairs would occupy more room than bonding electrons[14]; there are only one lone pair in NH₃ (Fig. 1 (a)) while two lone pairs in H₂O (Fig. 1 (b)). On the other hand, the latter aspect suggests that the bonding strength between O and H in H₂O molecule is stronger than that between N and H in NH₃.

In the following calculations, values for equilibrium constant K_f for H_nX gas molecules in ideal gas state at normal pressure listed in the JANAF Thermochemical Tables in form of log K_f[15,16] are used. For example, expression for K_f for ideal H₂S gas molecules is

(1)

where p^eq(H₂S), p^eq(H₂) and p^eq(S₂) refer to the equilibrium partial pressures of H₂S, H₂ and S₂, respectively, at a temperature T.

That is, lower the K_f value the higher the readiness for H_nX gas molecule to be dissociated into H₂ and X₂. According to the JANAF Thermochemical Tables[15,16], values of log K_f(NH₃) are negative at T higher than 500 K and values of log K_f(PH₃) are negative at entire range of T up to 6000 K implying readiness of these H₃X gas molecules to dissociation into H₂ and X₂. Thus, to gain high a(X) and high a(H) of these XH₃ gas molecules, it was necessary to carry out experiments under flowing XH₃ gas to suppress extent α of dissociation of XH₃ gas molecules[1-12,17,18]. When nitriding experiment of metals using NH₃ gas was undertaken in closed system to allow establishment of dissociation equilibrium among gas species, NH₃, N₂ and H₂, in the gas phase, N content in the reaction product became the one anticipated from p^eq(N₂) showing no effect of high a(N) of NH₃ gas molecules that was realized by suppressed extent α of dissociation (i.e. by uncracked NH₃)[6,8].

In contrast, values of log K_f(H₂S) are negative only at T higher than 1900 K and values of log K_f(H₂O) are negative only at T higher than 4400 K implying higher resistance of these H₂X type gas molecules against dissociation into H₂ and X₂ at relatively low temperatures. That is, for H₂S and H₂O, extent α of dissociation at T lower than 1500 K is considered to be inherently low not necessary to arrange flowing setup to realize low α for these gas species unlike for NH₃ and PH₃.

Anyway, to maintain formal consistency of the analysis procedure with that for the NH₃ gas molecules with suppressed α, parameter α is used in the following analysis for H₂S and H₂O.

2.2. Analysis for H₂S

In case of H₂S, dissociation reaction is represented by

(2)

Thus, for a given extent α of dissociation of H₂S, partial pressures, p(H₂S), p(S₂) and p(H₂), of H₂S, S₂ and H₂, respectively, in gas phase under condition of total pressure 1 bar would be represented by (in bar unit)and accordingly, following procedures presented in Ref.[9], a(S) and a(H) of H₂S with a specified extent α of dissociation being in equilibrium with S and H in metal (M) lattice are given by

(3)

(4)

(5)

(6)

(7)

To derive these relationships, equilibrium between S or H in metal lattice and H₂S in gas phase was assumed to be represented by

(8)

(9)

(10)

Calculated values of activities, a(S) and a(H), using K_p values listed in JANAF Thermochemical Tables[15,16] are plotted in Fig. 2 in form of isotherms as a function of α. As evident in Fig. 2, levels of a(S) and a(H) of H₂S do not seem to be specially high at any α under examined T up to 1300 K unlike in the cases with tri-hydrides H₃X of nitrogen-family element X (N, P or As)[9-12].

Hypothetical equilibrium activity a^eq(S) of S and equilibrium activity a^eq(H) of H of H₂S for given degree α^eq of the dissociation under equilibrium condition were calculated according to

(11)

(12)

The curves referring to these relationships are drawn in Fig. 2 with broken lines. It must be noted that these curves do not represent isothermal relationships unlike other curves drawn with full lines in these plots and thence a^eq(S) and a^eq(H) must be merely considered as the reference levels corresponding to the equilibrium partial pressure of the diatomic gas molecules, S₂ and H₂, respectively, for arbitrary α at different T under condition of total pressure 1 bar.

As such, the situation for H₂S regarding the extent of enhancement of a(S) and a(H) as a function of α is quite different from that for NH₃ as reproduced in Fig. 3[9,18]. As reproduced in Fig. 3, in case of NH₃ gas molecules, considerably higher levels of a(N) and a(H) compared with those under the hypothetical equilibrium state are realized over entire range of α at T higher than 600 K. In contrast, in case of H₂S gas molecules, a(S) and a(H) are considerably lower than the equilibrium levels over entire range of α even at T = 1300 K (Fig. 2). That is, enhanced a(S) and a(H) cannot be realized for H₂S gas molecules even at low α unlike for NH₃ gas molecules. Reproduced from Ref.[9] with superimposed hypothetical equilibrium curves reported in Ref.[18].

2.3. Analysis for H₂O

Similar calculations were made for H₂O and the results are plotted in Fig. 4. It is evident in Fig. 4 that a(O) vs. α and a(H) vs. α isotherms for H₂O gas molecules at T = 1300 K are comparable to or lower than a(S) vs. α and a(H) vs. α isotherms for H₂S gas molecules at T = 500 K. For H₂O, a^eq(O) and a^eq(H) isotherms locate by far above the plots in Fig. 4 and thence they are not drawn in Fig. 4. It means that enhanced a(O) and a(H) cannot be gained for H₂O gas molecules even at low α like for H₂S and unlike for NH₃. These evaluation results indicate that H₂X type gas molecules (X = VIb group element) is not at all unstable unlike H₃X type gas molecules (X = Vb group element) in spite of apparent similarity in electronic surrounding around X atom between the former and the latter as depicted in Fig. 1.

3. Discussion

According to molecular parameter values listed for H_nX type gas molecules in Table 1, bonding strength between O and H in H₂O must be by far stronger than that between N and H in NH₃. This is not in contradiction to the present evaluation results for H₂O suggesting low a(H) and a(O) even with suppressed α (Fig. 4) compared with very high a(N) and modestly enhanced a(H) for NH₃ even at comparatively high α (Fig. 3). The similar arguments for NH₃ and H₂O appear to be valid for PH₃ and H₂S as well.

As verified experimentally in the earlier works [6-8,10-12,17-20], where there are several species containing an element X coexisting in the reactants, X-containing chemical species possessing the highest a(X) in the reactants would determine the X content in the reaction product. For example, where amorphous carbon with a(C) > 1 is present in the reactant, C content in prepared carbide or carbonitride of metal would become higher than that under presence of graphite (reference state of C with a(C) = 1) alone [8,17-20] while N in NH₃ gas molecule in a state being away from equilibrium state determined a(N) to yield N-rich reaction products that are not synthesized in N₂ gas environment even at elevated pressure[1-12,17,18].

Thus, O content in the reaction product prepared in gas phase containing H₂O impurity as well as O₂ impurity must be determined by chemical potential a(O) of O of H₂O gas molecule represented by

(13)

or by a(O) of O₂ gas defined by

(14)

depending on whether a(O) defined by Eq.(13) or that defined by Eq.(14) is higher.

For example, commercial pure Ar gas of normal grade supplied in cylinder is typically with ppm order levels of impurity O₂ and H₂O. That is, a(O) of the O₂ impurity must be around 10^-3 while a(O) of H₂O would not be higher than 10^-8 even around 1000 K with α as small as 0.01 (cf. Fig. 4). Thus, a(O) of commercial grade Ar gas might be determined by p(O₂) defined by Eq.(14) rather than by a(O) of H₂O impurity given by Eq.(13).

Figure 2. Chemical activity a(S) of S and a(H) of H in H2S plotted as a function of extent α of dissociation of H2S

Figure 3. Chemical activity a(N) of N and a(H) of H in NH3 plotted as a function of extent α of dissociation of NH3

Figure 4. Chemical activity a(O) of O and a(H) of H in H2O plotted as a function of extent α of dissociation of H2O

Nevertheless, chemical inertness of H₂O gas molecule does not necessarily mean the electrochemical inertness of water in condensed state. Chemical reactivity and activity of condense water must be interpreted in terms of electrochemistry or solution chemistry rather than in terms of molecular chemistry. Under co-presence of H₂S and H₂O, yield of sulfuric acid H₂SO₄ is inevitable. Then, ionic species such as H⁺, SO₄^2- and OH^- in acidic solution would promote electrochemical process leading to corrosion. Chemical activity of element must be higher in form of ion than in form of neutral atom or molecule. As pointed out earlier in the text, the highest a(X) of the element X would determine the X content of the product in case that the element X exists in different forms in the reactant[6-12,17-20].

4. Conclusions

Thermodynamic evaluation for chemical activities, a(X) and a(H), in H₂X type gas molecules (X = S or O) was made as a function of extent α of dissociation of H₂X gas molecules following formally the procedure developed by Katsura for evaluation of a(N) and a(H) in NH₃ gas molecules with suppressed extent of dissociation[9] and for other XH₃ type gas molecules (X = P or As)[10-12]. Although the H₂X type gas molecules under consideration are resistant against spontaneous dissociation unlike the H₃X type tri-hydrides of nitrogen-family element X and thence direct comparison for the evaluation results for dependence of a(X) and a(H) on α between H₂X and H₃X might not be fully justifiable, the present evaluation results look rational indicating that both H₂S and H₂O gas molecules are quite inert in chemical sense in contrast to high chemical activities of constituents, X and H, in H₃X type nitrogen-family tri-hydrides under condition of suppressed dissociation.

As such, the present thermodynamic evaluation results for stable H₂X gas molecules together with the original analysis results for unstable H₃X gas molecules presented by Katsura[9] appear to suggest that chemical activities, a(X) and a(H), of these H_nX type gas molecules might be generally represented as functions of temperature T and extent α of dissociation.

The aspect of controlling a(C) in metal carburizing reaction through arbitrary varying partial pressures of constituent gas species in gas mixture consisting of CO and CO₂ or of CH₄ and H₂ was reported elsewhere[21-24] rather than through employment of amorphous carbon [8,18-20]. Thus, the evaluation results drawn in the present work for H₂S and H₂O demonstrating feasibility of determining the activities, a(S), a(O) and a(H), as functions of T and α must be considered valid and realistic.

For the inherently unstable gaseous molecular species, low α might be realized by simply arranging experimental setup with gas flow system to retard dissociation of the gas species. On the other hand, to realize low α condition for stable gas species H₂X (X = S or O), admixing with excess H₂ to gain high a(H) or admixing with X to gain high a(X) might be desirable.