A theoretical analysis of the spinodal decomposition in Fe- C martensite during aging stage of tempering
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I.
INTRODUCTION
TEMPERINGof martensite
in steels has long been studied. Increasing progress has been made in the last twenty years.il'z'l~ This is largely ascribed to the rapid development of experimental instruments. All of these developments enable us to have a clear enough picture of tempering. Olson and Cohen tll and K r a u s s [21 divided the tempering of martensite into seven stages, which designate the aging stages of tempering as A1, A2, A3 which correspond to clustering of carbon atoms, spinodal decomposition, and ordering, respectively, and the carbide forming stages of tempering as T1, T2, T3 . . . . . This classification system gives a good conclusion to our present understanding of tempering. But there is a gap in our knowledge of tempering: on the one hand, a lot of experimental results about tempering are known, but on the other hand, it must be pointed out that little quantitative and theoretical information and mathematical treatment about tempering is known. The present work is our first attempt to analyze tempering of Fe-C martensite in a theoretical way. In this article, we will focus only on the spinodal decomposition in Fe-C martensite. To do this, we must first set up a thermodynamic model for Fe-C martensite (which is essential for the analysis), because the present available models of martensite are unable to explain the spinodal decomposition in martensite.
Thus, the molar free energy of Fe-C martensite is composed of the following two terms: G = Gso1 + Gsub
[1]
where Gso~ and G,ub are molar free energy of Fe-C solid solution and energy of substructure in 1 mol martensite, respectively. For Fe-C solid solution, G~o~ = N c G c + NF~G~162 + A H -
TAS
[21
where Nc, NF, are mole fraction of carbon and iron, respecO O tively. N c + NF, = l, G c, G~.F~are the molar free energy of carbon and a-Fe in the standard state (pure graphite and pure ~-Fe), respectively. AH and AS are the mole enthalpy and entropy change of mixing. AH and AS are the mole enthalpy and entropy change of mixing. According to the calculation of the mixing entropy of interstitial solid solutions, - T A S can be expressed as follows: t31 -TAS
= RT(Nc In Nc + Nv~ In N w - N c In fl)
where fl is the ratio of the number of interstitial sites which can be occupied to the number of lattice atoms. For Fe-C solid solution (conforms to assumption (a)) /3--'2.
Thus, II. A THERMODYNAMIC MODEL OF Fe-C MARTENSITE Assumption: Fe-C martensite is a system which conforms to the following assumptions: (a) Fe-C martensite is an Fe-C solid solution (supersaturated). Carbon atoms occupy only octahedral interstitial sites in C-axis (experiment showed that 80 pct carbon atoms occupy one set of octahedral sites). (b) There exists a substructure (dislocations and twins) in martensite.
-TAS
= R T ( N c In Nc + NF~ In NF~ -- N c In 2)
[3]
For solid, AH - AU (AU is the molar internal energy change). J. Friedel t4j suggested that distortion energy W caused by the replacement of lattice atoms with foreign atoms equals AU or AH, AH -- AU --
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