On the electronic basis of the phosphorus intergranular embrittlement of iron
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G. B. Olson Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208-3112 (Received 2 March 1992; accepted 11 May 1992)
Using the all-electron full potential linearized augmented plane wave (FLAPW) total energy method, the influence of P impurity atoms on the cohesion of the Fe X 3 [ l i O ] ( l l l ) grain boundary is studied through direct comparison of phosphorus/iron interactions in the grain boundary and free surface environments. The calculated nearest P-Fe distance in P / F e ( l l l ) is 2.14 A—amounting to a 5% contraction compared to that (2.26 A) measured for the Fe 3 P compound and assumed for the P - F e grain boundary. The polar-covalent P - F e chemical bonding, which is a strong function of the P-Fe interatomic distance, is thus stronger on the F e ( l l l ) surface, while P reduces the spin polarization of the surrounding Fe atoms more efficiently in the grain boundary environment. These effects are examined in terms of the relative segregation energies affecting the work of boundary fracture.
I. INTRODUCTION Intergranular embrittlement of metals resulting from impurity segregation to grain boundaries (GB) is well documented.1'2 Based on a plausible thermodynamic description,3 the fracture mode of solids is determined by the competition between brittle interfacial cleavage separation and crack-tip blunting by dislocation emission. Brittle fracture occurs when the critical crack extension force (strain energy release rate), Gdish is larger than the Griffith work of the interfacial cleavage, yint; if Gdtsi < 2y,-n,, ductility prevails. The precise manner in which chemical segregants might modify Gdisi for dislocation emission still remains unclear today, while the definite role of segregation in determining the Griffith work of interfacial cleavage yint has emerged from applications of surface thermodynamics. Further, arguments have also been developed that yint is not only of crucial importance in governing the transition between brittle and ductile response, but even under conditions of substantial crack-tip plasticity the critical crack extension force for crack propagation can be a monotonic function of yint. Therefore, control of yint appears to be the most direct and effective way to enhance the interfacial fracture resistance. It has been revealed that3'4 for interfacial separation at a fixed boundary solute (impurity) coverage, V, nonlinear entropy contributions can be neglected and we obtain the relation = (2yint)0
- (Ag°b - Ag°s)T
(1)
J. Mater. Res., Vol. 7, No. 9, Sep 1992
http://journals.cambridge.org
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where (2y, nr ) 0 is the work of separation of the clean interface, and Ag° and Ag° are the free energies of segregation of the solute to the boundary and free surface, respectively. Obviously, a solute with greater (more negative) energy difference, Ag° - Ag°, will be a more potent embrittler. Due to their importance in practical applications, iron and iron-base alloys have been extensively studied, providing a relati
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