Long- and short-range structural order during thermal annealing of long-period Au4Zn alloys

We have used x-ray analysis to study the disordering and decomposition processes in Au₄Zn alloys which exhibit a long-period Ll₂(MM) superstructure at low temperatures. Several stages are observed during isothermal anneals of the alloy above T_c: I) disordering; II) an incubation period; and III) decomposition. The duration of each of these stages depends on the annealing temperature. It is shown that the disordering of the Ll₂(MM) superstructure always precedes the decomposition process, but the short-range order in the disordered solid solution resembles that of the Ll₂(MM) long-range order. State University of Architecture and Construction, Tomsk. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 56–62, August, 1997.     

Long-period incommensurate superstructures in Cu-Au alloys: Relation with short-period ordering

The nature of the stability of incommensurate long-period structures in alloys of the system Cu-Au is investigated on the basis of first-principles calculations of the electronic structure. It is shown that many structural properties of such formations can be explained only if the latter are treated as superstructures with respect to ordinary superstructures (L1₂ or L1₀): the electron spectrum of the superstructure and not that of the initial disordered alloy must serve as the initial spectrum. The observed dependence of the long period N on the degree η ?of the “short” long-range order is explained. The reasons why two-dimensional long-period superstructures from in the alloy Au₃Cu are found. Arguments supporting the fact that among quasicrystalline substances long-period superstructures fall between incommensurate systems and quasicrystals are presented.     

Relaxation processes in the incommensurate phase of a crystal with defects

The nature of the relaxation of the incommensurate superstructure of a ferroelectric to the equilibrium state is investigated experimentally. It is shown that near a phase transition the temperature dependence of the relaxation time of the incommensurate phase of the defective crystal is exponential. This law agrees qualitatively with the notion of domain wall motion in an inhomogeneous medium containing “random local phase-transition temperature” type defects. Fiz. Tverd. Tela (St. Petersburg) 41, 513–515 (March 1999)     

On the satellite extinction in incommensurate phase

For ZnP₂ and CdP₂ crystals in incommensurate phase selective superstructure X-ray reflections are observed. As shown a phason and amplitudon excitation modes do not result in this selective extinction of satellites. Apparently, it is associated with a modulation wave form in the incommensurate phase. The X-ray spectrum peculiarity of incommensurate crystals is discussed taking into consideration systematic and selective extinction of satellites.     

Fluctuation-induced broadening of Mn2+ EPR lines in the incommensurate phase of Rb2ZnCl4 crystals

The EPR spectra of Mn²⁺ ions in Rb₂ZnCl₄ crystals is investigated in the vicinity of the transition from the paraelectric phase to an incommensurate modulated phase. When these crystals are cooled below the transition temperature T _i =304 K, a splitting of the resonance lines is observed in the singular spectrum. A one-harmonic model is used to discuss the contributions that fluctuations in the amplitude and phase of the incommensurate displacement wave make to the local width of the singular spectra. It is shown that anomalies in the local width of the low-temperature singular peaks observed in the vicinity of T _i are caused by amplitude fluctuations. Fiz. Tverd. Tela (St. Petersburg) 41, 1668–1674 (September 1999)     

Evolution of charge ordering in manganites

Charge ordering phenomena in the manganites Ca_1-xSm_xMnO₃ have been studied for , using electron diffraction and lattice imaging, completed by magnetic and transport measurements. Three domains can be distinguished, depending on the nature of the structural transitions with temperature. For , the structural transition from a pseudo-tetragonal to a monoclinic form, with decreasing temperature, coincides with the competition between ferromagnetism and antiferromagnetism that is characterized by the temperature T_peak on the M ( T ) curves; short-range charge ordering is observed for manganites. For the second domain, , a structural transition from an orthorhombic to a long-range charge ordered state is clearly observed with decreasing temperature. The corresponding temperature T_CO coincides with the temperature T_peak deduced from magnetic measurements. This long range charge ordering, which appears along a, is either commensurate or incommensurate depending on the x value, with a modulation vector, q being close to x. These modulated superstructures correspond to a stacking of single Mn³⁺ stripes with multiple Mn⁴⁺ stripes along a, either in a commensurate or in an incommensurate manner. The third domain , is characterized by a transition to a charge ordered state with commensurate superstructure at low temperature. The latter can be described as a “partially” charge ordered state in which single “Mn³⁺” stripes alternate with mixed “Mn³⁺/Mn⁴⁺” stripes. Received 17 June 1998     

Long- and short-range order in the Pd<Subscript>6</Subscript>B monoclinic superstructure and M<Subscript>6</Subscript>X<Subscript>5</Subscript> and M<Subscript>6</Subscript>X allied superstructures

Symmetry analysis of the Pd₆B monoclinic superstructure (space group C2/c) formed in the cubic (with the B1 structure) solid solution of boron in palladium (PdB _y ) has been carried out. The formation of this superstructure proceeds as a first-order phase transition via the disorder-order channel including nine nonequivalent superstructure vectors of four stars {k ₁₀}, {k ₄}, {k ₃}, and {k ₀}. For the Pd₆B monoclinic super-structure (space group C2/c), the distribution function for boron atoms is calculated and the interval of admissible values of the long-range order parameters is defined. It is shown that the transition channel determined in this way coincides with the channel in which the M₆X monoclinic superstructure (space group C2) is formed; therefore, the Pd₆B superstructure can also be described in space group C2 to the same degree of accuracy. The higher symmetry of the monoclinic model (space group C2/c) suggests that it describes the structure of the Pd₆B phase (Pd₆B□₅), as well as of mutually inverse phases M₆X□₅ and M₆X₅□, more adequately than the model with space group C2. It is shown that superstructures of the M₆X□₅ type (space groups C2/c, C2, C2/m, and P3₁) and inverse superstructures of the M₆X₅□ type with the same space groups have the positions of the nearest surrounding of metal atoms by two types of nonmetallic sublattice sites located in the first and second coordination spheres.     

Model of periodic superstructure formation induced by mobile defects on a semiconductor surface

A model for forming a periodic superstructure on a semiconductor surface with mobile defects is proposed. It is shown that a self-organized system of such defects could lead to considerable modulation of incommensurate phase parameters in near-surface layers under the conditions of defect interaction with an incommensurate displacement wave. This type of defect system could induce a substantial energy decrease for the incommensurate phase and its additional stabilization on the one hand, and an increase in modulation amplitude that might be accompanied by a soliton-like nonsinusoidal incommensurate displacement wave on the other. The model allows us to explain the experimental results regarding the periodic superstructure discovered by G.V. Benemanskaya et al. on the surface of a GaN semiconductor. In particular, the model enables us to explain the nature of such superstructures based on the self-organization of mobile neutral triad-type defects, composed of negatively charged (3−) vacancies of the host lattice centers of Ga³⁺ and surface impurity ions of Cs⁺ and Ba²⁺, under conditions of triad interaction with an incommensurate displacement wave.     

Optical transmission coefficient of crystalline [N(CH<Subscript>3</Subscript>)<Subscript>4</Subscript>]<Subscript>2</Subscript>MeCl<Subscript>4</Subscript> in the incommensurate phase

This a study of the optical transmission of [N(CH₃)₄]₂ZnCl₄ and [N(CH₃)₄]₂CuCl₄ crystals in the incommensurate phase when a defect density wave is present. It is found that an anomalous reduction in the transmission coefficient is caused by scattering of light owing to a realignment of the superstructure during transitions between metastable states. When a defect density wave is present, the anomalous optical transmission of the crystal is related to the scattering of light on superstructure inhomogeneities produced by a superposition of existing modulation waves.     

Anomalous states of the structure of (NH4)2SO4 crystals in the temperature range 4.2–300 K

Crystals of the (NH₄)₂SO₄ ammonium sulfate are studied using x-ray diffractometry. It is revealed that the temperature dependence of the lattice parameters exhibits an anomalous behavior, namely, a global hysteresis, and an anomalous increase in the lattice parameter a and the unit cell volume at temperatures below the ferroelectric phase transition point (T _c=223 K). The series of superstructure reflections observed corresponds to an incommensurate composite structure. Analysis of the temperature behavior of the mismatch parameters for the matrix (host) and superstructure (guest) lattices demonstrates that the (NH₄)₂SO₄ compound undergoes a number of phase transitions, including a transition to a three-dimensionally incommensurate composite phase and transitions to commensurate (along one of the crystallographic directions) composite phases.     

Study of Mn2+ EPR spectra in the incommensurate phase of Rb2ZnCl4

An EPR study of Mn²⁺ centers in the incommensurate phase of rubidium tetrachlorozincate crystals is reported. It is shown that the temperature dependence of the high-field hyperfine line group M _S=3/2↔5/2 can be described in terms of a simple “local” model. The data obtained support the nonclassical type of critical behavior in Rb₂ZnCl₄ crystals corresponding to the three-dimensional Heisenberg model for a two-component order parameter. Fiz. Tverd. Tela (St. Petersburg) 41, 691–694 (April 1999)     

Monoclinic superstructure V<Subscript>14</Subscript>O<Subscript>6</Subscript> of the tetragonal solid solution of oxygen in vanadium

The monoclinic (space group C2/m) superstructure of V₁₄O₆, which is formed in the atom-vacancy ordering of the tetragonal solid solution of oxygen in vanadium, is studied by the methods of x-ray diffraction and symmetry analysis. It has been found that the channel of the order-disorder phase transition attributed to the formation of the monoclinic suboxide V₁₄O₆ includes six superstructure vectors belonging to three non-Lifshitz stars {k ₁₋₁}, {k ₁₋₂}, and {k _1–3} of one type {k ₁}. The distribution function of the O atoms in the V₁₄O₆ monoclinic superstructure has been calculated. It has been shown that the displacements of V atoms distort the body-centered tetragonal metal sublattice, thus preparing the formation of the fcc sublattice and the transition from the suboxide V₁₄O₆ to the cubic vanadium monoxide with the B1 structure.     

Symmetry analysis of the monoclinic Pd<Subscript>6</Subscript>B superstructure: Long- and short-range orders

A symmetry analysis of the monoclinic (space group C2/c) Pd₆B superstructure formed in the cubic (with structure B1) boron solid solution PdB _y in palladium has been performed. The formation of this superstructure occurs as a first-order phase transition via the disorder-order transition channel including nine nonequivalent superstructure vectors of four stars {k ₁₀}, {k ₄}, {k ₃}, and {k ₀}. For the monoclinic (space group C2) Pd₆B superstructure, the distribution function of boron atoms has been calculated and the interval of admissible values of long-range order parameters has been determined. It has been shown that the found transition channel is identical to the channel of the formation of the monoclinic (space group C2/c) M ₆ X superstructure; therefore, the Pd₆B superstructure can be described with the same accuracy in space group C2. The higher symmetry of the monoclinic (space group C2/c) model suggests that it more accurately describes the structure of the phase Pd₆B (Pd₆B□₅) and mutually inverse phases M ₆ X□₅ and M ₆ X ₅□ than the model with space group C2. It has been demonstrated that there are two types of the nearest environment of metal atoms with non-metal sublattice sites arranged in the first and second coordination spheres in M ₆ X□₅-type superstructures (space groups C2/c, C2, C2/m, and P3₁) and in inverse M ₆ X ₅□-type superstructures with the same space groups.     

Monoclinic superstructure V14O6 of the tetragonal solid solution of oxygen in vanadium

The monoclinic (space group C2/m) superstructure of V₁₄O₆, which is formed in the atom-vacancy ordering of the tetragonal solid solution of oxygen in vanadium, is studied by the methods of x-ray diffraction and symmetry analysis. It has been found that the channel of the order-disorder phase transition attributed to the formation of the monoclinic suboxide V₁₄O₆ includes six superstructure vectors belonging to three non-Lifshitz stars {k ₁₋₁}, {k ₁₋₂}, and {k _1–3} of one type {k ₁}. The distribution function of the O atoms in the V₁₄O₆ monoclinic superstructure has been calculated. It has been shown that the displacements of V atoms distort the body-centered tetragonal metal sublattice, thus preparing the formation of the fcc sublattice and the transition from the suboxide V₁₄O₆ to the cubic vanadium monoxide with the B1 structure. Original Russian Text ? A.I. Gusev, D.A. Davydov, 2007, published in Pis’ma v Zhurnal éksperimental’noĭ i Teoreticheskoĭ Fiziki, 2007, Vol. 86, No. 10, pp. 746–751.     

Incommensurate phase in the layered hexagonal crystal Cs3Bi2I9

An incommensurate phase is observed in a Cs₃Bi₂I₉ crystal, which belongs to the family of layered A₃B₂X₉ structures. Data from ¹²⁷I NQR and x-ray powder diffraction patterns show that the second-order normal phase—incommensurate phase transition at T _i=220 K is accompanied by a P6₃/mmc↔P2₁/m symmetry change and takes place at the center of the Brillouin zone. The nature of the instability leading to the appearance of this little-studied form of incommensurability is discussed. Fiz. Tverd. Tela (St. Petersburg) 39, 1105–1108 (June 1997)     

Superconductivity and magnetism in HoNi2B2C

The effect of magnetic ordering on superconductivity in HoNi₂B₂C is studied. It is concluded that the abrupt suppression of superconductivity in the region of incommensurate antiferromagnetic ordering is due to a modification of the wave functions of the conduction electrons by the long-range magnetic order. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 9, 702–707 (10 May 1996)     

Electronic spectra and phase transitions in thin [N(CH<Subscript>3</Subscript>)<Subscript>4</Subscript>]<Subscript>2</Subscript>CuCl<Subscript>4</Subscript> microcrystals

Optical absorption spectra in thin [N(CH₃)₄]₂CuCl₄ crystals in the thickness range 10 μm ≤ d < 100 μm have been studied. Strengthening of the crystal field has been found with a decrease in the [N(CH₃)₄]₂CuCl₄ crystal size. The reasons for absorption band shifts in the visible region depending on the [N(CH₃)₄]₂CuCl₄ crystal thickness and the manifestation of a size effect in crystals with an incommensurate superstructure are discussed.     

Order-disorder transformation theory in ternary alloys with F.C.C. lattice—III: The long- and short-range order in the alloys of quasi-binary section A3B-A3C

The long- and short-range order parameters as the functions of temperature were calculated for several compositions of ternary alloys which are ordered as the Ll₂ binary superstructure. The influence of different relations between the ordering energies in pairs on quantitative regularities of the change of the order parameters is discussed.     

LiKSO4的无公度相

本文用多晶X射线衍射配合差热分析的方法研究了LiKSO₄室温以上的相变。发现当温度在熔点以下到675℃之间,晶体结沟与α-K₂SO₄的高温相同构,α相最可能的空间群为P6₃/mmc.在T_i=675℃以下出现调制结构,类似K₂WO₄,K₂MoO₄等的无公度相;参数κ的值由0.492(640℃)而随温度变化。在470℃出现整合相变κ=0.500,整合后的结构为室温相的超点阵。然后在439℃转变为室温相(空间群为P6₃)。 关键词：