The stress driven instability in elastic crystals: Mathematical models and physical manifestations

Summary Equilibrium equations and stability conditions for the simple deformable elastic body are derived by means of considering a minimum of the static energy principle. The energy is supposed to be sum of the volume (elastic) and the surface terms. The ability to change relative positions of different material particles is taken into account, and appropriate natural definitions of the first and second variations of the energy are introduced and calculated explicitly. Considering the case of negligible magnitude of the surface tension, we establish that an equilibrium state of a nonhydrostatically stressed simple elastic body (of any physically reasonable elastic energy potential and of any symmetry) possessing any small smooth part of free surface is always unstable with respect to relative transfer of the material particles along the surface. Surface tension suppresses the mentioned instability with respect to sufficiently short disturbances of the boundary surface and thus can probably provide local smoothness of the equilibrium shape of the crystal. We derive explicit formulas for critical wavelength for the simplest models of the internal and surface energies and for the simplest equilibrium configurations. We also formulate the simplest problem of mathematical physics, revealing peculiarities and difficulties of the problem of equilibrium shape of elastic crystals, and discuss possible manifestations of the above-mentioned instability in the problems of crystal growth, materials science, fracture, physical chemistry, and low-temperature physics.     

Branched polymers in a wedge geometry in three dimensions

We investigate the statistical and dimensional properties of uniform star polymers attached by the branching vertex of degreef in a wedge geometry in three dimensions and described by the wedge angles and. We show that the growth constant is equal to ^f , where is the self-avoiding walk limit. Thef and (, ) dependences of the corresponding critical exponent _f (, ) are studied using Monte Carlo techniques. In the casef=1, our results are compared with existing predictions obtained from series expansion and renormalization group methods. We have also estimated the amplitudes for the mean square radius of gyration and the mean square end-to-end branch length. Our results for the ratio of the mean square radius of gyration of anf-star to that of a linear polymer of the same degree of polymerization attached in a similar wedge, and the analogous ratio for the mean square end-to-end branch length, are consistent with these ratios being lattice-independent quantities.     

Slow quenching for a one-dimensional kinetic Ising model: Residual energy and domain growth

A one-dimensional kinetic Ising model with Glauber dynamics subjected to a slow continuous quench to zero temperature is studied. For a rather general class of cooling schemes, described by a time-dependent temperatureT(t), the mean domain sizeL(t) is calculated along with the residual energye _res (r) as a function of the cooling rater. If the attempt frequency =₀ exp(–/kT), entering into the transition rates, is temperature dependent (i.e., the barrier is non-zero), the asymptotic growth ofL(t) is given byL()–L(t)~exp[–/kT(t)]. For this case the residual energy exhibits a power-law behaviore _res(r) ~r ^{/2(1 + )} forr small, where =4J/ andJ is the nearest neighbor coupling constant. For =0 and for certain cooling schemes the residual energy is zero andL(t)~t1/2, independent ofr.     

天然气和氧偶联制环氧乙烷催化剂的反应性能

研制了天然气和氧经偶联反应制环氧乙烷的Ａｇ－Ｂａ－Ｃｓ／Ａｌ２Ｏ３催化剂（ＮＥＯ－１）。用Ｎ２＋Ｏ２＋Ｃ２Ｈ４和偶联产物气加氧作原料气，在２５０℃，空速２５００ｈ＾－１时，乙烯转化率和ＥＯ选择性分别达到了３０％和８０％，ＮＥＯ－１催化具有适宜的比表面和孔结构，用ＸＰＳ分析发现，与新鲜的催化相比，经活化和反应后的催化剂表面的Ｂａ，Ｃｓ原子浓度增高，并具有较多的吸附氧物种。     

1-氨基环丙烷-1-羧酸的合成: 新型植物生长调节剂

本文报道了合成1-氨基环丙烷-1-羧酸的简便而价廉的方法,即乙酰乙酸乙酯法和α-氰乙酸乙酯法;并测定了产品的结构。     

取代硫脲化合物对作物的生长调节作用

取代脲类化合物已广泛用作除草剂、杀虫剂、杀鼠剂。根据结构活性关系,亦对烯丙基、甲基、二芳基取代硫脲衍生物的植物生长调节活性进行了研究。本文合成了3类取代硫脲化合物:R_1NHCSNHR_2,其中:R_1=苯基,α-萘基,叔丁基,R_2=α-苯基乙     

三硼酸锂晶体的生长形态

用自由生长系统研究了三硼酸锂ＬｉＢ_３Ｏ_５（ＬＢＯ）晶体的实际生长形态。实验表明，它的各晶面簇的重要性的顺序为：｛１１０｝＞｛０１１｝＞｛２０１｝＞｛１１１｝。讨论了ＬＢＯ晶体的生长习性与内部结构之间的关系并应用负离子配位多面体理论模型解释了ＬＢＯ晶体的生长形态。     

甲基丙烯酸全氟烷基代乙酯对天然橡胶乳液辐射改性研究

天然橡胶的性能与其组成中的C C双键有密切关系,由于C C双键的存在,为天然橡胶的改性提供了便利,大多数天然橡胶的改性方法,如氯化、氢氯化、环化、环氧化、接枝共聚等皆是建立在这一思路基础上的.White等[1]认为接枝天然橡胶的目的是提高天然橡胶的机械强度,赋予特殊的功能.作     

动,静态硫化（NR＋SBR）／PE共混体系的结构与性能

用TEM研究了(NR SBR)/PE共混体系经动、静态硫化后的形态结构及其与力学性能的关系。未硫化和静态硫化体系的形态结构与其组成有关,均以含量大的组份为连续相;对动态硫化体系,当(NR=SBR)/PE<70/30时,均以PE为连续相,其性能主要依赖于构成连续相组份的性质。 动态硫化体系的T_g值低于静态体系,随PE组份含量的增加变化不大,而静态硫化体系的T_g值则随PE含量增加向高温方向迁移。用DSC测得动态硫化体系的结晶度比静态体系的大。前者的应力-应变性能也低于后者。     

非线性光学材料──水草酸铵

一水草酸铵（简称ＡＯＭ）是一种优良的电光晶体￣［１］。文献￣［１，２］报道了该晶体的晶体结构，化学式为（ＮＨ＿４）＿２Ｃ＿２Ｏ＿２·Ｈ＿２Ｏ，属正交晶系，Ｐ２２２空间群，晶胞参数ａ＝０．８０３５ｎｍ，ｂ＝１。０３１ｎｍ，ｃ＝０．３８０１ｎｍ，ｚ＝２。本文拟报道ＡＯＭ单晶生长，热化学分析，透过波段以及非线性光学性质的初步研究。