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Thermodynamics of cementite layer formation
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Acta Materialia 57 (2009) 4074–4080 www.elsevier.com/locate/actamat
Thermodynamics of cementite layer formation H. Na¨fe * Max-Planck-Institut fu¨r Metallforschung, Pulvermetallurgisches Laboratorium, Heisenbergstraße 3, 70569 Stuttgart, Germany Received 2 September 2008; received in revised form 29 April 2009; accepted 1 May 2009 Available online 21 June 2009 Dedicated to my esteemed teacher and colleague D. Rettig on the occasion of his 75th birthday
Abstract The formation of cementite layers upon carburization of iron is described by a thermodynamic approach assuming the establishment of an equilibrium within the carburizing gas atmosphere and between the solid and the gas. Based on that, the suppression of soot formation by adding ammonia to the gas, which has recently been reported in the literature as a kinetically determined surprising phenomenon, can be explained sufficiently well and, hence, proves to be a thermodynamically predictable effect. Ó 2009 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Carburization; Cementite formation; Thermodynamics; Non-metal/metal solution; Sooting
1. Introduction Upon carburizing iron substrates, it has recently been found that massive cementite layers are formed if ammonia is deliberately added to the surrounding gas atmosphere, comprising carbon monoxide, hydrogen and nitrogen [1]. Without NH3, however, the cementite formation is accompanied by sooting of the substrate, i.e. disintegration of the iron surface by graphite precipitation. Hence, the addition of NH3 provides the possibility to suppress metal dusting. As an explanation, the authors suspect a kinetic effect of NH3 by accelerating the carbon adsorption at the solid/ gas interface and thus enhancing the carbon uptake by the iron substrate. This is supposed to result in an advanced cementite layer growth. Regarding the interpretation of the above observations the question arises as to which extent the phenomenon might be ascribed to thermodynamic rather than kinetic reasons. This question immediately comes to mind as the authors of [1] do not launch any serious attempt in order to consider thermodynamic aspects for an explanation.
*
Tel.: +49 711 689 3113; fax: +49 711 689 3131. E-mail address: [email protected]
It is the aim of the present paper to analyze the process of carburization under the above-mentioned conditions from a purely thermodynamic point of view. 2. Thermodynamic description of non-metal/metal solutions Thermodynamically, the binary iron–carbon system like the iron–nitrogen system and others are usually described as a solution of the non-metal An in the metal Me: 1 An ¢ ½AMe n
ð1Þ
where [A]Me denotes A dissolved in Me. An is commonly a mono-(n = 1) or biatomar (n = 2) element in its state of pure substance which is why its chemical potential is equal to the Raoultian standard chemical potential l0An (for details of the terminology cf. [2]). For [A]Me, the Henrian standard chemical potential l01½AMe is chosen, and therefore the relationship holds: 1 0 l ¼ l01½AMe þ RT ln a1½AMe n An
ð2Þ
with R and T being the gas constant and the absolute temperature. a1½AMe is the Henrian activity of the dissolved non-metal which, in many A–Me systems, because of fairly
1359-6454/$36.00 Ó 2009 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2009.05.001
H. Na¨fe / Acta Materialia 57 (2009) 4074–4080
low A solubilities, can be approximately set equal to the analytical concentration of [A]Me. The difference between the two standard chemical potentials in Eq. (2) is equal to the Gibbs free energy change associated with reaction (1), i.e. with the transfer of A from pure state to the infinitely dilute A–Me solution. In view of a single atomar entity of A, this transfer implies the removal of an A atom out of the bulk of the substance of A and subsequently the creation of a void within the solvent. Finally, it implies the replacement of the void by the A entity and the solvation of A by solvent species. The energetic and entropic effects associated with these processes result in the Gibbs free energy of solution of A in Me, i.e. DS G0½AMe . In the same way as for the thermodynamic description of [A]Me the Henrian standard state has been used in order to end up with Eq. (2), the Raoultian standard state ought to be applicable, too. This, however, provides the trivial identity: l0An ¼ l0An
ð3Þ
that does not contain any useful thermodynamic information. Eq. (3) means that the Raoultian activity of [A]Me is fixed to unity1: a½AMe ¼ 1
ð4Þ
Eq. (1) describes the equilibrium between two phases, the non-metal and the metal. Provided that An is e.g. molecular oxygen and Me is liquid sodium at e.g. 400 °C, the oxygen partial pressure that corresponds to the oxygen saturated sodium solution amounts to about 1050 bar. This extremely small value is the consequence of the strongly negative Gibbs free energy of formation of the compound between O and Na. In view of the statistical interpretation of the pressure of a gas, the value of 1050 bar can never be attributed to a gas phase. In this case, the non-metal does not represent an independent phase which is why the prerequisite for the establishment of the phase equilibrium (1) is no longer fulfilled. Due to the high affinity between O and Na, it is Na2O that gets dissolved in or precipitates out of the sodium melt rather than molecular O2. Provided that a compound MewAf exists between Me and An, the solution equilibrium (1) can without reservation be replaced by (w, f: stoichiometric numbers): ð5Þ Mew Af ! ½Mew Af Me
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whether MewAf or A is the solute. Since the solvent particles in the solvation shell of A are not distinguishable from the Me particles belonging either to the compound MewAf or to the solvation shell of MewAf, the final state of the liquid or solid solution remains the same. From this point of view, [MewAf]Me can be understood as synonymous to [A]Me. In order to simultaneously cover both compound formation and dissolution and in order to proceed from the same state of A as in Eq. (1) and end up with the same state of A as in Eq. (5), the formation reaction: f wMe þ An ! ½Mew Af Me n
ð6Þ
has to be considered. Reaction (6) means that after the formation of the pure substance MewAf from the constituent elements the product is dissolved in the solvent Me. Hence, Eq. (6) represents the standard formation reaction of [MewAf]Me. In terms of the Henrian standard state for the activity of [MewAf]Me, the thermodynamic description of reaction (6) yields: ln a1½Mew Af Me ¼
Df G01Mew Af RT
þ w ln aMe þ
f ln aAn n
ð7Þ
where Df G01Mew Af is the standard Gibbs free energy of formation of MewAf in the infinitely dilute solution of Me. Regarding Eq. (7) it is equally justified to apply the Raoultian standard state, as discussed in [2], to the description of the activity of MewAf dissolved in Me. Then the relationship reads: ln a½Mew Af
¼ Me
Df G0Mew Af RT
þ w ln aMe þ
f ln aAn n
ð8Þ
with Df G0Mew Af denoting the standard Gibbs free energy of formation of pure MewAf. Eq. (8) provides information about the Raoultian activity of the solute of a metallic solution which, in contrast to that of the formulation by Eq. (4), is not only restricted to the state of saturation but is generally valid. Since data on the standard Gibbs free energy of formation of a pure substance are known for most relevant compounds, relationship (8) is, moreover, useful from a practical point of view. 3. Thermodynamic conditions of cementite formation
The major difference between (1) and (5) is that in the former case dissolution and compound formation are combined, implying that the solvation energy additionally comprises the energy of the chemical bonding between A and Me, whereas (5) is solely a dissolution process. Nevertheless, there will not be a difference in the structure of the resulting solution regardless of
In view of the above remarks on the thermodynamic description of a non-metal/metal solution the formation reaction of cementite, Fe3C, from iron and carbon is considered: ð9Þ 3Fe þ C ! Fe3 C
1 Note that activity values larger than unity which can be encountered in the literature (cf. [3]) lose track of thermodynamic reality.
With this reaction proceeding toward the left hand side, sooting takes place. Thermodynamically, reaction (9) results in the following relationship:
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H. Na¨fe / Acta Materialia 57 (2009) 4074–4080
Df G0Fe3 C ¼ RT ln
a3Fe aC aFe3 C
ð10Þ
with Df G0Fe3 C being the standard Gibbs free energy of formation of pure cementite. aFe3 C , aFe and aC denote the Raoultian activities of the involved substances. Eq. (10) reveals that Fe3C, Fe and C may coexist in the state of pure substance, i.e. with ai = 1, only if Df G0Fe3 C ¼ 0. According to the quantitative data for Df G0Fe3 C [4] this is only given at one single temperature, i.e. at T = 589 °C. In the following this temperature will be named as Tsa. Above and below this temperature, the coexistence of all the three pure phases is impossible. As a consequence, reaction (9) is either completely on the right hand side or completely on the left one, which means that either the reaction product Fe3C exists alone or only the starting materials do coexist with each other. The reality, however, differs from these thermodynamic constraints. A cementite layer grown on the surface of a piece of iron that gets disintegrated by partially being converted into graphite implies the coexistence of all three substances simultaneously. This experimental fact strongly indicates that the condition ai = 1 is not unrestrictedly fulfilled in the system. There must be at least one substance for which the Raoultian activity deviates from unity. It is supposed that this applies to cementite. Cementite is present as a layer and thus as a part of the iron substrate rather than as a pure material. Hence, the activity of Fe3C in the cementite layer may deviate from that of the pure substance and is likely to be lower than unity which could be understood as an expression of non-stoichiometry in Fe3C, resulting in Fe3+dC. That the consideration of nonstoichiometry in cementite is not so far away has not only once been quoted in the literature [5–7]. The Fe3C-activity of the layer adjusted by the coexistence with pure iron and graphite, i.e. aFe = 1 and aC = 1, can be calculated from Eq. (10). For temperatures lower than or equal to Tsa, the following relationship holds: ln aFe3 C
Df G0Fe3 C ¼ RT
ðT 6 T sa Þ
ð11Þ
In the temperature region T P Tsa the situation is determined by the formation of pure Fe3C that sets in at Tsa and henceforth fixes the activity at a constant level, viz.: aFe3 C ¼ 1
ðT P T sa Þ
ð12Þ
Thus, Tsa is the temperature at which the Fe–C solution is saturated by Fe3C. Both of the curve branches representing Eqs. (11) and (12) are depicted in Fig. 1. The line describing the temperature dependence of aFe3 C at the same time defines the area within which soot either can be formed on the cementite surface or is impossible to be formed. In view of Eq. (10) the decomposition of Fe3C into Fe and C, with aFe = 1 and aC = 1, proceeds if aFe3 C is equal to or larger than the respective value of the coexistence line in Fig. 1. Below that line there is no chance from a mathematical point of view that the carbon activity
Fig. 1. Temperature dependence of the Raoultian Fe3C-activity of the cementite layer in coexistence with pure iron and graphite.
reaches the threshold aC = 1 while aFe = 1. Therefore, soot cannot be formed. Moreover, due to the numerical data of Df G0Fe3 C the concurrent establishment of the conditions aFe = 1 and aC = 1 is also impossible if the Fe3C-activity is confined to the constant level of Eq. (12) while the temperature is higher than the one at which Fe3C just starts to precipitate as a pure phase, i.e. Tsa. As a consequence, there is no chance for soot formation on the basis of Eq. (9) in the temperature interval T > Tsa. For the formulation of Eq. (9) it is assumed that the solid Fe–C solution represents a solution of Fe3C in Fe. It must be kept in mind, however, that apart from Fe3C another carbide exists, i.e. Fe2C [5]. Therefore, it is more realistic to consider the Fe–C solution as represented by a Fe–Fe2C–Fe3C solution from which graphite can also precipitate according to: 3Fe2 C ! ð13Þ 2Fe3 C þ C Consequently, the activities of both carbides are interrelated. For the condition aC = 1 the following relation is valid: ln
a3Fe2 C 2Df G0Fe3 C 3Df G0Fe2 C ¼ RT a2Fe3 C
ð14Þ
with aFe2 C and Df G0Fe2 C denoting the Raoultian activity of Fe2C and its standard Gibbs free energy of formation, respectively. Numerical data on Df G0Fe2 C are known from [5]. Based on Eq. (14) the Fe2C-activity of the Fe–Fe2C– Fe3C solution in equilibrium with pure graphite can be determined by taking either Eq. (11) and (12) into account. The result is: Df G0Fe2 C ðT 6 T sa Þ RT 2Df G0Fe3 C 3Df G0Fe2 C ðT P T sa Þ ¼ 3RT
ln aFe2 C ¼
ð15Þ
ln aFe2 C
ð16Þ
H. Na¨fe / Acta Materialia 57 (2009) 4074–4080
These two curve branches are depicted in Fig. 2. If aFe2 C is equal to or larger than the values representing the line of Fig. 2, soot is formed. This is true within the whole temperature interval covered by Fig. 2. Beyond that interval it is only true as long as the condition aFe2 C < 1 is fulfilled, i.e. below the saturation temperature of Fe2C. Due to the interdependence of aFe2 C and aFe3 C the line of Fig. 2 in terms of ln aFe2 C corresponds to the line of Fig. 1 in terms of ln aFe3 C . Both plots have the same relevance. As discussed above, upon increasing the temperature of the Fe–Fe2C–Fe3C solution, Tsa is the last temperature at which Fe and C coexist with each other. According to the laws of chemical equilibrium, slightly above this temperature any Fe particle in contact with C reacts with C to form Fe3C. Thermodynamically, this reaction must be complete with the consequence that at T > Tsa no iron is in equilibrium with carbon any more. Instead, the precipitation of carbon now obeys Eq. (12) implying that soot particles if formed are surrounded by Fe3C particles rather than Fe particles. Thus, the nature of the soot formation process alters which might be accompanied by a change in the kinetics of the process. Since the following considerations first of all focus on the behaviour of the system at temperatures lower than Tsa they will be confined to the activity of Fe3C only. The combination of Eq. (9) with the Boudouard equilibrium leads to: ð17Þ 3Fe þ 2CO ! Fe3 C þ CO2 According to reaction (17) the activity of Fe3C is fixed by the ratio between the partial pressures p of carbon monoxide and carbon dioxide in the carburizing atmosphere and by the respective values of the standard Gibbs free energies of formation: ln aFe3 C ¼
2Df G0CO
Df G0CO2 RT
Df G0Fe3 C
þ ln
p2CO pCO2
ð18Þ
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Depending on whether the value of the Fe3C-activity resulting from Eq. (18) is lying beyond the line of Fig. 1 or underneath, the carburizing gas causes soot to be produced out of the cementite layer or not. 4. Relevant gas equilibria In a gas mixture that contains ammonia, hydrogen and nitrogen, the formation and dissociation of NH3 will play a role: 3 1 NH3 ! H2 þ N2 2 2
ð19Þ
If H2, CO and CO2 are present, the water gas equilibrium has to be taken into consideration: H2 þ CO2 ! ð20Þ H2 O þ CO Moreover, in gaseous mixtures with constituents such as H2, H2O and CO there is some probability for the formation of hydrocarbons. In the present case, methane is regarded to be relevant for the behaviour of the atmosphere: ð21Þ 2H2 þ 2CO ! CH4 þ CO2 5. Thermodynamic constraints By assuming that reactions (19)–(21) are in thermodynamic equilibrium, the following relations hold: ln
1=2 3=2 Df G0NH3 p N2 p H2 ¼ pNH3 RT
ð22Þ
ln
pCO pH2 O Df G0CO2 Df G0CO Df G0H2 O ¼ pH2 pCO2 RT
ð23Þ
ln
pCH4 pCO2 2Df G0CO Df G0CH4 Df G0CO2 ¼ p2CO p2H2 RT
ð24Þ
with the partial pressures pk of each of the m different gas species k being defined by their mole numbers nk and the total pressure pt of the gas atmosphere: nk pt ð25Þ pk ¼ Pm j¼1 nj The mole numbers nk result from the values n0k , characterizing the starting concentrations of the carburizing gas mixture, and the change these numbers receive by the progress of reactions (19)–(21). Quantitatively, this change is expressed by nr, the extent of reaction, and is additionally governed by the stoichiometry characteristic of the respective reactions. Depending on whether the species under consideration are produced or consumed the stoichiometric numbers mk,r of the rth reaction are either positive or negative. Therefore, the relationship holds: Fig. 2. Phase stability regions for the decomposition of the Fe–Fe2C– Fe3C solid solution into iron and soot in terms of the Fe2C-activity.
nk ¼ n0k þ
3 X r¼1
mk;r nr
ð26Þ
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H. Na¨fe / Acta Materialia 57 (2009) 4074–4080
k stands for either NH3 or N2 or H2 or H2O or CO or CO2 or CH4 or Ar. r is equal to either 1 for reaction (19) or 2 for reaction (20) or 3 for reaction 21. The substitution of Eqs. (25) and (26) into Eqs. (22)–(24) results in a system of 3 non-linear equations in terms of the unknowns n1, n2 and n3. Numerically, this system of equations is restrained by the standard Gibbs free energies of formation of the involved substances, taken from [4,5,8], by the total pressure of the gas atmosphere as well as by the starting values for the concentration of the gaseous species. 6. Numerical calculations With numerical data for n1, n2 and n3 resulting from the zeros of the above-mentioned system of equations, the equilibrium composition of each constituent of the gas atmosphere is fixed by Eq. (26). Hence, the partial pressures of the gas species are also fixed, viz. by Eq. (25). In view of Eq. (18), the same is true for the Fe3C-activity established by the equilibrium according to Eq. (17), between the iron substrate, on the one hand, and carbon monoxide as well as carbon dioxide of the surrounding gas atmosphere, on the other hand. By plotting the results of the numerical calculations in terms of the logarithm of the Fe3C-activity as a function of the inverse temperature, the dashed lines of Figs. 3 and 4 are obtained. The numbers assigned to the lines stand for the gas compositions as specified in Table 1. The data for the compositions 1, 2, 3 and 4 of the gases that the iron samples are exposed to are identical with those of the gases used in [1] for the experimental investigations. Their initial compositions are characterized by an invariable H2 and CO concentration and, from 1 to 4, a growing substitution of N2 by NH3. According to Fig. 3, at T = 550 °C, curves 1 and 2 are lying within the region of soot formation whereas curve 4
Fig. 3. Fe3C-activity of the cementite layer after equilibrating with the carburizing gas atmosphere (dashed lines; gas compositions 1–4 according to the specifications of Table 1; pt = 1 bar) in comparison with the phase stability line (solid line).
Fig. 4. Fe3C-activity of the cementite layer after equilibrating with the carburizing gas atmosphere (dashed lines; gas compositions 5–8 according to the specifications of Table 1; pt = 1 bar) in comparison with the phase stability line (solid line).
Table 1 Initial values of the gas compositions used for the calculations the results of which are illustrated in Figs. 3–6. Gas
Initial gas composition (%) H2
CO
N2
NH3
CO2
Ar
1 2 3 4 5 6 7 8
58 58 58 58 58 75 15 15
20 20 20 20 20 15 2.0 1.8
22 15.4 8.8 – – – – –
– 6.6 13.2 22 – – – –
– – – – – – – 0.2
– – – – 22 10 83 83
is unambiguously outside this region. Curve 3 is close to the dividing line in between. Thus, it must be expected that the exposition of the iron/cementite layer to gas 1 or 2 causes graphite to be formed while gas 4 suppresses the graphite precipitation. These thermodynamically based predictions completely agree with the experimental observations reported in [1]. In particular, they demonstrate that the effect of ammonia on the suppression of the soot formation has mainly thermodynamic rather than kinetic reasons. There is only a slight difference between prediction and experiment insofar as the calculations let expect that the iron/cementite sample is barely sooted in gas 3 (cf. curve 3 of Fig. 3; T = 550 °C) whereas the authors of [1] describe the same gas composition as the one in which the gradual increase of the ammonia content just terminates the soot formation. This detail may indicate that other than thermodynamic aspects will also have an influence on the experimental behaviour, at least to a minor degree. The same is corroborated by considering the oxidation potential adjusted by the carburizing gas atmosphere under equilibrium conditions. According to the present thermo-
H. Na¨fe / Acta Materialia 57 (2009) 4074–4080
dynamic calculations, at T = 550 °C the oxidation potential, expressed as water to hydrogen partial pressure ratio, is slightly higher than the value established by the iron/ wustite equilibrium (cf. Fig. 5). Experimentally, it would mean that iron is to a certain extent oxidized during carburization which seems to contradict the reality. This contradiction may give another evidence that the experimental observations are widely but not totally in accordance with the thermodynamic description. Possibly, one or more of the reactions under consideration slightly deviate from their assumed equilibrium positions or additional reactions need to be taken into account for still better matching the experimental situation. Thermodynamically, the increase of the ammonia content in the carburizing gas results in an increasing inventory of molecular hydrogen and nitrogen in the system. Since ammonia is almost completely dissociated and since the dissociation is accompanied by doubling of the total number of gas molecules, the partial pressure of CO shrinks while that of H2 grows upon equilibration. As a result, the extent of both of the reactions (20) and (21) is affected. On the whole, the changes are such that the carburizing potential of the gas decreases with rising ammonia content. The preceding interpretation allows to conclude that the formation of massive cementite layers by suppressed sooting is not necessarily bound to the presence of ammonia as it has been stated in [1]. The ‘‘ammonia” effect can be simulated by other gases as well provided that they fulfill the same purpose regarding gas dilution and partial pressure shift. This is illustrated in Fig. 4 in which curves 5 and 6 represent the calculated Fe3C-activity of the cementite layer equilibrated with ammonia- and nitrogen-free gas atmospheres. Their initial compositions are chosen such that the data in terms of the CO and H2 partial pressure approximately correspond to the calculated equilibrium
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Fig. 6. Oxidation potential in terms of the partial pressure ratio between water and hydrogen of the carburizing gases 5–8 (dashed lines; gas compositions according to the specifications of Table 1; pt = 1 bar) in comparison with the oxidation potential of the iron/wustite phase equilibrium (solid line).
compositions established in gases 1 and 4. The effect is accomplished by using Ar as an inert diluting gas (cf. Table 1). In the same manner as the substitution of nitrogen by ammonia causes curve 1 of Fig. 3 to be shifted into the soot-free region toward the position of curve 4, curve 6 of Fig. 4 gets to be lying within this region due to a change in the initial CO and H2 partial pressures compared to those of gas 5. Interestingly, the calculations on the behaviour of the ammonia- and nitrogen-free gases also lead to an oxidation potential higher than that of the iron/wustite equilibrium (cf. curves 5 and 6 in Fig. 6 with curves 1 and 4 in Fig. 5). Therefore, as an example of gas compositions with a more reducing oxidation potential, gases 7 and 8 were chosen (cf. Figs. 4 and 6). 7. Conclusions The above considerations prove the experimental observations on the carburization of iron to be widely in accordance with thermodynamic calculations assuming equilibrium between the solid and the surrounding gas atmosphere as well as within the gas. In particular, the calculations enable to predict and to understand the observed suppression of soot formation by adding ammonia to the carburizing gas. As a consequence, the ‘‘ammonia” effect as prerequisite for the formation of massive cementite layers is not surprising but predictable and can be achieved by other means as well. References
Fig. 5. Oxidation potential in terms of the partial pressure ratio between water and hydrogen of the carburizing gases 1 and 4 (dashed lines; gas compositions according to the specifications of Table 1; pt = 1 bar) in comparison with the oxidation potential of the iron/wustite phase equilibrium (solid line).
[1] Gressmann T, Nikolussi M, Leineweber A, Mittemeijer EJ. Scripta Mater 2006;55:723. [2] Na¨fe H, Ber Bunsenges. Phys Chem 1994;98:1281. [3] Mittemeijer EJ, Slycke JT. Surface Eng 1996;2:152.
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H. Na¨fe / Acta Materialia 57 (2009) 4074–4080
[4] Barin I. Thermochemical data of pure substances. 3rd ed. Weinheim, New York: VCH Verlagsgesellschaft; 1995. [5] Richardson FD. J Iron Steel Inst 1953;175:33. [6] Banya S, Elliott JF, Chipman J. Met Trans 1970;1:1313.
[7] Chipman J. Met Trans 1972;3:55. [8] NIST-JANAF. Thermochemical tables. 4th ed. New York: American Chemical Society and American Institute of Physics and National Institute of Standards and Technology; 1998.
Acta Materialia 57 (2009) 4074–4080 www.elsevier.com/locate/actamat
Thermodynamics of cementite layer formation H. Na¨fe * Max-Planck-Institut fu¨r Metallforschung, Pulvermetallurgisches Laboratorium, Heisenbergstraße 3, 70569 Stuttgart, Germany Received 2 September 2008; received in revised form 29 April 2009; accepted 1 May 2009 Available online 21 June 2009 Dedicated to my esteemed teacher and colleague D. Rettig on the occasion of his 75th birthday
Abstract The formation of cementite layers upon carburization of iron is described by a thermodynamic approach assuming the establishment of an equilibrium within the carburizing gas atmosphere and between the solid and the gas. Based on that, the suppression of soot formation by adding ammonia to the gas, which has recently been reported in the literature as a kinetically determined surprising phenomenon, can be explained sufficiently well and, hence, proves to be a thermodynamically predictable effect. Ó 2009 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Carburization; Cementite formation; Thermodynamics; Non-metal/metal solution; Sooting
1. Introduction Upon carburizing iron substrates, it has recently been found that massive cementite layers are formed if ammonia is deliberately added to the surrounding gas atmosphere, comprising carbon monoxide, hydrogen and nitrogen [1]. Without NH3, however, the cementite formation is accompanied by sooting of the substrate, i.e. disintegration of the iron surface by graphite precipitation. Hence, the addition of NH3 provides the possibility to suppress metal dusting. As an explanation, the authors suspect a kinetic effect of NH3 by accelerating the carbon adsorption at the solid/ gas interface and thus enhancing the carbon uptake by the iron substrate. This is supposed to result in an advanced cementite layer growth. Regarding the interpretation of the above observations the question arises as to which extent the phenomenon might be ascribed to thermodynamic rather than kinetic reasons. This question immediately comes to mind as the authors of [1] do not launch any serious attempt in order to consider thermodynamic aspects for an explanation.
*
Tel.: +49 711 689 3113; fax: +49 711 689 3131. E-mail address: [email protected]
It is the aim of the present paper to analyze the process of carburization under the above-mentioned conditions from a purely thermodynamic point of view. 2. Thermodynamic description of non-metal/metal solutions Thermodynamically, the binary iron–carbon system like the iron–nitrogen system and others are usually described as a solution of the non-metal An in the metal Me: 1 An ¢ ½AMe n
ð1Þ
where [A]Me denotes A dissolved in Me. An is commonly a mono-(n = 1) or biatomar (n = 2) element in its state of pure substance which is why its chemical potential is equal to the Raoultian standard chemical potential l0An (for details of the terminology cf. [2]). For [A]Me, the Henrian standard chemical potential l01½AMe is chosen, and therefore the relationship holds: 1 0 l ¼ l01½AMe þ RT ln a1½AMe n An
ð2Þ
with R and T being the gas constant and the absolute temperature. a1½AMe is the Henrian activity of the dissolved non-metal which, in many A–Me systems, because of fairly
1359-6454/$36.00 Ó 2009 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2009.05.001
H. Na¨fe / Acta Materialia 57 (2009) 4074–4080
low A solubilities, can be approximately set equal to the analytical concentration of [A]Me. The difference between the two standard chemical potentials in Eq. (2) is equal to the Gibbs free energy change associated with reaction (1), i.e. with the transfer of A from pure state to the infinitely dilute A–Me solution. In view of a single atomar entity of A, this transfer implies the removal of an A atom out of the bulk of the substance of A and subsequently the creation of a void within the solvent. Finally, it implies the replacement of the void by the A entity and the solvation of A by solvent species. The energetic and entropic effects associated with these processes result in the Gibbs free energy of solution of A in Me, i.e. DS G0½AMe . In the same way as for the thermodynamic description of [A]Me the Henrian standard state has been used in order to end up with Eq. (2), the Raoultian standard state ought to be applicable, too. This, however, provides the trivial identity: l0An ¼ l0An
ð3Þ
that does not contain any useful thermodynamic information. Eq. (3) means that the Raoultian activity of [A]Me is fixed to unity1: a½AMe ¼ 1
ð4Þ
Eq. (1) describes the equilibrium between two phases, the non-metal and the metal. Provided that An is e.g. molecular oxygen and Me is liquid sodium at e.g. 400 °C, the oxygen partial pressure that corresponds to the oxygen saturated sodium solution amounts to about 1050 bar. This extremely small value is the consequence of the strongly negative Gibbs free energy of formation of the compound between O and Na. In view of the statistical interpretation of the pressure of a gas, the value of 1050 bar can never be attributed to a gas phase. In this case, the non-metal does not represent an independent phase which is why the prerequisite for the establishment of the phase equilibrium (1) is no longer fulfilled. Due to the high affinity between O and Na, it is Na2O that gets dissolved in or precipitates out of the sodium melt rather than molecular O2. Provided that a compound MewAf exists between Me and An, the solution equilibrium (1) can without reservation be replaced by (w, f: stoichiometric numbers): ð5Þ Mew Af ! ½Mew Af Me
4075
whether MewAf or A is the solute. Since the solvent particles in the solvation shell of A are not distinguishable from the Me particles belonging either to the compound MewAf or to the solvation shell of MewAf, the final state of the liquid or solid solution remains the same. From this point of view, [MewAf]Me can be understood as synonymous to [A]Me. In order to simultaneously cover both compound formation and dissolution and in order to proceed from the same state of A as in Eq. (1) and end up with the same state of A as in Eq. (5), the formation reaction: f wMe þ An ! ½Mew Af Me n
ð6Þ
has to be considered. Reaction (6) means that after the formation of the pure substance MewAf from the constituent elements the product is dissolved in the solvent Me. Hence, Eq. (6) represents the standard formation reaction of [MewAf]Me. In terms of the Henrian standard state for the activity of [MewAf]Me, the thermodynamic description of reaction (6) yields: ln a1½Mew Af Me ¼
Df G01Mew Af RT
þ w ln aMe þ
f ln aAn n
ð7Þ
where Df G01Mew Af is the standard Gibbs free energy of formation of MewAf in the infinitely dilute solution of Me. Regarding Eq. (7) it is equally justified to apply the Raoultian standard state, as discussed in [2], to the description of the activity of MewAf dissolved in Me. Then the relationship reads: ln a½Mew Af
¼ Me
Df G0Mew Af RT
þ w ln aMe þ
f ln aAn n
ð8Þ
with Df G0Mew Af denoting the standard Gibbs free energy of formation of pure MewAf. Eq. (8) provides information about the Raoultian activity of the solute of a metallic solution which, in contrast to that of the formulation by Eq. (4), is not only restricted to the state of saturation but is generally valid. Since data on the standard Gibbs free energy of formation of a pure substance are known for most relevant compounds, relationship (8) is, moreover, useful from a practical point of view. 3. Thermodynamic conditions of cementite formation
The major difference between (1) and (5) is that in the former case dissolution and compound formation are combined, implying that the solvation energy additionally comprises the energy of the chemical bonding between A and Me, whereas (5) is solely a dissolution process. Nevertheless, there will not be a difference in the structure of the resulting solution regardless of
In view of the above remarks on the thermodynamic description of a non-metal/metal solution the formation reaction of cementite, Fe3C, from iron and carbon is considered: ð9Þ 3Fe þ C ! Fe3 C
1 Note that activity values larger than unity which can be encountered in the literature (cf. [3]) lose track of thermodynamic reality.
With this reaction proceeding toward the left hand side, sooting takes place. Thermodynamically, reaction (9) results in the following relationship:
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H. Na¨fe / Acta Materialia 57 (2009) 4074–4080
Df G0Fe3 C ¼ RT ln
a3Fe aC aFe3 C
ð10Þ
with Df G0Fe3 C being the standard Gibbs free energy of formation of pure cementite. aFe3 C , aFe and aC denote the Raoultian activities of the involved substances. Eq. (10) reveals that Fe3C, Fe and C may coexist in the state of pure substance, i.e. with ai = 1, only if Df G0Fe3 C ¼ 0. According to the quantitative data for Df G0Fe3 C [4] this is only given at one single temperature, i.e. at T = 589 °C. In the following this temperature will be named as Tsa. Above and below this temperature, the coexistence of all the three pure phases is impossible. As a consequence, reaction (9) is either completely on the right hand side or completely on the left one, which means that either the reaction product Fe3C exists alone or only the starting materials do coexist with each other. The reality, however, differs from these thermodynamic constraints. A cementite layer grown on the surface of a piece of iron that gets disintegrated by partially being converted into graphite implies the coexistence of all three substances simultaneously. This experimental fact strongly indicates that the condition ai = 1 is not unrestrictedly fulfilled in the system. There must be at least one substance for which the Raoultian activity deviates from unity. It is supposed that this applies to cementite. Cementite is present as a layer and thus as a part of the iron substrate rather than as a pure material. Hence, the activity of Fe3C in the cementite layer may deviate from that of the pure substance and is likely to be lower than unity which could be understood as an expression of non-stoichiometry in Fe3C, resulting in Fe3+dC. That the consideration of nonstoichiometry in cementite is not so far away has not only once been quoted in the literature [5–7]. The Fe3C-activity of the layer adjusted by the coexistence with pure iron and graphite, i.e. aFe = 1 and aC = 1, can be calculated from Eq. (10). For temperatures lower than or equal to Tsa, the following relationship holds: ln aFe3 C
Df G0Fe3 C ¼ RT
ðT 6 T sa Þ
ð11Þ
In the temperature region T P Tsa the situation is determined by the formation of pure Fe3C that sets in at Tsa and henceforth fixes the activity at a constant level, viz.: aFe3 C ¼ 1
ðT P T sa Þ
ð12Þ
Thus, Tsa is the temperature at which the Fe–C solution is saturated by Fe3C. Both of the curve branches representing Eqs. (11) and (12) are depicted in Fig. 1. The line describing the temperature dependence of aFe3 C at the same time defines the area within which soot either can be formed on the cementite surface or is impossible to be formed. In view of Eq. (10) the decomposition of Fe3C into Fe and C, with aFe = 1 and aC = 1, proceeds if aFe3 C is equal to or larger than the respective value of the coexistence line in Fig. 1. Below that line there is no chance from a mathematical point of view that the carbon activity
Fig. 1. Temperature dependence of the Raoultian Fe3C-activity of the cementite layer in coexistence with pure iron and graphite.
reaches the threshold aC = 1 while aFe = 1. Therefore, soot cannot be formed. Moreover, due to the numerical data of Df G0Fe3 C the concurrent establishment of the conditions aFe = 1 and aC = 1 is also impossible if the Fe3C-activity is confined to the constant level of Eq. (12) while the temperature is higher than the one at which Fe3C just starts to precipitate as a pure phase, i.e. Tsa. As a consequence, there is no chance for soot formation on the basis of Eq. (9) in the temperature interval T > Tsa. For the formulation of Eq. (9) it is assumed that the solid Fe–C solution represents a solution of Fe3C in Fe. It must be kept in mind, however, that apart from Fe3C another carbide exists, i.e. Fe2C [5]. Therefore, it is more realistic to consider the Fe–C solution as represented by a Fe–Fe2C–Fe3C solution from which graphite can also precipitate according to: 3Fe2 C ! ð13Þ 2Fe3 C þ C Consequently, the activities of both carbides are interrelated. For the condition aC = 1 the following relation is valid: ln
a3Fe2 C 2Df G0Fe3 C 3Df G0Fe2 C ¼ RT a2Fe3 C
ð14Þ
with aFe2 C and Df G0Fe2 C denoting the Raoultian activity of Fe2C and its standard Gibbs free energy of formation, respectively. Numerical data on Df G0Fe2 C are known from [5]. Based on Eq. (14) the Fe2C-activity of the Fe–Fe2C– Fe3C solution in equilibrium with pure graphite can be determined by taking either Eq. (11) and (12) into account. The result is: Df G0Fe2 C ðT 6 T sa Þ RT 2Df G0Fe3 C 3Df G0Fe2 C ðT P T sa Þ ¼ 3RT
ln aFe2 C ¼
ð15Þ
ln aFe2 C
ð16Þ
H. Na¨fe / Acta Materialia 57 (2009) 4074–4080
These two curve branches are depicted in Fig. 2. If aFe2 C is equal to or larger than the values representing the line of Fig. 2, soot is formed. This is true within the whole temperature interval covered by Fig. 2. Beyond that interval it is only true as long as the condition aFe2 C < 1 is fulfilled, i.e. below the saturation temperature of Fe2C. Due to the interdependence of aFe2 C and aFe3 C the line of Fig. 2 in terms of ln aFe2 C corresponds to the line of Fig. 1 in terms of ln aFe3 C . Both plots have the same relevance. As discussed above, upon increasing the temperature of the Fe–Fe2C–Fe3C solution, Tsa is the last temperature at which Fe and C coexist with each other. According to the laws of chemical equilibrium, slightly above this temperature any Fe particle in contact with C reacts with C to form Fe3C. Thermodynamically, this reaction must be complete with the consequence that at T > Tsa no iron is in equilibrium with carbon any more. Instead, the precipitation of carbon now obeys Eq. (12) implying that soot particles if formed are surrounded by Fe3C particles rather than Fe particles. Thus, the nature of the soot formation process alters which might be accompanied by a change in the kinetics of the process. Since the following considerations first of all focus on the behaviour of the system at temperatures lower than Tsa they will be confined to the activity of Fe3C only. The combination of Eq. (9) with the Boudouard equilibrium leads to: ð17Þ 3Fe þ 2CO ! Fe3 C þ CO2 According to reaction (17) the activity of Fe3C is fixed by the ratio between the partial pressures p of carbon monoxide and carbon dioxide in the carburizing atmosphere and by the respective values of the standard Gibbs free energies of formation: ln aFe3 C ¼
2Df G0CO
Df G0CO2 RT
Df G0Fe3 C
þ ln
p2CO pCO2
ð18Þ
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Depending on whether the value of the Fe3C-activity resulting from Eq. (18) is lying beyond the line of Fig. 1 or underneath, the carburizing gas causes soot to be produced out of the cementite layer or not. 4. Relevant gas equilibria In a gas mixture that contains ammonia, hydrogen and nitrogen, the formation and dissociation of NH3 will play a role: 3 1 NH3 ! H2 þ N2 2 2
ð19Þ
If H2, CO and CO2 are present, the water gas equilibrium has to be taken into consideration: H2 þ CO2 ! ð20Þ H2 O þ CO Moreover, in gaseous mixtures with constituents such as H2, H2O and CO there is some probability for the formation of hydrocarbons. In the present case, methane is regarded to be relevant for the behaviour of the atmosphere: ð21Þ 2H2 þ 2CO ! CH4 þ CO2 5. Thermodynamic constraints By assuming that reactions (19)–(21) are in thermodynamic equilibrium, the following relations hold: ln
1=2 3=2 Df G0NH3 p N2 p H2 ¼ pNH3 RT
ð22Þ
ln
pCO pH2 O Df G0CO2 Df G0CO Df G0H2 O ¼ pH2 pCO2 RT
ð23Þ
ln
pCH4 pCO2 2Df G0CO Df G0CH4 Df G0CO2 ¼ p2CO p2H2 RT
ð24Þ
with the partial pressures pk of each of the m different gas species k being defined by their mole numbers nk and the total pressure pt of the gas atmosphere: nk pt ð25Þ pk ¼ Pm j¼1 nj The mole numbers nk result from the values n0k , characterizing the starting concentrations of the carburizing gas mixture, and the change these numbers receive by the progress of reactions (19)–(21). Quantitatively, this change is expressed by nr, the extent of reaction, and is additionally governed by the stoichiometry characteristic of the respective reactions. Depending on whether the species under consideration are produced or consumed the stoichiometric numbers mk,r of the rth reaction are either positive or negative. Therefore, the relationship holds: Fig. 2. Phase stability regions for the decomposition of the Fe–Fe2C– Fe3C solid solution into iron and soot in terms of the Fe2C-activity.
nk ¼ n0k þ
3 X r¼1
mk;r nr
ð26Þ
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k stands for either NH3 or N2 or H2 or H2O or CO or CO2 or CH4 or Ar. r is equal to either 1 for reaction (19) or 2 for reaction (20) or 3 for reaction 21. The substitution of Eqs. (25) and (26) into Eqs. (22)–(24) results in a system of 3 non-linear equations in terms of the unknowns n1, n2 and n3. Numerically, this system of equations is restrained by the standard Gibbs free energies of formation of the involved substances, taken from [4,5,8], by the total pressure of the gas atmosphere as well as by the starting values for the concentration of the gaseous species. 6. Numerical calculations With numerical data for n1, n2 and n3 resulting from the zeros of the above-mentioned system of equations, the equilibrium composition of each constituent of the gas atmosphere is fixed by Eq. (26). Hence, the partial pressures of the gas species are also fixed, viz. by Eq. (25). In view of Eq. (18), the same is true for the Fe3C-activity established by the equilibrium according to Eq. (17), between the iron substrate, on the one hand, and carbon monoxide as well as carbon dioxide of the surrounding gas atmosphere, on the other hand. By plotting the results of the numerical calculations in terms of the logarithm of the Fe3C-activity as a function of the inverse temperature, the dashed lines of Figs. 3 and 4 are obtained. The numbers assigned to the lines stand for the gas compositions as specified in Table 1. The data for the compositions 1, 2, 3 and 4 of the gases that the iron samples are exposed to are identical with those of the gases used in [1] for the experimental investigations. Their initial compositions are characterized by an invariable H2 and CO concentration and, from 1 to 4, a growing substitution of N2 by NH3. According to Fig. 3, at T = 550 °C, curves 1 and 2 are lying within the region of soot formation whereas curve 4
Fig. 3. Fe3C-activity of the cementite layer after equilibrating with the carburizing gas atmosphere (dashed lines; gas compositions 1–4 according to the specifications of Table 1; pt = 1 bar) in comparison with the phase stability line (solid line).
Fig. 4. Fe3C-activity of the cementite layer after equilibrating with the carburizing gas atmosphere (dashed lines; gas compositions 5–8 according to the specifications of Table 1; pt = 1 bar) in comparison with the phase stability line (solid line).
Table 1 Initial values of the gas compositions used for the calculations the results of which are illustrated in Figs. 3–6. Gas
Initial gas composition (%) H2
CO
N2
NH3
CO2
Ar
1 2 3 4 5 6 7 8
58 58 58 58 58 75 15 15
20 20 20 20 20 15 2.0 1.8
22 15.4 8.8 – – – – –
– 6.6 13.2 22 – – – –
– – – – – – – 0.2
– – – – 22 10 83 83
is unambiguously outside this region. Curve 3 is close to the dividing line in between. Thus, it must be expected that the exposition of the iron/cementite layer to gas 1 or 2 causes graphite to be formed while gas 4 suppresses the graphite precipitation. These thermodynamically based predictions completely agree with the experimental observations reported in [1]. In particular, they demonstrate that the effect of ammonia on the suppression of the soot formation has mainly thermodynamic rather than kinetic reasons. There is only a slight difference between prediction and experiment insofar as the calculations let expect that the iron/cementite sample is barely sooted in gas 3 (cf. curve 3 of Fig. 3; T = 550 °C) whereas the authors of [1] describe the same gas composition as the one in which the gradual increase of the ammonia content just terminates the soot formation. This detail may indicate that other than thermodynamic aspects will also have an influence on the experimental behaviour, at least to a minor degree. The same is corroborated by considering the oxidation potential adjusted by the carburizing gas atmosphere under equilibrium conditions. According to the present thermo-
H. Na¨fe / Acta Materialia 57 (2009) 4074–4080
dynamic calculations, at T = 550 °C the oxidation potential, expressed as water to hydrogen partial pressure ratio, is slightly higher than the value established by the iron/ wustite equilibrium (cf. Fig. 5). Experimentally, it would mean that iron is to a certain extent oxidized during carburization which seems to contradict the reality. This contradiction may give another evidence that the experimental observations are widely but not totally in accordance with the thermodynamic description. Possibly, one or more of the reactions under consideration slightly deviate from their assumed equilibrium positions or additional reactions need to be taken into account for still better matching the experimental situation. Thermodynamically, the increase of the ammonia content in the carburizing gas results in an increasing inventory of molecular hydrogen and nitrogen in the system. Since ammonia is almost completely dissociated and since the dissociation is accompanied by doubling of the total number of gas molecules, the partial pressure of CO shrinks while that of H2 grows upon equilibration. As a result, the extent of both of the reactions (20) and (21) is affected. On the whole, the changes are such that the carburizing potential of the gas decreases with rising ammonia content. The preceding interpretation allows to conclude that the formation of massive cementite layers by suppressed sooting is not necessarily bound to the presence of ammonia as it has been stated in [1]. The ‘‘ammonia” effect can be simulated by other gases as well provided that they fulfill the same purpose regarding gas dilution and partial pressure shift. This is illustrated in Fig. 4 in which curves 5 and 6 represent the calculated Fe3C-activity of the cementite layer equilibrated with ammonia- and nitrogen-free gas atmospheres. Their initial compositions are chosen such that the data in terms of the CO and H2 partial pressure approximately correspond to the calculated equilibrium
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Fig. 6. Oxidation potential in terms of the partial pressure ratio between water and hydrogen of the carburizing gases 5–8 (dashed lines; gas compositions according to the specifications of Table 1; pt = 1 bar) in comparison with the oxidation potential of the iron/wustite phase equilibrium (solid line).
compositions established in gases 1 and 4. The effect is accomplished by using Ar as an inert diluting gas (cf. Table 1). In the same manner as the substitution of nitrogen by ammonia causes curve 1 of Fig. 3 to be shifted into the soot-free region toward the position of curve 4, curve 6 of Fig. 4 gets to be lying within this region due to a change in the initial CO and H2 partial pressures compared to those of gas 5. Interestingly, the calculations on the behaviour of the ammonia- and nitrogen-free gases also lead to an oxidation potential higher than that of the iron/wustite equilibrium (cf. curves 5 and 6 in Fig. 6 with curves 1 and 4 in Fig. 5). Therefore, as an example of gas compositions with a more reducing oxidation potential, gases 7 and 8 were chosen (cf. Figs. 4 and 6). 7. Conclusions The above considerations prove the experimental observations on the carburization of iron to be widely in accordance with thermodynamic calculations assuming equilibrium between the solid and the surrounding gas atmosphere as well as within the gas. In particular, the calculations enable to predict and to understand the observed suppression of soot formation by adding ammonia to the carburizing gas. As a consequence, the ‘‘ammonia” effect as prerequisite for the formation of massive cementite layers is not surprising but predictable and can be achieved by other means as well. References
Fig. 5. Oxidation potential in terms of the partial pressure ratio between water and hydrogen of the carburizing gases 1 and 4 (dashed lines; gas compositions according to the specifications of Table 1; pt = 1 bar) in comparison with the oxidation potential of the iron/wustite phase equilibrium (solid line).
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[4] Barin I. Thermochemical data of pure substances. 3rd ed. Weinheim, New York: VCH Verlagsgesellschaft; 1995. [5] Richardson FD. J Iron Steel Inst 1953;175:33. [6] Banya S, Elliott JF, Chipman J. Met Trans 1970;1:1313.
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