Dense Random Packing Model Research Articles

On the structure and vibrational spectra of Cu-Zr alloy glasses

The radial distribution functions of CuxZr1-x (x=0.35, 0.50 and 0.65) have been calculated by the means of the relaxed dense random packing model. The calculated results agree well with the experimental data obtained by both X-ray and neutron diffraction. Based on the present model structures and the pair potentials, the vibrational densities of states have been calculated; from these the sound velocities and elastic constants were estimated. Agreement between theory and experiment is fairly good.

Optical conductivity of amorphous Ta and β-Ta films

Thin films of tantalum evaporated in high vacuum onto fused silica substrates at liquid-nitrogen temperature are amorphous, even after heating above room temperature. On room-temperature substrates, β-Ta, with a 30-atom tetragonal unit cell, is deposited. The electron-diffraction interference function of the amorphous a-Ta agreed best with dense random packing models, although a β-Ta microcrystalline model also gave fairly good agreement. The complex optical conductivity was determined from reflection and transmission measurements in the spectral range 0.5–6.5 eV at room temperature. The results for a-Ta and β-Ta were very similar to each other, differing significantly from bcc α-Ta (deposited onto heated substrates or crystallized from amorphous films), and they could be extrapolated to the measured dc conductivity at zero energy. After subtraction of a Drude contribution with an electron mean-free-path on the order of the interatomic distance, the remainder showed some features of the interband absorption in α-Ta, though somewhat smoothed and weakened. We conclude that the local arrangement of near neighbors is more important than whether long-range order exists.

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).

Partial pair correlation functions of La1− x( Al Ga Au) x metallic glasses from x-ray diffraction data

X-ray diffraction studies of La 1− x Al x , La 1− x ( Al 0.5 Ga 0.5 x , La 1− x Ga x and La 1− x Au x metallic glasses have been performed for x = 0.20, 0.24 and 0.28. Similarities in the radial distribution functions for these materials as well as other data suggest that these alloys are isostructural. Experimental data from different alloys have therefore been used to separate the three different pair distribution functions, which are then compared to dense random packing models and data for other metallic glasses.

Model Calculation for the Fe80B20 Alloy Glass

Abstract Three partial radial distribution functions [RDF’s] are calculated by means of relaxed dense-random packing models for a Fe80B20 glass. The model structures reproduce fairly well recently reported experimental partial RDF's derived from x-ray diffraction and neutron diffraction using isotopic substitutional methods. Most significantly, both the model calculated by means of relaxed dense-random packing models GBB (r), the appearance of a subpeak on the short distance side of the first peak.

Structural investigation of boron-containing metallic glasses

Structural investigations have been made of high boron-containing alloy glasses of compositions Co100−xBx withx=34, 36, 38 and 40 at % measured by X-ray diffraction. The characteristic second-peak splitting in the radial distribution function (RDF) is found for all samples presently investigated. The shoulders are also observed near the distances of 0.20 and 0.34 nm. The partial radial distribution functions of Co-Co and Co-B pairs have been derived from the measured total RDF data by applying the concentration method with the anomalous scattering technique, and the contributions from different atomic pairs to total RDF have been discussed. The calculation by the relaxed dense random packing model has been made for Fe-B alloy glasses with three different boron concentrations, i.e., 15, 25, and 40 at % boron and a comparison between the calculated and experimentally determined data is presented. The present model calculation could give the possible representation for the compositional dependence of the X-ray RDF for amorphous Fe-B alloys with boron contents of up to 40 at % as well as the different peak profile observed in the total RDF of X-ray data between Fe-B and Fe-P glasses.

非晶質固体の“結晶学” 完全非晶質固体の模型

The implications of the dense random packing (DRP) model are discussed, with an expectation that it may represent a possible structure model for perfect amorphous solids. The topological definition of the DRP is argued on the basis of Sadoc's idea that the DRP is an assembly of spheres, close-packed in a curved non-Euclidean space and mapped onto the linear Euclidean space. Thermal properties of the DRP, especially excess entropy, are also discussed in this context. Discussions are evidenced by the observed changes in structures and thermal properties of metallic glasses due to particle bombardments and cold works. Similar arguments prove to apply for systems such as amorphous silicon and amorphous silica.

Local structure and topology of a model amorphous metal

A dense random packing model of amorphous iron was analysed in terms of the Voronoi polyhedral statistics and the recently proposed local structure parameters, in particular stresses and site symmetry coefficients (Egami et al., 1980). The purpose of this study is to clarify the relationship between these two types of methods of describing the local structure of amorphous solids. It has been shown that the topology of the local structure represented by the Voronoi polyhedra is related to the local stresses and symmetry only through the coordination number. On the other hand, the degree of distortion of the environment, which is of primary importance to many physical properties and is well characterised by the local parameters, is practically independent of the polyhedral topology. It is concluded, therefore, that the topological description based upon the polyhedral statistics does not provide an unambiguous microscopic basis for relating the local structure of the dense random packing model to its physical properties and could even be misleading.

The electric field gradient in a random packing model of amorphous ionic materials

The electronic field gradient distribution at both the cation and anion sites has been computed for a dense random packing model of amorphous FeF 3 and analysed with particular reference to the sign of the principal component q. For the (large sphere) anion components twice as many sites are found with q>0 as with q<0 and the distribution of asymmetry parameter η is quite anomalous for the sites with positive q. These unusual features, and their essential absence at the (small sphere) cation sites, can be understood in terms of the local coordinations of the two types of ionic constituent and are likely to remain at least qualitatively valid for majority anions and minority cations in a wider context of amorphous ionic materials.

X-ray diffraction studies of the structure of LaA1Ga metallic glasses

The LaLa and LaA1 partial atomic distribution functions have been determined for glassy La 1− x A1 x from X-ray diffraction studies of isomorphous alloys of La 1− x A1 x , La 1− x (A1Ga), and La 1 − x Ga x for x = 0.20, 0.24 and 0.28. The atomic short range order of these La based metallic glasses is quite different from that of typical amorphous transition metal-metalloid alloys and from dense random packing models. A relatively short and well defined LaA1 nearest neighbor distance suggests some covalency in the bonds between unlike atoms and possible chemical ordering in the alloys.

Thermodynamic properties of coincidence boundaries in aluminum

Thermodynamic quantities of ∑ = 5 and ∑ = 11 grain boundaries were calculated as functions of temperature between zero and the bulk Debye temperature in aluminum. The local density of states (LDS) of individual atoms at the boundaries was computed by the recursion method, and the thermodynamic quantities were calculated from the LDS's. The functions calculated are the meansquare displacements of several atoms, the excess entropies, the excess free energies and the excess specific heats. These were analyzed in relation to the structural model that is the dense random packing model. The excess entropy of the boundary constructed by stacks of capped trigonal prism plus pentagonal bi-pyramids is much larger than that of stacks of capped trigonal prisms only. The resonant modes of the atoms at the boundaries produce a narrow peak at about 1 7 of the bulk Debye temperature in the graph of the excess specific heat vs temperature.

A Dislocation Model of Amorphous Metals

A dislocation model of amorphous metals is constructed to meet the requirement of global connectivity. Noncrystalline nature of atomic configurations at the screw dislocation core is discussed in connection with Bernal polyhedra and rings of fivefold symmetry which have been found in the dense random packing models. Relative population of trigonal prisms to that of tetragonal dodecahedra is determined by different degrees of symmetry breaking of the core structure. Pair distribution functions are calculated for the dislocation model after relaxation of atom positions and a good agreement with experiments is obtained for the dislocation density of 10 14 ∼10 15 cm -2 . For the high density the core structure is found to keep nearly the same local configuration as that of an isolated dislocation, and, thus, the dislocation model contains many Bernal polyhedra.

Crystallization and atomic scale structure of sputtered amorphous Fe-B films

We have used electron microscopy, electron diffraction and structure modelling techniques to investigate crystallization behavior and structure of sputtered Fe 100-x B x films (X = 16. - 24 at.%) of 100 A - 300 A thickness. Electron micrographs of most as deposited films showed a network of voids and low density regions. Areas of crystalline iron oxides were present on surfaces of most films, monoclinic e-Fe 2 O 3 as thin platelets ∼ 4000 A in diameter and cubic Fe 3 O 4 with 100A-200A granular morphology. Crystallization phenomena depended on heating rate and on whether oxide was present. Diffraction patterns and radial distribution functions of as-deposited films showed little dependence on B-content and were similar to those reported for liquid quenched Fe-B alloys. The average nearest neighbor distance for X = 24, at.% was 2.574A and increased by only 1.% with decreasing B content. The average nearest neighbor coordination number varied between 11.2 and 11.5. Binary dense random packing models for Fe-B alloys were generated using sphere diameters of 2.55A and 1.70A for Fe and B. No B-B nearest neighbor pairs were allowed, of the Fe configurations was controlled, and structures were relaxed with Lennard-Jones potentials. Models reproduced peak positions and relative peak heights of experimentally observed diffraction patterns and distribution functions only when different levels of tetrahedron perfection were used for model structures of different B content, indicating that the simple binary dense random packing algorithm does not adequately simulate effects of B on arrangements of Fe atoms in the amorphous alloys. Agreement achieved between experimental and model results became poorer with decreasing B content. Coordination numbers of the model structures were about 20% smaller than those obtained experimentally.

Electronic structure of the Ni-Pd-P and Ni-Pt-P metallic glasses: A pulsed NMR study

A pulsed NMR and magnetic susceptibility study of the electronic structure is reported for the rapidly quenched metallic glass systems: (Ni0.50Pd0.50)100-xPx (where 16≦x≦26.5), (NiyPd1-y)80P20 (where 0.20≦y≦0.80), and (NiyPt1-y)75P25 (where 0.20≦y≦0.68). The 31P Knight shift and nuclear spin-lattice relaxation rate in all three systems depend only on the P concentration, x, and not the Ni concentration, y, nor whether the second transition metal is Pd or Pt. Both the shift and relaxation rate for 31P are attributed solely to the direct contact hyperfine interaction. The 195Pt Knight shift and magnetic susceptibility for (NiyPt1-y)75P25 do depend on both the Ni concentration and temperature, enabling a determination of the contributions to the shift arising from the direct contact hyperfine and core polarization interactions. The results are discussed in terms of a rigid two-band picture with estimates being made for the s- and d-band densities of states and hyperfine coupling constants. There is strong evidence for a transfer of charge from the P metalloid atoms (M) to the d states of the transition-metal atoms (T), which is consistent with the dense random packing model for T100-xMx metallic glasses.

Electronic states in amorphous and liquid iron

Electronic density of states in amorphous and liquid iron is calculated for the systems of dense random packing model relaxed by means of the Pak-Doyama potential for crystalline alpha iron. The d orbital degeneracy is fully taken into account. An essential difference in the electronic structure is found between amorphous and liquid iron, i.e. the density of states for amorphous iron has double-peaked structure whereas that for liquid iron does not.

Structural analysis of amorphous Pd0.8Si0.2 alloy by the dense random packing model of differently sized compressible spheres

A structural model of the amorphous Pd0.8Si0.2 alloy is constructed by the relaxation of the dense random packing (DRP) model of differently sized compressible spheres. The density and the radial distribution function (RDF) of this model show good agreement with the observed one and the density variation seems to be eliminated. Das strukturelle Modell einer amorphen Pd0,8Si0,2-Legierung wird durch die Relaxation des DRP-Modells mit zusammendruckbaren Kugeln ungleicher Grose konstruiert. Die Dichte und radiale Verteilungsfunktion (RDF) in diesem Modell zeigen gute Ubereinstimmung mit den experimentellen Werten und die Dichteanderung scheint eliminiert zu werden.

Structural relaxation of the dense random packing model for amorphous iron

Using Johnson's potential of α-iron, three dense random packing (DRP) assemblies constructed by Ichikawa's method for k = 1.05, 1.2, and 1.4, are relaxed under a free boundary condition. The assembly with k = 1.2 is relaxed also by the potential obtained by Pak and Doyama and the long range oscillatory potential of liquid iron. The pair distribution function (PDF) of the relaxed model with k = 1.2 using Johnson's potential is in excellent agreement with the experimental PDF of the amorphous iron. On the other hand, the greatest packing fraction, η = 0.59, is achieved using the potential by Pak and Doyama. It is shown that the relaxation procedure using an appropriate potential is the indispensable process to construct realistic models of glassy metals. Mit Johnson's Potential fur α-Eisen werden drei statistisch dicht gepackte (DRP) Anordnungen, die mit Ichikawas Methode fur k = 1,05; 1,2 und 1,4 konstruiert wurden, unter freier Randbedingung relaxiiert. Die Anordung mit k = 1,2 wird ebenfalls mittels des von Pak und Doyama erhaltenen und des oszillatorischen langreichweitigen Potentials von flussigem Eisen relaxiiert. Die Paar-Verteilungsfunktion (PDF) des relaxiierten Modells mit k = 1,2 und dem Johnson-Potential befindet sich in ausgezeichneter Ubereinstimmung mit der experimentellen PDF von amorphem Eisen. Andererseits wird der groste Packungsanteil, η = 0,59, mit dem Potential von Pak und Doyama erhalten. Es wird gezeigt, das die Relaxationsmethode mit der Benutzung eines geeigneten Potentials der unerlasliche Prozes fur die Konstruktion realistischer Modelle glasartiger Metalle ist.

The Structure of Molten Nickel-Phosphorus Alloys

Abstract Detailed analyses of the x-ray scattering intensities of molten nickel-phosphorus alloys ranging from 0 to 30 at.% phosphorus have been carried out. The three partial structures required to characterize the binary alloys have been estimated. The interatomic distance of P -P pairs was found to be about 3.2 Å, and thus phosphorus atoms cannot exist as nearest neighbours in molten Ni-P alloys, at least within the present experimental composition range. It was confirmed that this arrangement of atoms contributed to the characterisic structure in which the expansion of the Ni -Ni distance was unavoidable. Calculations have also been carried out in terms of the dense random-packing model of binary spheres. The calculations were consistent with the experimental results.

Relaxed Bernal structure as a model of amorphous iron

Dense random packing models of Ichikawa with k=1.2 and k=1.4 have been relaxed using Johnston's potential for iron. The experimental pair distribution function of amorphous iron is in quite good agreement with the relaxed model of k=1.2. The results show that the relaxed structures are nearly the same and do not depend so strongly on the tetrahedral perfection k.

Hysteresis curves and magnetization processes in a model for an amorphous magnet with random uniaxial anisotropy

We consider the magnetic field behavior of a simple model for an amorphous ferromagnet with random single-ion anisotropy. The spins are taken as classical unit vectors located at sites of a dense random packing model and coupled via nearest-neighbor exchange interactions. An easy-axis direction is chosen at random for each site. For large anisotropy, the coercivity is very large and the hysteresis curves resemble those found for amorphous TbFe2 at low temperature. As the anisotropy is reduced, there is a fairly abrupt change in the behavior of the model indicating that sufficiently weak random anisotropy is effectively averaged away. We have examined the energy of metastable states. The results indicate that the canted aligned state is always more stable than low-moment spin-glass-like states. We also consider the magnetization process in the presence of imposed domain walls and find that wall motion is preceeded by magnetization rotation in the high-coercivity regime.