Dynamics of the formation of two-dimensional ordered structures

The growth of ordered domains in lattice gas models, which occurs after the system is quenched from infinite temperature to a state below the critical temperatureT _c, is studied by Monte Carlo simulation. For a square lattice with repulsion between nearest and next-nearest neighbors, which in equilibrium exhibits fourfold degenerate (2×1) superstructures, the time-dependent energy E(t), domain size L(t), and structure functionS(q, t) are obtained, both for Glauber dynamics (no conservation law) and the case with conserved density (Kawasaki dynamics). At late times the energy excess and halfwidth of the structure factor decrease proportional tot ^–x, whileL(t) t ^x, where the exponent x=1/2 for Glauber dynamics and x1/3 for Kawasaki dynamics. In addition, the structure factor satisfies a scaling lawS(k,t)=t ^2xS(kt^x). The smaller exponent for the conserved density case is traced back to the excess density contained in the walls between ordered domains which must be redistributed during growth. Quenches toT>T _c, T=T_c (where we estimate dynamic critical exponents) andT=0 are also considered. In the latter case, the system becomes frozen in a glasslike domain pattern far from equilibrium when using Kawasaki dynamics. The generalization of our results to other lattices and structures also is briefly discussed.     

分子拓扑指数在晶格能中的应用

分子拓扑指数在晶格能中的应用凌天才（重庆师范学院化学系重庆６３００４７）关键词拓扑指数，晶格能分子拓扑指数实际上是分子图的不变量。自ｗｉｅｎｅｒ￣［１］于１９４７年首次提出ｗｉｅｎｅｒ指数并用以关联烃类的沸点等数据以来，分子拓扑指数广泛用于关联与预测...     

Clusters,metastability, and nucleation: Kinetics of first-order phase transitions

We describe and interpret computer simulations of the time evolution of a binary alloy on a cubic lattice, with nearest neighbor interactions favoring like pairs of atoms. Initially the atoms are arranged at random; the time evolution proceeds by random interchanges of nearest neighbor pairs, using probabilities compatible with the equilibrium Gibbs distribution at temperatureT. For temperatures 0.59T_c, 0.81 T_c, and 0.89T _c, with density of A atoms equal to that in the B-rich phase at coexistence, the density C₁ of clusters ofl A atoms approximately satisfies the following empirical formulas: C₁ w(1 –)³ andC ₁, (1 –)⁴Q₁w¹ (2 l 10). Herew is a parameter and we defineQ _l = _K e ^–E(K) , where the sum goes over all translationally nonequivalentl-particle clusters andE(K) is the energy of formation of the clusterK. Forl > 10,Q ₁ is not known exactly; so we use an extrapolation formulaQ _l Aw _s ^–l l ^– exp(–bl ), wherew _s is the value ofw at coexistence. The same formula (withw > w _s) also fits the observed values of C, (for small values ofl) at densities greater than the coexistence density (forT=0.59T_c): When the supersaturation is small, the simulations show apparently metastable states, a theoretical estimate of whose lifetime is compatible with the observations. For higher supersaturation the system is observed to undergo a slow process of segregation into two coexisting phases (andw therefore changes slowly with time). These results may be interpreted as a more quantitative formulation (and confirmation) of ideas used in standard nucleation theory. No evidence for a spinodal transition is found.Supported by AFOSR Grant No. 73-2430D and by ERDA Contract No. EY-76-C-02-3077*000.     

High-density percolation: Exact solution on a Bethe lattice

A new percolation problem is posed where the sites on a lattice are randomly occupied but where only those occupied sites with at least a given numberm of occupied neighbors are included in the clusters. This problem, which has applications in magnetic and other systems, is solved exactly on a Bethe lattice. The classical percolation critical exponents=gg=1 are found. The percolation thresholds vary between the ordinary percolation thresholdp _c (m=1)=l/(z – 1) andp _c(m=z) =[l/(z – 1)]¹/(z–1). The cluster size distribution asymptotically decays exponentially withn, for largen, p p _c .Supported in part by National Science Foundation grant DMR78-10813.     

Synthesis and Crystal Structur of (4,4''-H2bipy)[CdBr4]·H2O

The title compound (4,4'-H2bipy)[CdBr4]·H2O 1 has been synthesized via hydrothermal reaction and characterized by X-ray diffraction. The crystal belongs to monoelinic,space group P21/c with a=8.260(3), b=23.926(7), c=9.774(2) (A), β=106.777(9)°,C10H12Br4CdN2O, Mr=608.26, V=1849.4(9)(A)3, Z=4, Dc=2.185 g/cm3, S=1.005, μ(MoKα)=9.814 mm-1, F(000)=1128, R=0.0646 and wR=0.0989. The crystal structure analysis of 1reveals that the title compound features an isolated structure, based on discrete 4,4'-H2bipy moieties and lattice water molecules which are linked by hydrogen bonds together with tetrahedral cadmium atoms terminally coordinated by four bromine atoms.     

Sr／Ca比变化对红色荧光粉Ca1-xSrxS：Eu^2＋的影响

在CO气氛下采用固相反应法合成了发红光的Ca1-xSrxS:Eu^2 荧光粉，研究了基质阳离子Sr／Ca比变化对其晶体性质及发光性能的影响。结果表明，随着Sr／Ca比的减少，荧光粉的晶胞参数逐渐降低；同时，由于受电子云膨胀效应和晶体场影响，发射主峰向长波方向移动，红色比逐渐增大，色纯度提高。     

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.     

Crystal Structure and Property of Perovskite-Type Oxides Containing Ion Vacancy

Studies on the role of oxygen vacancy in structural change of nonstoichiometric perovskites and a property of oxygen-deficient perovskite-related K₂NiF₄ compounds are reviewed.The structural changes on which the authors focused are cation ordering and lattice distortion. The relationship between the distortion and oxygen vacancy was investigated by comparing the structures of Sr₂(Sr_1-xM_x)TaO_6-d (M = Ca²⁺ and Nd³⁺) solid solutions. It was found that distortion of a perovskite-type lattice decreased with an increasing amount of oxygen vacancies. In order to investigate the relationship between the cation ordering on octahedral sites and oxygen vacancy, structures of stoichiometric Sr_2-xLa_xCo_1-yTa_1+yO₆ and oxygen-deficient Sr_2-xLa_xMg_1-yTa_1+yO_6-d solid solutions were compared. The authors' work reveals that the cation ordering affects the amount of oxygen vacancies in addition to cation charge and size.