
SHEMETOV YEVGENY. STUDIES OF PHASE TRANSITIONS IN THE UNITED A_{2}BX_{4} STRUCTURE βK_{2}SO_{4 }METHOD NUCLEAR QUADRUPOLE RESONANCE English abstract § 1.1 § 1.2 §1.3 § 1.4 § 2.1 § 2.2 §2.3 §2.4 § 3.1 § 3.2 § 3.3 § 3.4 § 4.1 § 4.2 § 4.3 § 4.4 Reference Template pdf abstract
CONTENTS
INTRODUCTION Studies of the structure of the crystal structures, the nature of phase transitions recently reached a qualitatively new level. By theoretical and experimental work has been formulated a universal approach to the description of phase state on the basis of solving discrete field theory models. In the language of the theory of interacting nodes on harmonic lattice spins have been found and studied nonlinear solutions in the form of fermions. At the same time, as it turned out, the system can be represented by the normal fermion modes. The theory of the soft mode condensation Goldstounovskogo boson is just a special case of solutions in the form of singleparticle fermion states  for example, the spinwave or soliton. Theoretical and experimental studies carried out for the external magnetic field and take into account only the spinspin interaction in the framework of models with different dimensionality, showed that the behavior of the system depends not only on the spin and spatial dimension of the system, but must be considered a significant radius interspin interaction. It has been found that in this case there are classes of solutions to form the longperiod structure, and observed experimentally. In recent years, were discovered and studied compounds with charge density waves, quasione organic semiconductors and dielectrics, in which it was found ordering various elements of the structure similar to the longperiod form of magnets. Unlike magnetic systems in dielectric crystals at the forefront of the dipoledipole interaction and the dimension of the spin variable gives way pseudospin ordering chemical bonds. In crystalline dielectrics with a structure of βK_{2}SO_{4} were first detected with an incommensurate phase, compared with the original sample intervals. From Xray data indicated that the emerging superstructure reflections can be characterized by a temperature dependent parameter disparity. Change the local environment of the structural units in phases with such features more optimal way to observe change of the electric field, or its constituents. Therefore, the method of nuclear quadrupole resonance (NQR) observed in the nucleus with the quadrupole moment and depends on the electric field gradient at the nucleus under study, is optimal for the study of incommensurate structures. Nucleus Cl, Br, J in crystals of the family A_{2}BX_{4} occupy a convenient structural position and allow to obtain information about the origin of the primary structural disproportion, the type of phase transition, modulation features. With the participation of the author have been made one of the first such studies, including those under the influence of high hydrostatic pressure. Involvement of the latter, as an additional parameter allows you to get a new nontrivial information about the incommensurate phase. The objectives of this thesis include studies by nuclear quadrupole resonance of halogens (Cl, Br, J), and other methods, crystals family βK_{2}SO_{4} with structural disproportion. Elucidation of changes in the spectral features of the resonance parameters in phase transitions and symmetry transformations, the analysis of the local environment and the nucleus of its transformation into different compounds of this series with temperature and high hydrostatic pressure. Investigation of the processes of the spin dynamics. In combination with other methods of analysis of changes in the crystal symmetry at structural phase transitions.
Chapter 1. Incommensurately modulated phases in dielectrics with structure type βK_{2}SO_{4.}
§ 1.1.Theory of phase transitions and incommensurate phases. Phase transition is called structural when changescrystallographic structure of matter. Symmetry of the crystal lattice, as it is known, in the general case described simorfnymi 230 space groups. Change in the symmetry of the crystal at the phase transition seemed, until recently, in the framework of the LandauDevonshire, as a change of some function, called the order parameter, by the loss of the symmetry elements and decreasing the initial symmetry G_{o} to a certain subgroup of the symmetry group G_{1} G_{o.} From the point of view of the atomic structure of the crystal, this means that the asymmetric atoms in the G_{1} phase, shifted relative to the equilibrium positions which they occupy at the high phase. The structure of the new phase G_{1} is a superposition of the displacements corresponding frozen soft mode and structure of G_{0} phase. Hence the structure of the new phase is uniquely determined by the structure of the initial phase and the vector of the soft mode (the symmetry of the soft mode). According to Anderson's theory [1], phase transitions caused by the instability of the crystal relative to some of its normal modes in the hightemperature phase. The frequency of this mode decreases when approaching the critical temperature T_{i,} and the restoring force for displacements corresponding to such a fashion tends to zero as long as the phonon does not condense on the stability boundary. Consequently, the static displacements of atoms at the transition from phase G_{0} to G_{1} phase are frozen vibrational displacement codes corresponding to the soft phonon (q_{s).} However, this concept is applicable when the displacements of atoms from the highsmall positions (phase transitions of bias) and becomes less useful for large displacements (phase transitions of the orderdisorder). In the latter case, structural changes are usually described in the framework of the Ising model, which deals with largescale motions and entered the (pseudo) spin variables describing the position of atoms or groups. The results of this approach generally boil down to the fact that the phase transition occurs at the wave vector q_{s,} which corresponds to a maximum of interactions J(q) between objects Ising nodes. Parallel  the development of theory undertaken considerable experimental efforts to study the microscopic nature structure phase transitions. Most known results of the classical study of the temperature dependences of q_{s} in βK_{2}SO_{4} [2]. Neytron  diffraction method on this crystal were shot dispersion curves q(ω) at different temperatures Figure 1.1. Temperature dependence of q for S_{2} fashion shows that the wave rector q_{s} can have values between zero and the wave vector at the Brillouin zone boundary. In this case, the value q_{s}, corresponding to a minimum the dispersion curve, the symmetry is not fixed and typically depends on the temperature. Changes in the structure of the crystal in this case determined by the symmetry of highG_{0} phase, followed by some pretransitional area corresponding mitigation fashion responsible for the phase transition at T_{i.} Below T_{i} there is a phase where the minimum of the soft mode varies near the symmetrical point of reciprocal space G*, and when they correspond exactly q_{s} G*, at T_{c} transition occurs in the lowsymmetry structure. The phase between T_{i} and T_{c} is called, incommensurat because values of the wave vector q_{s,} when it is a continuous change can take irrational values, which corresponds to an infinitely large unit cell of the crystal. In this case the crystal is represented threedimensionally periodic structure, where any inside – crystalline function in one or more directions superimposed longwavelength spatial modulation period is generally not a multiple of the period of the unit cell of highsymmetry phase. Displacement of nucleus of symmetric function of the order parameter in this
0 0.5 q_{s } 1.0 q
Figure 1.1. Dispersion curves for the soft mode in K_{2}SeO_{4} at different temperatures and the dependence q_{s}1/3(1δ)2π/a.
case, can be represented by an expansion in the eigenvectors of the soft mode [2,3]: (1.1.) where e_{k}^{l}  eigen vectors irreducible representation G*; G*; А'l, Аl  amplitude eigenvectors; X (lk) – lst position of the atom, the center of mass of kth group in the pth unit cell; jwave phase modulation. Analysis of the interaction of atoms in an external periodic potential shown [4,5] that the period of the structure is fixed on the true meaning and proportioned incommensurate phase is not realized. The resulting wave vector, depending on the "pressure", varies continuously, but Nonanalytic. For this strange behavior, mathematicians devised a very original name  "Devil's Staircase" (devil or Satan staircase) [5]. However, initially there was no hope to explore different types of nonanalytic behavior numerically, and even more so by experiment. In addition to the theory of Aubrey [5,6], in [7,8,9], to describe the transition from incommensurate (Jc) to the commensurate phase were introduced "domain" wall or soliton theory and developed the idea as part of Macmillan Ising models with solitons, phasons and "devil's staircase". Results McMillan, reduced to the fact that the transition from J_{C} in the commensurate phase can be represented by a picture of solitonlike structure of the atomic displacements described by the soliton (domain) wall ^{:} u = A cosφ(x); φ(х)  k/p arctg(exp(ax/p )) (1.2) φ(х) = 2π/р; р = 1,2,...k.; These walls separate regions with different values of the phase shifts of atoms φ(х) = 2p/р; р = 1,2,...k.. Shape of the phase function in the incommensurate (incommensurate) phase is given by: φ(х) = φ_{о} + φ(хmb) (1.3) where φ_{о}  the phase shift; b  distance between the walls, m = 1,2,3, ... p. When the temperature decreases, the width of the soliton wall and a^{1} is a continuous transition to the commensurate state. . Order parameter in this case is the number of solitons. In real crystals, if the width of the soliton is a few lattice periods, the center of the soliton is energetically advantageous to have at some point in the unit cell [10]. In this case, the transition to the final as symmetrical, the system will experience a sequence of phase transitions of the first kind, until you reach the main phase with p = k. In addition, there are often a few stars of the wave vectors that lead to the existence of incommensurate walls of various types, and can be carried out transitions between different configurations of the soliton structure. There are other types of nonlinear numerical solutions (kinks, wobblers, etc.), describing the shape of the atomic displacements in the incommensurate phase. Such as NaNO_{2,} the structure seems almost plane waves, and up to T _{C} no harmonics incommensurate wave vector [11]. McMillan ideas were developed Janson[8] Aubrey [12]and Buck [13] These authors studied the behavior of soliton solutions of the discrete problem in Isinglike systems with the interaction up to three neighbors (ANNNI  model). In this case, the deviation of the wave vector q_{δ} = (1 )*/3 proportioned values can be represented by a rational number x = M/N, and the structure of solutions (steps "devil's staircase") may be associated with symmetry interconnected sublattices with symmetry restrictions on the values of the numbers N and M. Then the transition from the highG_{0} in the lowsymmetry phase G_{i,} between the phase diagram there is a region where the structure is represented by a cascade of intermediate or longperiod incommensurate states with discrete or continuous variation of the wave vector q_{δ} (Fig.4.38 and 4.39). The regions of these states are very sensitive to external (theoretical) effects. By this time the state of the theory of symmetry was enough to make its results for the classification of all possible types of theoretical incommensurate structures [15] and classify them into different classes incommensurate space groups in the theory of supersymmetry [16]. Supersymmetry transformation rules allow you to specify the direction of the transformation and permissible types of symmetry of incommensurate structures that can realistically be implemented in each class Fedorovskoye crystal structure. As an illustration, we give an outline of possible directions changes in lattice symmetry Brillouin highly symmetric group D_{2h}^{16} (Pnma), Figure 1.2. In the circles of indexed figures experimentally realized soft modes for crystals 1) Tb_{2}(Mo0_{4})_{3,} k_{m} = p (110) 2) RbD_{3}(Se0_{3})_{2,} k_{z} = p (001) 3) K_{2}SeO_{4} , k = 2p (m00) m»1/3 In [18] is a diagram indicating the possible ways of symmetry transformations structure Pnma (D_{2h}^{16})^{.} From the experimental data revealed that the sequence of phase transitions in crystals with highsymmetry group symmetry Pnma structure βK_{2}SO_{4 }defines mitigation dispersion curve along the S . line. There are four irreducible representations of S_{1}, S_{2}, S_{3}, S_{4 }of this group. In K_{2}SeO_{4,} for example, the soft mode associated with the representation of S_{2}: Eline Eline (D_{2}_{h}^{16}) (Pnma) ► Jc modulation ►C_{2}_{v}^{9 }(Pna2_{1}) m»1/3 along the xaxis m»1/3 Later in other compounds of the family A_{2}BX_{4} type structure βK_{2}SO_{4,} installed other possible sequences of symmetry transformations, which are determined by another basis of irreducible representations of (Table 1.1). Given the possibility of experimental observation of the behavior of "devil's staircase" or to account for the influence of concomitant and secondary order parameters, the analysis of experimental structural data necessary to know the various ways allowed symmetry transformations of the structure, taking into account the parity ratio x= N/M in the case of longperiod structures . The analysis performed in Refs [17, 18], which indicates all possible subgroups generated representations S_{i}, L_{i}, G_{i } The above theory of solids based on the adiabatic or BornOppenheimer approximation, where the kinetic energy of the nucleus T (R_{n)} is actually neglected. However, as the last experimental studies [23], the characteristic times of nuclear motions can be compared with the electronic. Arise in this case, the vibronic interaction, even in the case of mixed singlet states, lead to JahnTeller distortions, which crystal system can be a source of instability and dipole explain the nature of ferroelectricity [22]. From the standpoint of the vibronic theory postulates soft mode are consequences of the cooperative pseudoJahnTeller effect. In the framework of this theory can be explained and the disproportionate nature of the state in dielectric crystals. Interaction of the electron or nuclear state leads to interaction pseudosoft phonon modes of different symmetry, localized near a variety of provisions of the reciprocal lattice symmetry [8, 94]. In the hightemperature phase G_{0,} these modes do not interact, but below the temperature will determine the resonant interaction of the two components of the structure, phaseshifted.
Figure 1.2. Symmetric points and directions of the lattice Brillouin grupy D_{2}_{h}^{16} (Pnma).
the standpoint of the atomic arrangement of this will lead to cooperation between the two sublattices of the crystal with different periods and realized a disproportionate or mosaiccluster state. Recently, efforts have been made to combine the universality hypothesis and cluster theory of phase transitions. In this way on the basis of experimental data for the theoretical foundations of association phase transitions of receiving and orderdisorder [19,20]. There are reasonable grounds to believe that these transitions differ only in magnitude of the contribution from the phonon modes and pseudospin. This theory considers the equilibrium configurations of atoms in direct space: (1.4) with singleparticle potential:
In contrast to the models discussed above is introduced varying degrees of anharmonicity motion near doublewell potential. In the case where the value of g = V°_{s}/k_{S}T_{C} (ratio of the depth of the pit to the local thermal energy) is small, the offset describes weakly damped mode, otherwise the soft mode From is strongly overdamped, and there is strong anharmonicity of the atomic motion in the potential V_{s} (g>l). In the latter case, at low temperatures (below T_{C)} one of the holes has a large population. As numerical calculations before T_{C} there Pretransitional area where there are buds (clusters), whose structure is similar to the structure of the lowtemperature phase. Finite lifetime and size correlated moving clusters form different from that of the matrix, a dynamic structure, which is manifested in the spectral response function of the system. Molecular dynamics method were obtained solving the equations of motion with the Hamiltonian (4) as a nonlinear soliton solutions. In case of submission of solitons in the form of pseudoideal gas particles, the spectral function of the system is described as a phonon spectrum plus scattering due to slower movement of clusters (Gallo, diffuse bands on radiographs). When the speed of the cluster (or its borders) greater than the change in its size, there is a critical narrowing of the spectral components (central peak). Or, in the case of bias, if the fluctuations around quasi offset provisions are large compared with the quasiequilibrium by the local displacements. Even for small fluctuations in the presence of correlated moving regions should lead to redistribution contribution to the spectral response function between the quasiharmonic frequencies and part responsible for the cluster scale movement. Thus, even if the bias (g « 1), the spectral function of the coordinate ordering Q completely changed at T_{i}> T_{C} with decreasing T. For T <T_{i} soft phonon spectrum into the growth of the central peak. In systems offset soft mode has a resonant nature, although it may be a bit muted (Re and Im parts different from zero). In systems of orderdisorder imaginary part of the soft mode is always different from zero, a Re part only if the quantum mechanical ground state splitting (tunneling, Hbonds). Cluster pattern in the transition of the displacement type allows crossover from mode to mode bias orderdisorder at T> T_{c,} as a result of the coherence of atomic motions. Temporal and spatial correlation functions of clusters, also have considerable scale range. Maximum size and lifetime limited correlation length and time, and the minimum value  the size of embryos and their lifetime in development threshold temperature fluctuations. If the system causes an increase in the size of preventing germs зародышей time structural redistribution could increase significantly and experimentally observed complete or partial freezing of nonequilibrium state of the system (windows). In the thermodynamic sense, the surface free energy of the system in the microscopic space of external parameters is represented by many local minimums separated by high energy barriers which may exist for a long time longlived metastable phases overlapped with the topological structure (quasiergodic behavior) [21]. The problem of implementation of some elements of the crystal structure in a state such as glass, under quasiergodic assumptions led to the development of new approaches in the thermodynamic description of phase transitions. Quasiergodic system under certain conditions can evolve different structural timedependent pathways in megascopic (cluster) and the macroscopic sense. In this case also, there is certain temperature Т_{к}, the separating region with various types of thermodynamic behavior.
English abstract Avtoreferat § 1.1 § 1.2 §1.3 § 1.4 § 2.1 § 2.2 §2.3 §2.4 § 3.1 § 3.2 § 3.3 § 3.4 § 4.1 § 4.2 § 4.3 § 4.4 Reference Template pdf abstract
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