Structural Unit Model Research Articles

Atomic structure of (001) twist boundaries in f.c.c metals Structural unit model

Abstract The applicability of the structural unit model, developed for tilt boundaries by Sutton and Vitek (1983), to (001) twist boundaries in f.c.c. metals is investigated. The model is found to be useful in discussing the continuity of boundary structure with misorientation and the Burgers vectors of screw grain boundary dislocations. A surprising result is that the structures of low-angle boundaries (with misorientation, less than 22–62°) vary discontinuously with misorientation, in the sense that different boundary units appear in boundaries with slightly (in the limit infinitesimally) different misorientations, in accordance with a simple geometrical rule. At higher misorientations the boundary structure varies smoothly with misorientation and two non-equivalent decompositions into structural units can always be found. One of these decompositions is invariant with respect to the symmetry elements of the overall boundary structure, while the other is not. The continuity of boundary structure and grai...

Interatomic Forces and Structure of Grain Boundaries

ABSTRACTOver the past two decades, grain boundary structures have been investigated, with increasing frequency, using computer simulation techniques. The accuracy of the potentials used to describe the interaction between atoms is essential to the success of any computer modelling and practically all these studies have been made assuming that the atoms exert pair-wise forces on each other. This paper discusses the applicability and limitations of this assumption and the validity and applicability of the simulation results obtained with pair-potentials. First, it is shown that certain structural features of grain boundaries are independent of the potential used. Such results form, for example, the basis of the structural unit model which relates the structures of boundaries corresponding to different misorientations. Secondly, the multiplicity of boundary structures and its physical implications are discussed. In particular, we report on the complexities of the structure of Σ=5 [001] twist boundaries and on alternative structures of [111] twist boundaries near the Σ=3 twin orientation, both found by computer modelling. These results, which are of general nature, are compared with experimental observations by X-ray diffraction and transmission electron microscopy and a very good agreement is found. However, exact positions of atoms in calculated structures depend on the potential used. Hence, to study properties sensitively dependent on these positions requires to go beyond the pair-potentials.

A computer simulation study of 〈001〉 and 〈111〉 tilt boundaries: the multiplicity of structures

The sources of the multiplicity of metastable structures of grain boundaries are discussed using a recently developed structural unit model of grain boundary structure. Two sets of computer calculations of symmetrical tilt boundaries are presented and it is shown that the calculated multiplicity of metastable structures is readily predicted by the structural unit model. This multiplicity is likely to be very extensive in the case of general grain boundaries. The implications of the structural multiplicity of grain boundaries for various grain boundary phenomena as well as for interpretation of “direct observations” of grain boundary structure are discussed.

Structural Unit Models for High Angle Symmetrical Tilt Boundaries in Ordered Compounds with the Ll2 Structure

ABSTRACTHard sphere models were used to determine densest configurations in symmetrical [100] and [110] tilt boundaries in compounds with the Ll2 structure. The minimum allowed interatomic distances used in these models were estimated from interatomic potentials and the structures of the intermetallic phases in the binary system. The structural unit model is used to analyze the possible ground states for ordering.Two different cases were analyzed corresponding to compounds with “soft” potentials (i.e. Cu3 Au) and “hard” potentials (i.e. Ni3Al). For the Cu3Au type the grain boundary structures obtained were similar to those reported by other investigators for pure fcc metals. Several boundaries were found to be a “two phase” structure, differing in composition and ordering state. This leads to a certain degree of clustering in the boundaries. The contribution of clustering to the grain boundary energy is calculated in a point approximation based on the first coordination shell.For compounds of the Ni3Al type the structures that are densest were found to be generally diffetent from the low energy configurations of boundaries in, pure fcc metals and Cu3 Au. These configurations preserve order, but are much less dense. The possibility of grain boundary “phases” that are not present in other fcc materials may constitute an explanation for the extreme GB weakness observed in Ni3Al and other Ll2 compounds with high ordering energy.

Simple structural unit model for core-dependent properties of symmetrical tilt boundaries

Consider any physical property, p, of a grain boundary, which depends primarily on the atomic structure of the core, e.g., the boundary diffusivity or the core energy. This paper demonstrates that the recently determined structural unit model for the core structure allows one to estimate p for any boundary in a series of symmetrical tilt boundaries possessing a range of tilt angles if values of p for a few particular boundaries in the series are known. More specifically, we shall show that p for all boundaries with misorientations between those of two so-called ''favored boundaries'' can be estimated from a knowledge of the values of p for the two favored boundaries and the intermediate boundary made up of equal numbers of the structural units comprising the two favored boundaries. Applications of the results to measurements of boundary diffusivities and boundary energies are indicated briefly.

Similarities in amorphous and crystalline transition metal–metalloid alloy structures

In many amorphous and glassy systems the local structure seems to be essentially the same in amorphous and crystalline phases. It thus becomes possible to define a ‘local structural unit’, such as the SiO4 group in silicates. Determination of the structure then reduces to the problem of describing how the local units are connected and packed in the medium-range structure. There is mounting evidence that alloys of transition metals with metalloids are more adequately described by arrangements of stereo-chemically-defined structural units than by alternative descriptions in terms of random packing of atoms. There are three phases, Fe3C, Ti3P and Fe3P, which may serve as models of local structural units. These lattices differ to a small degree in the symmetry of the metalloid nearest-neighbour shell but there are major differences in the arrangement of local structural units. Although the experimental evidence is limited, it seems that the distinctive features of the local and medium-range topologies of the crystalline phases are represented in the structures of each of the corresponding glasses.

Chloromethylated polystyrene reaction with tris(2‐hydroxyethyl)amine. I. Crosslinked polymers prepared by chloromethylated polystyrene with tris(2‐hydroxyethyl)amine

AbstractA multifunctional crosslinked polymer resulted from a chloromethylated polystyrene reaction with tris(2‐hydroxyethyl)amine. A benzyl chloride reaction (chosen as a structural unit model) with tris(2‐hydroxyethyl)amine was investigated to explain the reasons for the crosslinking. Amino‐ethers and tris(2‐hydroxyethyl)amine hydrochloride in addition to ammonium quaternary salt were isolated from this reaction. The formation of amino‐ethers proved that an ammonium quaternary salt rearrangement also takes place during the quaternization reaction. This rearrangement leads to chloromethylated polystyrene during its reaction with tris(2‐hydroxyethyl)amine.

Simple kinetic model diffusion controlled decay of free radical in highly crystalline polyolefins

AbstractA simple kinetic model for the diffusion controlled decay of radicals in two‐phase high crystalline polyolefins is proposed. The analysis of the kinetic system was carried out taking into consideration a structural unit model containing all the structural properties of the macroscopic system. Radical decay in the amorphous phase and on the surface of lamellae has been discussed taking into account Wait's theory of diffusion controlled reactions, radiation boundary conditions, and the flux of radicals through lamellae surfaces.A rough computer calculation using the derived equation and the experimental data of Kashiwabara on radical decay in γ‐irradiated polyethylene was carried out leading to DA values equal to 10−9 cm2/sec, which favors the interchain hydrogen atom “hopping” mechanism of radical migration.

Grain boundary faceting of 〈101̄0〉 tilt boundaries in zinc—II

Observations of faceting of high-angle 〈101̄0〉 tilt grain boundaries in zinc have been made in the misorientation range 3° < θ < 36.5°. A structural unit model of the atomic configurations in these low energy faceted boundaries has been developed which accurately describes the observed changes in facet inclination with boundary misorientation. Following the predictions of the model, faceting of 〈101̄0〉 tilt boundaries in zinc in the misorientation range 49.5° < θ < 55.2° was looked for and was found as anticipated. The predicted change in facet morphology with boundary misorientation was observed here also. The structural units in the model are taken to be short segments of 〈101̄0〉 coincidence or near-coincidence tilt boundaries which combine to form the asymmetric tilt boundaries making up the facets. Characteristics of the structural units and the manner in which they combine to produce low-energy atomic configurations are discussed.

Evaluation of Mechanical Anisotropy of Uniaxially Stretched PVA Films

The mechanical anisotropy of uniaxially stretched PVA films was investigated experimentally and theoretically. The theoretical calculation of the mechanical anisotropy of the films was carried out of two structural models. The first calculation was performed by averaging the mechanical anisotropies of the oriented structural units on the basis of homogeneous stress hypothesis. On this calculation, a structural unit model was constructed by combining the orthorhombic crystallite with the isotropic amorphous phase in parallel or series to the reference axis. The other theoretical calculation of the mechanical anisotropy of the films was carried out of an averaged structural model which was obtained by averaging the orientations of crystallites and amorphous chains, respectively, and combining the averaged crystalline unit with the averaged amorphous phase in parallel and series to the stress direction. The anisotropy of amorphous phase in the averaged structural model was considered by assuming the affine deformation mechanism.The result obtained from every theoretical calculation shows the experimental results of the uniaxially stretched PVA films in good agreement with each other.

Study of Young's Modulus of Polymer Film Filled with Fragmented Glass Fibers

There have been several papers hitherto published relating to young's modulus of polymer film filled fragmented glass fibers to the moduli of its constituents. Few of them have, however, taken the orientation distribution of the glass fibers into consideration in calculating the bulk modulus.In this paper, the effect of orietation distribution of the glass fiber upon the bulk modulus is first formulated on a basis of the homogeneous stress hypothesis for an aggregate model of concentric structural units consisting of the glass fiber surrounded by the polymer component. Then, the structural unit is corrected so that the normal stress in the fiber varies along the fiber axis.The anisotropy of Young's modulus calculated upon the above given model agrees fairly well with that observed for polyethylene and polyester films both filled with glass fibers in a range of volume fractions less than 30%.