Thermodynamic calculation and experimental verification of the carbonitride-austenite equilibrium in Ti-Nb microalloyed
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I.
INTRODUCTION
IT is well known that the carbonitrides of transition metals play an important role in improving the overall properties of microalloyed steels. Thermodynamic analysis is an important method for optimizing both the chemistry and process design of microalloyed steels for thermomechanical processing. Thermodynamic representations of the multicomponent phase diagram Fe-~MiEXj of dilute iron alloys containing any number of solutes have been developed by a number of authors [1-121 (here, M is the substitutional transition metal Ti, Nb, and V and X is the interstitial element C and N). None of these models has taken capillarity into account. The surface tension effect can be significant as a consequence of the typically tiny particle sizes (5 to 10 nm), which raises the matrix composition at the interface in equilibrium with the precipitates and thereby reduces the mole fraction of precipitates. Many experimental studies [5-1sl on the multicomponent carbonitride compositions have been carried out in the past decade. Almost all of them were restricted to measurements of metallic compositions (e.g., the x in Ti~Nb~_x) (CyNl_y)*
in terms of binary compounds at a given temperature, and the residual solute contents in microalloyed steels. The compositions of the extracted particles (both the x and y in (TixNbl_x) (CyNl-y)) w e r e determined by two complementary techniques: energy dispersive X-ray spectrometry (EDX) and electron energy loss spectrum (EELS). II.
With the inclusion of the capillarity term for spherical particles, the following four chemical potential equalities in terms of the composition of the two phases define the austenite-carbonitride equilibrium: ~12J RT In [XcXTi] = AG~ic + RT In [xy] + AG(1 - x) 4o-V~
9 ( l - y ) + 1)(1 - y ) 2 + _ _ r
[la]
RTIn [XcXNb] = AG~bc + RTln [(1 - x)y] - AG(x) 9 (1 - y )
*In this article, (Ti~Nb~ x) (CyNl--y) is frequently simplified as (TiNb) (CN). The complete formula will be used only in the case when precise knowledge of the compositions of the precipitates is required.
in the complex compounds. In the present study, the sublattice-regular solution model proposed by Hillert and Staffansson tl61 has been modified with the inclusion of the capillarity effect and applied to Fe-Ti-Nb-C-N alloys. The purposes of the thermodynamic analysis are to calculate the effective contents of Ti, Nb, C, and N available for the formation of the complex carbonitride precipitates during aging, the compositions and mole fractions of these precipitates
THE AUSTENITE-Ti-Nb EQUILIBRIUM
CARBONITRIDE
4o'V~
+ f~(1 _ y ) 2 + _ _ r
[lbl RTIn [XNXTi ] = m a g i N -1- RTIn Ix(1 - y)] 4o-Vc
- AG(1 - x) (y) + ~y2 + __
F
[lc]
J
RTln [Xrogwo] = AG~br~+ RTln [(1 - x) (1 - y)] 4o'Vc + AG(x)(y) + OAy 2 + - -
[1 d]
F HEILONG ZOU, formerly Research Associate, with the Institute for Materials Research, McMaster University, is Research Scientist, with Atomic Energy of Canada, Limited, Chalk River, ON, Canada. J.S. KIRKALDY, Emeritus Professor, is with the Institute for Materials
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