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On the definitions of paraequilibrium and orthoequilibrium
Scripta Materialia 50 (2004) 697–699 www.actamat-journals.com
On the definitions of paraequilibrium and orthoequilibrium gren M. Hillert *, J. A Department of Materials Science and Engineering, Division of Physical Metallurgy, Brinellvagen 23, KTH, SE-10044 Stockholm, Sweden Received 15 October 2003; received in revised form 15 October 2003; accepted 6 November 2003
Abstract Hultgren’s terminology of paraferrite and paracementite in alloy steels and his definition of paraequilibrium are reviewed. They are not completely compatible due to the possibility of forming ferrite with the initial alloy content (paraferrite) even under full local equilibrium (local orthoequilibrium). That has caused some confusion. Ó 2003 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Paraequilibrium; Steels; Carbon; Thermodynamics; Diffusion
When studying the transformation of austenite to ferrite and cementite, Hultgren concluded that the product phases sometimes formed with the same alloy content as the parent austenite [1]. He called such products paraferrite and paracementite without any theoretical interpretation. However, in addition he hypothesized that the paraphases had formed under special conditions which he called ‘‘paraequilibrium’’, i.e., equilibrium for carbon but with the same ratio of the alloying elements to iron in the growing phase as in the parent phase. It is evident that paraequilibrium defines conditions at the migrating interface, i.e., a kind of so-called local equilibrium. Hillert [2] examined the thermodynamics of this condition, drawing a common tangent to the Gibbs energy surfaces of a and c in an Fe– C–X system. It went through the C-axis and the axis for an Fe–X composition with the same Fe/X ratio as in the parent phase. It was thus evident that not only the chemical potential of carbon is the same on the two sides of the product/parent interface but also the weighted average of the chemical potentials of iron and the alloying elements. Rudberg [3] extended this study and emphasized that even the chemical potential of any component defined with a composition having the same Fe/X ratio must be the same in the two phases at paraequilibrium. Hultgren used the terms orthoferrite and orthocementite when the product phases had the compositions
*
Corresponding author. Tel.: +46-8-7908385; fax: +46-8-207681. E-mail address: [email protected] (M. Hillert).
expected from full equilibrium, which he called ‘‘orthoequilibrium’’ in this context. In a second paper [4] he gave more detailed discussions. There he assumed that tempering of martensite would first produce paracementite but it would change into orthocementite after a sufficiently long time. Here he used the term orthoequilibrium for the final state and discussed the ‘‘local orthoequilibrium’’ being established in thin layers of the phases at an early stage of tempering. However, in recent times the prefix ‘‘local’’ has been dropped and the term orthoequilibrium is frequently used to mean full local equilibrium at a migrating interface. In order to avoid misinterpretations, it might be possible to accept the use of orthoequilibrium only for the local conditions at interfaces and to use full equilibrium for a state of the whole system. However, there seems to be no good reason to use the term orthoequilibrium at all. Full equilibrium and full local equilibrium are quite adequate terms and do not need any special explanations. It should be realized that local orhtoequilibrium at the interface can very well result in the formation of a product phase with the same alloy content as the bulk of the parent phase if it grows behind a local pile-up of the alloying elements in the parent phase [5]. With Hultgren’s definition such a product would still be called paraferrite or paracementite. Consequently, the term paraequilibrium on one hand and paraferrite or paracementite, on the other, are not completely compatible. In order to resolve this conflict it was first proposed that such growth conditions should be called false paraconditions [5] or quasi-paraequilibrium conditions [6] because they result in paraferrite but without
1359-6462/$ - see front matter Ó 2003 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.scriptamat.2003.11.020
698
M. Hillert, J. Agren / Scripta Materialia 50 (2004) 697–699
paraequilibrium being established. The term NPLE (no partition, local equilibrium) has also been proposed [7] but does not relate to the prefix ‘‘para’’ in paraferrite and paracementite. The tie-line between the two filled circles in Fig. 1 illustrates the local conditions at the a=c interface when a is growing into c of composition (u0C , u0X ) under quasiparaequilibrium conditions. The composition variable ui is related to the ordinary mole fraction by ui ¼ xi =ð1 xC Þ. The phase boundaries for paraequilibrium are also included in Fig. 1 as dashed lines and it is shown that they are situated inside the stable two-phase field. The horizontal tie-line between the two squares represents the paraequilibrium between the two phases. Similar diagrams can be found in Refs. [5,7–11]. Speer et al. [12] have recently discussed the equilibration of carbon between martensite and retained austenite occurring on tempering after an initial quench to form martensite, if the carbide precipitation can be prevented. Since martensite has inherited the composition of the parent austenite, the resulting ferrite after the
Fig. 1. Schematic picture of an isothermal section of the Fe rich corner of an Fe–C–X phase diagram when X stabilizes c. The tie-line between the filled circles illustrates the local equilibrium at the a=c interface during growth of a under quasi-paraequilibrium conditions (NPLE) in a c specimen of initial alloy content u0X . The right-hand part shows the local pile-up of X in front of the advancing interface and illustrates the absence of long-range diffusion of X. The lower part shows the C profile with a rapid change close to the interface, due to a variation of the activity coefficient in the pile-up, and then a slower approach to the initial C content, u0C , due to long-range diffusion of C. That diffusion is driven by the difference in carbon activity between the isoactivity line and the initial alloy (u0C , u0X ). Local conditions under paraequilibrium (no diffusion of X relative to Fe and local equilibrium for C and for the constant mixture of X and Fe) in the same alloy is represented by the two squares. Orthoequilibrium (i.e., full equilibrium in the whole system) is represented by the open circles.
excess carbon has diffused into the retained austenite should have the same alloy content as the parent austenite. Speer et al. thus regarded it as paraferrite which may be justified by Hultgren’s definition. They realized that it had not formed under paraequilibrium and proposed that the state obtained after complete carbon equilibration under tempering of a quenched specimen should be referred to as constrained paraequilibrium (CPE). However, that term is misleading for the following reasons. (a) Paraequilibrium is already a constrained equilibrium. (b) Paraequilibrium is defined by three conditions at the interface: (1) same ratio of the alloying elements to iron in both phases, (2) equal chemical potential of carbon as well as (3) of the weighted average of iron and the alloying elements. Instead, CPE was defined by replacing the third condition with the requirement of minimum of the Gibbs energy of the whole system, subject to the constraint that the martensite(ferrite)/austenite interface is immobile during the equilibration of carbon in the whole system. The relation to paraequilibrium would thus seem very weak because paraequilibrium refers to the conditions at a migrating interface. (c) Redistribution of the alloying elements close to the interface can hardly be avoided during the long tempering required for equilibration of carbon in the whole system. This was realized already by Hultgren when using the term ‘‘local orthoequilibrium’’ for the conditions established already ‘‘at an early stage of tempering or annealing, while the bulk of each phase still is of paracomposition’’. (d) Due to the requirement of minimum in Gibbs energy, the term CPE is applicable only to the final state whereas the term paraequilibrium applies to the growth of the new phase. (e) If there is some redistribution of the alloying elements at the martensite(ferrite)/austenite interface, it would have a negligible effect on the distribution of carbon between the bulk of the two phase, which is controlled by their activity coefficients for carbon. The result of equilibration of carbon is thus independent of the conditions at the ferrite/austenite interface. This further emphasizes the difference between CPE and paraequilibrium. As a consequence, there seems to be no relation of CPE to paraequilibrium. In conclusion it should first be emphasized that the concept of paraequilibrium was defined by Hultgren as a special constrained local equilibrium at migrating interfaces in Fe–C–X systems where X represents one or more substitutional alloying elements. In that context he used the concept of orthoequilibrium to mean full equilibrium. That term should be used only as a counterpart to paraequilibrium. Even such usage can be misleading because paraequilibrium refers
M. Hillert, J. Agren / Scripta Materialia 50 (2004) 697–699
to the local conditions at a migrating interface and orthoequilibrium was originally used to describe the state of equilibrium in the whole system. It is now proposed that the term orthoequilibrium should not be used at all but be replaced by ‘‘full equilibrium’’ or ‘‘full local equilibrium’’, depending on the context. It has here been shown that the concept ‘‘constrained paraequilibrium’’ (CPE), which was recently proposed, has no relation to paraequilibrium. One should find another term. It must be accepted that Hultgren’s terminology of paraferrite and paracementite and his definition of paraequilibrium are not completely compatible. That has caused confusion already in the past and to the present authors there seemed to be a need of clarification. The risk of misunderstandings may be decreased but not eliminated if one stops using the term orthoequilibrium. In order to eliminate the risk completely one may have to drop the terms paraferrite and paracementite. However, those terms are useful and should be retained.
699
References [1] [2] [3] [4] [5] [6]
[7] [8]
[9] [10]
[11] [12]
Hultgren A. Trans ASM 1947:915. Hillert M. Jernkont Ann 1952;136:25. Rudberg E. Jernkont Ann 1952;136:91. (a) Hultgren A. Jernkont Ann 1951;135:403 (in Swedish); (b) Hultgren A, Handlingar KVA. Ser 4 Bd. 4, 1953. Hillert M. Paraequilibrium, Internal Report, Swedish Inst Metal Research, 1953. Hillert M. Phase equilibria, phase diagrams and phase tranformations––their thermodynamic basis. Cambridge: Cambridge University Press; 1998. Coates DE. Metall Trans 1973;4:2313. Hillert, M. Paraequilibrium and other restricted equilibria. In: Bennet LH, Massalski TB, Giessen BC, editors. Alloy phase diagrams, Materials Research Society Symposium Proceedings, vol. 19. 1983. p. 295–309. Purdy GR, Weichert DH, Kirkaldy JS. Trans AIME 1964;230:1025. Aaronson HI, Enomoto M, Reynolds Jr RT. In: Embury JD, Purdy GR, editors. Advances in phase transitions. Oxford: Pergamon Press; 1988. p. 20–36. Gosh G, Olson GB. Metall Mater Trans 2001;32A:455. Speer JG, Matlock DK, De Cooman BC, Schroth JG. Acta Mater 2003;51:2611.
On the definitions of paraequilibrium and orthoequilibrium gren M. Hillert *, J. A Department of Materials Science and Engineering, Division of Physical Metallurgy, Brinellvagen 23, KTH, SE-10044 Stockholm, Sweden Received 15 October 2003; received in revised form 15 October 2003; accepted 6 November 2003
Abstract Hultgren’s terminology of paraferrite and paracementite in alloy steels and his definition of paraequilibrium are reviewed. They are not completely compatible due to the possibility of forming ferrite with the initial alloy content (paraferrite) even under full local equilibrium (local orthoequilibrium). That has caused some confusion. Ó 2003 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Paraequilibrium; Steels; Carbon; Thermodynamics; Diffusion
When studying the transformation of austenite to ferrite and cementite, Hultgren concluded that the product phases sometimes formed with the same alloy content as the parent austenite [1]. He called such products paraferrite and paracementite without any theoretical interpretation. However, in addition he hypothesized that the paraphases had formed under special conditions which he called ‘‘paraequilibrium’’, i.e., equilibrium for carbon but with the same ratio of the alloying elements to iron in the growing phase as in the parent phase. It is evident that paraequilibrium defines conditions at the migrating interface, i.e., a kind of so-called local equilibrium. Hillert [2] examined the thermodynamics of this condition, drawing a common tangent to the Gibbs energy surfaces of a and c in an Fe– C–X system. It went through the C-axis and the axis for an Fe–X composition with the same Fe/X ratio as in the parent phase. It was thus evident that not only the chemical potential of carbon is the same on the two sides of the product/parent interface but also the weighted average of the chemical potentials of iron and the alloying elements. Rudberg [3] extended this study and emphasized that even the chemical potential of any component defined with a composition having the same Fe/X ratio must be the same in the two phases at paraequilibrium. Hultgren used the terms orthoferrite and orthocementite when the product phases had the compositions
*
Corresponding author. Tel.: +46-8-7908385; fax: +46-8-207681. E-mail address: [email protected] (M. Hillert).
expected from full equilibrium, which he called ‘‘orthoequilibrium’’ in this context. In a second paper [4] he gave more detailed discussions. There he assumed that tempering of martensite would first produce paracementite but it would change into orthocementite after a sufficiently long time. Here he used the term orthoequilibrium for the final state and discussed the ‘‘local orthoequilibrium’’ being established in thin layers of the phases at an early stage of tempering. However, in recent times the prefix ‘‘local’’ has been dropped and the term orthoequilibrium is frequently used to mean full local equilibrium at a migrating interface. In order to avoid misinterpretations, it might be possible to accept the use of orthoequilibrium only for the local conditions at interfaces and to use full equilibrium for a state of the whole system. However, there seems to be no good reason to use the term orthoequilibrium at all. Full equilibrium and full local equilibrium are quite adequate terms and do not need any special explanations. It should be realized that local orhtoequilibrium at the interface can very well result in the formation of a product phase with the same alloy content as the bulk of the parent phase if it grows behind a local pile-up of the alloying elements in the parent phase [5]. With Hultgren’s definition such a product would still be called paraferrite or paracementite. Consequently, the term paraequilibrium on one hand and paraferrite or paracementite, on the other, are not completely compatible. In order to resolve this conflict it was first proposed that such growth conditions should be called false paraconditions [5] or quasi-paraequilibrium conditions [6] because they result in paraferrite but without
1359-6462/$ - see front matter Ó 2003 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.scriptamat.2003.11.020
698
M. Hillert, J. Agren / Scripta Materialia 50 (2004) 697–699
paraequilibrium being established. The term NPLE (no partition, local equilibrium) has also been proposed [7] but does not relate to the prefix ‘‘para’’ in paraferrite and paracementite. The tie-line between the two filled circles in Fig. 1 illustrates the local conditions at the a=c interface when a is growing into c of composition (u0C , u0X ) under quasiparaequilibrium conditions. The composition variable ui is related to the ordinary mole fraction by ui ¼ xi =ð1 xC Þ. The phase boundaries for paraequilibrium are also included in Fig. 1 as dashed lines and it is shown that they are situated inside the stable two-phase field. The horizontal tie-line between the two squares represents the paraequilibrium between the two phases. Similar diagrams can be found in Refs. [5,7–11]. Speer et al. [12] have recently discussed the equilibration of carbon between martensite and retained austenite occurring on tempering after an initial quench to form martensite, if the carbide precipitation can be prevented. Since martensite has inherited the composition of the parent austenite, the resulting ferrite after the
Fig. 1. Schematic picture of an isothermal section of the Fe rich corner of an Fe–C–X phase diagram when X stabilizes c. The tie-line between the filled circles illustrates the local equilibrium at the a=c interface during growth of a under quasi-paraequilibrium conditions (NPLE) in a c specimen of initial alloy content u0X . The right-hand part shows the local pile-up of X in front of the advancing interface and illustrates the absence of long-range diffusion of X. The lower part shows the C profile with a rapid change close to the interface, due to a variation of the activity coefficient in the pile-up, and then a slower approach to the initial C content, u0C , due to long-range diffusion of C. That diffusion is driven by the difference in carbon activity between the isoactivity line and the initial alloy (u0C , u0X ). Local conditions under paraequilibrium (no diffusion of X relative to Fe and local equilibrium for C and for the constant mixture of X and Fe) in the same alloy is represented by the two squares. Orthoequilibrium (i.e., full equilibrium in the whole system) is represented by the open circles.
excess carbon has diffused into the retained austenite should have the same alloy content as the parent austenite. Speer et al. thus regarded it as paraferrite which may be justified by Hultgren’s definition. They realized that it had not formed under paraequilibrium and proposed that the state obtained after complete carbon equilibration under tempering of a quenched specimen should be referred to as constrained paraequilibrium (CPE). However, that term is misleading for the following reasons. (a) Paraequilibrium is already a constrained equilibrium. (b) Paraequilibrium is defined by three conditions at the interface: (1) same ratio of the alloying elements to iron in both phases, (2) equal chemical potential of carbon as well as (3) of the weighted average of iron and the alloying elements. Instead, CPE was defined by replacing the third condition with the requirement of minimum of the Gibbs energy of the whole system, subject to the constraint that the martensite(ferrite)/austenite interface is immobile during the equilibration of carbon in the whole system. The relation to paraequilibrium would thus seem very weak because paraequilibrium refers to the conditions at a migrating interface. (c) Redistribution of the alloying elements close to the interface can hardly be avoided during the long tempering required for equilibration of carbon in the whole system. This was realized already by Hultgren when using the term ‘‘local orthoequilibrium’’ for the conditions established already ‘‘at an early stage of tempering or annealing, while the bulk of each phase still is of paracomposition’’. (d) Due to the requirement of minimum in Gibbs energy, the term CPE is applicable only to the final state whereas the term paraequilibrium applies to the growth of the new phase. (e) If there is some redistribution of the alloying elements at the martensite(ferrite)/austenite interface, it would have a negligible effect on the distribution of carbon between the bulk of the two phase, which is controlled by their activity coefficients for carbon. The result of equilibration of carbon is thus independent of the conditions at the ferrite/austenite interface. This further emphasizes the difference between CPE and paraequilibrium. As a consequence, there seems to be no relation of CPE to paraequilibrium. In conclusion it should first be emphasized that the concept of paraequilibrium was defined by Hultgren as a special constrained local equilibrium at migrating interfaces in Fe–C–X systems where X represents one or more substitutional alloying elements. In that context he used the concept of orthoequilibrium to mean full equilibrium. That term should be used only as a counterpart to paraequilibrium. Even such usage can be misleading because paraequilibrium refers
M. Hillert, J. Agren / Scripta Materialia 50 (2004) 697–699
to the local conditions at a migrating interface and orthoequilibrium was originally used to describe the state of equilibrium in the whole system. It is now proposed that the term orthoequilibrium should not be used at all but be replaced by ‘‘full equilibrium’’ or ‘‘full local equilibrium’’, depending on the context. It has here been shown that the concept ‘‘constrained paraequilibrium’’ (CPE), which was recently proposed, has no relation to paraequilibrium. One should find another term. It must be accepted that Hultgren’s terminology of paraferrite and paracementite and his definition of paraequilibrium are not completely compatible. That has caused confusion already in the past and to the present authors there seemed to be a need of clarification. The risk of misunderstandings may be decreased but not eliminated if one stops using the term orthoequilibrium. In order to eliminate the risk completely one may have to drop the terms paraferrite and paracementite. However, those terms are useful and should be retained.
699
References [1] [2] [3] [4] [5] [6]
[7] [8]
[9] [10]
[11] [12]
Hultgren A. Trans ASM 1947:915. Hillert M. Jernkont Ann 1952;136:25. Rudberg E. Jernkont Ann 1952;136:91. (a) Hultgren A. Jernkont Ann 1951;135:403 (in Swedish); (b) Hultgren A, Handlingar KVA. Ser 4 Bd. 4, 1953. Hillert M. Paraequilibrium, Internal Report, Swedish Inst Metal Research, 1953. Hillert M. Phase equilibria, phase diagrams and phase tranformations––their thermodynamic basis. Cambridge: Cambridge University Press; 1998. Coates DE. Metall Trans 1973;4:2313. Hillert, M. Paraequilibrium and other restricted equilibria. In: Bennet LH, Massalski TB, Giessen BC, editors. Alloy phase diagrams, Materials Research Society Symposium Proceedings, vol. 19. 1983. p. 295–309. Purdy GR, Weichert DH, Kirkaldy JS. Trans AIME 1964;230:1025. Aaronson HI, Enomoto M, Reynolds Jr RT. In: Embury JD, Purdy GR, editors. Advances in phase transitions. Oxford: Pergamon Press; 1988. p. 20–36. Gosh G, Olson GB. Metall Mater Trans 2001;32A:455. Speer JG, Matlock DK, De Cooman BC, Schroth JG. Acta Mater 2003;51:2611.