Investigation of nematic order by coherent neutron scattering

The mathematical relationship between the orientational order parameters and the coherent neutron scattering cross section for a nematic liquid crystal is given. For deuterated para-azoxyanisole the single-molecule part of the cross section is evaluated within the meanfield approximation and combined with experimental results to give information about molecular orientational order in terms of P ₂, P ₄ and P ₆. Both P ₂ and P ₄ are found necessary for describing the molecular order. Discrepancies between experimental and theoretical results are interpreted as possibly reflecting the inadequacy of the meanfield theory of Maier and Saupe.     

Effect of bias field on the dielectric properties of 0.7Pb(Mg1/3Nb2/3)O3-0.3PbTiO3 single crystals with different orientations

Microdomain-macrodomain transformations and phase transitions in 0.7Pb(Mg_1/3Nb_2/3)O₃-0.3PbTiO₃ single crystals were investigated by studying their relative permittivity under various dc bias at constant heating and cooling rates. The orientation dependence of the bias field effect was revealed by examining the temperature dependence of relative permittivity as a function of crystal orientation (the 111, 011 and 001 directions) and dc bias field. The crystals have a microdomain rhombohedral ferroelectric state in the ferroelectric phase under zero dc bias. External bias field could modulate the domain state and induce a macrodomain state in the crystals. Also, it is proposed that the dc bias applied along the 001 or 011 direction could induce a tetragonal ferroelectric phase or an orthorhombic ferroelectric phase, respectively, in an intermediate temperature range. PACS 77.80.-e; 77.22.-d; 81.40.-z     

Molecular dynamics study of nematic liquid crystal orientation ordering

Molecular dynamics investigations of distribution functions of orientation, order parameters P ₂, P ₄ and selfdiffusion tensor components for nematic liquid crystal model were performed. Our results are in good agreement with experimental data for p-azoxyanisole (PAA). Applied molecular dynamics model is perspective for investigations of structure characteristics and transport coefficients of nematic phase.     

The lattice deformation and the energy of antiphase boundaries in Fe-Si alloys

The lattice deformation across the antiphase boundary and the energy of both types (a/2111 anda(100) of antiphase boundaries lying in {110} plane are calculated using a series of three interatomic potentials fitted to experimental data. It is shown that the relaxation of atomic planes in the vicinity of antiphase boundary is important for thea/2111 antiphase boundary and is negligible for a 100 antiphase boundary in the DO₃ structure.The author is grateful to Dr. F.Kroupa and to Dr. A.Gemperle for valuable discussions.     

Mixing properties,differentiability of the free energy and the central limit theorem for a pure phase in the Ising model at low temperature

For the Ising model with nearest neighbour interaction it is shown that the spin correlations _{A B} - _{A B} decrease exponentially asd(A, B) in a pure phase when the temperature is well belowT _c. This is used to prove that the free energyF(,h) is infinitely differentiable in and has one sided derivatives inh of all orders forh=0. The bounds are also used to prove that the central limit theorem holds for several variables such as e.g. the total energy and the total magnetization of the system, the limit distribution being gaussian with variances determined by the second derivatives ofF(,h).     

Investigation of nematic order by coherent neutron scattering

The mathematical relationship between the orientational order parameters and the coherent neutron scattering cross section for a nematic liquid crystal is given. For deuterated para-azoxyanisole the single-molecule part of the cross section is evaluated within the meanfield approximation and combined with experimental results to give information about molecular orientational order in terms of P ₂, P ₄ and P ₆. Both P ₂ and P ₄ are found necessary for describing the molecular order. Discrepancies between experimental and theoretical results are interpreted as possibly reflecting the inadequacy of the meanfield theory of Maier and Saupe.     

Ray theory of the impulse response of randomly bent multimode fibres

A ray theory based on the time-independent Fokker-Planck equation and the integration of time along ray trajectories provides analytical expressions for the average arrival time and spread of optical pulses propagating in randomly distorted, multimode, optical fibres. A clear physical picture emerges from the theory. The analytical expressions obtained for t and t ² coincide with the ones obtained by Olshansky from coupled-mode theory. The t ³ and t ⁴ moments of the impulse response are also calculated. Simple closed-form formulae are given for the step-index slab. The coupling between all modes is effectively taken into account in our ray theory.On leave of absence at the Laboratoire des Signaux et Systèmes.     

Thes-f model with Coulomb repulsion: Thermodynamics of two atomic cluster. Spin 1/2

A cluster of two atoms described by thes-f model with Coulomb repulsion has been considered. The interaction between localized 4f electrons (S=1/2) is taken in the molecular field approximation. The thermodynamic quantities like magnetization, specific heat and correlation functions n , n , S ^z n , S ^z n , S ^z (n –n ), n n and S ⁺ a ⁺ a as functions of temperature are presented for different band fillingN=0, 0.5, 1, 1.5, 2. The dependence of Curie temperature onN is calculated. The phase diagram forN=1 (T=0K) shows the possibility of existence of two phases: paramagnetic and ferromagnetic.The Curie temperature and the specific heat as functions ofN exhibit similar trends as found in experiments on doped magnetic semiconductors.     

Random walk with persistence

The exact analytic result is obtained for the Fourier transform of the generating functionF(R,s)= _n=0 s ⁿ P(R,n), whereP(R,n) is the probability density for the end-to-end distanceR inn steps of a random walk with persistence. The moments R ²(n), R ⁴(n), and R ⁶(n) are calculated and approximate results forP(R,n) and R ^–1(n) are given.     

Atomic in-plane disorder in Co/Pt superlattices

We have studied 111 and 001 oriented Co(3 Å)/Pt(18 Å) superlattices grown by molecular beam epitaxy via X-ray diffraction using synchrotron radiation. The diffraction peak shapes, for the scattering vector Q parallel to the film planes, were found to be characteristically different between these two films. For the 111 oriented sample, this broadening is characterized by a Lorentzian peak shape with a positional correlation length of the order of 50 Å. The data further indicate that the atomic correlation in the 111 sample has a long range orientational but only short range positional order.     

Langevin dynamic simulation of hysteresis in a field-swept Landau potential

Numerical simulations are done of Langevin dynamics for a uniform-orderparameter, field-swept Landau model,= –|a/2|m ²+|b/4|m ⁴–mh(t) , to study hysteresis effects. The field is swept at a constant rateh(t)=h(0)+ht. The stochastic jump values of the field {h_J from an initially prepared metastable minimumm(0) are recorded, on passage to a global minimum m(). The results are: (a) The mean jump¯h _J(h) increases (hysteresis loop widens) with h, confirming a previous theoretical criterion based on rate competition between field-sweep and inverse mean first-passage time (FPT); (b) The broad jump distribution(h _J,h) is related to intrinsically large FPT fluctuations ( ²–²)/ ² O(1), and can be quantitatively understood. Possible experimental tests of the ideas are indicated.     

Renormalized transport equations for the bistable potential model

Renormalized transport equations for general Fokker-Planck systems are derived and applied to the bistable potential model. The exact equation for the expectation value x _t can be evaluated in both domains Dx _± and xD ₀ outside and between the potential minima, leading to drastic differences of the dynamics prevailing inD _± andD ₀, respectively.     

Correlation inequalities for the truncated two-point function of an Ising ferromagnet

We establish the following new correlation inequalities for the truncated twopoint function of an Ising ferromagnet in a positive external field: _j ; _l ^T _j ; _k ^T _k ; _l ^T , and _j ; _l ^T _{k K j} ; _k ^T _{k l} , whereK is any set of sites which separatesj froml. The inequalities are also valid for the pure phases with zero magnetic field at all temperatures. Above the critical temperature they reduce to known inequalities of Griffiths and Simon, respectively.NSERC Postgraduate Fellow, 1978–1981. Research supported in part by NSF Grant No. PHY-78-25390-A02.     

Average coordination-number dependence of glass-transition temperature in Ge-In-Se chalcogenide glasses

Twenty-six glassy compositions, belonging to the Ge_xIn₆Se_94-x and Ge_xIn₁₂Se_88-x families of the Ge-In-Se system, were prepared from high purity constiment elements. Differential Scanning Calorimetry (DSC) measurements were carried out on these glasses. The DSC thermograms were used to determine the glass transition temperatures (T _g) for the compositions examined. TheT _g-composition dependence of the Ge_xIn₆Se_94-x family shows a minimum inT _g at a value of the average coordination number, r, equal to 2.4. For both families of the glasses examined, theT _g-r dependence displays maxima at r=2.75 and r=2.83 for Ge_xIn₆Se_94-x and Ge_xIn₁₂Se_88-x families, respectively. These results are interpreted by using the Phillips model of rigidity percolation and Chemically Ordered Covalent Network (COCN) model.     

The growth of crystalline vapor deposited carbon-60 thin films

Thin films (25-2500 Å) of C₆₀ molecules have been deposited on both (001) NaCl and mica substrates at varying temperatures by resistive evaporation. Both electron diffraction and high resolution microscopy have been used to assess the degree of crystallinity, the orientational ordering and the nature of the defects present in these face-centered-cubic films. For NaCl, optimum conditions yielded polycrystalline films with a tendency towards a 110 orientation, while for mica, extended single crystal films have been fabricated which exhibit a 111 direction normal to the film surface.     

Magnetic moments of proton drip-line nuclei13O and9C

The magnetic moments of the proton drip-line nuclei¹³O(I = 3/2^–,T _1/2 = 8.6 ms) and 9C(I = 3/2^–,T _1/2 = 126 ms) have been determined for the first time through the combined techniques of polarized radioactive nuclear beams and-NMR detection. The observed magnetic moments are ¦(¹³O)¦ = 1.3891 ±0.0003 _N and ¦(⁹C)¦ = 1.3914 ±0.0005 _N. Spin expectation values are deduced to be 0.76 and 1.44 for¹³O and⁹C, respectively. While the of¹³O is consistent with the systematics from isospinT= 1/2 mirror pairs, the of⁹C is unusually large, even far larger than the single particle value, = 1.     

Fast helium production in interactions of 3.7 A GeV <Superscript>24</Superscript>Mg with emulsion nuclei

We have studied the properties of the relativistic helium fragments emitted from the projectile in the interactions of ²⁴Mg ions accelerated at an energy of 3.7 A GeV with emulsion nuclei. The total, partial nuclear cross-sections and production rates of helium fragmentation channels in relativistic nucleus-nucleus collisions and their dependence on the mass and energy of the incident projectile nucleus are investigated. The yields of multiple helium projectile fragments disrupted from the interactions of ²⁴Mg projectile nuclei with hydrogen H, light CNO and heavy AgBr groups of target emulsion nuclei are discussed and they indicate that the breakup mechanism of the projectile seems to be independent of the target mass. Limiting fragmentation behavior of fast-moving helium fragments is observed in both the projectile and target nuclei. The multiplicity distributions of helium projectile fragments emitted in the interactions of ²⁴Mg projectile nuclei with the different target nuclei of the emulsion are well described by the KNO scaling presentation. The mean multiplicities of the different charged secondary particles, normally defined shower, grey and black ( n_s, n_g and n_b) emitted in the interactions of 3.7 A GeV ²⁴Mg with the different groups of emulsion nuclei at different ranges of projectile fragments are decreasing when the number of He fragments stripped from projectile increases. These values of n_i ( i = s, g, b and h particles) in the events where the emission of fast helium fragments were accompanied by heavy fragments having Z 3 seem to be constant as the He multiplicity increases, and exhibit a behavior independent of the He multiplicity.     

Deformation and annealing textures of rolled nickel single crystals

Textural and structural analysis is conducted on nickel single crystals of unstable orientation in a compression deformed (=83%) and annealed state. The formation of different deformation textures (DT) on opposite surfaces of compressed crystals is established. The relief and band structure corresponds to two-component DT {110} 112, observed in the compression plane. Annealing (573°K) leads to the appearance of recrystallization grains on the two component DT side {110} 112. Orientationally, the first recrystallization grains correspond to the intersection of the peripheral portions of the texture maxima associated with both components of DT. On the side with DT {123} 212, indications of recrystallization were not observed. Application of the texture method with defocus allowed the comparison of the state of the lattice in the regions of the crystal having different orientations. The experimentally observed inhomogeneity of the development of the structure for primary recrystallization is explained by the inhomogeneity of the deformed structure and by orientational factors.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 45–50, June, 1986.     

Isotonic and isobaric dependencies of nuclear charge radii for rare-earth nuclei

Isotonic and isobaric dependencies of nuclear charge radii in the region between Z=54 and Z=70 are obtained from the analysis of isotope shift data r² and muonic and electron scattering data on r². They are compared with the predictions of the droplet model and the Hartree-Fock calculations. The isobaric dependencies of r² have proven to be especially sensitive to the choice of an effective nucleon-nucleon interaction.     

Target mass dependence of mean slow particle multiplicity in high energy hadron-nucleus interaction

This work presents a study on the dependence of mean slow particle multiplicity (N_h) on the mass numberA of the target nucleus for a wide range of target mass and energy. It has been shown that this dependence can be best expressed by the relation N _h= 0.57A^0.61.The author would like to express his indebtedness to Prof. A. Herz (CERN), Prof. K. D. Tolostov (JINR), Prof. R. Wilkes (University of Washington) for kindly supplying the exposed emulsion plates.