Continuous Random Network Model Research Articles

Structure changes in amorphous silica by neutron irradiation

Wide angle, small angle, and very-small angle X-ray scatterings (WAXS, SAXS and VSAXS) as well as optical microscopy are observed for amorphous silica before and after neutron irradiation [3×10 10 n th/cm 2, (48±2)°C]. The results are analyzed by employing the continuous random network (CRN) model [Zachariasen, J. Am. Chem. Soc. 54 (1932) 3841] that is topologically equivalent to the dense random packing (DRP) model for metallic glass (hard spheres being replaced by deformable spheres containing Si 2O 4 structural units). The effects of irradiation, as deduced from the broadening of the innermost haloes in WAXS, are interpreted in terms of an enhancement of randomness in the packing of the spheres materializing the structural unit, and in the internal structures of the spheres. This involves the rearrangements of the OSiO network that results in the local invalidation of the CRN-DRP equivalence. Consequently, small (25 Å) and large ( 2×10 5 A ̊ ) structural inhomogeneities are produced that can effectively be disclosed by WAXS, SAXS, VSAXS, and optical microscopy. Arguments are advanced in which these structural changes are viewed as deviations from the DRP-equivalent CRN model in an analogous way as interpreting the radiation effects of amorphous Pd 80Si 20 (Doi et al., J. Non-Crystalline Solids 34 (1979) 405).

Amorphous semiconductors: Structural models

The structure of amorphous semiconductors has become the subject of intense study in recent years. In this paper, the models, that have been constructed and applied to represent the structures, have been briefly reviewed. Details of the construction of continuous random network (CRN) models have been presented and a comparative study of the microcrystallite model and the random network model has been made in the light of their recent applications.

Distortion energy distributions in the random network model of amorphous silicon

Distortion energy distributions (DEDs) in the relaxed Polk-Boudreaux 519-atom continuous random network model (PB model) of amorphous silicon (a-Si) have been obtained. The Keating potential was used for the relaxation and calculation of the DEDs. It is found that the bond stretching DEDs over bonds and atoms fit f 1( χ 2) and f 4( χ 2) type functions, which are the chi-square distribution functions with 1 and 4 degrees of freedom, respectively. The bond bending DEDs over angles and atoms fit f 1( χ 2) and f 5( χ 2 type functions, respectively. The fact that both the bond stretching and the bond bending DEDs fit chi-square distribution functions confirms the true randomness of the relaxed PB model. The mean value of the bond bending distortion energy of an atom is found to account for the major part of the observed heat of crystallization per atom.

A continuous random network model for vitreous boron trioxide

The structure of glassy boron trioxide B 2 O 3 is a subject of debate since it is not yet established which of two possibilities, either -BO 3 triangles or -B 3 O 6 ‘boroxol’ rings, forms the structural unit of a continuous random network describing the structure. We describe the construction of the first hand-built ‘ball-and-stick’ structural model to simulate the structure of glassy B 2 O 3 . It is composed solely of -BO 3 triangles with no boroxol rings whatsoever; the calculated scattering properties of the model agree very well with experimental X-ray and neutron data, although the density of the model is some 17 % higher than the experimental value. This might be reduced either by relaxing the constraint placed during construction that the model be made as dense as possible, or by incorporating a small proportion of boroxol units.

A structural model for the interface between amorphous and (100) crystalline silicon

Abstract A structural model for the interface between amorphous and (100) crystalline Si has been constructed by building a model of a continuous random network (CRN) on a crystalline substrate. In relaxing the atomic coordinates to minimize the elastic energy, the Keating Potential was used for the interatomic interactions. The interface consists of 121 atoms on the amorphous and 230 atoms on the crystalline side. In the 121-atom CRN model, the r.m.s. deviations of the bond lengths and bond angles are 1·05% and 6·86° respectively, and the bond-angle distribution, dihedral-angle distribution, and reduced intensity function F(s) are similar to a bulk CRN model. The principal results characterizing the interface are (a) the r.m.s. bond-angle deviation in the crystal is 3·52° (not zero), and (b) the r.m.s. bond-angle deviation on the boundary surface between the amorphous and crystalline sections is 9·05° indicating a larger distortion than in the bulk CRN model.

Structural and vibrational properties of a model of vitreous As 2O 3

We have constructed and analyzed a 635-atom continuous random network model of vitreous As 2O 3. Computer relaxations of the strain energy carried out for different distributions of bond angles indicate that bond angles in the glass are similar to those found in crystalline forms of As 2O 3. Vibrational spectra calculated for the model reproduce the main features seen in recent measurements of the infrared and Raman spectra of vitreous As 2O 3 but suggest an intermediate range order more like that found in crystalline forms.

Physical and chemical properties of SiSiO 2 transition regions

Current understanding on physical and chemical properties of Si-SiO 2 transition regions is reviewed from the viewpoints of the morphology and the chemical structure of the transition region and the interface trap states. Normal and cross-sectional transmission microscopies have revealed the interface asperity which is consistent with the study of the carrier mobility in surface layers. Various analytical measurements, such as ion-scattering spectrometry and electron spectroscopy, have indicated an abrupt transition model for the SiSiO 2 systems. The transition region includes strained SiO 2, monolayer of SiO x as a connective region from the bulk SiO 2 to Si and disordered Si layers in the Si substrate. The abrupt transition model has been used for theoretical calculation of the interface trap states originated by bonding defects, and also does not conflict with the continuous random network model for the SiSiO 2 transition region.

The pentagonal dodecahedral model of vitreous silica and its compatibility with diffraction experiments

AbstractROBINSON's pentagonal dodecahedral model represents a very interesting non‐crystallographical heterogeneous description of atomic arrangement in vitreous silica. The pair function distribution of this model has been calculated and compaired with a measured pair function distribution of vitreous silica. The pentagonal dodecahedral model seems to be a little better than cristallite models but cannot bear comparison with the continuous random network model.

Pulsed NQR in amorphous, orthorhombic and rhombohedral arsenic

Pulsed nuclear-quadrupole-resonance (NQR) measurements have been performed on rhombohedral, orthorhombic, and amorphous (a −) arsenic. Measurements of T 1 provide evidence of low-frequency disorder modes in a-As. The NQR frequencies indicate that the bonding is predominately p-like in all three solids. The asymmetric NQR line shape of a-As is consistent with the distribution of dihedral angles implicit in the continuous random network models. The bond-angle distributions inferred from x-ray scattering and continuous-random-network models do not result primarily from a distribution in bond hybridizations.

Thermodynamics and lattice vibrations of minerals: 3. Lattice dynamics and an approximation for minerals with application to simple substances and framework silicates

The principles of lattice dynamics are briefly reviewed in this paper, and from these principles a simple, generally applicable lattice vibrational spectrum is proposed for minerals. The spectrum can be used to calculate the thermodynamic functions in the harmonic approximation. The model proposed is consistent with lattice dynamics and is sufficiently detailed in its assumptions about the distribution of modes that the thermodynamic functions are closely specified. The primitive unit cell, containing s atoms, is chosen as the fundamental vibrating unit; it has 3s degrees of freedom, three of which are acoustic modes. Anisotropy of these modes is included by use of anisotropic shear velocities for the two shear branches: dispersion is included by use of a sinusoidal dispersion relation between frequency and wave vector for all three acoustic branches. Optic modes, which comprise 3s–3 degrees of freedom, are represented by a uniform continuum, except for ‘intramolecular’ stretching modes (such as Si‐O stretching modes) which can be enumerated and identified as being isolated from the optic continuum. Parameters for the model are obtained from elastic and spectroscopic data; the model is independent of any calorimetric data. It is applied to give the temperature dependence of Cv over the range 0°–1000°K of halite, periclase, brucite, corundum, spinel, quartz, cristobalite, silica glass, coesite, stishovite, rutile, albite, and microcline. The specific heat of the simple Debyelike substances, halite and periclase, is reproduced well by the model. The influence of the additional formula unit of H2O on the vibrational and thermodynamic properties of brucite, as compared to periclase, is discussed. The heat capacities of the relatively simple minerals, spinel and corundum, are given accurately by the model. The heat capacities of quartz, cristobalite, and coesite are accurately predicted from spectroscopic data through the model. The heat capacity of silica glass is discussed in terms of the classic continuous random network (CRN) model and a paracrystalline model, the pentagonal dodecahedral (PD) model of Robinson (1965). The PD model appears to be more consistent with measured Cv data than the CRN model. The heat capacity data of rutile are reasonably reproduced by the model as are the data for stishovite at temperatures above 50°K. Measured data for stishovite below 50°K appear to contain an excess heat capacity relative to the model; this excess may arise from surface energy contributions, as was suggested by Holm et al. (1967), and it is suggested that the model provides a better estimate of the low‐temperature vibrational heat capacity of stishovite than the measured data. The heat capacities of albite and microcline are reproduced well by the model. The model is only a simple approximation to real lattice vibrational spectra, but it appears to work well for a large number of minerals and is therefore useful in correlating structural, compositional, elastic, spectroscopic, and thermodynamic properties for purposes of extrapolation and prediction of these properties.

Structural description of iron-silicon amorphous alloys

Abstract Typical Fe x Si1-x amorphous alloys have been studied by electron diffraction and resistivity measurements in a wide concentration range (0 ≤ x ≤ 0·75). A description of the short-range order in these systems is proposed in terms of a dense random packing of hard spheres, as in pure amorphous metals, if x ≥ 0·3. In the small iron concentration range (x ≤ 0·2) the structure becomes progressively similar to an amorphous semiconductor, as pictured by a continuous random network model. Iron and silicon atoms appear to be distributed without chemical correlations.

Chemical bonding effects on the diffraction intensities in amorphous silicon and carbon

Abstract The X-ray and electron diffraction intensities from amorphous silicon and carbon cannot be accounted for solely from consideration of a model structure and the appropriate atomic scattering factor. Therefore the aim of the present work is to study the effects of chemical bonding on these diffraction intensities. The linear combination of atomic orbitals description of a covalent bond has been modelled as a superposition of two (identical) spherical charge distributions centred on the nuclei and a third (different) spherical distribution at the bond centre. Using this model of the covalent bond density, plus nuclear‐nuclear, nuclear-bond centre and bond centre–bond centre partial structure factors, the diffraction intensities are calculable without further approximation. The partial structure factors have been calculated from two models: (a) a continuous random network (CRN) model including odd membered rings; and (b) an ordered units (polytetrahedral) model. The principal conclusions are (i) that...

On the topological and electronic structure of amorphous semiconductors

Using a basis of bonding orbitals and tight-binding matrix elements depending on the local topology the author has calculated the valence band densities of states (VBDOS) appropriate to a series of seven continuous random network (CRN) models of the structure of a-Si. Comparison with experimental data allows quantitative bounds to be put on the average number of 'wrong bonds' present in a-Si. A surprisingly large number of 'wrong bonds' are required before significant deviations from the form of the VBDOS of a purely even-ringed CRN are obtained. It is argued that in studies of the topological disorder of other such systems only two or three models of very different topologies need be considered in order to identify a typical topological structure.

Vibrational spectra and topological structure of tetrahedrally bonded amorphous semiconductors

Abstract Calculations of the vibrational spectra of continuous random network models of tetrahedrally bonded amorphous semiconductors are presented. Nearest neighbour central and non-central force constants are used. The results show that the shape of the TO-like peak of the spectrum depends on both the topology and bondangle distribution of the network. Comparison with experimental data suggests that a-Ge contains slightly fewer odd-membered rings than the Polk model and an average bond-angle distortion of 10° or more. On the other hand the shape of the TA-like peak depends more directly on the topology of the network, giving a clearer distinction between the results for structures containing both odd and evenmembered rings and those containing even rings only. Tentative comparison with experimental data for a-GaAs suggests a structure containing very few oddmembered rings, while the data for a-Ge indicate a significant number of oddmembered rings.

Optical spectra and local order in amorphous TlCl and TlBr

AbstractThe optical absorption spectra of amorphous TlCl and TlBr films are investigated in the photon energy range near the absorption edge. Annealing the films and tracing the spectra with annealing temperature discontinuous changes in the shape of the spectra are observed at two different annealing temperatures. A continuous random network model is presented for the structure of the amorphous TlCl and TlBr films, which is in agreement with recent structural data. The annealing dependence of the spectra is understood by assuming the existence of two disordered modifications with different short‐range order.

One-band density of states for some models for amorphous semiconductors

The authors use the equation-of-motion method to obtain directly the one-band density of states, projected on interior atoms, for three approximately 500-unit continuous random network models for amorphous group IV semiconductors and one 533-atom continuous random network model for amorphous arsenic. The presence of a sharp peak in the lower part of the band and the retreat of the lower band-edge are correlated with the concentration of five-membered rings of bonds.

Structural model for amorphous solid water

We construct two continuous random network models for amorphous solid water and compute their x-ray and neutron diffraction properties. The results for one type of network accord well with experiment. This implies that there are important relatively long-range, as well as short-range, positional correlations in the solid amorphous phase of water.

Relaxed continuous random network models (II): Scattering properties

We report here the result of our calculations on the scattering properties of two random networks. One of these is the 519 atom model due to Polk and the other a 201 atom model generated by Steinhardt et al. We compare experimental and calculated values of the reduced intensity function and the influence of relaxation of a network on the reduced intensity function. We present calculations of the structure factor, dark field and interference images for these models. As in our earlier findings there is at least orientation in each random network which shows a considerable degree of order and can qualitatively account for the contrast observed in electron micrographs. In the latter calculations we also explore effects of aperture geometry on the image results.

Kinematical theory of images from polycrystalline and random-network structures

Kinematical electron microscope images to be expected from the Polk continuous random-network model and from a polycrystalline cluster have been computed. Dark-field images of both models show qualitatively similar speckle patterns. Fringes are observed in bright-field images of thin polycrystals (t≲ 40Å), but they disappear in thicker samples and are not observed in any of the Polk-model images. The experimental observation of fringes therefore cannot be explained by the current theory, possibly because it does not take account of the angular spread of illumination. Except perhaps in very thin specimens, it seems impossible at present to draw any reliable conclusions about the local atomic arrangement in amorphous materials by simple examination of electron micrographs.

Continuous Random Network Model for Amorphous Solid Water

Continuous random network models representing amorphous solid water have been constructed. The x-ray and neutron scattering predictions for one type of model agree quite well with experimental results.