The effect of Ag, Pb and Bi impurities on grain boundary sliding and intergranular decohesion in Copper

We investigate the changes in grain boundary sliding (GBS) and intergranular decohesion in copper (Cu), due to the inclusion of bismuth (Bi), lead (Pb) and silver (Ag) substitutional impurity atoms at a symmetric tilt grain boundary (GB), using a first-principles concurrent multiscale approach. We first study the segregation behavior of the impurities by determining the impurity segregation energy in the vicinity of the GB. We find that the energetically preferred sites are on the GB plane. We investigate the intergranular decohesion of Cu by Bi and Pb impurities and compare this to the effect of Ag impurities by considering the work of separation, and the tensile strength, . Both and decrease in the presence of Bi and Pb impurities, indicating their great propensity for intergranular embrittlement, whilst the presence of Ag impurities has only a small effect. We consider GBS to assess the mechanical properties in nanocrystalline metals and find that all three impurities strongly inhibit GBS, with Ag having the biggest effect. This suggests that Ag has a strong effect on the mechanical properties of nanocrystalline Cu, even though its effect on the intergranular decohesion properties of coarse-grained Cu is not significant.

[1]  P. Blöchl,et al.  Electrostatic decoupling of periodic images of plane‐wave‐expanded densities and derived atomic point charges , 1995 .

[2]  E. Carter,et al.  First principles local pseudopotential for silver: towards orbital-free density-functional theory for transition metals. , 2005, The Journal of chemical physics.

[3]  E Weinan,et al.  Multiscale simulations in simple metals: A density-functional-based methodology , 2004, cond-mat/0404414.

[4]  Lu,et al.  Superplastic extensibility of nanocrystalline copper at room temperature , 2000, Science.

[5]  E. Kaxiras,et al.  Sulfur-induced embrittlement of nickel: a first-principles study , 2012 .

[6]  M. Tschopp,et al.  Quantifying the energetics and length scales of carbon segregation to α-Fe symmetric tilt grain boundaries using atomistic simulations , 2012, 1206.5385.

[7]  Matthias Krack,et al.  Pseudopotentials for H to Kr optimized for gradient-corrected exchange-correlation functionals , 2005 .

[8]  M. Tschopp,et al.  Atomistic Investigation of the Role of Grain Boundary Structure on Hydrogen Segregation and Embrittlement in α-Fe , 2013, Metallurgical and Materials Transactions A.

[9]  James R. Rice,et al.  Dislocation Nucleation from a Crack Tip" an Analysis Based on the Peierls Concept , 1991 .

[10]  James R. Rice,et al.  Ductile versus brittle behaviour of crystals , 1974 .

[11]  Robert J. Asaro,et al.  Toward a quantitative understanding of mechanical behavior of nanocrystalline metals , 2007 .

[12]  Michele Parrinello,et al.  Quickstep: Fast and accurate density functional calculations using a mixed Gaussian and plane waves approach , 2005, Comput. Phys. Commun..

[13]  P. Gumbsch,et al.  Accommodation processes during deformation of nanocrystalline palladium , 2010 .

[14]  Michael W. Finnis,et al.  Bismuth embrittlement of copper is an atomic size effect , 2004, Nature.

[15]  G. Lu,et al.  Quantum mechanics/molecular mechanics methodology for metals based on orbital-free density functional theory , 2007 .

[16]  J. Nocedal Updating Quasi-Newton Matrices With Limited Storage , 1980 .

[17]  J. Rice,et al.  Dislocation emission from cracks in crystals or along crystal interfaces , 1986 .

[18]  Emily A. Carter,et al.  Toward an orbital-free density functional theory of transition metals based on an electron density decomposition , 2012 .

[19]  Y. Ivanisenko,et al.  First Direct In Situ Observation of Grain Boundary Sliding in Ultrafine Grained Noble Metal , 2014 .

[20]  A. Paxton,et al.  Boron in copper: A perfect misfit in the bulk and cohesion enhancer at a grain boundary , 2007, 0711.1629.

[21]  G. Duscher,et al.  Bismuth-induced embrittlement of copper grain boundaries , 2004, Nature materials.

[22]  David L. McDowell,et al.  Tensile strength of 〈1 0 0〉 and 〈1 1 0〉 tilt bicrystal copper interfaces , 2007 .

[23]  Prosper Matković,et al.  Physical Metallurgy I , 2009 .

[24]  E. Kaxiras,et al.  Modeling Brittle and Ductile Behavior of Solids from First-Principles Calculations , 2000 .

[25]  Grain Boundary Segregation of Interstitial and Substitutional Impurity Atoms in Alpha-Iron , 2013, 1310.3413.

[26]  K. Jacobsen,et al.  A Maximum in the Strength of Nanocrystalline Copper , 2003, Science.

[27]  Arthur F. Voter,et al.  Structural stability and lattice defects in copper: Ab initio , tight-binding, and embedded-atom calculations , 2001 .

[28]  Xin Sun,et al.  Probing grain boundary sink strength at the nanoscale: Energetics and length scales of vacancy and interstitial absorption by grain boundaries in α -Fe , 2012 .

[29]  J. E. Glynn,et al.  Numerical Recipes: The Art of Scientific Computing , 1989 .

[30]  U. Waghmare,et al.  Effect of dopants on grain boundary decohesion of Ni: A first-principles study , 2008 .

[31]  M. Halliday,et al.  Some observations of grain-boundary sliding in aluminium bicrystals tested at constant strain rate and constant rate of stress increase , 1971 .

[32]  John C. Slater,et al.  Atomic Radii in Crystals , 1964 .

[33]  E. D. Hondros,et al.  Grain boundary segregation , 1973, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[34]  B. Kieback,et al.  Elemental distribution, solute solubility and defect free volume in nanocrystalline restricted-equilibrium Cu–Ag alloys , 2013, Journal of physics. Condensed matter : an Institute of Physics journal.

[35]  R. Averback,et al.  Quantitative description of plastic deformation in nanocrystalline Cu: Dislocation glide versus grain boundary sliding , 2008 .

[36]  Foiles,et al.  Embedded-atom-method functions for the fcc metals Cu, Ag, Au, Ni, Pd, Pt, and their alloys. , 1986, Physical review. B, Condensed matter.

[37]  H. Müllejans,et al.  Bismuth segregation at copper grain boundaries , 1999 .

[38]  Subra Suresh,et al.  Mechanical behavior of nanocrystalline metals and alloys , 2003 .

[39]  Teter,et al.  Separable dual-space Gaussian pseudopotentials. , 1996, Physical review. B, Condensed matter.

[40]  A. Bower,et al.  The Effect of Solute Atoms on Aluminum Grain Boundary Sliding at Elevated Temperature , 2011 .

[41]  Joost VandeVondele,et al.  Gaussian basis sets for accurate calculations on molecular systems in gas and condensed phases. , 2007, The Journal of chemical physics.

[42]  L. Szász,et al.  Density-Functional Formalism , 1975 .

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

[44]  J. Degmová,et al.  Grain boundary sliding and migration in copper: Vacancy effect , 2005 .

[45]  S. Whang,et al.  Effect of interstitials on tensile strength and creep in nanostructured Ni , 2005 .

[46]  Chen Huang,et al.  Orbital-free density functional theory simulations of dislocations in aluminum , 2009 .

[47]  H. V. Swygenhoven,et al.  Intergranular fracture in nanocrystalline metals , 2002 .

[48]  F. Flores,et al.  Interfaces in crystalline materials , 1994, Thin Film Physics and Applications.

[49]  D. Farkas,et al.  Non-planar grain boundary structures in fcc metals and their role in nano-scale deformation mechanisms , 2014 .

[50]  Stefan Goedecker,et al.  Efficient solution of Poisson's equation with free boundary conditions. , 2006, The Journal of chemical physics.

[51]  A. Dick Beiträge zur Metallurgie des Kupfers , 1856 .

[52]  R. O. Jones,et al.  The density functional formalism, its applications and prospects , 1989 .

[53]  F. Nabarro The physics of creep , 1995 .

[54]  G. Lu,et al.  Effect of vacancy on the sliding of an iron grain boundary , 2011 .

[55]  James R. Rice,et al.  Embrittlement of interfaces by solute segregation , 1989 .

[56]  R. Selvam,et al.  Atomistic simulation of grain boundary energetics – Effects of dopants , 2005 .

[57]  E. Hall,et al.  The Deformation and Ageing of Mild Steel: III Discussion of Results , 1951 .

[58]  Hideo Kaburaki,et al.  Grain Boundary Decohesion by Impurity Segregation in a Nickel-Sulfur System , 2005, Science.

[59]  M. Seah Segregation and the strength of grain boundaries , 1976, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[60]  K. Jacobsen,et al.  Atomic-scale simulations of the mechanical deformation of nanocrystalline metals , 1998, cond-mat/9812102.

[61]  A. Bower,et al.  Aluminum Σ3 grain boundary sliding enhanced by vacancy diffusion , 2010 .

[62]  N. Petch,et al.  The Cleavage Strength of Polycrystals , 1953 .

[63]  M. Tschopp,et al.  Atomic-scale analysis of liquid-gallium embrittlement of aluminum grain boundaries , 2013, 1312.2160.

[64]  Peter M. Derlet,et al.  Grain-boundary sliding in nanocrystalline fcc metals , 2001 .

[65]  W. P. Green,et al.  Deformation and failure of a superplastic AA5083 aluminum material with a cu addition , 2006 .

[66]  E. Kaxiras,et al.  Effects of alloying on the ductility of MoSi2 single crystals from first-principles calculations , 1998 .

[67]  Stefan Goedecker,et al.  Efficient and accurate three-dimensional Poisson solver for surface problems. , 2007, The Journal of chemical physics.

[68]  K. Jacobsen,et al.  Softening of nanocrystalline metals at very small grain sizes , 1998, Nature.

[69]  Michele Parrinello,et al.  A hybrid Gaussian and plane wave density functional scheme , 1997 .

[70]  H. Grabke Segregation at Interfaces , 1987 .

[71]  Structural and chemical embrittlement of grain boundaries by impurities: A general theory and first-principles calculations for copper , 2006, cond-mat/0608508.

[72]  Efthimios Kaxiras,et al.  Kinetic energy density functionals for non-periodic systems , 2002 .

[73]  Jorge Nocedal,et al.  On the limited memory BFGS method for large scale optimization , 1989, Math. Program..

[74]  F. Weinberg Grain boundary shear in aluminum , 1954 .

[75]  V. Heine,et al.  Sliding mechanisms in aluminum grain boundaries , 1997 .

[76]  John R. Rice,et al.  Ductile vs brittle behavior of crystals , 1973 .