Diffusional Phase Transformations in the Solid State

Abstract This chapter deals with diffusional phase transformations. We first define a phase and move on to discuss various ways of classifying phase transformations. We then discuss in detail the energetics (thermodynamics) and kinetics of diffusional phase transformations. Transformations discussed include: precipitation, atomic ordering, spinodal decomposition, massive and cellular transformations in the light of the sections on energetics and kinetics. A final section of the role of symmetry in developing microstructure concludes the chapter.

[1]  C. Dollins Nucleation on dislocations , 1970 .

[2]  A. Ardell,et al.  On the modulated structure of aged Ni-Al alloys: with an Appendix On the elastic interaction between inclusions by J. D. Eshelby , 1966 .

[3]  Paul Shewmon,et al.  Diffusion in Solids , 2016 .

[4]  G. H. Meier,et al.  Microstructural behaviour and mechanical hardening in a Cu-Ni-Cr alloy , 1978 .

[5]  M. Hillert,et al.  Formation of modulated structures in copper-nickel-iron alloys , 1961 .

[6]  H. Aaronson,et al.  Proceedings of an International Conference on Solid [to] Solid Phase Transformations , 1982 .

[7]  D. Kirkwood,et al.  Precipitate number density in a NiAl alloy at early stages of ageing , 1970 .

[8]  M. P. Shaskolskaya,et al.  Fundamentals of Crystal Physics , 1983 .

[9]  J. W. Martin,et al.  Stability of microstructure in metallic systems , 1976 .

[10]  J. Nutting,et al.  Direct observation of the strain field produced by coherent precipitated particles in an age-hardened alloy , 1958 .

[11]  P. D. Merica,et al.  Heat Treatment and Constitution of Duralumin , 1968 .

[12]  G. Thomas,et al.  Structure and properties of spinodally decomposed Cu-Ni-Fe alloys , 1970 .

[13]  D. Laughlin,et al.  Effects of Cu content and preaging on precipitation characteristics in aluminum alloy 6022 , 2000 .

[14]  I. Prigogine,et al.  From Being to Becoming: Time and Complexity in the Physical Sciences , 1982 .

[15]  J. V. Bee,et al.  The cellular reaction in dilute copper-titanium alloys , 1980 .

[16]  P. Shewmon Transformations in metals , 1969 .

[17]  W. Soffa,et al.  The structure and properties of age hardened Cu-Ti alloys , 1976 .

[18]  R. Sinclair,et al.  Spinodal decomposition of a nickel-titanium alloy , 1974 .

[19]  L. Girifalco Statistical physics of materials , 1973 .

[20]  U. Dehlinger Chemische Physik der Metalle und Legierungen , 1939 .

[21]  P. Wang,et al.  Nucleation kinetics of the α→γM massive transformation in a Ti-47.5 at.% Al alloy , 2003 .

[22]  J. Cahn The later stages of spinodal decomposition and the beginnings of particle coarsening , 1966 .

[23]  R. Weiss,et al.  Components of the Thermodynamic Functions of Iron , 1956 .

[24]  F. Nabarro The influence of elastic strain on the shape of particles segregating in an alloy , 1940 .

[25]  Samuel Glasstone,et al.  The Theory Of Rate Processes , 1941 .

[26]  F. Ham Diffusion‐Limited Growth of Precipitate Particles , 1959 .

[27]  R. Williams Long-period superlattices in the copper-gold system as two-phase mixtures , 1980 .

[28]  U. Dahmen Phase Transformations, Crystallographic Aspects , 1986 .

[29]  J. Nutting,et al.  The Structure of Metals , 1960 .

[30]  M. Notis,et al.  Spinodal decomposition, ordering transformation, and discontinuous precipitation in a Cu-15Ni-8Sn alloy , 1998 .

[31]  D. Fontaine k-Space symmetry rules for order-disorder reactions , 1975 .

[32]  N. Tanaka,et al.  High Resolution Lattice Images of Ordered Structures in Al–Li Alloys , 1988 .

[33]  P. Auger,et al.  Atom Probe Studies of the Fe–Cr System and Stainless Steels Aged at Intermediate Temperature: A Review , 2000 .

[34]  A. Khachaturyan,et al.  Spatially periodic distributions of new phase inclusions caused by elastic distortions , 1974 .

[35]  A. Virkar,et al.  Massive Transformation in the Y2O3‐Bi2O3 System , 1994 .

[36]  R. Trivedi,et al.  The role of interfacial free energy and interface kinetics during the growth of precipitate plates and needles , 1970, Metallurgical and Materials Transactions B.

[37]  Larry Kaufman,et al.  The lattice stability of metals—III. Iron☆ , 1963 .

[38]  R. Fournelle,et al.  The genesis of the cellular precipitation reaction , 1972 .

[39]  T. B. Massalski,et al.  The surprising role of magnetism on the phase stability of Fe (Ferro) , 2009 .

[40]  E. S. Machlin,et al.  An Introduction to Aspects of Thermodynamics and Kinetics: Relevant to Materials Science , 1991 .

[41]  R. Becker Die Keimbildung bei der Ausscheidung in metallischen Mischkristallen , 1938 .

[42]  H. Stanley,et al.  Introduction to Phase Transitions and Critical Phenomena , 1972 .

[43]  J. D. Eshelby The determination of the elastic field of an ellipsoidal inclusion, and related problems , 1957, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[44]  Srikumar Banerjee,et al.  Phase transformations : examples from titanium and zirconium alloys , 2007 .

[45]  W. Soffa,et al.  Decomposition of a Cu-Ni-Cr ternary alloy , 1991 .

[46]  Hiroshi Imamura,et al.  The formation of “γ′ precipitate doublets” in NiAl alloys and their energetic stability , 1982 .

[47]  and B Ditchek,et al.  Applications of Spinodal Alloys , 1979 .

[48]  Discontinuous coarsening of aligned eutectoids , 1974 .

[49]  G. D. Preston The diffraction of X-rays by age-hardening aluminium copper alloys. , 1938, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[50]  K. Laidler,et al.  Application of the Theory of Absolute Reaction Rates to Overvoltage , 1939 .

[51]  J. Gibbs On the equilibrium of heterogeneous substances , 1878, American Journal of Science and Arts.

[52]  A. Khachaturyan,et al.  Theoretical analysis of strain-induced shape changes in cubic precipitates during coarsening , 1988 .

[53]  J. Cahn Coherent fluctuations and nucleation in isotropic solids , 1962 .

[54]  C. Liu,et al.  Solid-solution theory and spinodal decomposition , 1971 .

[55]  P. Camus,et al.  Phase separation and coarsening in FeCrCo alloys , 1984 .

[56]  J. E. Burke,et al.  RECRYSTALLIZATION AND GRAIN GROWTH , 1952 .

[57]  Andrei Linde,et al.  A new inflationary universe scenario: A possible solution of the horizon , 1982 .

[58]  J. E. Hilliard,et al.  Free Energy of a Nonuniform System. I. Interfacial Free Energy , 1958 .

[59]  Robert W. Balluffi,et al.  Kinetics Of Materials , 2005 .

[60]  I. Lifshitz,et al.  The kinetics of precipitation from supersaturated solid solutions , 1961 .

[61]  A. J. Bradley X-ray evidence of intermediate stages during precipitation from solid solution , 1940 .

[62]  H. Hardy,et al.  Report on precipitation , 1954 .

[63]  John W. Cahn,et al.  On Spinodal Decomposition , 1961 .

[64]  R. Trivedi,et al.  The effects of crystallographic anisotropy on the growth kinetics of Widmanstätten precipitates , 1975 .

[65]  H. Lipson,et al.  An X-ray study of the dissociation of an alloy of copper, iron and nickel , 1943, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[66]  A. Guinier Structure of Age-Hardened Aluminium-Copper Alloys , 1938, Nature.

[67]  W. C. Johnson,et al.  Characteristics of phase equilibria in coherent solids , 1991 .

[68]  D. Williams,et al.  Experimental observations on the nucleation and growth of δ′ (Al3Li) in dilute Al-Li alloys , 1985 .

[69]  D. Laughlin,et al.  Interplay of ordering and spinodal decomposition in the formation of ordered precipitates in binary fcc alloys: Role of second nearest-neighbor interactions , 2010 .

[70]  M. Rajković,et al.  Ordering transformations in Fe-50Co based alloys , 1981 .

[71]  R. Grüne Decomposition of Ni-12 at.% Ti by atom-probe field-ion microscopy , 1988 .

[72]  W. G. Burgers,et al.  Mechanism and kinetics of the allotropic transformation of tin , 1957 .

[73]  J. Cahn Nucleation on dislocations , 1957 .

[74]  V. Radmilović,et al.  Massive transformation and the formation of the ferromagnetic L10 phase in manganese-aluminum-based alloys , 2002 .

[75]  V. Vasudevan,et al.  Kinetics and thermodynamics of the α→γm massive transformation in a Ti–47.5 at.% Al alloy , 1999 .

[76]  Charles M. Elliott,et al.  Spinodal decomposition in Fe-Cr alloys: Experimental study at the atomic level and comparison with computer models—III. Development of morphology , 1995 .

[77]  D. Laughlin,et al.  High-strength age hardening copper–titanium alloys: redivivus , 2004 .

[78]  B. Vonnegut Variation with temperature of the nucleation rate of supercooled liquid tin and water drops. , 1948, Journal of colloid science.

[79]  G. Vineyard Frequency factors and isotope effects in solid state rate processes , 1957 .

[80]  M. Miller,et al.  Spinodal decomposition of iron-32 at.% chromium at 470°C☆ , 1982 .

[81]  John W. Cahn,et al.  On spinodal decomposition in cubic crystals , 1962 .

[82]  Eckhard Nembach,et al.  Particle Strengthening of Metals and Alloys , 1996 .

[83]  M. Avrami Kinetics of Phase Change. II Transformation‐Time Relations for Random Distribution of Nuclei , 1940 .

[84]  R. Asimow Clustering kinetics in binary alloys , 1963 .

[85]  W. C. Johnson,et al.  The Thermodynamics of Elastically Stressed Crystals , 2004 .

[86]  J. Langer,et al.  Kinetics of nucleation in near-critical fluids , 1980 .

[87]  J. Cahn,et al.  A linear theory of thermochemical equilibrium of solids under stress , 1973 .

[88]  B. Lesage,et al.  The influence of temperature on slip and twinning in uranium , 1971 .

[89]  H. Bethe Statistical Theory of Superlattices , 1935 .

[90]  John W. Cahn,et al.  The kinetics of grain boundary nucleated reactions , 1956 .

[91]  N. Mott,et al.  An attempt to estimate the degree of precipitation hardening, with a simple model , 1940 .

[92]  C. Rao PHASE TRANSITIONS IN SOLIDS , 2008 .

[93]  M. Hillert,et al.  A solid-solution model for inhomogeneous systems , 1961 .

[94]  David Turnbull,et al.  Rate of Nucleation in Condensed Systems , 1949 .

[95]  D. Turnbull Correlation of Liquid‐Solid Interfacial Energies Calculated from Supercooling of Small Droplets , 1950 .

[96]  David J. Young,et al.  Diffusion in the Condensed State , 1988 .

[97]  G. Kostorz,et al.  Phase separation in Ni-rich Ni–Ti: the metastable states , 2003 .

[98]  D. Laughlin,et al.  Re-Examination of A1 → L10 Ordering: Generalized Bragg-Williams Model with Elastic Relaxation , 2011 .

[99]  R. Williams The calculation of coherent phase equilibria , 1984 .

[100]  C. M. Wayman,et al.  A theoretical basis for spinodal decomposition in ordered alloys , 1980 .

[101]  Samuel M. Allen,et al.  Mechanisms of phase transformations within the miscibility gap of Fe-rich Fe-Al alloys , 1976 .

[102]  C. M. Elliott,et al.  Spinodal decomposition in Fe-Cr alloys: Experimental study at the atomic level and comparison with computer models—I. Introduction and methodology , 1995 .

[103]  W. Bragg,et al.  The effect of thermal agitation on atomic arrangement in alloys , 1935 .

[104]  David B. Williams,et al.  Grain boundary discontinuous precipitation reactions , 1981 .

[105]  G. M. Pound,et al.  Nucleation of a second solid phase along dislocations , 1973, Metallurgical and Materials Transactions B.

[106]  D. Turnbull An approximate crystal structure for the beta phase of uranium. , 1950 .

[107]  C. Zener Impact of Magnetism Upon Metallurgy , 1955 .

[108]  A. G. Guy Elements of physical metallurgy , 1951 .

[109]  G. D. Preston Structure of Age-Hardened Aluminium-Copper Alloys , 1938, Nature.

[110]  H. Ino A pairwise interaction model for decomposition and ordering processes in B.C.C. binary alloys and its application to the Fe-Be system , 1978 .

[111]  A. Wilm Physikalisch-metallurgische Untersuchungen über magnesiumhaltige Aluminiumlegierungen , 1911 .

[112]  S. K. Pabi,et al.  Discontinuous reactions in solids , 2001 .

[113]  P. Germain,et al.  Nucleation in Condensed Matter , 1983 .

[114]  R. Wagner,et al.  Homogeneous Second‐Phase Precipitation , 2013 .

[115]  J. L. Meijering,et al.  Calculs thermodynamiques concernant la nature des zones Guinier-Preston dans les alliages aluminium-cuivre , 1952 .

[116]  P. Koppad,et al.  Small-angle scattering from GP zones in Al-Cu alloy , 2011 .

[117]  Dimo Kashchiev,et al.  Nucleation : basic theory with applications , 2000 .

[118]  J. Cahn,et al.  Spinodal decomposition in age hardening copper-titanium alloys , 1975 .

[119]  M. Glicksman Diffusion in solids : field theory, solid-state principles, applications , 2000 .

[120]  V. Radmilović,et al.  Spinodal decomposition of Al-rich Al-Li alloys , 1989 .

[121]  G. W. Greenwood The growth of dispersed precipitates in solutions , 1956 .

[122]  V. Ginzburg,et al.  Comments on the region of applicability of the landau theory for structural phase transitions , 1987 .

[123]  A. Ardell,et al.  Coherent equilibrium in alloys containing spherical precipitates , 1995 .

[124]  A. G. Khachaturi︠a︡n Theory of structural transformations in solids , 1983 .

[125]  A. Shiryayev On The Statistical Theory of Metal Crystallization , 1992 .

[126]  J. Cornie,et al.  An electron microscopy study of precipitation in Cu-Ti sideband alloys , 1973 .

[127]  Bellon,et al.  Irradiation-induced formation of metastable phases: A master-equation approach. , 1988, Physical review. B, Condensed matter.

[128]  John W. Cahn,et al.  Free Energy of a Nonuniform System. II. Thermodynamic Basis , 1959 .

[129]  J. Burke,et al.  The kinetics of phase transformations in metals , 1965 .

[130]  T. Hakkarainen Formation of coherent Cu4Ti precipitates in copper-rich copper-titanium alloys , 1971 .

[131]  C. L. Corey,et al.  The ordering transition in Ni3Al alloys , 1973 .

[132]  R. E. Smallman,et al.  Modern Physical Metallurgy , 1962 .

[133]  M. Avrami Granulation, Phase Change, and Microstructure Kinetics of Phase Change. III , 1941 .

[134]  Brun J-Y,et al.  Cu-Ti and Cu-Ti-Al solid state phase equilibria in the Cu-rich region. , 1983 .

[135]  M. Fine,et al.  Precipitation studies in Ni-10 at.% Ti☆ , 1963 .

[136]  J. C. Jaeger,et al.  Conduction of Heat in Solids , 1952 .

[137]  Clarence Zener,et al.  Interference of Growing Spherical Precipitate Particles , 1950 .

[138]  Andrew Putnis,et al.  An Introduction to Mineral Sciences , 1992 .

[139]  A. Ardell,et al.  The effect of volume fraction on particle coarsening: theoretical considerations , 1972 .

[140]  K. Easterling,et al.  Phase Transformations in Metals and Alloys , 2021 .

[141]  A. Khachaturyan Ordering in substitutional and interstitial solid solutions , 1978 .

[142]  David S. Wilkinson,et al.  Mass Transport in Solids and Fluids , 2000 .

[143]  D. Laughlin,et al.  Decomposition and ordering processes involving thermodynamically first-order order → disorder transformations , 1989 .

[144]  P. Haasen,et al.  Nucleation and growth of γ′-Precipitates in Ni-14 at.% Al , 1983 .

[145]  H. Aaronson,et al.  Influence of crystallography upon critical nucleus shapes and kinetics of homogeneous f.c.c.-f.c.c. nucleation—IV. Comparisons between theory and experiment in CuCo alloys , 1984 .

[146]  T. B. Massalski,et al.  The nature and role of incoherent interphase interfaces in diffusional solid-solid phase transformations , 2006 .

[147]  M. Doi,et al.  The effect of elastic interaction energy on the morphology of ?'precipitates in nickel-based alloys , 1984 .

[148]  H. I. Aaronson,et al.  Mechanisms of Diffusional Phase Transformations in Metals and Alloys , 2010 .

[149]  P. Voorhees,et al.  A graphical method for constructing coherent phase diagrams , 1991 .

[150]  M. Stowell Precipitate nucleation: does capillarity theory work? , 2002 .

[151]  W. Shockley,et al.  Order-Disorder Transformations in Alloys , 1938 .

[152]  Robert E. Reed-Hill,et al.  Physical Metallurgy Principles , 1972 .

[153]  D. Laughlin Spinodal decomposition in nickel based nickel-titanium allols , 1976 .

[154]  A. B. Pippard,et al.  The Elements of Classical Thermodynamics , 1958 .

[155]  G. Inden The role of magnetism in the calculation of phase diagrams , 1981 .

[156]  M. Fine,et al.  Precipitation in Ni-11.1 at.% Al and Ni-13.8 at.% Al alloys☆ , 1972 .

[157]  G. Inden The effect of continous transformations on phase diagrams , 1982 .

[158]  John E. Hilliard,et al.  Free Energy of a Nonuniform System. III. Nucleation in a Two‐Component Incompressible Fluid , 1959 .

[159]  M. Avrami Kinetics of Phase Change. I General Theory , 1939 .

[160]  Charles M. Elliott,et al.  Spinodal decomposition in Fe-Cr alloys: Experimental study at the atomic level and comparison with computer models—II. Development of domain size and composition amplitude , 1995 .

[161]  Long-Qing Chen,et al.  Computer simulation of the kinetics of order-disorder and phase separation during precipitation of δ′ (Al3Li) in AlLi alloys , 1997 .