Frederick Milstein

Mechanical properties of silica aerogels

Abstract Aerogels are extremely low density solids that are characterized by a high porosity and pore sizes in the order of nanometers. The mechanical behavior of silica aerogel was investigated with hardness, compression, tension and shear tests. The influences of testing conditions, storage environment and age were examined, with particular attention paid to the effects of processing parameters, including fiber-reinforcement. Good correlation was found between hardness and compressive strength over a wide range of processing parameters. Increasing fiber reinforcement generally retarded shrinkage during fabrication and yielded smaller matrix densities for a given target density. For a given fiber content, hardness, compressive strength and elastic moduli increased and strain at fracture decreased with increasing matrix density. In the lower ranges of matrix density, fiber reinforcement increased strain at fracture and elastic moduli. The mechanical response was also sensitive to environment and storage history. With age, the compressive strength and elastic moduli increased while the strain at fracture decreased. Tension and shear results indicate that shear strength of aerogels exceeds tensile strength which is consistent with brittle materials response.

Theoretical elastic behaviour of crystals at large strains

Current knowledge in the subject of the theoretical mechanical behaviour of perfect single crystals under load is reviewed. Examples of computations of load, lattice deformation, elastic moduli, and elastic stability are discussed, and qualitatively interesting (and sometimes surprising) phenomena are noted. Although computational techniques are reviewed briefly, the emphasis is upon the collation and interpretation of various computational results that have appeared in the literature. Special consideration is given to the topics of lattice stability and the definition and computation of elastic moduli of crystals under load, as well as branching from one path of deformation to another under a prescribed mode of loading. Possible applications in materials science include deformation of whiskers, twinning, martensitic transformations, very rapid shock deformation, powder technology and size reduction, and mechanical properties of small structures such as metallized integrated circuits.

Applicability of exponentially attractive and repulsive interactomic potential functions in the description of cubic crystals

The well‐known Morse function φ(r) = D {exp [−2α(r−r0)] −2 exp [−α(r−r0)]} can be considered to be a particular case of the general family of potential functions with exponential attraction and exponential repulsion, viz., φm(r) = [D/(m−1)] {exp[−mα(r−r0)] −m × exp[−α(r−r0)]}. This study examines the suitability of applying the functions φm (r) to the description of mechanical properties of cubic crystals. For bcc lattices, the ratio C11/C12 for the theoretical model of the crystal made up of atoms with φm (r) interatomic interactions is shown to be too small to provide a realistic description of bcc metals; also, the bcc crystals are found to be inherently unstable for larger values of αa0, where a0 is the lattice parameter of the crystal. For fcc lattices, however, the theoretical model of the crystal is found to be mechanically stable for arbitrary (i.e., m>1) exponentially attractive and repulsive interactions and the elastic moduli C11 and C12 of the theoretical fcc crystals are found to be capable o...

Theoretical strength of a perfect crystal with exponentially attractive and repulsive interatomic interactions

Numerical calculations are made of the theoretical strength of fcc crystals with two‐body exponentially attractive and exponentially repulsive interatomic interactions; the crystals are subjected to unconstrained (100) uniaxial tension and compression. The calculations are made from the point of view of mechanical lattice stability; the general theory has been presented in an earlier paper. The numerical values of the parameters characterizing the interatomic interactions were calculated from the elastic moduli C11 and C12 and the stress‐free equilibrium value of lattice parameter for Ni; the element Ni was selected for this purpose because (i) the Cauchy condition is not severely violated for Ni, (ii) the correct (i.e., experimental) linear elastic stress‐strain behavior is exhibited by the theoretical model of the crystal, and (iii) reasonably good agreement is obtained between theoretically calculated and experimentally observed anharmonic pressure‐vs‐volume behavior. Calculations are carried out using...

Correlation between mercuric iodide detector performance and crystalline perfection

X-ray, neutron and gamma ray diffraction rocking curves; X-ray topography; microhardness; and optical microscopic measurements have been performed directly on several mercuric iodide (Hgl2) nuclear radiation detectors fabricated from single crystals grown from the vapor phase. Two types of detectors were measured: spectrometer types (grades A and B), which had resolutions of 5–10% for the 662 keV photopeak of 137Cs, or radiation counters (grades C and D), where the spectral resolution ranged from 11% to no resolution. A good correlation has been found between the detector grade and the full width at half maximum (FWHM) of both the X- and gamma ray rocking curves (i.e., the higher the detector grade (A or B), the narrower the FWHM of the diffraction peak). X-ray topography also correlated with well both the FWHM of the diffraction X-ray rocking curve and the detector grade. The uniformity of the microhardness of the HgI2 detectors was found to be proportional to the nuclear performance of the detector. The better spectrometer-grade detectors were softer and much more uniform in microhardness than the most inferior detectors. The better detectors were also found to have much smoother surfaces than the poorer detectors, as observed by optical microscopy studies.

Plastic deformation and dislocation structure of single crystal mercuric iodide

A systematic investigation of plasticity in single crystal mercuric iodide was carried out. Over eighty compression tests were performed on single crystal specimens oriented variously with respect to the axis of loading. Three characteristic loading responses were observed and classified according to crystal orientation, as follows: (a) the direction of load was perpendicular to the [001] axis, (b) the loading direction was parallel to [001] and (c) the load was neither parallel nor perpendicular to [001]. In cases a and b, under sufficient load, the samples always exhibited brittle failure (without prior plastic deformation) whereas, in case c, the samples were always easily plastically deformed by slip of (001) planes. The case c plastic deformation also exhibited work hardening. A dislocation model for plasticity in mercuric iodide is induced from the experimental results. The model consists of “easy glide” dislocations, the cores of which are parallel to (001) planes, and “hard glide” dislocations that intersect the (001) planes. Movement of the easy glide dislocations causes the (001) slip in case c, whereas interactions between the easy and hard glide dislocations account for the work hardening. The results of other experiments (including creep, annealing, microscopic observation of dislocation etch pits, and bending) are consistent with the model. Deformation during large angle bending tests is a particularly remarkable phenomenon.

Compressive Response of Lightweight Ceramic Ablators: Phenolic Impregnated Carbon Ablator

Lightweight ceramic ablators are porouse brousceramicsubstrates impregnated with organicresins. Thematerialsweredevelopedforuseasheatshieldsforplanetaryentry.Thecompressiveresponseandhardnessofaphenolic impregnated carbon ablator and its e brous substrates are reported. Results are also given for charred specimens of the ablator. Fibers in the substrate tend to be randomly and uniformly aligned parallel to a preferred plane. Two characteristic compressive responses were observed, depending on the orientation of the load with respect to the preferred e ber-alignment plane. When the load was parallel to this plane, the stress increased approximately linearly with increasing strain to strains of about 2%. The stress then followed an erratic “ horizontal” path with increasing strain as the materials apparently failed by an internal separation and buckling mechanism. In contrast, during compression transverse to the e ber-alignment plane, the materials underwent signie cant, nonlinear, plastic deformation, wherein the stress increased with increasing strain to strains of over 50% without indications of fracture. Considerable energy was absorbed during compression, particularly for materials subjected to the transverse loading condition. Resin impregnation substantially strengthens the ablator material; this effect was prominent for specimens loaded transverse to the e ber-alignment plane.

Mechanics and energetics of the Bain transformation

Abstract The general mechanics and energetics of the Bain transformation are presented. The Bain transformation takes a crystal from its b.c.c. configuration into its f.c.c. structure, or vice versa, by means of homogeneous axial deformations. The crystal remains b.c.t. on the transformation path, and different types of Bain transformation may be distinguished by the response of the transverse lattice parameters to incremental changes in the longitudinal lattice parameter. A rational means of comparing the various types is made possible by defining the longitudinal stretch as the independent variable or degree of transformation. It is shown that, among possible Bain transformations, the one that occurs under a uniaxial-loading environment has the lowest binding energy at any given stage of transformation. In addition, the lowest possible barrier energy for any Bain transformation occurs when the crystal passes through a special unstresssd tetragonal state that resides at a local energy maximum on the unia...

Dislocation activity in single crystal Hgl2

An etchant of 5% alcohol in trichloroethylene (TCE) allows greater resolution of dislocation etch pits in vapour-grown single crystals of Hgl2 than the “traditional” alcohol etches. The improved etchant has made possible the identification of etch pits, on the (001) faces of single-crystal Hgl2, that are associated with dislocations on {100}-type slip planes. The evidence for this conclusion includes (a) the geometric and crystallographic features of the etch pits, (b) the manner in which they are induced by deformation, and (c) their regularity in passing through the crystal, perpendicular to the (001) plane.

Anharmonicity and symmetry in crystals

Abstract A number of investigators have observed anharmonic (i.e. non-linear) behaviour in stress-strain curves of metallic whiskers: For f.c.c. metals, in general, the non-linearities are ordered according to l″100 > 0 > l″111 > l″110, where l″ is the second derivative of stress with respect to strain and the subscripts indicate the axial, crystallographic direction of loading. (It is of particular interest to note that the stress-strain curve is concave upward in [100] loading.) In the present work, this behaviour is explained in terms of the influence of crystal symmetries occurring on the primary loading paths (specifically, in terms of the existence of multiple zeros—or unstressed states—and bifurcations or branchings among paths of different symmetry). Theoretical computations for lattice models of Ni and Cu in [100], [110] and [111] loading are presented as examples. The agreement between the results of theory and experiment is excellent. It is suggested that such symmetry considerations may be val...