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NASA NTRS1990

A review of nonlinear constitutive models for metals

Over the past two decades a number of thermomechanical constitutive theories have been proposed for viscoplastic metals. These models are in most cases similar in that they utilize a set of internal state variables which provide locally averaged representations of microphysical phenomena such as dislocation rearrangement and grain boundary sliding. The state of development of several of these models is now at the point where accurate theoretical solutions can be obtained for a wide variety of structural problems at elevated temperatures. The fundamentals of viscoplasticity are briefly reviewed and a general framework is outlined. Several of the more prominent models are reviewed, and predictions from models are compared to experimental results.

Allen, David H.↗

NASA NTRS1976

Computer simulation of screw dislocation in aluminum

The atomic structure in a 110 screw dislocation core for aluminum is obtained by computer simulation. The lattice statics technique is employed since it entails no artificially imposed elastic boundary around the defect. The interatomic potential has no adjustable parameters and was derived from pseudopotential theory. The resulting atomic displacements were allowed to relax in all three dimensions.

Esterling, D. M.↗

NASA NTRS2006

Quantitative Assessment of Fatigue Damage Accumulation in Wavy Slip Metals from Acoustic Harmonic Generation

A comprehensive, analytical treatment is presented of the microelastic-plastic nonlinearities resulting from the interaction of a stress perturbation with dislocation substructures (veins and persistent slip bands) and cracks that evolve during high-cycle fatigue of wavy slip metals. The nonlinear interaction is quantified by a material (acoustic) nonlinearity parameter beta extracted from acoustic harmonic generation measurements. The contribution to beta from the substructures is obtained from the analysis of Cantrell [Cantrell, J. H., 2004, Proc. R. Soc. London A, 460, 757]. The contribution to beta from cracks is obtained by applying the Paris law for crack propagation to the Nazarov-Sutin crack nonlinearity equation [Nazarov, V. E., and Sutin, A. M., 1997, J. Acoust. Soc. Am. 102, 3349]. The nonlinearity parameter resulting from the two contributions is predicted to increase monotonically by hundreds of percent during fatigue from the virgin state to fracture. The increase in beta during the first 80-90 percent of fatigue life is dominated by the evolution of dislocation substructures, while the last 10-20 percent is dominated by crack growth. The model is applied to the fatigue of aluminium alloy 2024-T4 in stress-controlled loading at 276MPa for which experimental data are reported. The agreement between theory and experiment is excellent.

Cantrell, John H.↗

NASA NTRS2001

Electro-Thermal Simulation Studies of SiC Junction Diodes Containing Screw Dislocations Under High Reverse-Bias Operation

The objective of this work was to conduct a modeling study of SiC P-N junction diodes operating under high reverse biased conditions. Analytical models and numerical simulation capabilities were to be developed for self-consistent electro-thermal analysis of the diode current-voltage (I-V) characteristics. Data from GRC indicate that screw dislocations are unavoidable in large area SiC devices, and lead to changes in the SiC diode electrical response characteristics under high field conditions. For example, device instability and failures linked to internal current filamentation have been observed. The physical origin of these processes is not well understood, and quantitative projections of the electrical behavior under high field and temperature conditions are lacking. Thermal calculations for SiC devices have not been reported in the literature either. So estimates or projections of peak device temperatures and power limitations do not exist. This numerical study and simulation analysis was aimed at resolving some of the above issues. The following tasks were successfully accomplished: (1) Development of physically based models using one- and two-dimensional drift-diffusion theory for the transport behavior and I-V characteristics; (2) One- and two-dimensional heat flow to account for internal device heating. This led to calculations of the internal temperature profiles, which in turn, were used to update the electrical transport parameters for a self-consistent analysis. The temperature profiles and the peak values were thus obtainable for a given device operating condition; (3) Inclusion of traps assumed to model the presence of internal screw dislocations running along the longitudinal direction; (4) Predictions of the operating characteristics with and without heating as a function of applied bias with and without traps. Both one and two-dimensional cases were implemented; (5) Assessment of device stability based on the operating characteristics. The presence of internal non-uniformities, particularly filamentary structures, was probed and demonstrated; (6) Cause and physical origins of filamentary behavior and unstable I-V characteristics were made transparent; (7) It was demonstrated that diodes containing defects would be more prone to thermal breakdown associated with the temperature dependent decrease in the thermal conductivity; and (8) Finally, negative differential resistance (S-shaped NDR) which can potential lead to device instability and filamentary behavior was shown to occur for diodes containing a line of defects such as could be associated with a screw dislocation line.

Joshi, R. P.↗

NASA NTRS1974

Surface recrystallization theory of the wear of copper in liquid methane

Copper was subjected to sliding against 440C in liquid methane. The normal load range was from 1/4 to 2 kilograms, and the sliding velocity range was from 3.1 to 25 meters per second. Over this range of experimental parameters, the wear rate of the copper rider was found to be proportional to the sliding velocity squared and to the normal load. Transmission electron microscopy was used to study the dislocation structure in the copper very near the wear scar surface. It was found that near the wear scar surface, the microstructure was characterized by a fine-cell recrystallized zone in which individual dislocations could be distinguished in the cell walls. The interiors of the cells, about 0.5 micrometer in diameter, were nearly dislocation free. Below the recrystallized layer was a zone that was intensely cold worked by the friction process. With increasing depth, this intensely cold worked zone gradually became indistinguishable from the partially cold worked bulk of the copper, representative of the initial condition of the material.

Bill, R. C.↗

NASA NTRS1999

Step Bunching: Influence of Impurities and Solution Flow

Step bunching results in striations even at relatively early stages of its development and in inclusions of mother liquor at the later stages. Therefore, eliminating step bunching is crucial for high crystal perfection. At least 5 major effects causing and influencing step bunching are known: (1) Basic morphological instability of stepped interfaces. It is caused by concentration gradient in the solution normal to the face and by the redistribution of solute tangentially to the interface which redistribution enhances occasional perturbations in step density due to various types of noise; (2) Aggravation of the above basic instability by solution flowing tangentially to the face in the same directions as the steps or stabilization of equidistant step train if these flows are antiparallel; (3) Enhanced bunching at supersaturation where step velocity v increases with relative supersaturation s much faster than linear. This v(s) dependence is believed to be associated with impurities. The impurities of which adsorption time is comparable with the time needed to deposit one lattice layer may also be responsible for bunching; (4) Very intensive solution flow stabilizes growing interface even at parallel solution and step flows; (5) Macrosteps were observed to nucleate at crystal corners and edges. Numerical simulation, assuming step-step interactions via surface diffusion also show that step bunching may be induced by random step nucleation at the facet edge and by discontinuity in the step density (a ridge) somewhere in the middle of a face. The corresponding bunching patterns produce the ones observed in experiment. The nature of step bunching generated at the corners and edges and by dislocation step sources, as well as the also relative importance and interrelations between mechanisms 1-5 is not clear, both from experimental and theoretical standpoints. Furthermore, several laws controlling the evolution of existing step bunches have been suggested, though unambiguous conclusions are still missing. Addressing these issues is the major goal of the present project. The theory addressing the above problem, experimental methods, several figures which include: (1) the spatial wave numbers at which the system is neutrally stable as a function of growth velocity for linear kinetics and supersaturation for nonlinear kinetics; (2) a schematic of the experiment of lysozyme crystal growing under conditions of natural convection; (3) fluctuations in time, t, of the normal growth rate, R(t), vicinal slope, p(t) and Fourier Spectra of R(t), discussions and conclusions are presented.

Chernov, A. A.↗

NASA NTRS1986

The crack layer approach to toughness characterization in steel

In a study of the laws of crack propagation and toughness characterization, it is feasible to employ two alternative approaches, including the fracture mechanics approach and the material science approach. The crack layer (CL) theory discussed by Khandogin and Chudnovsky (1978) and Chudnovsky (1980) considers the crack together with the surrounding defects as one system which has several degrees of freedom. It is pointed out that the CL theory defines the relationship between the parameters of fracture mechanics and the characteristics of microstructural changes which are the subject of material science. Experiments are described, taking into account a toughness characterization test and microscopic studies. Attention is given to a phenomenological study of toughness characterization, the morphology of crack layer, and the evaluation of energy stored in the dislocation network.

Bessendorff, M.↗

NASA NTRS1998

Determining the Molecular Growth Mechanisms of Tetragonal Lysozyme Crystals

Studies of the growth of tetragonal lysozyme crystals employing atomic force microscopy (AFM) have shown the advantages of this technique in investigating the growth mechanisms of protein crystals [1]. The resolution of these studies was in the micron range, which revealed surface features such as the occurrence of dislocations and 2D nucleation islands, similar to those found in inorganic systems. They clearly showed that the crystals grew by these surface growth mechanisms. However, the studies also revealed some surprising features, such as bimolecular growth step heights and pronounced growth anisotropies on the (110) face, which could not be explained. In previous studies we employed Periodic Bond Chain (PBC) theory to tetragonal lysozyme crystal growth and found that the crystals were constructed by strongly bonded molecular chains forming helices about the 43 axes [2,3]. The helices were connected to each other with weaker bonds. The growth process was shown to proceed by the formation of these 43 helices, resulting in bimolecular growth steps on the (110) face. It was also shown to explain many other observations on tetragonal lysozyme crystal growth. Although PBC analysis is not a new technique [4], it has not been widely used as the mechanisms predicted from it could not be experimentally verified. In this study the growth process of these crystals was investigated, particularly for the (110) face, employing some newly developed high resolution AFM techniques. These techniques allowed individual lysozyme molecules on the crystal faces to be resolved and predictions from PBC analyses to be tested. The analyses had shown that of the two possible packing arrangements on (110) faces, only one would actually occur. Employing the first of the newly developed techniques, these faces were scanned by high resolution AFM. The resulting images were then compared with the theoretically constructed images for the two possible packing arrangements on the (110) face. The theoretical images were constructed by convolution of the crystal surface shape obtained from crystallographic data with the AFM tip shape. The comparison confirmed the prediction that the molecular packing arrangement of these faces corresponded to that for complete 43 helices. The second AFM technique that was developed was used to follow the growth process by measuring the dimensions of individual growth units on the (110) face. Linescans across a growth step, performed near the saturation limit of the crystals, allowed the growth unit dimensions to be measured. These measurements showed that growth on the (110) face proceeded by the formation of new 43 helices from the addition of at least tetramer units in the [110] direction. In the [001] direction growth proceeded by the addition of various aggregate units corresponding to the 4(sub 3) helices.

Li, Huayu↗

NASA NTRS2012

Influence of Containment on the Growth of Silicon-Germanium: A Materials Science Flight Project

A series of Ge(1-x)Si(x) crystal growth experiments are planned to be conducted in the Low Gradient Furnace (LGF) onboard the International Space Station. The primary objective of the research is to determine the influence of containment on the processing-induced defects and impurity incorporation in germanium-silicon alloy crystals. A comparison will be made between crystals grown by the normal and "detached" Bridgman methods and the ground-based float zone technique. Crystals grown without being in contact with a container have superior quality to otherwise similar crystals grown in direct contact with a container, especially with respect to impurity incorporation, formation of dislocations, and residual stress in crystals. "Detached" or "dewetted" Bridgman growth is similar to regular Bridgman growth in that most of the melt is in contact with the crucible wall, but the crystal is separated from the wall by a small gap, typically of the order of 10-100 microns. Long duration reduced gravity is essential to test the proposed theory of detached growth. Detached growth requires the establishment of a meniscus between the crystal and the ampoule wall. The existence of this meniscus depends on the ratio of the strength of gravity to capillary forces. On Earth, this ratio is large and stable detached growth can only be obtained over limited conditions. Crystals grown detached on the ground exhibited superior structural quality as evidenced by measurements of etch pit density, synchrotron white beam X-ray topography and double axis X-ray diffraction. The plans for the flight experiments will be described.

Volz, M. P.↗

NASA NTRS2014

Influence of Containment on the Growth of Silicon-Germanium (ICESAGE): A Materials Science ISS Investigation

A series of Ge(1-x)Si(x) crystal growth experiments are planned to be conducted in the Low Gradient Furnace (LGF) onboard the International Space Station. The primary objective of the research is to determine the influence of containment on the processinginduced defects and impurity incorporation in germanium-silicon alloy crystals. A comparison will be made between crystals grown by the normal and "detached" Bridgman methods and the ground-based float zone technique. Crystals grown without being in contact with a container have superior quality to otherwise similar crystals grown in direct contact with a container, especially with respect to impurity incorporation, formation of dislocations, and residual stress in crystals. "Detached" or "dewetted" Bridgman growth is similar to regular Bridgman growth in that most of the melt is in contact with the crucible wall, but the crystal is separated from the wall by a small gap, typically of the order of 10-100 microns. Long duration reduced gravity is essential to test the proposed theory of detached growth. Detached growth requires the establishment of a meniscus between the crystal and the ampoule wall. The existence of this meniscus depends on the ratio of the strength of gravity to capillary forces. On Earth, this ratio is large and stable detached growth can only be obtained over limited conditions. Crystals grown detached on the ground exhibited superior structural quality as evidenced by measurements of etch pit density, synchrotron white beam X-ray topography and double axis X-ray diffraction. The plans for the flight experiments will be described.

Volz, M. P.↗

NASA NTRS2014

Influence of Containment on the Growth of Silicon-Germanium (ICESAGE): A Materials Science Investigation

A series of Ge Si crystal growth experiments are planned to be conducted in the Low 1-x x Gradient Furnace (LGF) onboard the International Space Station. The primary objective of the research is to determine the influence of containment on the processing-induced defects and impurity incorporation in germanium-silicon alloy crystals. A comparison will be made between crystals grown by the normal and "detached" Bridgman methods and the ground-based float zone technique. Crystals grown without being in contact with a container have superior quality to otherwise similar crystals grown in direct contact with a container, especially with respect to impurity incorporation, formation of dislocations, and residual stress in crystals. "Detached" or "dewetted" Bridgman growth is similar to regular Bridgman growth in that most of the melt is in contact with the crucible wall, but the crystal is separated from the wall by a small gap, typically of the order of 10-100 microns. Long duration reduced gravity is essential to test the proposed theory of detached growth. Detached growth requires the establishment of a meniscus between the crystal and the ampoule wall. The existence of this meniscus depends on the ratio of the strength of gravity to capillary forces. On Earth, this ratio is large and stable detached growth can only be obtained over limited conditions. Crystals grown detached on the ground exhibited superior structural quality as evidenced by measurements of etch pit density, synchrotron white beam X-ray topography and double axis X-ray diffraction.

Volz, M. P.↗

NASA NTRS2015

Crystal Growth of Germanium-Silicon Alloys on the ISS

A series of Ge(1-x)Si(x) crystal growth experiments are planned to be conducted in the Low Gradient Furnace (LGF) onboard the International Space Station. The experiments are part of the investigation "Influence of Containment on the Growth of Silicon-Germanium" (ICESAGE). The primary objective of the research is to determine the influence of containment on the processing-induced defects and impurity incorporation in germanium-silicon alloy crystals. A comparison will be made between crystals grown by the normal and "detached" Bridgman methods and the ground-based float zone technique. Crystals grown without being in contact with a container have superior quality to otherwise similar crystals grown in direct contact with a container, especially with respect to impurity incorporation, formation of dislocations, and residual stress in crystals. "Detached" or "dewetted" Bridgman growth is similar to regular Bridgman growth in that most of the melt is in contact with the crucible wall, but the crystal is separated from the wall by a small gap, typically of the order of 10-100 microns. Long duration reduced gravity is essential to test the proposed theory of detached growth. Detached growth requires the establishment of a meniscus between the crystal and the ampoule wall. This meniscus can exist over a much larger range of processing parameters in microgravity and the meniscus is more stable under microgravity conditions. The plans for the flight experiments will be described.

Volz, M. P.↗

NASA NTRS2016

Detached Solidification of Germanium-Silicon Crystals on the ISS

A series of Ge(sub 1-x) Si(sub x) crystal growth experiments are planned to be conducted in the Low Gradient Furnace (LGF) onboard the International Space Station. The primary objective of the research is to determine the influence of containment on the processing-induced defects and impurity incorporation in germanium-silicon alloy crystals. A comparison will be made between crystals grown by the normal and "detached" Bridgman methods and the ground-based float zone technique. Crystals grown without being in contact with a container have superior quality to otherwise similar crystals grown in direct contact with a container, especially with respect to impurity incorporation, formation of dislocations, and residual stress in crystals. "Detached" or "dewetted" Bridgman growth is similar to regular Bridgman growth in that most of the melt is in contact with the crucible wall, but the crystal is separated from the wall by a small gap, typically of the order of 10-100 microns. Long duration reduced gravity is essential to test the proposed theory of detached growth. Detached growth requires the establishment of a meniscus between the crystal and the ampoule wall. The existence of this meniscus depends on the ratio of the strength of gravity to capillary forces. On Earth, this ratio is large and stable detached growth can only be obtained over limited conditions. Crystals grown detached on the ground exhibited superior structural quality as evidenced by measurements of etch pit density, synchrotron white beam X-ray topography and double axis X-ray diffraction.

Volz, M. P.↗

NASA NTRS2016

Detached Solidification of Germanium-Silicon Crystals on the ISS

Volz, M. P.↗

NASA NTRS1978

Modified lattice-statics approach to dislocation calculations. II - Application

The atomic structure of a screw dislocation core of the 110 line type in aluminum is calculated by the modified lattice-statics method developed in the preceding paper. The method includes anharmonic as well as harmonic forces and permits relaxation of the atoms in all three dimensions. All forces used in the present calculations were derived from a first-principles interatomic pair potential obtained via pseudopotential theory. Several significant differences from the ordinary lattice statics results are noted, including the displacement field, Peierl's energy barrier, and the equilibrium core-center location.

Esterling, D. M.↗

NASA NTRS1985

On the use of internal state variables in thermoviscoplastic constitutive equations

The general theory of internal state variables are reviewed to apply it to inelastic metals in use in high temperature environments. In this process, certain constraints and clarifications will be made regarding internal state variables. It is shown that the Helmholtz free energy can be utilized to construct constitutive equations which are appropriate for metallic superalloys. Internal state variables are shown to represent locally averaged measures of dislocation arrangement, dislocation density, and intergranular fracture. The internal state variable model is demonstrated to be a suitable framework for comparison of several currently proposed models for metals and can therefore be used to exhibit history dependence, nonlinearity, and rate as well as temperature sensitivity.

Allen, D. H.↗

NASA NTRS1991

Analyses of near- and far-field two-lobe patterns outside the output endface of a two-mode fiber

The behaviors of the near- and far-field two-lobe radiation patterns from a circular-core two-mode fiber are studied by using both the mode and Kirchhoff diffraction theories. The electric field outside the output endface of the fiber is derived from the electric field distribution of the LP sub 01 and LP sub 11 modes at the fiber endface using the Kirchhoff diffraction formula. Different phenomena are studied by solving this expression numerically at near-and far-fields. The Gouy phase shifts are quantitatively evaluated at cross-sections of the near field. The results reveal the distortion and dislocation of the far-field two-lobe pattern induced by an inclination angle of the fiber endface.

Wang, A.↗

NASA NTRS1985

Molecular beam epitaxial growth and transmission electron microscopy studies of thin GaAs/InAs(100) multiple quantum well structures

GaAs/InAs(100) multiple interface structures involving 7.4 percent lattice mismatch have been fabricated via molecular beam epitaxy and examined via transmission electron microscopy. It is found that high-quality, dislocation-free interfaces involving such high lattice mismatch can indeed be experimentally realized for very thin layers provided proper care is given to achieve a balance between the growth kinetics and the thermodynamics leading to the equilibrium ground state of the strained layer. The compressive strain is homogeneously accommodated and a tetragonal distortion is induced in the InAs layer with a perpendicular lattice constant in close agreement with that expected on the basis of the continuum theory and elastic constants of bulk InAs.

Grunthaner, F. J.↗