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NASA NTRS1983

Ignition of a combustible half space

A half space of combustible material is subjected to an arbitrary energy flux at the boundary where convection heat loss is also allowed. An asymptotic analysis of the temperature growth reveals two conditions necessary for ignition to occur. Cases of both large and order unity Lewis number are shown to lead to a nonlinear integral equation governing the thermal runaway. Some global and asymptotic properties of the integral equation are obtained.

Olmstead, W. E.↗

NASA NTRS1992

On the nonlinear development of three-dimensional instability waves in natural transition

The nonlinear development of a pair of symmetrical three-dimensional oblique instability waves in transitioning boundary layers is investigated based on critical-layer nonlinearity (CLN). Particular emphasis is placed on understanding the mechanisms leading to the naturally occurring transition in which the amplitudes of the plane and oblique modes can be of the same order. Results indicate that the self-interaction of the oblique waves reduces their growth rate. A relatively large oblique mode can either suppress or enhance the growth of the plane mode, depending on the initial phase difference. If the plane mode amplitude is not negligible with respect to that of the oblique modes, it causes a strong amplification of the oblique mode at the subharmonic frequency. The comparison with observations are quite encouraging and several novel features of the natural transition process are revealed.

Mankbadi, Reda R.↗

NASA NTRS1999

The Measurement of Sulfur Oxidation Products and Their Role in Homogeneous Nucleation

An improved version of a transverse ion source was developed which uses selected ion chemical ionization mass spectrometry techniques inside of a particle nucleation flow tube. These new techniques are very unique, in that the chemical ionization is done inside of the flow tube rather than by having to remove the compounds and clusters of interest which are lost on first contact,with any surfaces. The transverse source is also unique because it allows the ion reaction time to be varied over more than an order of magnitude, which in turn makes possible the separation of ion induced cluster growth from the charging of preexisting molecular clusters. As a result of combining these unique capabilities, the first ever measurements of prenucleation molecular clusters were performed. These clusters are the intermediate stage of growth in the gas-to-particle conversion process. This new technique provides a means of observing clusters containing 2, 3, 4, ... and up to about 8 sulfuric acid molecules, where the critical cluster size under these measurement conditions was about 4 or 5. Thus, the nucleation process can now be directly observed and even growth beyond the critical cluster size can be investigated. The details of this investigation are discussed in a recently submitted paper, which is included as Appendix A. Measurements of the diffusion coefficient of sulfuric acid and sulfuric acid clustered with a water molecule have also been performed. The measurements are also discussed in more detail in another recently submitted paper which is included as Appendix B. The empirical results discussed in both of these papers provide a critical test of present nucleation theories. They also provide new hope for resolving many of the huge discrepancies between field observation and model prediction of particle nucleation. The second part of the research conducted under this project was directed towards the development of new chemical ionization techniques for measuring sulfur oxidation products.

Eisele, F. L.↗

NASA NTRS2002

Health Monitoring for Airframe Structural Characterization

This study established requirements for structural health monitoring systems, identified and characterized a prototype structural sensor system, developed sensor interpretation algorithms, and demonstrated the sensor systems on operationally realistic test articles. Fiber-optic corrosion sensors (i.e., moisture and metal ion sensors) and low-cycle fatigue sensors (i.e., strain and acoustic emission sensors) were evaluated to validate their suitability for monitoring aging degradation; characterize the sensor performance in aircraft environments; and demonstrate placement processes and multiplexing schemes. In addition, a unique micromachined multimeasure and sensor concept was developed and demonstrated. The results show that structural degradation of aircraft materials could be effectively detected and characterized using available and emerging sensors. A key component of the structural health monitoring capability is the ability to interpret the information provided by sensor system in order to characterize the structural condition. Novel deterministic and stochastic fatigue damage development and growth models were developed for this program. These models enable real time characterization and assessment of structural fatigue damage.

Munns, Thomas E.↗

NASA NTRS2004

Migration of the Cratering Flow-Field Center with Implications for Scaling Oblique Impacts

Crater-scaling relationships are used to predict many cratering phenomena such as final crater diameter and ejection speeds. Such nondimensional relationships are commonly determined from experimental impact and explosion data. Almost without exception, these crater-scaling relationships have used data from vertical impacts (90 deg. to the horizontal). The majority of impact craters, however, form by impacts at angles near 45 deg. to the horizontal. While even low impact angles result in relatively circular craters in sand targets, the effects of impact angle have been shown to extend well into the excavation stage of crater growth. Thus, the scaling of oblique impacts needs to be investigated more thoroughly in order to quantify fully how impact angle affects ejection speed and angle. In this study, ejection parameters from vertical (90 deg.) and 30 deg. oblique impacts are measured using three-dimensional particle image velocimetry (3D PIV) at the NASA Ames Vertical Gun Range (AVGR). The primary goal is to determine the horizontal migration of the cratering flow-field center (FFC). The location of the FFC at the time of ejection controls the scaling of oblique impacts. For vertical impacts the FFC coincides with the impact point (IP) and the crater center (CC). Oblique impacts reflect a more complex, horizontally migrating flow-field. A single, stationary point-source model cannot be used accurately to describe the evolution of the ejection angles from oblique impacts. The ejection speeds for oblique impacts also do not follow standard scaling relationships. The migration of the FFC needs to be understood and incorporated into any revised scaling relationships.

Anderson, J. L. B.↗

NASA NTRS2020

Assessment of Sustainability Development in Urban Areas of Morocco

In Morocco, the last census counted 70% of houses in cities, with seven cities accounting for 25% of the total population and 41% of the urban population. This paper questioned the sustainability indicator in Moroccan cities using a novel methodology based on Earth observations and census data. We estimated the indicator for the 25 largest urban areas between 2003 and 2013. A stratification based on urbanization fractions allowed for the definition and comparison of hierarchically ordered zones consistent across urban areas and scales. We found no systematic pattern of growth between cities. However, three categories of development were identified: a group of large cities with an indicator less than unity and land consumption commensurate to population growth, a group of medium-sized cities trending moderately towards unsustainability with an indicator between one and two, and a group including small cities with significant departure from sustainability. The disparate sustainability levels between urban areas appear to be related to the rapid economic growth, typical of an emerging economy. Our results indicate a continuous population growth pushing outwards the perimeters of existing urban areas. Unless regulated, land consumption is increasing faster than the population in most parts of Morocco, in line with global trends.

Lahouari Bounoua↗

NASA NTRS1993

Growth of Si spherical crystals and the surface oxidation (M-9)

Nearly 90 percent of semiconductor devices are produced with Si single crystals as the starting materials. For instance, the integrated circuits (IC), which are used in almost all electronic equipments such as TV, tape recorders, audio amplifiers, etc., are made after various processings of Si single crystal wafers. In these wafers, the same controlled amounts of impurities are added and the uniformities in their distributions are extremely important. Growth under microgravity makes it possible to eliminate the buoyancy-driven convection in the melt, which is one of the main origins of convections which results in non-uniformity of the impurity. Another source of convection is known as Marangoni convection which is driven on the free surface when a temperature gradient occurs. One of the merits of microgravity experimentation is that the detailed study of this convection becomes possible. Another important advantage of microgravity is that growth of crystals without a crucible is possible. This makes it possible to study melt growth without the strain which is usually introduced on the ground. Nevertheless, we should repeat and analyze many growth experiments in space to get reliable results. However, since in the FMPT, the time for the experiment is limited, we plan to carry out two kinds of very simple and basic experiments as the first step for the semiconductor growth experiment. In the first experiment, we use single crystal Si sphere as the starting material and as shown, this sphere is heated in the furnace at a slightly higher temperature than the melting point. After the melting front moves nearly half way to its center, the temperature is decreased to stop the melting and to start the growth from the seed for which we use the unmelted solid party of the sphere. The sphere is centered by quartz protuberances inside of the quartz crucible. There exists the possibility of temperature fluctuations being introduced when the molten sphere occasionally touches the protuberances. The total time needed for the melting and the growth processes is estimated to be 30 minutes. Infrared emission from the sphere is monitored in order to prevent the accidental loss of the central solid core. The schematical illustration of the second experient is shown. A single crystal, Si rod is used as the starting material. In the first stage, the rod is melted from one end to obtain a liquid sphere. In the second stage, the single crystal is grown by decreasing the temperature from the unmelted part of the rod which is used as the seed. The second experient somewhat resembles the Czochralski method used on the ground; however, in the space experiment, no crucible is employed and the temperature uniformity is much superior. In both experiments, phosphorous is doped to allow observation of the change in the shape of the liquid solid interface during crystal growth and the impurity striations, if any.

Nishinaga, Tatau↗

NASA NTRS2025

PSE-Based Aerodynamic Flow Transition Prediction Using Automated Unstructured CFD Integration

Accurate, robust, and efficient prediction of transition in viscous flows is a significant challenge in computational fluid dynamics. We present a coupled, high-fidelity, iterative approach that leverages the FUN3D flow solver and the LASTRAC stability code to predict transition in low-disturbance environments, initiated by the linear growth of boundary-layer instability modes. Our method integrates the ability of FUN3D to compute mixed laminar-transitional-turbulent mean flows via transition-sensitized Reynolds-Averaged Navier-Stokes equations with the ability of LASTRAC to perform linear stability analysis, all within an automated framework that requires no intermediate user involvement. Unlike conventional frameworks that rely on classical stability theory or reduced-order metamodels, our approach employs the parabolized stability equations to provide more accurate and reliable estimates of disturbance growth for multiple instability mechanisms, including Tollmien-Schlichting, Kelvin-Helmholtz, and crossflow modes. By accounting for the effects of mean-flow nonparallelism as well as the surface curvature, this approach lays the foundation for improved N-factor correlations for transition onset prediction in a broad class of flows. We apply this method to three distinct flow configurations: 1) flow over a zero-pressure-gradient flat plate, 2) the NLF-0416 airfoil with both natural and separation-induced transitions, and 3) a 6:1 prolate spheroid, where transition is primarily driven by crossflow instability. For the two-dimensional cases, a formulated intermittency distribution is used to model the transition zone in between the laminar and fully turbulent flows. The results include comparisons with experimental measurements, similar numerical approaches, and transport-equations-based models, demonstrating good agreement in surface pressure coefficients, transition onset locations, and skin-friction coefficients for all three configurations. Besides contributing a couple of new insights into boundary-layer transition in these canonical cases, this study provides a powerful tool for transition modeling in both research and design applications in aerodynamics.

Transition Prediction↗

NASA NTRS2009

Stability of Detached Solidification

Bridgman crystal growth can be conducted in the so-called "detached" solidification regime, where the growing crystal is detached from the crucible wall. A small gap between the growing crystal and the crucible wall, of the order of 100 micrometers or less, can be maintained during the process. A meniscus is formed at the bottom of the melt between the crystal and crucible wall. Under proper conditions, growth can proceed without collapsing the meniscus. The meniscus shape plays a key role in stabilizing the process. Thermal and other process parameters can also affect the geometrical steady-state stability conditions of solidification. The dynamic stability theory of the shaped crystal growth process has been developed by Tatarchenko. It consists of finding a simplified autonomous set of differential equations for the radius, height, and possibly other process parameters. The problem then reduces to analyzing a system of first order linear differential equations for stability. Here we apply a modified version of this theory for a particular case of detached solidification. Approximate analytical formulas as well as accurate numerical values for the capillary stability coefficients are presented. They display an unexpected singularity as a function of pressure differential. A novel approach to study the thermal field effects on the crystal shape stability has been proposed. In essence, it rectifies the unphysical assumption of the model that utilizes a perturbation of the crystal radius along the axis as being instantaneous. It consists of introducing time delay effects into the mathematical description and leads, in general, to stability over a broader parameter range. We believe that this novel treatment can be advantageously implemented in stability analyses of other crystal growth techniques such as Czochralski and float zone methods.

Mazuruk, K.↗

NASA NTRS2018

Coupled Thermomechanical Micromechanics Modeling of the Influence of Thermally Grown Oxide Layer in an Environmental Barrier Coating System

Environmental Barrier Coatings (EBCs) have emerged as a promising means of protecting critical components for high temperature applications (e.g., aircraft engines). EBCs are often used to protect an underlying material (substrate) from extreme thermal/chemical environments. However, systems that utilize EBCs are susceptible to a number of failure modes including oxidation/delamination. Environmental Barrier Coatings (EBCs) have emerged as a promising means of protecting silicon based ceramic matrix composite (CMC) components for high temperature applications (e.g., aircraft engines). EBCs are often used to protect an underlying material (substrate) such as silicon carbide from extreme thermal/chemical environments. In a typical CMC/EBC system, an EBC may or may not be adhered to an underlying substrate with a bond coat (e.g., silicon). Irrespective, systems that utilize EBCs are susceptible to a number of failure modes including oxidation/delamination, recession, chemical attack and dissolution, thermo-mechanical degradation, erosion, and foreign object damage. Current work at NASA Glenn Research Center is aimed at addressing these failure modes in EBC systems and developing robust analysis tools to aid in the design process. The Higher-Order Theory for Functionally Graded Materials (HOTFGM), a precursor to the High-Fidelity Generalized Method of Cells micromechanics approach, was developed to investigate the coupled thermo-mechanical behavior of functionally graded composites and will be used herein to assess the development and growth of a low-stiffness thermally grown oxide (TGO) layer in EBC/CMC systems without a silicon bond coat. To accomplish this a sensitivity study is conducted to examine the influence of uniformly and non-uniformly grown oxide layer on the associated driving forces leading to mechanical failure (spallation) of EBC layer when subjected to isothermal loading, recession, chemical attack and dissolution, thermomechanical degradation, erosion, and foreign object damage. Current work at NASA Glenn Research Center is aimed at addressing these failure modes in EBC systems and developing robust analysis tools to aid in the design process. The Higher-Order Theory for Functionally Graded Materials (HOTFGM), a precursor to the High-Fidelity Generalized Method of Cells micromechanics approach, was developed to investigate the coupled thermo-mechanical behavior of functionally graded composites (Aboudi et al., 1999, Composites B). For example, HOTFGM was previously used (Arnold et al, 1995, NASA CP 10178, paper 34), to assess interlaminar stresses (including free edge effects) in a substrate with a thermal barrier coating (TBC). In this study, HOTFGM micromechanics analyses will be used to assess the development and growth of a low-stiffness thermally grown oxide (TGO) layer between a silicon carbide substrate and a ytterbium disilicate EBC. In order to realistically simulate TGO growth, an evolution law will be incorporated into HOTFGM. In addition, the effect of TGO roughness will be explored consistent with previous TBC work (Pindera et al., 2000. Material Science and Engineering, A284, pp. 158-175). This model represents a first step in developing a robust analysis tool that can ultimately be used to design durable EBC systems. Additional failure modes will be considered as part of a future work.

environmental barrier coating↗

NASA NTRS1989

A numerical study of a class of TVD schemes for compressible mixing layers

At high Mach numbers the two-dimensional time-developing mixing layer develops shock waves, positioned around large-scale vortical structures. A suitable numerical method has to be able to capture the inherent instability of the flow, leading to the roll-up of vortices, and also must be able to capture shock waves when they develop. Standard schemes for low speed turbulent flows, for example spectral methods, rely on resolution of all flow-features and cannot handle shock waves, which become too thin at any realistic Reynolds number. The performance of a class of second-order explicit total variation diminishing (TVD) schemes on a compressible mixing layer problem was studied. The basic idea is to capture the physics of the flow correctly, by resolving down to the smallest turbulent length scales, without resorting to turbulence or sub-grid scale modeling, and at the same time capture shock waves without spurious oscillations. The present study indicates that TVD schemes can capture the shocks accurately when they form, but (without resorting to a finer grid) have poor accuracy in computing the vortex growth. The solution accuracy depends on the choice of limiter. However a larger number of grid points are in general required to resolve the correct vortex growth. The low accuracy in computing time-dependent problems containing shock waves as well as vortical structures is partly due to the inherent shock-capturing property of all TVD schemes. In order to capture shock waves without spurious oscillations these schemes reduce to first-order near extrema and indirectly produce clipping phenomena, leading to inaccuracy in the computation of vortex growth. Accurate simulation of unsteady turbulent fluid flows with shock waves will require further development of efficient, uniformly higher than second-order accurate, shock-capturing methods.

Sandham, N. D.↗

NASA NTRS1990

Cyclotron maser and plasma wave growth in magnetic loops

Cyclotron maser and plasma wave growth which results from electrons accelerated in magnetic loops are studied. The evolution of the accelerated electron distribution is determined by solving the kinetic equation including Coulomb collisions and magnetic convergence. It is found that for modest values of the column depth of the loop the growth rates of instabilities are significantly reduced and that the reduction is much larger for the cyclotron modes than for the plasma wave modes. The large decrease in the growth rate with column depth suggests that solar coronal densities must be much lower than commonly accepted in order for the cyclotron maser to operate. The density depletion has to be similar to that which occurs during auroral kilometric radiation events in the magnetosphere. The resulting distributions are much more complicated than the idealized distributions used in many theoretical studies, but the fastest growing mode can still simply be determined by the ratio of electron plasma to gyrofrequency, U=omega(sub p)/Omega(sub e). However, the dominant modes are different than for the idealized situations with growth of the z-mode largest for U approximately less than 0.5, and second harmonic x-mode (s=2) or fundamental o-mode (s=1) the dominant modes for 0.5 approximately less than U approximately less than 1. The electron distributions typically contain more than one inverted feature which could give rise to wave growth. It is shown that this can result in simultaneous amplification of more than one mode with each mode driven by a different feature and can be observed, for example, by differences in the rise times of the right and left circularly polarized components of the associated spike bursts.

Hamilton, Russell J.↗

NASA NTRS2013

Carbon Nanotube Microarrays Grown on Nanoflake Substrates

This innovation consists of a new composition of matter where single-walled carbon nanotubes (SWNTs) are grown in aligned arrays from nanostructured flakes that are coated in Fe catalyst. This method of growth of aligned SWNTs, which can yield well over 400 percent SWNT mass per unit substrate mass, exceeds current yields for entangled SWNT growth. In addition, processing can be performed with minimal wet etching treatments, leaving aligned SWNTs with superior properties over those that exist in entangled mats. The alignment of the nanotubes is similar to that achieved in vertically aligned nanotubes, which are called "carpets. " Because these flakes are grown in a state where they are airborne in a reactor, these flakes, after growing SWNTs, are termed "flying carpets. " These flakes are created in a roll-to-roll evaporator system, where three subsequent evaporations are performed on a 100-ft (approx. =30-m) roll of Mylar. The first layer is composed of a water-soluble "release layer, " which can be a material such as NaCl. After depositing NaCl, the second layer involves 40 nm of supporting layer material . either Al2O3 or MgO. The thickness of the layer can be tuned to synthesize flakes that are larger or smaller than those obtained with a 40-nm deposition. Finally, the third layer consists of a thin Fe catalyst layer with a thickness of 0.5 nm. The thickness of this layer ultimately determines the diameter of SWNT growth, and a layer that is too thick will result in the growth of multiwalled carbon nanotubes instead of single-wall nanotubes. However, between a thickness of 0.5 nm to 1 nm, single-walled carbon nanotubes are known to be the primary constituent. After this three-layer deposition process, the Mylar is rolled through a bath of water, which allows catalyst-coated flakes to detach from the Mylar. The flakes are then collected and dried. The method described here for making such flakes is analogous to that which is used to make birefringent ink that is coated on U.S. currency. After deposition, the growth is carried out in a hot-filament chemical vapor deposition apparatus. A tungsten hot filament placed in the flow of H2 at a temperature greater than 1,600 C creates atomic hydrogen, which serves to reduce the Fe catalyst into a metallic state. The catalyst can now precipitate SWNTs in the presence of growth gases. The gases used for the experiments reported are C2H2, H2O, and H2, at rates of 2, 2, and 400 standard cubic centimeters per minute (sccm), respectively. In order to retain the flakes, a cage is constructed by spot welding stainless steel or copper mesh to form an enclosed area, in which the flakes are placed prior to growth. This allows growth gases and atomic hydrogen to reach the flakes, but does not allow the flakes, which rapidly nucleate SWNTs, to escape from the cage.

Schmidt, Howard K.↗

NASA NTRS1998

Effect of Measured Welding Residual Stresses on Crack Growth

Welding residual stresses in thin plate A516-70 steel and 2219-T87 aluminum butt weldments were measured by the strain-gage hole drilling and X-ray diffraction methods. The residual stress data were used to construct 3D strain fields which were modeled as thermally induced strains. These 3D strain fields were then analyzed with the WARP31) FEM fracture analysis code in order to predict their effect on fatigue and on fracture. For analyses of fatigue crack advance and subsequent verification testing, fatigue crack growth increments were simulated by successive saw-cuts and incremental loading to generate, as a function of crack length, effects on crack growth of the interaction between residual stresses and load induced stresses. The specimen experimental response was characterized and compared to the WARM linear elastic and elastic-plastic fracture mechanics analysis predictions. To perform the fracture analysis, the plate material's crack tearing resistance was determined by tests of thin plate M(T) specimens. Fracture analyses of these specimen were performed using WARP31D to determine the critical Crack Tip Opening Angle [CTOA] of each material. These critical CTOA values were used to predict crack tearing and fracture in the weldments. To verify the fracture predictions, weldment M(T) specimen were tested in monotonic loading to fracture while characterizing the fracture process.

Hampton, Roy W.↗

NASA NTRS2002

Near-term lander experiments for growing plants on Mars: requirements for information on chemical and physical properties of Mars regolith

In order to support humans for long-duration missions to Mars, bioregenerative Advanced Life Support (ALS) systems have been proposed that would use higher plants as the primary candidates for photosynthesis. Hydroponic technologies have been suggested as the primary method of plant production in ALS systems, but the use of Mars regolith as a plant growth medium may have several advantages over hydroponic systems. The advantages for using Mars regolith include the likely bioavailability of plant-essential ions, mechanical support for plants, and easy access of the material once on the surface. We propose that plant biology experiments must be included in near-term Mars lander missions in order to begin defining the optimum approach for growing plants on Mars. Second, we discuss a range of soil chemistry and soil physics tests that must be conducted prior to, or in concert with, a plant biology experiment in order to properly interpret the results of plant growth studies in Mars regolith. The recommended chemical tests include measurements on soil pH, electrical conductivity and soluble salts, redox potential, bioavailability of essential plant nutrients, and bioavailability of phytotoxic elements. In addition, a future plant growth experiment should include procedures for determining the buffering and leaching requirements of Mars regolith prior to planting. Soil physical tests useful for plant biology studies in Mars regolith include bulk density, particle size distribution, porosity, water retention, and hydraulic conductivity.

NASA Center JSC↗

NASA NTRS1982

Diffusive-convective physical vapor transport of PbTe from a Te-rich solid source

Crystal growth of PbTe by physical vapor transport (sublimation) in a closed ampoule is governed by the vapor species in thermal equilibrium with the solid compound. Deviations from stoichiometry in the source material cause diffusion limitation of the transport rate, which can be modified by natural (gravity-driven) convection. Mass-transport experiments have been performed using Te-rich material wherein sublimation rates have been measured in order to study the effects of natural convection in diffusion-limited vapor transport. Linear velocities for both crystal growth and evaporation (back sublimation) have been measured for transport in the direction of gravity, horizontally, and opposite to gravity. The experimental results are discussed in terms of both the one-dimensional diffusive-advective model and current, more sophisticated theory which includes natural convection. There is some evidence that convection effects from radial temperature gradients and solutal density gradients have been observed.

Zoutendyk, J.↗

NASA NTRS2003

Analysis of Plasma-Sprayed Thermal Barrier Coatings With Homogeneous and Heterogeneous Bond Coats Under Spatially Uniform Cyclic Thermal Loading

This report summarizes the results of a numerical investigation into the spallation mechanism in plasma-sprayed thermal barrier coatings observed under spatially-uniform cyclic thermal loading. The analysis focuses on the evolution of local stress and inelastic strain fields in the vicinity of the rough top/bond coat interface during thermal cycling, and how these fields are influenced by the presence of an oxide film and spatially uniform and graded distributions of alumina particles in the metallic bond coat aimed at reducing the top/bond coat thermal expansion mismatch. The impact of these factors on the potential growth of a local horizontal delamination at the rough interface's crest is included. The analysis is conducted using the Higher-Order Theory for Functionally Graded Materials with creep/relaxation constituent modeling capabilities. For two-phase bond coat microstructures, both the actual and homogenized properties are employed in the analysis. The results reveal the important contributions of both the normal and shear stress components to the delamination growth potential in the presence of an oxide film, and suggest mixed-mode crack propagation. The use of bond coats with uniform or graded microstructures is shown to increase the potential for delamination growth by increasing the magnitude of the crack-tip shear stress component.

Arnold, Steven M.↗

NASA NTRS1994

Convective flow effects on protein crystal growth

The long-term stability of the interferometric setup for the monitoring of protein morphologies has been improved. Growth or dissolution of a crystal on a 100 A scale can now be clearly distinguished from dimensional changes occurring within the optical path of the interferometer. This capability of simultaneously monitoring the local interfacial displacement at several widely-spaced positions on the crystal surface with high local depth resolution, has already yielded novel results. We found with lysozyme that (1) the normal growth rate is oscillatory, and (2) the mean growth step density is greater at the periphery of a facet than in its center. The repartitioning of Na(+) and Cl(-) ions between lysozyme solutions and crystals was studied for a wide range of crystallization conditions. A nucleation-growth-repartitioning model was developed to interpret the large body of data in a unified way. The results strongly suggests that (1) the ion to lysozyme ratio in the crystal depends mostly on kinetic rather than crystallographic parameters, and (2) lysozyme crystals possess a salt-rich core with a diameter on the order of 10 microns. The computational model for diffusive-convective transport in protein crystallization (see the First Report) has been applied to a realistic growth cell geometry, taking into account the findings of the above repartitioning studies. These results show that some elements of a moving boundary problem must be incorporated into the model in order to obtain a more realistic description. Our experimental setup for light scattering investigations of aggregation and nucleation in protein solutions has been extensively tested. Scattering intensity measurements with a true Rayleigh scatterer produced systematically increased forward scattering, indicating problems with glare. These have been resolved. Preliminary measurements with supersaturated lysozyme solutions revealed that the scatterers grow with time. Work has begun on a computer program for the unified evaluation of simultaneously obtained, multi-angle static and dynamic light scattering data.

Rosenberger, Franz↗