David J. Srolovitz

Structural defects in amorphous solids Statistical analysis of a computer model

Abstract The possibility of defining structural defects in amorphous solids in terms of parameters such as atomic-level internal stresses and local symmetry coefficients was proposed in a previous paper (Egami, Maeda and Vitek 1980). Using a model amorphous structure generated by a computer, these parameters are statistically analysed in the present paper. It is shown that the stress and the symmetry coefficients are closely correlated and that spatial correlations of various kinds exist. The structural defects are then defined as regions in which the corresponding characterizing parameter deviates significantly from its average value. Two distinct classes of defects were found; (i) positive (p-type defects) and negative (n-type defects) local density fluctuations; and (ii) regions of large shear stresses and large deviations from spherical symmetry. Defects consisting of pairs of p-type and n-type defects separated by regions of large shear stresses are also common. The effect of annihilation of p- and n...

An atomistic study of deformation of amorphous metals

Abstract The computer simulation of a shear deformation of a model monoatomic amorphous metal has been performed. The strain was applied incrementally, relaxing the structure at each step. The complete stress-strain curve was thus obtained. A large number of microscopic deformation events have been observed and analyzed using the description of the local atomic structure by the atomic level stresses. Although no temperature effects have been included in the present study the calculated stress-strain curve is in very good agreement with the stress-strain curves measured experimentally at or above room temperature. The common feature of these experiments and present calculations is, however, the homogeneity of the deformation. Hence, it is argued that fundamental microscopic deformation mechanisms are the same at low and high temperatures and the macroscopic differences arise owing to the strain localization in the former case. The regions of inhomogeneous atomic movement which results in plastic deformation, have not been found to be correlated with local density fluctuations in contrast with assumptions of the models based on free volume theory. They are, however, correlated with regions of high shear stresses, called τ-defects. These defects are formed during the deformation, are sustained by the applied stress and appear to act as stress concentrators in the vicinity of which a localized viscous flow develops.

Local structural fluctuations in amorphous and liquid metals: a simple theory of the glass transition

A method of describing the thermal fluctuations in the local atomic structure of liquid and amorphous metals in terms of the fluctuations in the atomic level stresses is proposed. The energy of the system is expressed in terms of these stresses in the elastic approximation. The temperature dependence of the second moments of the stresses is then calculated and shown to be linear with temperature. The glass transition is assumed to take place when the second moments freeze to certain values determined by computer simulation. It is shown that the pressure fluctuations and the shear fluctuations freeze at different temperatures. The glass transition, in the normal sense, is described by the freezing of the pressure fluctuation. This method provides a reasonable estimate of the glass transition temperature, and predicts it to be proportional to the product of atomic volume and bulk modulus. It furthermore provides an explanation of the different relaxation behaviours between the pressure and shear fluctuations.

Grain boundaries exhibit the dynamics of glass-forming liquids

Polycrystalline materials are composites of crystalline particles or “grains” separated by thin “amorphous” grain boundaries (GBs). Although GBs have been exhaustively investigated at low temperatures, at which these regions are relatively ordered, much less is known about them at higher temperatures, where they exhibit significant mobility and structural disorder and characterization methods are limited. The time and spatial scales accessible to molecular dynamics (MD) simulation are appropriate for investigating the dynamical and structural properties of GBs at elevated temperatures, and we exploit MD to explore basic aspects of GB dynamics as a function of temperature. It has long been hypothesized that GBs have features in common with glass-forming liquids based on the processing characteristics of polycrystalline materials. We find remarkable support for this suggestion, as evidenced by string-like collective atomic motion and transient caging of atomic motion, and a non-Arrhenius GB mobility describing the average rate of large-scale GB displacement.

Engineering the shape and structure of materials by fractal cut

Significance Most materials can be stretched to a small degree, depending on their elastic limits and failure properties. For most materials the maximum elastic dilatation is very small, implying that the macroscopic shapes to which an elastic body can be deformed is severely limited. The present work addresses the simple modification of any material via hierarchical cut patterns to allow for extremely large strains and shape changes and a large range of macroscopic shapes. This is an important step in the development of shape-programmable materials. We provide the mathematical foundation, simulation results, and experimental demonstrations of the concept of fractal cut. This approach effectively broadens the design space for engineered materials for applications ranging from flexible/stretchable devices and photonic materials to bioscaffolds. In this paper we discuss the transformation of a sheet of material into a wide range of desired shapes and patterns by introducing a set of simple cuts in a multilevel hierarchy with different motifs. Each choice of hierarchical cut motif and cut level allows the material to expand into a unique structure with a unique set of properties. We can reverse-engineer the desired expanded geometries to find the requisite cut pattern to produce it without changing the physical properties of the initial material. The concept was experimentally realized and applied to create an electrode that expands to >800% the original area with only very minor stretching of the underlying material. The generality of our approach greatly expands the design space for materials so that they can be tuned for diverse applications.

Atomistic Simulation of Materials

All materials are made of atoms. This simple and powerful statement will serve as the scientific basis of this course. We will model the interaction between atoms or their parts using different methods. We will implement these models into computer programs for doing numerical experiments. Then, we will analyze the results of these numerical experiments to gain understanding about the macroscopic properties of materials: their structure, vibrational properties, electronic properties, and more.

Nanowire Failure: Long = Brittle and Short = Ductile

Experimental studies of the tensile behavior of metallic nanowires show a wide range of failure modes, ranging from ductile necking to brittle/localized shear failure-often in the same diameter wires. We performed large-scale molecular dynamics simulations of copper nanowires with a range of nanowire lengths and provide unequivocal evidence for a transition in nanowire failure mode with change in nanowire length. Short nanowires fail via a ductile mode with serrated stress-strain curves, while long wires exhibit extreme shear localization and abrupt failure. We developed a simple model for predicting the critical nanowire length for this failure mode transition and showed that it is in excellent agreement with both the simulation results and the extant experimental data. The present results provide a new paradigm for the design of nanoscale mechanical systems that demarcates graceful and catastrophic failure.

Measurement of the cleavage energy of graphite

The basal plane cleavage energy (CE) of graphite is a key material parameter for understanding many of the unusual properties of graphite, graphene and carbon nanotubes. Nonetheless, a wide range of values for the CE has been reported and no consensus has yet emerged. Here we report the first direct, accurate experimental measurement of the CE of graphite using a novel method based on the self-retraction phenomenon in graphite. The measured value, 0.37±0.01 J m−2 for the incommensurate state of bicrystal graphite, is nearly invariant with respect to temperature (22 °C≤T≤198 °C) and bicrystal twist angle, and insensitive to impurities from the atmosphere. The CE for the ideal ABAB graphite stacking, 0.39±0.02 J m−2, is calculated based on a combination of the measured CE and a theoretical calculation. These experimental measurements are also ideal for use in evaluating the efficacy of competing theoretical approaches.

Mechanisms of Failure in Nanoscale Metallic Glass

The emergence of size-dependent mechanical strength in nanosized materials is now well-established, but no fundamental understanding of fracture toughness or flaw sensitivity in nanostructures exists. We report the fabrication and in situ fracture testing of ∼70 nm diameter Ni-P metallic glass samples with a structural flaw. Failure occurs at the structural flaw in all cases, and the failure strength of flawed samples was reduced by 40% compared to unflawed samples. We explore deformation and failure mechanisms in a similar nanometallic glass via molecular dynamics simulations, which corroborate sensitivity to flaws and reveal that the structural flaw shifts the failure mechanism from shear banding to cavitation. We find that failure strength and deformation in amorphous nanosolids depend critically on the presence of flaws.

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.