Structure, energetics, and mechanical stability of Fe-Cu bcc alloys from first-principles calculations

Atomic volumes, magnetic moments, mixing energies, and the elastic properties of bcc Fe1–xCux solid solutions are studied by ab initio calculations based on the cluster expansion framework. For the calculation of concentration-dependent elastic moduli in disordered solid solutions, we introduce a generalization of the cluster expansion technique that is designed to handle tensorial quantities in high-symmetry phases. Calculated mixing energies, atomic volumes, and magnetic moments are found to be in good agreement with available measurements for metastable alloys prepared through nonequilibrium processing techniques. Additionally, the predicted variations of the bulk modulus and shear moduli C44 and C[prime] with respect to copper concentration are calculated for the disordered bcc phase. While the bulk modulus and C44 are positive for all concentrations, C[prime] is predicted to be positive only for Cu concentration less than 50 atomic %, and negative otherwise. Our results thus indicate that the mechanical instability of bcc Cu persists over a wide range of compositions. The implications of the present results are discussed in relation to the observed metastability of bcc Fe-Cu alloys, and the strengthening mechanism of nanoscale bcc precipitates in an alpha-Fe matrix.

[1]  D. Bacon,et al.  Computer simulation of the core structure of the screw dislocation in α-iron containing copper precipitates: I. structure in the matrix and a precipitate , 2002 .

[2]  D. Fontaine.  Cluster Approach to Order-Disorder Transformations in Alloys , 1994 .

[3]  J. S. Perrin,et al.  Effects of radiation on materials , 1981 .

[4]  E. Wigner.  On the Interaction of Electrons in Metals , 1934 .

[5]  G. Speich,et al.  Elastic constants of binary iron-base alloys , 1972 .

[6]  Paxton,et al.  High-precision sampling for Brillouin-zone integration in metals. , 1989, Physical review. B, Condensed matter.

[7]  D. Seidman,et al.  Nanoscale studies of segregation at coherent heterophase interfaces in α‐Fe based systems , 2004 .

[8]  M. G. Hetherington,et al.  A study of the precipitation of copper particles in a ferrite matrix , 1987 .

[9]  Matthias Militzer,et al.  Precipitation Kinetics and Strengthening of a Fe-0.8wt%Cu Alloy , 2001 .

[10]  Wang,et al.  Accurate and simple analytic representation of the electron-gas correlation energy. , 1992, Physical review. B, Condensed matter.

[11]  A. Reuss,et al.  Berechnung der Fließgrenze von Mischkristallen auf Grund der Plastizitätsbedingung für Einkristalle . , 1929 .

[12]  A. van de Walle,et al.  Automating First-Principles Phase Diagram Calculations , 2002 .

[13]  W. Johnson,et al.  Mechanically driven alloying and grain size changes in nanocrystalline Fe-Cu powders , 1993 .

[14]  L. Brown,et al.  A dispersion strengthening model based on differing elastic moduli applied to the iron-copper system , 1972 .

[15]  Tian,et al.  Low-energy electron diffraction and photoemission study of epitaxial films of Cu on Ag{001} , 1991, Physical review. B, Condensed matter.

[16]  Graeme Ackland,et al.  Computer simulation of point defect properties in dilute Fe—Cu alloy using a many-body interatomic potential , 1997 .

[17]  J. Connolly,et al.  Density-functional theory applied to phase transformations in transition-metal alloys , 1983 .

[18]  B. Segall,et al.  Application of generalized gradient-corrected density functionals to iron. , 1992, Physical review. B, Condensed matter.

[19]  Cohen,et al.  Iron at high pressure: Linearized-augmented-plane-wave computations in the generalized-gradient approximation. , 1994, Physical review. B, Condensed matter.

[20]  G. Kresse,et al.  From ultrasoft pseudopotentials to the projector augmented-wave method , 1999 .

[21]  E. M. Lopasso,et al.  Phase diagram of an empirical potential: The case of Fe-Cu , 2003 .

[22]  S. R. Goodman,et al.  An FIM-atom probe study of the precipitation of copper from lron-1.4 at. pct copper. Part I: Field-ion microscopy , 1973 .

[23]  M. Gillan,et al.  First principles calculations on crystalline and liquid iron at Earth's core conditions , 1997 .

[24]  Blöchl,et al.  Projector augmented-wave method. , 1994, Physical review. B, Condensed matter.

[25]  Jackson,et al.  Atoms, molecules, solids, and surfaces: Applications of the generalized gradient approximation for exchange and correlation. , 1992, Physical review. B, Condensed matter.

[26]  H. Monkhorst,et al.  SPECIAL POINTS FOR BRILLOUIN-ZONE INTEGRATIONS , 1976 .

[27]  W. Voigt,et al.  Lehrbuch der Kristallphysik , 1966 .

[28]  W. Hergert,et al.  TOTAL ENERGY AND MAGNETIC MOMENTS IN DISORDERED FEXCU1-X ALLOYS , 1998 .

[29]  R. E. Watson,et al.  Structural instabilities of excited phases , 1997 .

[30]  S. R. Goodman,et al.  An FIM-atom probe study of the precipitation of copper from lron-1.4 at. pct copper. Part II: Atom probe analyses , 1973 .

[31]  S. H. Vosko,et al.  Accurate spin-dependent electron liquid correlation energies for local spin density calculations: a critical analysis , 1980 .

[32]  E. Kneller.  Magnetic and Structural Properties of Metastable Fe‐Cu Solid Solutions , 1964 .

[33]  P. Pareige,et al.  Synthesis of atom probe experiments on irradiation-induced solute segregation in French ferritic pressure vessel steels , 2000 .

[34]  Y. Kawazoe,et al.  Ab initio studies on the structural and magnetic properties of FeCu superlattices , 1999 .

[35]  W. Johnson,et al.  Thermal stability and grain growth behavior of mechanically alloyed nanocrystalline Fe-Cu alloys , 1993 .

[36]  S. Louie,et al.  Ab initio study of iron and iron hydride: I. Cohesion, magnetism and electronic structure of cubic Fe and FeH , 1998 .

[37]  L. Wang,et al.  Structural stability of higher-energy phases and its relation to the atomic configurations of extended defects: The example of Cu , 1999 .

[38]  P. J. Craievich,et al.  Vibrational free energy in the Ni-Cr system , 1997 .

[39]  J. H. He,et al.  Overlapping solid solubility in mechanically alloyed Fe-Ni and Fe-Cu , 2003 .

[40]  F. Ducastelle,et al.  Generalized cluster description of multicomponent systems , 1984 .

[41]  Li,et al.  Epitaxial growth of a metastable modification of copper with body-centered-cubic structure. , 1987, Physical review. B, Condensed matter.

[42]  P. Marcus,et al.  Pressure instability of bcc iron , 2002 .

[43]  C. Domain,et al.  Ab initio calculations of defects in Fe and dilute Fe-Cu alloys , 2001 .

[44]  Burke,et al.  Generalized Gradient Approximation Made Simple. , 1996, Physical review letters.

[45]  Marcus,et al.  Elastic constants of Cu and the instability of its bcc structure. , 1993, Physical review. B, Condensed matter.

[46]  G. Ackland,et al.  Simple N-body potentials for the noble metals and nickel , 1987 .

[47]  B. Fultz,et al.  Two-phase coexistence in Fe–Cu alloys synthesized by ball milling , 1998 .

[48]  E. Kröner.  Berechnung der elastischen Konstanten des Vielkristalls aus den Konstanten des Einkristalls , 1958 .

[49]  T. Yoshitake,et al.  Magnetic Properties of Metastable bcc and fcc Fe-Cu Alloys Produced by Vapor Quenching , 1984 .

[50]  J. H. He,et al.  Two-phase coexistence region in mechanically alloyed Cu-Fe: An X-ray absorption near-edge structure study , 1999 .

[51]  Ab initio pseudopotential study of Fe, Co, and Ni employing the spin-polarized LAPW approach. , 1995, Physical review. B, Condensed matter.

[52]  A. Sutton,et al.  The bcc-to-9R martensitic transformation of Cu precipitates and the relaxation process of elastic strains in an Fe-Cu alloy , 2000 .

[53]  G. Kresse,et al.  Ab initio molecular dynamics for liquid metals. , 1993 .

[54]  B. Wirth,et al.  Composition and magnetic character of nanometre-size Cu precipitates in reactor pressure vessel steels: Implications for nuclear power plant lifetime extension , 2002 .

[55]  A. Yavari,et al.  Mechanically driven alloying of immiscible elements. , 1992, Physical review letters.

[56]  R. Hoffmann,et al.  Bcc and Fcc transition metals and alloys: a central role for the Jahn-Teller effect in explaining their ideal and distorted structures. , 2002, Journal of the American Chemical Society.

[57]  Georg Kresse,et al.  Norm-conserving and ultrasoft pseudopotentials for first-row and transition elements , 1994 .

[58]  D. Bacon,et al.  Hardening due to copper precipitates in α-iron studied by atomic-scale modelling , 2004 .

[59]  J. Rayne,et al.  Elastic Constants of Iron from 4.2 to 300°K , 1961 .

[60]  Siegfried Schmauder,et al.  Comput. Mater. Sci. , 1998 .

[61]  Watson,et al.  Local stability of nonequilibrium phases. , 1994, Physical review letters.

[62]  D. Bacon,et al.  Computer simulation of the core structure of the screw dislocation in α-iron containing copper precipitates: II. dislocation–precipitate interaction and the strengthening effect , 2002 .

[63]  G. Smith,et al.  High-resolution electron microscopy studies of the structure of Cu precipitates in α-Fe , 1994 .

[64]  R. Hill.  The Elastic Behaviour of a Crystalline Aggregate , 1952 .

[65]  W. C. Overton,et al.  Temperature Variation of the Elastic Constants of Cubic Elements. I. Copper , 1955 .

[66]  S. Esterby.  American Society for Testing and Materials , 2006 .

[67]  G. Smith,et al.  Transmission electron microscope investigations of the structure of copper precipitates in thermally-aged Fe—Cu and Fe—Cu—Ni , 1991 .

[68]  W. Johnson,et al.  Incipient chemical instabilities of nanophase Fe-Cu alloys prepared by mechanical alloying , 1996 .

[69]  Börje Johansson,et al.  Ab initio calculation of the elastic properties of Al1-xLix (x≤0.20) random alloys , 2005 .

[70]  E. Ma,et al.  Magnetic moment and atomic volume in supersaturated Fe–Cu solid solutions: Ab initiocalculations compared with experiments , 2000 .

[71]  Yi Wang,et al.  Ab initio lattice stability in comparison with CALPHAD lattice stability , 2004 .

[72]  G. Grimvall,et al.  Dynamical and thermodynamical instabilities in the disordered Re x W 1 − x system , 1999 .

[73]  D. Isheim,et al.  Origin of copper precipitation strengthening in steel revisited , 2005 .

[74]  B. Alder,et al.  THE GROUND STATE OF THE ELECTRON GAS BY A STOCHASTIC METHOD , 2010 .

[75]  E. Ma,et al.  Thermodynamic and magnetic properties of metastable FexCu100−x solid solutions formed by mechanical alloying , 1993 .

[76]  Faraday Discuss , 1985 .

[77]  Kojiro F. Kobayashi,et al.  Mechanical Alloying in the Fe-Cu System , 1992 .

[78]  Zhenyu Zhang,et al.  Instability of higher-energy phases in simple and transition metals , 2003 .