Theoretical study of interface structure and energetics in semicoherentFe(001)/MX(001)systems (

Dan Fors

¹

,

Göran Wahnström

²

Abstract

We perform a systematic ab initio study of the electronic and atomic structure of semicoherent interfaces between bcc Fe and NaCl MX ͑M = Sc, Ti, V, Cr, Zr, Nb, Hf, Ta; X = C or N͒. The interface energetics is accessed by using a Peierls-Nabarro framework, in which ab initio data for the chemical interactions across the interface are combined with a continuum description to account for the elastic distortions. The key factors to the trends in the interface energy are identified and discussed with respect to the size of the misfit and the electronic structure of the MX phase. Our approach shows that the inclusion of lattice misfit can have a significant contribution to the interface energy ͑up to 1.5 J / m 2 ͒ and must therefore be thoroughly accounted for in the interface description. The results will have important bearings on our ability to understand and describe precipitate stability in steels.

Strengthening Mechanisms in Thermomechanically Processed NbTi-Microalloyed Steel

“…where M = 3 is the matrix orientation factor, b = 0.286 nm is Burgers vector, c is the matrix-particle interface energy assumed for the Fe-NbC interface to be c = 1 Jm À2 , [44] and f is the particle volume fraction. The variation in precipitation strengthening (Table III) followed the trend for particle volume fraction in the corresponding particle size ranges (Table I): for >20 nm particles, the maximum precipitation strengthening contribution was observed for the 1248 K (975°C) temperature schedule; and for <20 nm particles, the contribution decreased with a decrease in the finish deformation temperature.…”

“…For the measured particle volume fractions (Table I) and the unit cell sizes a Ti3Nb1C2N2 = 0.64 nm (on average from [42] ), a NbC = 0.44 nm, [43][44][45] and a bccFe = 0.286 nm, the C contents in all particles were calculated to be 0.063 at. pct (0.014 wt pct), 0.068 at.…”

“…Assuming stoichiometric 50/50 pct concentration of Nb and C atoms in the <20 nm NbC particles with fcc crystal structure, [43][44][45] the <20 nm particle volume fraction can be related to the Nb and C atomic fractions in these particles in the following way:…”

Transition of the Interface between Iron and Carbide Precipitate From Coherent to Semi-Coherent

“…Johansson et al developed a method for determining the interface energy using a few points of γ surface [18][19][20]. They showed that the strain energy should be relieved by forming a semi-coherent precipitate for thicker precipitates, since the elastic energy caused by the coherent strain increases with the thickness of the precipitate.…”

“…Many first-principles calculations have been performed for the interfaces between body-centered cubic (bcc) iron and carbide or nitride precipitates with an NaCl-type structure [10][11][12][13][14][15][16][17][18][19][20], and the bonding nature between these interfaces has been discussed in the literature. Hartford investigated the chemical bond across the interface and interface energies for the coherent interface between VN and bcc iron [10].…”