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Register a new userBasal-plane Incommensurate Phases in HCP Structures
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Authors
I. Lukyanchuk
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An Ising model with competing interaction is used to study the appearance of incommensurate phases in the basal plane of an hexagonal closed-packed structure. The calculated mean-field phase diagram reveals various 1q-incommensurate and lock-in phases. The results are applied to explain the basal-plane incommensurate phase in some compounds of the AABX_4 family, like K_2MoO_4, K_2WO_4, Rb_2WO4 and to describe the sequence of high-temperature phase transitions in other compounds of this family.
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The paper continues a series of papers devoted to treatment of the crystalline state on the basis of the approach in equilibrium statistical mechanics proposed earlier by the author. This paper is concerned with elaboration of a mathematical apparatus in the approach for studying second-order phase transitions, both commensurate and incommensurate, and properties of emerging phases. It is shown that the preliminary symmetry analysis for a concrete crystal can be performed analogously with the one in the Landau theory of phase transitions. After the analysis one is able to deduce a set of equations that describe the emerging phases and corresponding phase transitions. The treatment of an incommensurate phase is substantially complicated because the symmetry of the phase cannot be described in terms of customary space groups. For this reason, a strategy of representing the incommensurate phase as the limit of a sequence of long-period commensurate phases whose period tends to infinity is worked out. The strategy enables one to obviate difficulties due to the devils staircase that occurs in this situation.
Three different special quasirandom structures (SQS) of the substitutional hcp $A_{1-x}B_x$ binary random solutions ($x=0.25$, 0.5, and 0.75) are presented. These structures are able to mimic the most important pair and multi-site correlation functions corresponding to perfectly random hcp solutions at those compositions. Due to the relatively small size of the generated structures, they can be used to calculate the properties of random hcp alloys via first-principles methods. The structures are relaxed in order to find their lowest energy configurations at each composition. In some cases, it was found that full relaxation resulted in complete loss of their parental symmetry as hcp so geometry optimizations in which no local relaxations are allowed were also performed. In general, the first-principles results for the seven binary systems (Cd-Mg, Mg-Zr, Al-Mg, Mo-Ru, Hf-Ti, Hf-Zr, and Ti-Zr) show good agreement with both formation enthalpy and lattice parameters measurements from experiments. It is concluded that the SQSs presented in this work can be widely used to study the behavior of random hcp solutions.
We report the chemical reaction of single-layer graphene with hydrogen atoms, generated in situ by electron-induced dissociation of hydrogen silsesquioxane (HSQ). Hydrogenation, forming sp3 C-H functionality on the basal plane of graphene, proceeds at a higher rate for single than for double layers, demonstrating the enhanced chemical reactivity of single sheet graphene. The net H atom sticking probability on single layers at 300 K is at least 0.03, which exceeds that of double layers by at least a factor of 15. Chemisorbed hydrogen atoms, which give rise to a prominent Raman D band, can be detached by thermal annealing at 100~200 degrees C. The resulting dehydrogenated graphene is activated when photothermally heated it reversibly binds ambient oxygen, leading to hole doping of the graphene. This functionalization of graphene can be exploited to manipulate electronic and charge transport properties of graphene devices.
An incommensurate phase refers to a solid state in which the period of a superstructure is incommensurable with the primitive unit cell. Recently the incommensurate phase is induced by applying an in-plane strain to hexagonal manganites, which demonstrates single chiral modulation of six domain variants. Here we employ Landau theory in combination with the phase-field method to investigate the incommensurate phase in hexagonal manganites. It is shown that the equilibrium wave length of the incommensurate phase is determined by temperature and the magnitude of the applied strain, and a temperature-strain phase diagram is constructed for the stability of the incommensurate phase. Temporal evolution of domain structures reveals that the applied strain not only produces the force pulling the vortices and anti-vortices in opposite directions, but also results in the creation and annihilation of vortex-antivortex pairs.
We establish the qualitative behavior of the incommensurability $epsilon$, optimal domain wall filling $ u$ and chemical potential $mu$ for increasing doping by a systematic slave-boson study of an array of vertical stripes separated by up to $d=11$ lattice constants. Our findings obtained in the Hubbard model with the next-nearest neighbor hopping $t=-0.15t$ agree qualitatively with the experimental data for the cuprates in the doping regime $xlesssim 1/8$. It is found that $t$ modifies the optimal filling $ u$ and triggers the crossover to the diagonal (1,1) spiral phase at increasing doping, stabilized already at $xsimeq 0.09$ for $t=-0.3t$.
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