When a crystal is subjected to a periodic potential, under certain circumstances (such as when the period of the potential is close to the crystal periodicity; the potential is strong enough, etc.) it might adjust itself to follow the periodicity of the potential, resulting in a, so called, commensurate state 1-3 .Such commensurate-incommensurate transitions are ubiquitous phenomena in many areas of condensed matter physics: from magnetism and dislocations in crystals, to vortices in superconductors, and atomic layers adsorbed on a crystalline surface 1 . Of particular interest might be the properties of topological defects between the two commensurate phases: solitons 2,4 , domain walls 1 , and dislocation walls 5-7 . Here we report a commensurate-incommensurate transition for graphene on top of hexagonal boron nitride (hBN) 8,9 . Depending on the rotational angle between the two hexagonal lattices, graphene can either stretch to adjust to a slightly different hBN periodicity (the commensurate state found for small rotational angles) or exhibit little adjustment (the incommensurate state). In the commensurate state, areas with matching lattice constants are separated by domain walls that accumulate the resulting strain. Such soliton-like objects present significant fundamental interest 1 , and their presence might explain recent observations when the electronic, optical, Raman and other properties of graphene-hBN heterostructures have been notably altered 10 .

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Local perturbations of the crystal and magnetic structure of gamma-iron near carbon interstitial impurity is investigated by ab initio electronic structure calculations. It is shown that the carbon impurity creates locally a region of ferromagnetic ordering with substantial tetragonal distortions. Exchange integrals and solution enthalpy are calculated, the latter being in very good agreement with experimental data. The effect of the local distortions on the carbon-carbon interactions in gamma-iron is discussed.

Energetics of the fcc (γ) -bcc (α) lattice transformation by the Bain tetragonal deformation is calculated for both magnetically ordered and paramagnetic (disordered local moment) states of iron. The first-principle computational results manifest a relevance of the magnetic order in a scenario of the γ -α transition and reveal a special role of the Curie temperature of α-Fe, TC , where a character of the transformation is changed. At a cooling down to the temperatures T < TC one can expect that the transformation is developed as a lattice instability whereas for T > TC it follows a standard mechanism of creation and growth of an embryo of the new phase. It explains a closeness of TC to the temperature of start of the martensitic transformation, Ms.PACS numbers: 61.50. Ks, 64.70.kd, 75.30.Et, 75.50.Bb, 71.20.Be Deeper understanding of mechanisms of polymorphous γ -α transformation in iron and its alloys is of fundamental importance for both metallurgical technologies [1,2] and for a general theory of phase transitions in solids [3,4,5]. Despite numerous investigations an issue of a mechanism of a new phase nucleation in the course of γ -α transformation remains open (see, e.g., discussion in Ref. 4).

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Grain boundaries with dangling bonds (DBGB) in graphene are studied by atomistic Monte Carlo and molecular dynamics simulations in combination with density functional (SIESTA) calculations. The most stable configurations are selected and their structure is analyzed in terms of grain boundary dislocations. It is shown that the grain boundary dislocation with the core consisting of pentagon, octagon and heptagon (5-8-7 defect) is a typical structural element of DBGB with relatively low energies. Electron energy spectrum and magnetic properties of the obtained DBGB are studied by density functional calculations. It is shown that the 5-8-7 defect is magnetic and that its magnetic moment survives after hydrogenation. The effects of hydrogenation and of out of plane deformations on the magnetic properties of DBGB are studied.Comment: 10 pages, 11 figures, 4 tables, the final version accepted in pr

We present a general scheme for analyzing the structure and mobility of dislocations based on solutions of the Peierls-Nabarro model with a two component displacement field and restoring forces determined from the ab-initio generalized stacking fault energetics (ie., the so-called γ-surface). The approach is used to investigate dislocations in L10 TiAl and CuAu; predicted differences in the unit dislocation properties are explicitly related with features of the γ-surface geometry. A unified description of compact, spread and split dislocation cores is provided with an important characteristic "dissociation path" revealed by this highly tractable scheme. 61.72.Lk, 61.72.Bb, 61.72.Nn, 61.82.Bg, 62.20.Fe

Diversity of mesostructures formed in steel at cooling from high temperature austenite (γ) phase is determined by interplay of shear reconstructions of crystal lattice and diffusion of carbon. Combining first-principle calculations with large-scale phase-field simulations we demonstrate a decisive role of magnetic degrees of freedom in the formation of energy relief along the Bain path of γ-α transformation and, thus, in this interplay. We show that there is the main factor, namely, magnetic state of iron and its evolution with temperature which controls the change in character of the transformation. Based on the computational results we propose a simple model which reproduces, in a good agreement with experiment, the most important curves of the phase transformation in Fe-C, namely, the lines relevant to a start of ferrite, bainite, and martensite transformations. Phase field simulations within the model describe qualitatively typical patterns at these transformations.