Random walks on inhomogeneous lattices

For lattices with two kinds of points (black and white), distributed according to a translation-invariant joint probability distribution, we study statistical properties of the sequence of consecutive colors encountered by a random walker moving through the lattice. The probability distribution for the single steps of the walk is considered to be independent of the colors of the points. Several exact results are presented which are valid in any number of dimensions and for arbitrary probability distributions for the coloring of the points and the steps of the walk. They are used to derive a few general properties of random walks on lattices containing traps.Presented at the Symposium on Random Walks, Gaithersburg, MD, June 1982.     

THE CORRELATION EFFECT ON THE CHAIN MOTION CONTRIBUTION TO IONIC TRANSPORT IN POLYMER ELECTROLYTES

The ionic transport process in polymer electrolytes (such as polyethylene oxide) wassimulated numerically on a two dimensional square lattice where charge carriers areaccommodated by the lattice sites connected randomly with available bonds to represent theamorphous chain configuration. Following the dynamic bond percolation theory(DBPT),the chainmotion contribution to the ionic conduction was incorporated via periodical renewal of the randombond configuration. To check and extend the prediction made by DBPT employing global abruptbond renewal,spatial correlation of the bond reassignment was introduced to the system by: 1)regional bond renewal and 2) organized bond motion. It is found that the difference between thediffusivities simulated involving regional bond renewal and those of DBPT becomes negligiblewhen the bond renewal rate approaches the carrier hopping rate.     

Low temperature synthesis and characterization of porous anatase TiO2 nanoparticles

An ethanol solution of Ti-peroxy compounds was prepared from the ethanol solution of titanium isopropoxide (Ti(O-iPr)4) and H2O2. Heating of the ethanol solution of the Ti-peroxy compounds at 348 K formed a Ti-peroxy gel, and heat treatment of the gel at 348 K for more than 6 h formed gels that consisted of anatase nanoparticles. The diameter of the anatase nanoparticles increased from 9 to 15 nm as the heating time increased from 6 to 48 h. According to the results of the N2 adsorption measurement, the anatase nanoparticles had micropores, and the specific surface area (SBET) was in the range of 254 to 438 m2/g. The particle size, lattice strain, specific surface area, and photocatalytic activity of the anatase nanoparticles can be regulated by the heating time of the Ti-peroxy gel at 348 K.     

Methane Decomposition in a Barium Titanate Packed-Bed Nonthermal Plasma Reactor

The behavior of lattice oxygen species of the ferroelectric material during methane oxidation was investigated using a nonthermal plasma reactor packed with BaTiO ₃ pellets. Lattice oxygen species in BaTiO ₃ play an important role in the formation of N ₂ O and the oxidation of CH ₄ . The oxidation products such as CO and CO ₂ were formed from independent reaction pathways. Lattice oxygen species were able to preferentially oxidize the carbon species deposited on the pellet surface into CO. Also, N ₂ O and NO _x were independently formed in the N ₂–O ₂ reaction, suggesting that different oxygen species give N ₂ O and NO _x. N ₂ O was produced by the oxidation of molecular nitrogen with lattice oxygen species.     

用重复卷积法求解物理宽化函数

用重复卷积法求解物理宽化函数吴万国,林嘉　（福州大学中心实验室,福州３５０００２）（中国（福建）对外贸易中心集团,福州３５０００１）关键词Ｘ射线衍射,晶粒度,晶格畸变,重复卷积粉末试样的Ｘ射线衍射谱线一般具有一定的宽度,引起话线宽化的主要原因有仪器致...     

General analysis of the measurements of the lateral crystal lattice moduli of semicrystalline polymers by x-ray diffraction and the application to nylon 6

A mathematical representation based on a linear elastic theory is proposed by which one may investigate the dependences of molecular orientation and crystallinity on the crystal lattice moduli and linear thermal expansion coefficients in the direction perpendicular to the chain axis as commonly measured by x-ray diffraction. In the theoretical calculation, a previously introduced model was employed in which oriented crystalline phase is surrounded by oriented amorphous phase and the strains of the two phases at the boundary are identical. The mathematical analysis indicated that the lateral crystal lattice moduli and linear thermal coefficients as measured by x-ray diffraction may be different from the intrinsic crystal moduli and linear thermal coefficients of a crystal unit cell, depending on the structure of the polymer solid. The numerical calculation was applied to nylon 6. As a result, it may be confirmed that the lateral crystal lattice moduli measured by x-ray diffraction are sensitive to the morphology of the bulk speciments and close to the intrinsic crystal moduli if the morphology of the test specimen can be represented by a parallel model with respect to the original stretching longitudinal direction.     

Metastable systems driven by colored noise: The stationary state

The influence of the Bardeen-Herring back-jump correlations on the Fermi-Dirac statistics of the one-dimensional nonhomogeneous fermionic lattice gas is studied by the Monte Carlo simulation technique and semianalytically. The resulting distribution is obtained, exhibiting increased population of the lower levels in comparison to the Fermi-Dirac statistics.     

Molecular intercalates

The paper deals with the relations between host lattices and guest molecules. Several types of interaction of the guest molecules and the host material are explained and some conclusions are made about the arrangement of various guest molecules in the van der Waals' gap.     

Relations between site percolation thresholds

By decomposing certain lattices into two sublattices, and examining at percolation threshold the structure of their infinite clusters, an approximate relation between p _c ⁰ , of the original lattice and p _c ¹ , of the sublattice is established: p _c ⁰ (p _c ¹ )^1/2. It is conjectured that an inequality always holds: p _c ⁰ (p _c ¹ )^1/2, and heuristic arguments are given to substantiate it. By similar considerations good estimates forp _c of certain correlated percolation problems are also obtained.     

Lattice dynamical study of body-centred tetragonal indium

The phonon dispersion curves, phonon frequency distribution function as well as the lattice specific heat of body-centred tetragonal indium have been deduced using a lattice dynamical model which includes central, angular and volume forces. Six elastic constants, four zone boundary frequencies and an equilibrium condition were used in the evaluation of the force constants. It is shown that this model is elastically consistent and satisfies the symmetry requirements of the lattice, the phonon frequencies of indium deduced from it are in very good agreement with the experimental values of Reichardt and Smith and the theoretical values of Garrett and Swihart, and theθ _D values compare well with the experimental values over a wide temperature range. The apparent discrepancies in the phonon dispersion curves and theθ _D-T curves obtained from deficient models, importance of umklapp processes and the significance of angular forces in the lattice dynamical models are discussed.