Short-range order and twins in ordered titanium monoxide

The structure of annealed titanium monoxide TiO_1.087 containing monoclinic ordered phase Ti₅O₅ was studied by electron diffraction. Along with the set of structural, superstructural, and extra reflections, the diffraction pattern of titanium monoxide shows a set of plane diffuse fringes in the (112)_B1* section of the reciprocal lattice of the basis cubic structure B1. It is shown that some of the extra reflections are due to the twinning of the monoclinic superstructure along the (?1?11) plane of the reciprocal lattice of the basis cubic structure. The diffuse contours enclose plane areas of the reciprocal space with the fixed values of wave vectors K₁₀₀ ～ ±(h+0.07)k₁₀₀, K₀₁₀ ～ ±(k+0.07)k₀₁₀, and K₀₀₁ ～± (l+0.07)k₀₀₁ of the B1 structure. Their appearance is associated with the short-range displacement order.     

Diffraction of electrons in the CubicTi5O5 superstructure of titanium monoxide

Annealed titanium monoxide TiO_1.087 has been studied by the electron diffraction method. A cubic model of the Ti₅O₅ superstructure (Ti₅O₅ (Ti₉₀?₁₈O₉₀??₁₈)) of nonstoichiometric titanium monoxide Ti _x O _z has been proposed on the basis of experimental data and representations about the disorder-order transition channel. It has been shown that reflections observed on the electron diffraction pattern are identified in the space group $Pm\bar 3m$ . The period of the unit cell of the cubic Ti₅O₅ superstructure is larger than that for the B1 basic disordered structure of Ti _x O _z monoxide by a factor of 3. The disorder-order transition channel Ti _x O _z (space group $Fm\bar 3m$ )-Ti₅O₅ (space group $Pm\bar 3m$ ) includes 75 superstructure vectors of seven stars {k ₁₀}, {k ₇}, {k ₆₍₁₎}, {k ₆₍₂₎}, {k ₄₍₁₎}, {k ₄₍₂₎}, and {k ₁}. The distribution functions of Ti and O atoms over the sites of the cubic Ti₅O₅ (space group $Pm\bar 3m$ ) superstructure have been calculated.     

Aging effect in CaLaBa{Cu1???xFex}3O7???�� with 0 �� x �� 0.07 studied by M?ssbauer spectroscopy

In this work, we study the long-term aging effect caused by Fe atoms in the superconductor CaLaBa{Cu_1???xFe_x}₃O_7????? with 0 ?? x ?? 0.07. XRD confirms that this system has a YBCO-like structure. The critical temperature (T_c) is strongly affected by aging and depends on the amount of Fe in the structure. Room temperature Mössbauer spectroscopy reveals the presence of the typical species A, B?CB ??, C and new species E ?? and F. Interestingly; A, which corresponds to the Fe^3?+? atom located in the Cu(1) of the chains with spin S _z = 3/2, shows a drastic reduction which means migration to the species B, B ?? and C. Species B and B ?? correspond to the Fe^3?+? in the Cu(2) site forming planar quasi-octahedral and planar square pyramidal, while the C specie is a square pyramidal with O(5) respectively (spin S_z = 3/2 in all these cases). Aging causes loss of superconductivity in the samples with 5 and 7% of iron content.     

Magnetostriction and thermal expansion of HoAl3(BO3)4

The magnetostriction and thermal expansion of rare-earth aluminoborate HoAl₃(BO₃)₄ have been studied theoretically. The calculated field and temperature dependences of the multipole moments of the Ho³⁺ ion in HoAl₃(BO₃)₄ made it possible to describe the known experimental data and to predict possible anomalies of thermal expansion. It has been shown that, for the direction of the field B ‖ c, the nonmonotonic character of magnetostriction along the axis a is determined by the multipole moments, the main of which is β _J 〈O ₄ ⁰ 〉. For B ‖ a and B ‖ b, the maximum moments are β _J 〈O ₄ ² 〉and α _J 〈O ₂ ² 〉; their variation with the field and temperature explain well the form of magnetostriction. It has been established that the greater value of magnetostriction Δa/a for B ‖ b than for B ‖ a and the greater value of magnetostriction for the field in the basal plane than for B ‖ c are caused by greater variations in the field of actual multipole moments.     

Short-wavelength atomic-displacement modulation preceding the <Emphasis Type="Italic">B</Emphasis>2 → <Emphasis Type="Italic">B</Emphasis>19′ martensitic transformation in a TiNi-based alloy

Neutron diffraction studies of the fine structure of a Ti₄₉Ni₅₁ single crystal are performed before the onset of the B2 → B19′ martensitic transformation (temperature of the onset of the transformation M _s =200 K). Upon cooling below 460 K, extra reflections are found to form; their positions in the B2-phase reciprocal lattice correspond to the full non-Lifshitz star of the wave vector q=0.225〈112〉. At temperatures below 430 K, 0.45〈110〉 extra reflections appear, corresponding to second-order diffraction effects. In the temperature range 300–460 K, reversible and nonhysteretic changes in the intensities and positions of both types of extra reflections are observed. Analysis of the intensities and spatial distribution of the extra reflections in the B2-phase reciprocal lattice indicates that a displacive superstructure dominated by longitudinally polarized atomic-displacement waves with q=0.225〈112〉 arises in the single crystal in the pretransition temperature range.     

Exact solution of the Boltzmann equation in the relaxation approximation,existence of negative differential conductivity for certain types of energy bands and its implication for the fluctuation spectrum and the noise temperature

The Boltzmann equation for the distributionf _k of a system of charged particles obeying classical statistics in a uniform fieldF, $$\frac{{\partial f_k }}{{\partial t}} + F\frac{{\partial f_k }}{{\partial k}} = \smallint d^3 k'(W_{kk'} f_{k'} - W_{k'k} f_k ),$$ will be solved analytically for a special class of transition ratesW _kk′=const·h _k ·ν _k ·ν _k′ for any initial distribution.h _k is the Maxwell distribution andν _k >0 can be interpreted as ak-dependent relaxation frequency. The constant relaxation approximation (ν _k =ν) will be used to discuss the drift velocitiesu for all the fields and temperaturesT for certain types of band structuresE(k). Bands with lineark-dependence for largek give rise to drift velocities saturating for large fields. For bands with the periodicity of the reciprocal lattice, the zero drift-theorem has been proved. It states that $$\mathop {\lim }\limits_{F \to \infty } u (F,T) = \mathop {\lim }\limits_{T \to \infty } u (F,T) = 0$$ for all the periodic band structures. This theorem is even correct for a generalW _kk′ if certain restrictions are made. Finally, making use of the Markov character of the conditional probability (Green's function) solution of the Boltzmann equation, the velocity fluctuation spectrumS is calculated forE(k)=A(1?cosa k). It will be shown thatS(F, T, 0) remains positive for the critical field and all temperatures, and therefore the noise temperature diverges on approaching the critical field.     

Spatial dispersion in polariton spectra of CuGaS2 crystals

The unmodulated and wavelength-modulated reflectivity spectra of CuGaS₂ crystals for the polarization E ‖ c, k ⊥ c at 77 and 8 K have been studied. The states n=1, 2, and 3 of A excitons and n=1 and 2 of B and C excitons are established. The luminescence spectra from the surface at k ‖ c and k ⊥ c are obtained. The fine structure of the reflectivity spectra of excitons are analyzed with due regard for the normal and oblique incidence of light onto the crystal surface. The main parameters of the A, B, and C excitonic series are determined such as the energies of the longitudinal and transverse excitons Γ₄ (E ‖ c) for states n=1 and 2, the longitudinal and the transverse mass of excitons in CuGaS 2, and the effective masses of electrons (m _c1*) and holes (m _v1*, m _v2*, m _v3*). It is shown that the mass m _v1* in the upper valence band at k ‖ c equals (0.7–0.8)m ₀ and at k ⊥ c, 1.87m ₀.     

Atomic-vacancy ordering in the lowest tungsten carbide W2C

Atomic-vacancy ordering in the lowest tungsten carbide W₂C with an L′3-type basic hexagonal structure has been studied by neutron diffraction and X-ray diffraction. In the temperature range 2700–1370 K, the only ordered phase of the lowest tungsten carbide is shown to be the trigonal ?-W₂C phase (space group P $\overline 3 $ 1m). This trigonal ?-W₂C phase is found to form via a disorder-order phase transition channel, which includes three superstructure vectors (k ₁₅ ⁽¹⁾ , k ₁₅ ⁽²⁾ , k ₁₇ ⁽¹⁾ ) of two Lifshitz stars ({k ₁₅}, {k ₁₇}, and to be described by two long-range order parameters (η₁₅, η₁₇). The distribution function of carbon atoms in the trigonal ?-W₂C superstructure is calculated, and the corresponding region of the allowable values of the long-range order parameters η₁₅ and η₁₇ is found. Symmetry analysis of other possible superstructures of the lowest tungsten carbide W₂C is performed, and the physically acceptable sequence of phase transformations in W₂C is determined.     

Anisotropic resonant magnetoplasticity of NaCl crystals in the Earth’s magnetic field

Resonant relaxation of the dislocation structure under the action of crossed magnetic fields, i.e., constant magnetic field of the Earth (B _Earth) and alternating radio-frequency field ( $\tilde B$ ), has been experimentally studied in a series of dielectric (NaCl) crystals with various compositions of impurities under variations in the frequency, direction of the pumping field $\tilde B$ , and orientation of the samples in the Earth’s magnetic field. The frequency dependence of the dislocation path length l(ν) exhibits peaks with various heights (l _max) and resonant frequencies (ν_res). The maximum resonant effect has been observed for dislocations with the direction L orthogonal to the plane of crossed magnetic fields in a configuration of mutually perpendicular vectors {L, $\tilde B$ , B _Earth} belonging, together with sample edges {a, b, c}, to the 〈100〉 system. Variation of the concentration C of calcium impurity in crystals of the NaCl_Ca series only influenced the resonant peak height as $l_{\max } \propto 1/\sqrt C $ . Rotation of the magnetic field $\tilde B$ in the (b, c) plane from direction $\tilde B$ ⊥ B _Earth to $\tilde B$ ∥ B _Earth also did not influence the frequency of the resonance but changed its amplitude. Depending on the crystal type, this influence changed from rather insignificant (in crystals of the NaCl_LOMO series) to complete suppression of the effect for $\tilde B$ ∥ B _Earth (in the NaCl_Nik series). The resonant frequency ν_res is sensitive to orientation of the sample with respect to B _Earth. Upon rotation of the crystal by the angle θ = ∠(c, B _Earth) about the a ⊥ B _Earth edge, the initial peak for dislocations L ‖ a at the crystal orientation θ = 0 and the frequency ν _res ⁰ is replaced by a pair of peaks at frequencies ν_{1, 2} ≈ ν _res ⁰ cosθ_{1, 2}, where θ₁ = 90° ? θ and θ₂ = θ. Previously, these peaks were observed separately in NaCl_Nik crystals for $\tilde B$ ∥ c and $\tilde B$ ∥ b. In the present study, these peaks have been observed simultaneously for both orientations of $\tilde B$ in NaCl_LOMO and NaCl_Ca crystals, where the resonance is not completely suppressed for $\tilde B$ ∥ B _Earth.     

Resonant dislocation motion in NaCl crystals in the EPR scheme in the Earth’s magnetic field with pulsed pumping

Resonant dislocation motions in NaCl(Ca) crystals under the simultaneous action of the Earth’s magnetic field B _Earth (～66 μT) and a pulsed pump field $\tilde B$ of sufficient amplitude $\tilde B_m $ and certain duration τ have been detected and studied. The measured dislocation path peaks l(τ) have a maximum at τ = τ _r ≈ 0.53 μs. The resonance criterion has been found to be the ordinary EPR condition in which the g-factor is close to 2 and the optimum inverse pulse duration τ _r ^?1 is used instead of the harmonic pump field frequency ν _r . The largest peak l(τ) height is reached at mutually orthogonal dislocation (L) and magnetic field (B _Earth and $\tilde B$ ) orientations. Pulsed field rotation to the position $\tilde B$ ‖ B _Earth significantly decreases but does not “kill” the effect. For dislocations parallel to the Earth’s field (L ‖ B _Earth), the resonance almost disappears even at $\tilde B$ ⊥ B _Earth. In the optimum geometry of experiments, as the pump field amplitude $\tilde B_m $ decreases from 17.6 to 10 μT, the path peak height l _r = l(τ _r ) decreases only by 7.5%, remaining at the level of l _r ～ 10² μm, and at a $\tilde B_m $ further fall-off to 4 μT, it rapidly decreases to background values. In this case, the relative density of mobile dislocations similarly decreases from ～90 to 40%. Possible physical mechanisms of the observed effect have been discussed.     

Some estimates for magnetic fluctuations in a turbulent medium

A new integral relationship between the fluctuations b(r, t) of a magnetic field and its mean B ₀(r, t) is derived for the steady-state magnetic field in a turbulent medium. This formula provides the estimate 〈b?curlb〉=?B ₀?curlB ₀. Simultaneously, the coefficient of amplification of the mean magnetic field α effect) is obtained: α=(η+β)B ₀? curlB ₀/B ₀ ² . The formula for α allows for a decrease in this coefficient owing to the back action of the magnetic field on the turbulent velocity field. It is shown that the Zel’dovich’s estimate 〈 b ²〉?β/η B ₀ ² for two-dimensional turbulence holds for magnetic fields at the instant the fluctuations 〈a ²〉 of the vector potential, rather than 〈b ²〉, reach a maximum. Here, η and β are the ohmic (molecular) and turbulent diffusion coefficients, respectively. This estimate is refined with allowance made for the fact that the condition for diffusion approximation itself relates the β, b, and B ₀ quantities to each other.     

Two-dimensional representation of position, velocity and acceleration by PFG-NMR

A novel view on the presentation of pulsed field-gradient nuclear magnetic resonance experiments to encode position and translational displacements is given. A conventional diffusion or flow experiment employing two magnetic field gradients of effective areak ₁, andk ₂ separated by a time interval Δ can formally be expressed as a means to probek space in a two-dimensional way. While for most applications, a full coverage of the [k ₁,k ₂] space is not necessary, an experiment withk ₁ = ?k ₂ can be regarded as a sampling of the secondary diagonal in [k ₁,k ₂] space. Likewise, the main diagonal is represented by the conditionk ₁ =k ₂ and encodes position. Thus, the [r ₁,r ₂] space conjugate to [k ₁,k ₂], which is obtained by Fourier transformation, can be transferred into a position/displacement correlation plot simply by rotation of the coordinate system by an angle of 45°. While displacementR =r ₂ ?r ₁ corresponds to an average velocity? =R/Δ, an extension towards higher-order derivations such as acceleration is straightforward by modification of the pulse sequence. We discuss this new concept in a general way, treating both the magnetic field and the particle position by Taylor expansions with respect to space and time, respectively, and present examples for fluid flowing through capillary systems in the light of the suggested interpretation.     

Ti5O5 superstructures of cubic titanium monoxide

A cubic model is proposed for the Ti₅O₅ (Ti₅?O₅□ ≡ Ti₉₀?₁₈O₉₀□₁₈) superstructure of nonstoichiometric titanium monoxide Ti _x O _z with double imperfection. The unit cell of the cubic Ti₅O₅ superstructure has the threefold lattice parameter of the unit cell of the basis disordered B1 structure of Ti _x O _z monoxide and belongs to space group $Pm\bar 3m$ . The channel of the disorder-order transition, i.e., Ti _x O _z (space group $Fm\bar 3m$ )-Ti₅O₅ (space group $Pm\bar 3m$ ), includes 75 superstructure vectors of seven stars {k ₁₀}, {k ₇}, {k ₆₍₁₎}, {k ₆₍₂₎}, {k ₄₍₁₎}, {k ₄₍₂₎}, and {k ₁}. The distribution functions of Ti and O atoms over the sites of the cubic Ti₅O₅ superstructure are calculated. A comparison of the X-ray and electron diffraction data obtained for ordered TiO_1.087 monoxide with the theoretical simulation results supports the existence of the cubic Ti₅O₅ superstructure. The cubic (space group $Pm\bar 3m$ ) Ti₅O₅ superstructure is shown to be a high-temperature structure relative to the well-known monoclinic (space group C2/m) superstructure of the same type.     

T-odd correlations in (n, αγ) reactions

The T-odd correlation (k _α · [σ × k _γ])(k _α · k _γ), where σ is the vector of the neutron polarization and the symbols k denote the respective linear momenta (all vectors are unit ones), in the sequential alpha-gamma cascade induced by a thermal-neutron capture is studied. The study is performed in the one-resonance approximation. Both the final-state interaction of the alpha particle with the residual nucleus and the actual T-noninvariant phase shift are considered as possible origins of the correlation. The problem of suitable target isotopes is analyzed. Related correlations in other neutron- and proton-induced reactions are discussed.     

A Real Quaternion Spherical Ensemble of Random Matrices

One can identify a tripartite classification of random matrix ensembles into geometrical universality classes corresponding to the plane, the sphere and the anti-sphere. The plane is identified with Ginibre-type (iid) matrices and the anti-sphere with truncations of unitary matrices. This paper focusses on an ensemble corresponding to the sphere: matrices of the form Y=A ^?1 B, where A and B are independent N×N matrices with iid standard Gaussian real quaternion entries. By applying techniques similar to those used for the analogous complex and real spherical ensembles, the eigenvalue joint probability density function and correlation functions are calculated. This completes the exploration of spherical matrices using the traditional Dyson indices β=1,2,4. We find that the eigenvalue density (after stereographic projection onto the sphere) has a depletion of eigenvalues along a ring corresponding to the real axis, with reflective symmetry about this ring. However, in the limit of large matrix dimension, this eigenvalue density approaches that of the corresponding complex ensemble, a density which is uniform on the sphere. This result is in keeping with the spherical law (analogous to the circular law for iid matrices), which states that for matrices having the spherical structure Y=A ^?1 B, where A and B are independent, iid matrices the (stereographically projected) eigenvalue density tends to uniformity on the sphere.     

Magnetic properties of erbium iron garnet in high magnetic fields up to 150kOe

The magnetic properties of single crystals of erbium iron garnet (ErIG) were studied in applied fields up to 150kOe between 1.4 and 300K. At low temperature, the macroscopic easy direction of the bulk magnetization is [100]; below the compensation temperature (80±2K), the magnetization presents non-linear field evolution. On the assumption of an isolated ground doublet, the anisotropy constantsK _i (i=1,2) of ErIG are given byK _i (Er)+K _i (YIG); theK _i are calculated as a function of theG andg tensor components. It is worthwhile noting that theK _i (Er) are strongly temperature dependent; so at low temperature the anisotropy of the garnet is determined by the rare earth ions, while in the 50 K regionK ₁(Er) becomes comparable toK ₁(YIG) with the opposite sign which results in a very weak anisotropy of the garnet. Above 50 K,K ₁(YIG) is predominant and the Fe³⁺ ions determine the garnet anisotropy.     

Rotation of the plane of polarization and linear birefringence of sound in hematite below the morin point

The linear antiferromagnetic birefringence of sound in hematite (α-Fe₂O₃) residing in the collinear easy-axis phase (L ‖ C ₃) below the Morin point is experimentally studied. The plane of polarization of a linearly polarized transverse acoustic wave propagating along the trigonal axis C ₃ of a hematite crystal placed in a magnetic field H applied in the basal plane (H ⊥ C ₃, 3.5 ≤ H ≤ 15 kOe) is found to rotate after a temperature-driven orientational phase transition to the easy-axis state. The angle of rotation exhibits a 180° angular dependence on the direction of the magnetic field in the basal plane and varies from zero to ～π/2. Numerical estimates suggest that the conditions necessary for rotation of the plane of polarization through appreciable angles (～π/2) can be satisfied in the easy-axis phase at orientational phase transition temperatures close to the Morin point, which actually takes place in the fields employed. The results obtained are described sufficiently well by the theory of linear antiferromagnetic birefringence of sound (E.A. Turov) and confirm its main conclusions.     

Hyperfine structure investigations of some odd levels of Co I by level crossing and optical methods

Using the level crossing technique the ratios and absolute values of the hyperfine structure (hfs) constants of the levelsz ⁴F_9/2 andz ⁴F_7/2 of the configuration 3d ⁷4s4p of Co I were measured:z ⁴ F _9/2: ¦A¦=(811±12)MHz; ¦B¦=(48±93) MHz;B/A=?0.06±0.11 A>0; B<0z ⁴ F _7/2: ¦A¦ = (659 ±11)MHz; ¦B¦=(33±84)MHz;B/A=?0.05±0.13 A>0; B<0. In addition the hfs constants of three other excited levels of Co I could be determined by optical methods:z ⁴ F _9/2:A=525±26 MHz;B=200 MHzy ⁴ F _9/2:A=300±30 MHz;B=?500 MHzy ⁴ G _11/2:A=315±20 MHz;B=400 MHz. The experimental results are compared with known experimental and also with theoretical values which where calculated using the parametric potential method.     

Evaluating the validity of parametrized relativistic wave equations

We wish to determine the correct partial differential equation(s) for describing a relativistic particle. A physical foundation is presented for using a parametrized wave equation with the general form $$i\frac{{\partial \psi }}{{\partial s}} = K\psi$$ where s is the invariant evolution parameter. Several forms have been proposed for the generator K of evolution parameter translations. Of the proposed generators, only the generator K ₂ which is proportional to the inner product P _μ P ^μ of fourmomentum operators can be derived from first principles, notably a probabilistic basis. Although experimental tests must be made to establish the validity of K ₂,we conclude that K ₂ is the leading theoretical candidate for the form of a generator of evolution parameter translations.     

On the temperature behavior of second sound and Poiseuille flow

The linearized Peierls equation for the phonon densityN (k λ,r t) is solved by replacing the collision operator in the subspace orthogonal to the collision invariants byk-dependent relaxation rates. For the normal process relaxation time the behaviorτ _N (k λ)∝|k|^?p for smallk is assumed. Taking into account thisk-dependence ofτ _N explicitly and avoiding an expansion with respect toΩτ _N (kλ) before performing the necessary integration overk yields new, non-analytic, terms in the hydrodynamic equations describing second sound and Poiseuille flow. It is shown that this may lead to a temperature dependence of second sound damping and thermal conductivity in the Poiseuille flow region differing from the usual theoretical predictions and in better agreement with experiments.