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  • 1.
    Borgenstam, Annika
    et al.
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
    Edmonds, D.
    Hillert, Mats
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
    Eutectoids with cementite as the major constituent in Fe-C-M alloys2016In: Acta Materialia, ISSN 1359-6454, E-ISSN 1873-2453, Vol. 103, p. 280-289Article in journal (Refereed)
    Abstract [en]

    The addition of a third element to hypereutectoid Fe-C alloys may cause inclusions of a minor constituent in the precipitate of cementite from austenite even if the initial austenite is supersaturated only with cementite. Cementite will often become the major constituent of this kind of microstructure. For Fe-C-Cu alloys this has been explained as the result of precipitation from supersaturated cementite. An alternative mechanism could be that the mixture of cementite and a minor constituent forms by simultaneous and cooperative growth of the two phases, i.e., by a reaction that may be regarded as eutectoid. This mechanism has already been applied to explain the occurrence of eutectoid colonies with cementite as the major constituent and a minor constituent for which there was no supersaturation initially. This phenomenon has been observed in hypereutectoid ternary Fe-C alloys with Al, Mn or Si. The necessary requirements on the ordinary isothermal phase diagram are now examined with a graphical method based on the slopes of tie-lines. It predicts the phenomenon in all cases where it has been observed, including Fe-C-Cu and not in the Fe-C-Ni and Fe-C-Cr systems where it has not been observed. The requirements become more evident when the calculated phase equilibria are plotted as an isothermal phase diagram with the alloy content as a function of the carbon activity instead of carbon content. Finally, a comparison is made with bainite in Fe-C alloys where ferrite is the major and cementite the minor constituent. The same two explanations have been proposed for that case.

  • 2.
    Borgenstam, Annika
    et al.
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
    Hedström, Peter
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
    Hillert, Mats
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
    Kolmskog, Peter
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
    Stormvinter, Albin
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
    Ågren, John
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
    On the Symmetry Among the Diffusional Transformation Products of Austenite2011In: Metallurgical and Materials Transactions. A, ISSN 1073-5623, E-ISSN 1543-1940, Vol. 42A, no 6, p. 1558-1574Article in journal (Refereed)
    Abstract [en]

    Information on the diffusional transformation products of austenite in high-carbon steels is reviewed and supplemented with new microscopic studies. A comparison with transformation products in low-carbon steels indicates that there is a symmetry with pearlite in the middle, where ferrite and cementite are equal partners, and with acicular ferrite or cementite on each side. They both form with a surface relief, and at lower temperatures, each one is the leading phase in a eutectoid microstructure, bainite and inverse bainite, respectively. However, there is an asymmetry because at low temperatures bainite appears in high-carbon steels but inverse bainite never appears in low-carbon steels. At a constant high carbon content, there is another kind of symmetry, which is related to temperature. At intermediate temperatures the eutectoid reaction results in spherical nodules in which the cementite constituent originates from Widmanstatten plates. It turns spiky at both higher and lower temperatures with the leading phase in the spikes being cementite at higher temperatures and ferrite at lower temperatures. In the first kind of symmetry, there is an abrupt change among the three reaction products; in the second kind of symmetry, there is a gradual change. Accepting that all the eutectoid microstructures form by diffusion of carbon, one may explain the existence of both symmetries by the variation of the ratio of the supersaturations of ferrite and cementite with carbon content and with temperature.

  • 3.
    Borgenstam, Annika
    et al.
    KTH, Superseded Departments, Materials Science and Engineering.
    Hillert, Mats
    KTH, Superseded Departments, Materials Science and Engineering.
    Activation energy for isothermal martensite in ferrous alloys1997In: Acta Materialia, ISSN 1359-6454, E-ISSN 1873-2453, Vol. 45, no 2, p. 651-662Article in journal (Refereed)
    Abstract [en]

    The experimental information on isothermal α martensite in ferrous alloys is reviewed. From the kinetics one can clearly distinguish between three groups of alloys yielding isothermal martensite. The first group contains high alloy steels with a low Ms temperature. They form isothermal martensite with a temperature dependence corresponding to a very low activation energy, possibly 7 kJ/mol. The second group contains steels with an appreciable amount of carbon. Its rate of formation of isothermal martensite can be explained by assuming that it is triggered by submicroscopic plates of bainite formed with a rate controlled by carbon diffusion. The third group contains Fe---Ni alloys with up to about 25% Ni. There the temperature dependence corresponds to an activation energy of about 80 kJ/mol. It is proposed that their transformation is related to the transformation causing plateau II in experiments with very rapid cooling, a transformation which has previously been proposed to be related to the formation of bainite.

  • 4.
    Borgenstam, Annika
    et al.
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
    Hillert, Mats
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
    Kinetics of bainite transformation in steels2012In: Phase Transformations in Steels, Elsevier, 2012, Vol. 1, p. 468-501Chapter in book (Refereed)
    Abstract [en]

    The main kinetic features of the formation of bainite are discussed, firstly in relation to two incompatible hypotheses for the growth mechanism of bainitic ferrite. One is based on diffusionless growth of bainitic ferrite but diffusional growth of Widmanstätten ferrite. The other is based on the assumption that there is only one kind of acicular ferrite and it grows under simultaneous diffusion of carbon into the interior of the parent austenite. The kinetics of the first stage of bainite formation, the growth of acicular ferrite, is treated in detail because it has been subject to the more intensive research. The kinetics of the reactions by which cementite forms and the subsequent reactions, by which the transformation to bainite is completed, have been subject to less research.

  • 5.
    Borgenstam, Annika
    et al.
    KTH, Superseded Departments, Materials Science and Engineering.
    Hillert, Mats
    KTH, Superseded Departments, Materials Science and Engineering.
    Model for nucleation of isothermal martensite2001In: Scripta Materialia, ISSN 1359-6462, E-ISSN 1872-8456, Vol. 45, no 8, p. 917-922Article in journal (Refereed)
    Abstract [en]

    Kaufman and Cohen's model for thermally activated growth of preexisting embroys of isothermal martensite was defined with a series of obstacles but they only considered jumps in one direction. Jumps in both directions across obstacles were recently considered and the activation energy for the net reaction was described. That nucleation model is now developed further.

  • 6.
    Borgenstam, Annika
    et al.
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
    Hillert, Mats
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
    Ågren, John
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
    Metallographic evidence of carbon diffusion in the growth of bainite2009In: Acta Materialia, ISSN 1359-6454, E-ISSN 1873-2453, Vol. 57, no 11, p. 3242-3252Article in journal (Refereed)
    Abstract [en]

    There are two paradigms regarding the formation of bainite. One is based on the first stage being rapid, diffusionless growth or acicular ferrite and the subsequent formation of carbide occurring by precipitation from the supersaturated ferrite. All assumption that the first stage occurs as a series of subsequent rapid steps resulting in sub-units plays an important role as an explanation of the not so rapid growth observed macroscopically. The other paradigm is based on the first stage being the formation of acicular ferrite under carbon diffusion and on the subsequent growth of carbide and ferrite side by side. Metallographic observations are presented that support the second paradigm. It is difficult to see how they can be accounted for by the first paradigm, in particular the observation of the shapes of sub-units.

  • 7. Dahle, A. K.
    et al.
    Hillert, Mats
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
    Discussion of "nucleation mechanism of eutectic phases in aluminum-silicon hypoeutectic alloys"2005In: Metallurgical and Materials Transactions. A, ISSN 1073-5623, E-ISSN 1543-1940, Vol. 36, no 6, p. 1612-1613Article in journal (Refereed)
    Abstract [en]

    A previous study tried to prove that each plate of Si in the ordinary Al-Si eutectic is nucleated individually by the action of a small iron-containing particle. The study justified the need for a more complete understanding of the Al-Si eutectic reaction in the absence of chemical modifiers in order to shed light on the complicated mechanisms operating in chemically modified Al-Si alloys. Reacting to this claim, the present authors state that the mechanisms of the ordinary eutectic reaction of Al-Si alloys have been well understood for several decades, thus a very strong evidence is required to justify a revision of that understanding. For their part, the authors of the first study justified their claim for a revision by considering results of thermal analyses, optical microscopy, scanning and transmission electron microscopy, and selected area electron diffraction (SAED) analyses and elemental X-ray mapping performed on samples of precisely controlled chemistry.

  • 8. Dahle, A. K.
    et al.
    Hillert, Mats
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
    Reply to discussion on "Nucleation mechanism of eutectic phases in aluminum-silicon hypoeutectic alloys'2006In: Metallurgical and Materials Transactions. A, ISSN 1073-5623, E-ISSN 1543-1940, Vol. 37A, no 4, p. 1353-1353Article in journal (Refereed)
  • 9. De Graef, M.
    et al.
    Kral, M. V.
    Hillert, Mats
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
    A modern 3-D view of an "Old" pearlite colony2006In: JOM: The Member Journal of TMS, ISSN 1047-4838, E-ISSN 1543-1851, Vol. 58, no 12, p. 25-28Article in journal (Refereed)
    Abstract [en]

    This paper describes the three-dimensional (3-D) microstructure of a pearlite colony in a carburized electrolytic iron. The original data was obtained by serial sectioning methods around 1960, and is revisited with modern 3-D visualizations. After a brief historical introduction, the structure of the pearlite colony is discussed, using surface renderings and blue-red stereoscopic images.

  • 10. Hallstedt, Bengt
    et al.
    Dupin, Nathalie
    Hillert, Mats
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
    Höglund, Lars
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
    Lukas, Hans Leo
    Schuster, Julius C.
    Solak, Nuri
    Thermodynamic models for crystalline phases. Composition dependent models for volume, bulk modulus and thermal expansion2007In: Calphad, ISSN 0364-5916, E-ISSN 1873-2984, Vol. 31, no 1, p. 28-37Article in journal (Refereed)
    Abstract [en]

    The thermodynamic modelling of solid (crystalline) phases forms a central topic within the Calphad approach and a variety of aspects have been discussed at previous Ringberg workshops. At the present Ringberg workshop, modelling of volume and its temperature, pressure and composition dependence formed a major part of the discussions. In addition, modelling of the heat capacity above the (equilibrium) melting temperature, sublattice modelling of complex phases, modelling of ordering and interstitial solutions in the bcc lattice and the effect of magnetism were addressed.

  • 11.
    Hillert, M.
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
    Discussion of "A Commentary on Reaction Kinetics in Processes of Nucleation and Growth"*2011In: Metallurgical and Materials Transactions. A, ISSN 1073-5623, E-ISSN 1543-1940, Vol. 42A, no 11, p. 3241-3241Article in journal (Refereed)
  • 12.
    Hillert, Mats
    KTH, Superseded Departments, Materials Science and Engineering.
    A model-based continuum treatment of ordering and spinodal decomposition2001In: Acta Materialia, ISSN 1359-6454, E-ISSN 1873-2453, Vol. 49, no 13, p. 2491-2497Article in journal (Refereed)
    Abstract [en]

    Using the absolute reaction rate theory, a continuum treatment of ordering and spinodal decomposition is derived from the original planar discrete lattice model which was based on a Bragg-Williams type of approach. For small amplitudes the result agrees with Cahn's linearized equation for spinodal decomposition. The kinetic equation for ordering has a factor not included in the Allen-Cahn equation which depends on the local degree of order and may have important consequences.

  • 13.
    Hillert, Mats
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
    An application of irreversible thermodynamics to diffusional phase transformations2006In: Acta Materialia, ISSN 1359-6454, E-ISSN 1873-2453, Vol. 54, no 1, p. 99-104Article in journal (Refereed)
    Abstract [en]

    The method of transforming the set of flux equations for two simultaneous processes into a new set of processes is reviewed and applied to diffusion in one-phase materials where the two primary equations describe the individual diffusion of the components and the new ones describe the migration of Kirkendall markers and interdiffusion. It is then modified to apply to a two-phase material with a diffusional transformation and the new equations then describe the migration of the phase interface and interdiffusion across the interface. Comparison is made with previous attempts. In order to treat the transition from diffusion-controlled to partitionless growth it may be necessary to introduce a third primary flux equation. It is possible to incorporate this third flux within the other two, in which case it will contribute substantially to their cross-coefficients.

  • 14.
    Hillert, Mats
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
    Comments on "Eutectic solidification of gray cast iron"2005In: Scripta Materialia, ISSN 1359-6462, E-ISSN 1872-8456, Vol. 52, no 3, p. 249-250Article in journal (Refereed)
    Abstract [en]

    Applying a new technique for studying the orientation of austenite at room temperature, where it would normally transform to martensite, Rivera et al. have studied the solidification of gray cast iron. Their conclusions are in general agreement with the classical work in this field.

  • 15.
    Hillert, Mats
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
    Deviation from local equilibrium2005In: Solid-Solid Phase Transformations in Inorganic Material 2005, Vol 2 / [ed] Howe, JM; Laughlin, DE; Lee, JK; Dahmen, U; Soffa, WA, 2005, p. 327-338Conference paper (Refereed)
    Abstract [en]

    In order to learn more about the atomic mechanisms of the migration of phase interfaces one should study the kinetic equations. They are based on the driving forces which can be obtained from the deviation from local equilibrium at the migrating interface. The thermodynamic and mechanistic background of the deviation from local equilibrium will be described and illustrated with molar Gibbs energy diagrams. It will be discussed how the flux equations for individual components can be formulated in order to represent various causes of friction. The discussion will be based on the sharp interface model but its shortcomings will be emphasized.

  • 16.
    Hillert, Mats
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
    Discussion of "A Personal Commentary on Transformation of Austenite at Constant Subcritical Temperatures"2011In: Metallurgical and Materials Transactions. A, ISSN 1073-5623, E-ISSN 1543-1940, Vol. 42A, no 3, p. 541-542Article in journal (Refereed)
  • 17.
    Hillert, Mats
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
    Evaluation of the EMF from a potential phase diagram for a quaternary system2008In: The SGTE Casebook: Second Edition: Thermodynamics At Work, Elsevier, 2008, p. 228-230Chapter in book (Refereed)
  • 18.
    Hillert, Mats
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
    Fundamentals of diffusion in phase transformations2012In: Phase Transformations in Steels, Elsevier, 2012, Vol. 1, p. 94-125Chapter in book (Refereed)
    Abstract [en]

    An atomistic model in the lattice-fixed frame of reference is the basis for the present discussion of the fundamentals of diffusion. It is shown that cross terms appear when gradients of some composition variable are introduced. It is demonstrated that an equation describing the movement of Kirkendall markers must be included in the new set of flux equations when the frame of reference is changed. It is argued that one should store information of mobilities rather than diffusivities and one should make calculations of diffusion in the lattice-fixed frame.

  • 19.
    Hillert, Mats
    KTH, Superseded Departments, Materials Science and Engineering.
    Nature of local equilibrium at the interface in the growth of ferrite from alloyed austenite2002In: Scripta Materialia, ISSN 1359-6462, E-ISSN 1872-8456, Vol. 46, no 6, p. 447-453Article in journal (Refereed)
    Abstract [en]

    The increase over the years of experimental information on the effect of alloying elements on the transformation of austenite to ferrite and of the theoretical understanding is reviewed. The prediction of two kinds of transitions in behavior is described and the importance of exploring them experimentally is stressed.

  • 20.
    Hillert, Mats
    KTH, Superseded Departments, Materials Science and Engineering.
    Nature of massive transformation2004In: Metallurgical and Materials Transactions. A, ISSN 1073-5623, E-ISSN 1543-1940, Vol. 35A, no 1, p. 351-352Article in journal (Refereed)
    Abstract [en]

    A description of massive transformation is presented. Massive transformation is defined as a kind of composition-invariant nucleation-and-growth formation of a solid phase from another solid phase. The nature of massive transformation is often described as diffusional. The concentration of nucleation to grain boundaries in the parent phase is a significant feature of massive transformation.

  • 21.
    Hillert, Mats
    KTH, Superseded Departments, Materials Science and Engineering.
    Paradigm shift for bainite2002In: Scripta Materialia, ISSN 1359-6462, E-ISSN 1872-8456, Vol. 47, no 3, p. 175-180Article in journal (Refereed)
    Abstract [en]

    One of the pictures of the mechanism of the bainitic transformation has been based upon the paradigm that it is closely related to the martensitic transformation. It has resulted in an unjustified belief in high growth velocity and high supersaturation of carbon in bainitic ferrite. It seems that the time is now right for abandoning that paradigm.

  • 22.
    Hillert, Mats
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
    Phase equilibria, phase diagrams and phase transformations: Their thermodynamic basis, second edition2007Book (Other academic)
    Abstract [en]

    Computational tools allow material scientists to model and analyze increasingly complicated systems to appreciate material behavior. Accurate use and interpretation however, requires a strong understanding of the thermodynamic principles that underpin phase equilibrium, transformation and state. This fully revised and updated edition covers the fundamentals of thermodynamics, with a view to modern computer applications. The theoretical basis of chemical equilibria and chemical changes is covered with an emphasis on the properties of phase diagrams. Starting with the basic principles, discussion moves to systems involving multiple phases. New chapters cover irreversible thermodynamics, extremum principles, and the thermodynamics of surfaces and interfaces. Theoretical descriptions of equilibrium conditions, the state of systems at equilibrium and the changes as equilibrium is reached, are all demonstrated graphically. With illustrative examples - many computer calculated - and worked examples, this textbook is an valuable resource for advanced undergraduates and graduate students in materials science and engineering.

  • 23.
    Hillert, Mats
    KTH, Superseded Departments, Materials Science and Engineering.
    Solute drag and entropy production - Two approaches to the same phenomenon2004In: RECRYSTALLIZATION AND GRAIN GROWTH, PTS 1 AND 2 / [ed] Bacroix, B; Driver, JH; LeGall, R; Maurice, C; Penelle, R; Regle, H; Tabourot, L, ZURICH-UETIKON: TRANS TECH PUBLICATIONS LTD , 2004, Vol. 467-470, p. 3-8Conference paper (Refereed)
    Abstract [en]

    The historical development of the two approaches to the interaction between solute atoms and a migrating interface, based on dissipation of Gibbs energy and on solute drag, are reviewed and compared. In the way the solute drag was formulated long ago for recrystallization and grain growth, it does not apply to phase transformations. With a new solute drag equation, which was recently proposed, it turns out that the two approaches are completely equivalent for phase transformations as well as grain boundary migration.

  • 24.
    Hillert, Mats
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
    Solute drag illustrated graphically2005In: Zeitschrift für Metallkunde, ISSN 0044-3093, Vol. 96, no 2, p. 104-107Article in journal (Refereed)
    Abstract [en]

    There are two approaches to the interaction between solute atoms and migrating interfaces. A comparison between the two is illustrated with molar Gibbs energy diagrams. It is demonstrated that the present treatments of solute drag are equivalent to the treatment based on dissipation of Gibbs energy for grain boundary migration but not for phase transformations. A new treatment of solute drag is equivalent to the dissipation approach for both cases. It predicts that the solute drag changes sign for phase transformations and acts as a driving force.

  • 25.
    Hillert, Mats
    KTH, Superseded Departments, Materials Science and Engineering.
    Solute drag in grain boundary migration and phase transformations2004In: Acta Materialia, ISSN 1359-6454, E-ISSN 1873-2453, Vol. 52, no 18, p. 5289-5293Article in journal (Refereed)
    Abstract [en]

    Cahn's equation for solute drag has recently been applied to phase transformations but the method of application has been disputed. A new equation for solute drag is now proposed, which is more general and applies to multicomponent systems. It yields the same result for the migration of grain boundaries but a different result for phase transformations. It has the advantage of being equivalent to the approach based on the dissipation of Gibbs energy. (C) 2004 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

  • 26.
    Hillert, Mats
    KTH, Superseded Departments, Materials Science and Engineering.
    The compound energy formalism2001In: Journal of Alloys and Compounds, ISSN 0925-8388, E-ISSN 1873-4669, Vol. 320, no 2, p. 161-176Article in journal (Refereed)
    Abstract [en]

    The compound energy formalism for solution phases with sublattices is very flexible and thermodynamic models for a large variety of phases have been constructed within this formalism. The range of applications is reviewed and the methods of handling various problems are examined. Recent developments including treatments of short range order within the compound energy formalism are reviewed.

  • 27.
    Hillert, Mats
    et al.
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
    Borgenstam, Annika
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
    Centennial of the Diffusionless Paradigm of Bainite2012In: Metallurgical and Materials Transactions. A, ISSN 1073-5623, E-ISSN 1543-1940, Vol. 43A, no 12, p. 4487-4495Article in journal (Refereed)
    Abstract [en]

    The diffusionless growth model of bainite formation was included in an international consensus in 1912 that all transformation products of austenite form by an initial transformation to martensite. The introduction of isothermal treatment revealed that all the products form directly. However, for bainite, the idea of some relation to martensite survived and developed into the diffusionless paradigm. Zener introduced the T (o) concept for predicting the start temperature of lower bainite, but also described diffusional growth of upper bainite. The present description of the diffusionless growth model is now examined and criticized.

  • 28.
    Hillert, Mats
    et al.
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
    Borgenstam, Annika
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
    Ågren, John
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
    Do bainitic and Widmanstatten ferrite grow with different mechanisms?2010In: Scripta Materialia, ISSN 1359-6462, E-ISSN 1872-8456, Vol. 62, no 2, p. 75-77Article in journal (Refereed)
    Abstract [en]

    Caballero et al. recently presented new evidence for different growth mechanisms of Widmanstatten and bainitic ferrite. Their argument was based on Zener's hypothesis of diffusionless growth of bainitic ferrite. It is now demonstrated that Bhadeshia's model, based on Zener's hypothesis, predicts that some of the new measurements, claimed to fall above B-s and to be due to Widmanstatten ferrite, actually fall within the predicted temperature range of bainite, indicating that they cannot be used as new support for Bhadeshia's model.

  • 29.
    Hillert, Mats
    et al.
    KTH, Superseded Departments, Materials Science and Engineering.
    Höglund, Lars
    KTH, Superseded Departments, Materials Science and Engineering.
    Comments on kinetics model of isothermal pearlite formation in a 0.4C-1.6Mn steel2004In: Scripta Materialia, ISSN 1359-6462, E-ISSN 1872-8456, Vol. 50, no 1, p. 171-173Article in journal (Refereed)
    Abstract [en]

    A recent attempt to use the volume fraction of isothermally formed pearlite to decide how Mn partitions between ferrite and cementite is criticized. An alternative method is proposed.

  • 30.
    Hillert, Mats
    et al.
    KTH, Superseded Departments, Materials Science and Engineering.
    Höglund, Lars
    KTH, Superseded Departments, Materials Science and Engineering.
    Comments on Reply to comments on kinetics model of isothermal pearlite formation in a 0.4C-1.6Mn steel2004In: Scripta Materialia, ISSN 1359-6462, E-ISSN 1872-8456, Vol. 51, no 1, p. 77-78Article in journal (Refereed)
    Abstract [en]

    A recent statement that the correction of a serious error in a thermodynamic calculation was not relevant to the interpretation is shown to be caused by the use of an incorrect equation instead of the lever rule.

  • 31.
    Hillert, Mats
    et al.
    KTH, Superseded Departments, Materials Science and Engineering.
    Höglund, Lars
    KTH, Superseded Departments, Materials Science and Engineering.
    Melting of a peritectic phase2004In: Scripta Materialia, ISSN 1359-6462, E-ISSN 1872-8456, Vol. 50, no 7, p. 1055-1059Article in journal (Refereed)
    Abstract [en]

    The reverse of a peritectic reaction belongs to the class of eutectic and eutectoid reactions and the same theory is now applied after modification for the fact that the predominating diffusion occurs within one of the growing phases, here the liquid one. The complications caused by the metastable congruent melting point are examined.

  • 32.
    Hillert, Mats
    et al.
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
    Höglund, Lars
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
    Mobility of alpha/gamma phase interfaces in Fe alloys2006In: Scripta Materialia, ISSN 1359-6462, E-ISSN 1872-8456, Vol. 54, no 7, p. 1259-1263Article in journal (Refereed)
    Abstract [en]

    Information on the mobility of alpha/gamma phase interfaces in Fe alloys has been scarce and one has long relied on an evaluation for alpha/alpha grain boundaries. New and old information is now reviewed. There are strong indications that the mobility is much lower than for alpha/alpha grain boundaries.

  • 33.
    Hillert, Mats
    et al.
    KTH, Superseded Departments, Materials Science and Engineering.
    Höglund, Lars
    KTH, Superseded Departments, Materials Science and Engineering.
    Schalin, M.
    Computer simulation of cooling curves for solidification2000In: Materials transactions, JIM, ISSN 0916-1821, Vol. 41, no 8, p. 1098-1103Article in journal (Refereed)
    Abstract [en]

    The method of simulating cooling curves for solidifying alloys is examined. Usually, a simulation program only results in a curve showing the fraction solidified material as a function of temperature. In order to predict the cooling curve, i.e. temperature as a function of time, it is necessary to use a simulation program that also evaluates the changes of enthalpy during solidification and takes into account the possible variation of the rate of heat extraction with temperature or with a temperature difference between a crucible and a furnace. By comparing predicted cooling curves obtained in that way with experiments it was investigated how to take into account the heat capacity of the crucible. Two simulation programs were used; one based on the Gulliver-Scheil approximations and the other taking back diffusion into account, using a finite difference technique. In both cases the enthalpy was evaluated continuously during cooling.

  • 34.
    Hillert, Mats
    et al.
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
    Höglund, Lars
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
    Ågren, John
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
    Diffusion in interstitial compounds with thermal and stoichiometric defects2005In: Journal of Applied Physics, ISSN 0021-8979, E-ISSN 1089-7550, Vol. 98, no 5Article in journal (Refereed)
    Abstract [en]

    The ordinary flux equation for diffusion, which considers the composition gradient as the driving force, is seldom of much use in studying closely stoichiometric phases. Depending on the defect structure it would instead be profitable to use an appropriate function of the activity. Such functions will now be derived and it will be shown how the operating defect mechanism of diffusion can be identified from information on the variation of the activity inside a phase during diffusion. However, it is usually very difficult to measure the activity profile inside a phase. It will be shown how it can be obtained by combining results from several experiments. The method will be used to analyze experimental information on the formation of surface layers of Fe4N and Fe3C.

  • 35.
    Hillert, Mats
    et al.
    KTH, Superseded Departments, Materials Science and Engineering.
    Höglund, Lars
    KTH, Superseded Departments, Materials Science and Engineering.
    Ågren, John
    KTH, Superseded Departments, Metallurgy.
    Diffusion-controlled lengthening of Widmanstatten plates2003In: Acta Materialia, ISSN 1359-6454, E-ISSN 1873-2453, Vol. 51, no 7, p. 2089-2095Article in journal (Refereed)
    Abstract [en]

    Various treatments of the diffusion-controlled lengthening of plates during precipitation from a supersaturated solid solution are compared numerically. Serious doubts are raised about the validity of Trivedi's treatment which has been generally accepted. A recent treatment based directly on Ivantsov's solution gives results in between those of Trivedi's equation and Zener's equation, as modified by Hillert.

  • 36. Hillert, Mats
    et al.
    Höglund, Lars
    KTH, Superseded Departments, Materials Science and Engineering.
    Ågren, John
    Escape of carbon from ferrite plates in austenite1993In: ACTA METALL MATER, ISSN 0956-7151, Vol. 41, no 7, p. 1951-1957Article in journal (Refereed)
    Abstract [en]

    A newly developed computer program for the simulation of diffusional transformations has been applied to study the escape of carbon from a plate of ferrite assuming that the plate initially formed by a partitionless reaction from an Fe-C austenite. Thereafter the ferrite austenite interface was assumed to be immobile and local equilibrium was assumed for carbon but not for iron. The process first follows a parabolic rate law and is there controlled by the rate of diffusion in ferrite. Later stages are not parabolic and are controlled by the diffusivity in austenite. Its concentration dependence was taken into account. It was found that the rate could be estimated analytically using the maximum value rather than the average value.

  • 37.
    Hillert, Mats
    et al.
    KTH, Superseded Departments, Materials Science and Engineering.
    Höglund, Lars
    KTH, Superseded Departments, Materials Science and Engineering.
    Ågren, John
    KTH, Superseded Departments, Metallurgy.
    Role of carbon and alloying elements in the formation of bainitic ferrite2004In: Metallurgical and Materials Transactions. A, ISSN 1073-5623, E-ISSN 1543-1940, Vol. 35A, no 12, p. 3693-3700Article in journal (Refereed)
    Abstract [en]

    One approach to the prediction of the carbon content of austenite, remaining after the precipitation of bainitic ferrite, is based on the assumption that bainitic ferrite during growth inherits the carbon content of the parent austenite. An alternative approach is based on the assumption that bainitic ferrite grows with a low carbon content and there is no major difference between Widmanstatten ferrite and bainitic ferrite. The two approaches are now compared using information from alloyed steels with considerable amounts of Si, where the formation of cementite is retarded. The former approach does not account for the effect of Mn and fails severely at low alloy contents. The latter approach seems more promising but is not without difficulties. In particular, in order to explain the effects of Cr and Mo, it seems necessary to introduce a kinetic effect, presumably caused by solute drag.

  • 38.
    Hillert, Mats
    et al.
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
    Jonsson, Stefan
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
    Prediction of a quasiternary section of a quaternary phase diagram2008In: The SGTE Casebook: Thermodynamics At Work, Elsevier, 2008, 2, p. 114-117Chapter in book (Refereed)
  • 39.
    Hillert, Mats
    et al.
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
    Kjellqvist, Lina
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
    Mao, Huahai
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
    Selleby, Malin
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
    Sundman, Bo
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
    Parameters in the compound energy formalism for ionic systems2009In: Calphad, ISSN 0364-5916, E-ISSN 1873-2984, Vol. 33, no 1, p. 227-232Article in journal (Refereed)
    Abstract [en]

    The compound energy formalism, CEF, involves many model parameters. They are evaluated to give the best fit to the experimental information. The optimisation is simpler if less parameters need to be adjusted.The maximum number of independent parameters that can be evaluated depends on the information available. The best choice of parameters is first discussed for simple ionic substances with an internal variable, then for solutions of two or four such substances.

    To reduce the number of parameters, independent parameters are conveniently defined as combinations of primary model parameters. That may be possible when there is an internal variable,which can take only one value, the value that minimizes the Gibbs energy. Such combinations may be regarded as the true optimisation parameters and they may be used actively during an optimisation. The present discussion deals with substances with an internal variable and mixtures, which may have more than one internal variable.

    The conclusions apply equally well to non-ionic systems if the information is limited to stoichiometric compositions. The optimisation parameters should then be defined for stoichiometric overall compositions.

  • 40.
    Hillert, Mats
    et al.
    KTH, Superseded Departments, Materials Science and Engineering.
    Odqvist, Joakim
    KTH, Superseded Departments, Materials Science and Engineering.
    Ågren, John
    KTH, Superseded Departments, Materials Science and Engineering.
    Interface conditions during diffusion-controlled phase transformations2004In: Scripta Materialia, ISSN 1359-6462, E-ISSN 1872-8456, Vol. 50, no 4, p. 547-550Article in journal (Refereed)
    Abstract [en]

    Considerations of the driving force on the interface in diffusional phase transformations are usually limited to diffusion in the parent phase. Diffusion in both phases is now considered. Equations are derived for the calculation of the composition of the material crossing the interface and the driving force acting on the interface.

  • 41.
    Hillert, Mats
    et al.
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
    Qiu, Caian
    Prediction of loss of corrosion resistance in austenitic stainless steels2008In: The SGTE Casebook: Thermodynamics At Work, Elsevier, 2008, 2, p. 106-113Chapter in book (Refereed)
  • 42.
    Hillert, Mats
    et al.
    KTH, Superseded Departments, Materials Science and Engineering.
    Schalin, M.
    Modeling of solute drag in the massive phase transformation2000In: Acta Materialia, ISSN 1359-6454, E-ISSN 1873-2453, Vol. 48, no 2, p. 461-468Article in journal (Refereed)
    Abstract [en]

    The role of solute drag in the massive phase transformation is evaluated through the dissipation of Gibbs energy by diffusion. As an introduction, the solute drag in grain boundary migration is first examined using the wedge-shaped energy function considered by Cahn and by Lucke and Stuwe. The effect of a diffusivity varying from a low value in the bulk to a high value in the center of the boundary is examined. It decreases the solute drag drastically. For the massive phase transformation it is demonstrated how the solute drag increases by the tendency for segregation and by a high diffusivity in the interface but it decreases if the diffusivity is lower than in the parent phase. The most important contribution to solute drag comes from the spike of solute atoms in the parent phase being pushed forward by the advancing interface. The spike is thus an obstacle for growth that must be broken through in order for diffusion-controlled growth to turn partitionless. The possibility of dynamic nucleation is also discussed.

  • 43.
    Hillert, Mats
    et al.
    KTH, Superseded Departments, Materials Science and Engineering.
    Schwind, M.
    Selleby, Malin
    KTH, Superseded Departments, Materials Science and Engineering.
    Trapping of vacancies by rapid solidification2002In: Acta Materialia, ISSN 1359-6454, E-ISSN 1873-2453, Vol. 50, no 12, p. 3283-3291Article in journal (Refereed)
    Abstract [en]

    A model has been developed for the process of trapping of vacancies in rapid solidification of pure metals, which includes the effect of solute drag where vacancies play the role of solute. Within a reasonable range of parameter values it predicts that substantial trapping cannot occur unless the solidification velocity is 1 m/s or higher. It is demonstrated that the intrinsic mobility of the liquid/solid interface should not be evaluated without considering the effects of vacancy trapping and solute drag caused by vacancies. The model is applied to copper and unknown parameters are evaluated from information on the solidification velocity as a function of undercooling.

  • 44.
    Hillert, Mats
    et al.
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
    Selleby, Malin
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
    Discussion of cementite layer formation and sooting2010In: Scripta Materialia, ISSN 1359-6462, E-ISSN 1872-8456, Vol. 63, no 11, p. 1037-1040Article in journal (Refereed)
    Abstract [en]

    A thermodynamic explanation was recently proposed for the formation of massive layers of cementite without any graphite by gas carburization of steels at 550 degrees C if the gas contains NH(3). That explanation is now criticized. It is proposed that a kinetic factor, based on the difficulty of precipitating graphite inside a solid matrix, may contribute to the inhibition of metal dusting in the presence of NH3.

  • 45.
    Hillert, Mats
    et al.
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
    Selleby, Malin
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
    Methods for storage of Gibbs energy data of substances2016In: Calphad, ISSN 0364-5916, E-ISSN 1873-2984, Vol. 53, p. 146-150Article in journal (Refereed)
    Abstract [en]

    There are two popular methods for storing Gibbs energy data for pure substances. They are inspired by Planck and by Lewis and Randall and may appear as very different but it will be demonstrated that they only differ by the choice of references. The derivation of functions to be stored will then be described and a crude but very simple method for extending them to 0. K by interpolation instead of extrapolation will be presented.

  • 46.
    Hillert, Mats
    et al.
    KTH, Superseded Departments, Materials Science and Engineering.
    Ågren, John
    KTH, Superseded Departments, Metallurgy.
    Discussion on local equilibrium at solid/liquid interfaces during melting2002In: Scripta Materialia, ISSN 1359-6462, E-ISSN 1872-8456, Vol. 46, no 6, p. 455-457Article in journal (Refereed)
    Abstract [en]

    Melting experiments were recently used to support the assumption of considerable deviation from local equilibrium. It is now claimed that the observed velocities of melting were low enough to allow diffusion in the solid to give a well developed spike of the solute in front of the migrating interface making a strong deviation from local equilibrium unlikely.

  • 47.
    Hillert, Mats
    et al.
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
    Ågren, John
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
    Extremum principles for irreversible processes2006In: Acta Materialia, ISSN 1359-6454, E-ISSN 1873-2453, Vol. 54, no 8, p. 2063-2066Article in journal (Refereed)
    Abstract [en]

    Hamilton's extremum principle is a powerful mathematical tool in classical mechanics. Onsager's extremum principle may play a similar role in irreversible thermodynamics and may also become a valuable tool. His principle may formally be regarded as a principle of maximum rate of entropy production but does not have a clear physical interpretation. Prigogine's principle of minimum rate of entropy production has a physical interpretation when it applies, but is not strictly valid except for a very special case.

  • 48.
    Hillert, Mats
    et al.
    KTH, Superseded Departments, Metallurgy.
    Ågren, John
    KTH, Superseded Departments, Metallurgy.
    On the definitions of paraequilibrium and orthoequilibrium2004In: Scripta Materialia, ISSN 1359-6462, E-ISSN 1872-8456, Vol. 50, no 5, p. 697-699Article in journal (Refereed)
    Abstract [en]

    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.

  • 49.
    Hillert, Mats
    et al.
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
    Ågren, John
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
    Reply to comments on "On the definition of paraequilibrium and orthoequilibrium"2005In: Scripta Materialia, ISSN 1359-6462, E-ISSN 1872-8456, Vol. 52, no 1, p. 87-88Article in journal (Refereed)
    Abstract [en]

    In the equilibrium conditions called CPE the letters PE stand for paraequilibrium. However, paraequilibrium plays no important role in the process for which CPE was introduced. The essential feature is the equilibration of carbon between a and γ under the constraint that the interface is immobile. In order to avoid confusion regarding the nature of paraequilibrium, the term CCE (constrained carbon equilibrium) is proposed instead of CPE.

  • 50.
    Jeppsson, Johan
    et al.
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
    Ågren, John
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
    Hillert, Mats
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
    Modified mean field models of normal grain growth2008In: Acta Materialia, ISSN 1359-6454, E-ISSN 1873-2453, Vol. 56, no 18, p. 5188-5201Article in journal (Refereed)
    Abstract [en]

    Models of normal grain growth can either start from a postulated kinetic law for individual grains and yield a distribution of grain sizes or they can start from a postulated distribution and the kinetic law may be derived. Both methods are studied and a whole family of distributions based on new kinetic laws are derived using the first method. Both methods have recently been applied using Onsager's extremum principle but it is now shown that more classical procedures are sufficient. Kinetic laws give an indication of what physical factors govern the growth or shrinkage of individual grains. A Rayleigh's distribution seems to indicate that large grains are surrounded by grains smaller than the critical size and small grains are surrounded by grains larger than the critical size. The effects of the new family of kinetic laws on the development of grain size distributions are studied by numerical simulations.

12 1 - 50 of 75
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