Mineralogy and chemistry of the earth's upper mantle based on the partial fusion-partial crystallization model
Mineralogy and chemistry of earth upper mantle, using partial fusion-partial crystallization model
Carter, J. L.↗
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Modelling crystal growth: Convection in an asymmetrically heated ampoule
The objective was to develop and implement a numerical method capable of solving the nonlinear partial differential equations governing heat, mass, and momentum transfer in a 3-D cylindrical geometry in order to examine the character of convection in an asymmetrically heated cylindrical ampoule. The details of the numerical method, including verification tests involving comparison with results obtained from other methods, are presented. The results of the study of 3-D convection in an asymmetrically heated cylinder are described.
Alexander, J. Iwan D.↗
Multiscale Modeling of Structurally-Graded Materials Using Discrete Dislocation Plasticity Models and Continuum Crystal Plasticity Models
A multiscale modeling methodology that combines the predictive capability of discrete dislocation plasticity and the computational efficiency of continuum crystal plasticity is developed. Single crystal configurations of different grain sizes modeled with periodic boundary conditions are analyzed using discrete dislocation plasticity (DD) to obtain grain size-dependent stress-strain predictions. These relationships are mapped into crystal plasticity parameters to develop a multiscale DD/CP model for continuum level simulations. A polycrystal model of a structurally-graded microstructure is developed, analyzed and used as a benchmark for comparison between the multiscale DD/CP model and the DD predictions. The multiscale DD/CP model follows the DD predictions closely up to an initial peak stress and then follows a strain hardening path that is parallel but somewhat offset from the DD predictions. The difference is believed to be from a combination of the strain rate in the DD simulation and the inability of the DD/CP model to represent non-monotonic material response.
Saether, Erik↗
An Integrated Approach to Laser Crystal Development
Norfolk State University has developed an integrated research program in the area of laser crystal development, including crystal modeling, crystal growth, spectroscopy, and laser modeling. This research program supports a new graduate program in Chemical Physics, designed in part to address the shortage of minority scientists.
Ries, Heidi R.↗
Validation of a Crystal Plasticity Model Using High Energy Diffraction Microscopy
High energy diffraction microscopy is used to measure the crystallographic orientation and evolution of lattice strain in an Al Li alloy. The relative spatial arrangement of the several pancake-shaped grains in a tensile sample is determined through in situ and ex situ techniques. A model for crystal plasticity with continuity of lattice spin is posed, where grains are represented by layers in a finite element mesh following the arrangement indicated by experiment. Comparison is drawn between experiment and simulation.
Beaudoin, A. J.↗
Evaluation of a Thermodynamic Ice Crystal Accretion Model using Experimental Data from NASA’s 2nd Fundamental Ice Crystal Icing Test
A thermodynamic model describing ice crystal icing is evaluated using experimental data collected at NASA Propulsion Systems Laboratory. The model makes the distinction between ice accretions that are "freeze-dominated" and "melt-dominated". Freeze-dominated icing occurs when partially melted ice crystals impact a surface and freeze. This type of icing is characterized by strong adhesion. This contrasts with melt-dominated icing, where un-melted ice crystals adhere to a surface. This type of icing is characterized by weak adhesion. In this paper, the thermodynamic model is used to analyze the ice growth rates and facility conditions to explain possible phenomena such as mass loss as well as the melting and freezing fractions. Previous analyses assumed a collection efficiency of unity at the leading edge of the experimental model. LEWICE is used to determine a better estimate of the collection efficiency at the model leading edge as ice accretion grows in time. The result shows that the sticking efficiency could change in a greater percent with time than previously reported.
Ice Crystal Icing↗
Czochralski growth of crystals - Simple models for growth rate and interface shape
A simple model for the crystal growth by the Czochralski (CZ) process has been proposed based on semiquantitative arguments. The model provides empirical relationships for the dependence of the pulling rate and the interface shape on the important process variables such as crystal radius, crucible temperature, height of the melt level, and the height of the exposed portion of the crucible wall. The parameters of the model can be evaluated by matching the results obtained from a detailed mathematical model of the CZ process or from extensive experimental data. The model has, therefore, the potential application for determining the best process conditions and for on-line control and optimization of the crystal puller to grow crystals with constant diameter and nearly planar interface.
Srivastava, R. K.↗
Structure development in silicon sheet by shaped crystallization
Models are presented for the development of a parallel twinned structure of the 110 plane type and the 112 line type in silicon ribbons. The models are believed to be mutually compatible and operable. The first model relates the requirements for super-cooling during crystallization. The existence of reentrant angles associated with the twin structure is proposed to provide a rough interface to reduce super-cooling. The spacing of the twins is proposed to be limited by the geometrical relationship between the thermal gradient in the liquid and the dimensions of the twinned crystallization front. The second model relates the thermal stress configuration to detail dislocation reactions which would be expected to develop twins. While a specific dislocation mechanism cannot yet be defined, a number of alternatives are presented. All of these various dislocation mechanisms would result in the observed crystalline configuration and the choice among them is not critical.
Leipold, M. H.↗
A contact rule for rigid-sphere models of crystal structures
Contact rule for rigid-sphere models of crystal structures
Shlichta, P. J.↗
Czochralski crystal growth: Modeling study
The modeling study of Czochralski (Cz) crystal growth is reported. The approach was to relate in a quantitative manner, using models based on first priniciples, crystal quality to operating conditions and geometric variables. The finite element method is used for all calculations.
Dudukovic, M. P.↗
Evaluation of a Thermodynamic Ice Crystal Icing Model Using Experimental Ice Accretion Data
This paper presents the evaluation of a thermodynamic ice crystal icing model, previously presented to describe the possible mechanisms of icing within the core of a turbofan jet engine. It has been proposed that there are two types of distinct ice accretions based on a surface energy balance: freeze-dominated icing and melt-dominated icing. In the former, ice accretion occurs where a freeze fraction (0 to 1) of melted ice crystals freezes on a surface, along with the existing ice of the impinging water and ice mass. This freeze-dominated icing is characterized by having strong adhesion to the surface. In the latter, icing occurs from accumulated unmelted ice on a surface, where a melt fraction (0 to 1) dictates the amount of unmelted impinged ice. This melt-dominated icing is characterized by weakly bonded surface adhesion. The experimentally observed ice growth rates suggest that only a small fraction of the impinging ice remains on the surface, implying a mass loss mechanism such as splash, runback, bounce, or erosion. This mass loss parameter must be determined in conjunction with the fraction of freezing liquid water or fraction of melting ice on an icing surface. This loss parameter, however, along with the freeze and melt fraction, are the only experimental parameters that are currently not measured directly. Using reported icing growth rates from published ice crystal icing experiments, a methodology is proposed to determine these unknown parameters. This work takes reported ice accretion data from tests conducted by the National Aeronautics and Space Administration (NASA) in 2016 and tests NASA collaborated on with the National Research Council (NRC) of Canada in 2012 that examined the fundamental physics of ice crystal icing. Those research efforts sought to generate icing conditions representative of those that occur inside a jet engine when ingesting ice crystals. This paper presents the fundamental equations of the thermodynamic model, the methodology used to determine the aforementioned unknown icing parameters, and results from model evaluation using experimental data. In addition, this paper builds on the previously proposed model by adding a transient conduction term to explain ice growth behavior at the onset of experimental tests that was observed to be different from steady-state ice growth that occurred later in the test run.With the addition of this energy term, this becomes a quasi-steady model. A key finding from this work suggests that mass loss fractions can exceed 0.90 for steady ice growth periods. In addition, due to conductive heat fluxes when using a warmer-than-freezing airfoil, lower mass loss fraction values were calculated during the initial transient period.
Ice-Crystal Ice Accretion↗
Numerical modeling of crystal growth on a centrifuge for unstable natural convection configurations
The fluid mechanics associated with crystal growth processes on centrifuges is modeled using 2D and 3D models. Two-dimensional calculations show that flow bifurcations exist in such crystal growth configurations where the ampoule is oriented in the same direction as the resultant gravity vector and a temperature gradient is imposed on the melt. A scaling analysis is formulated to predict the flow transition point from the natural convection dominated regime to the Coriolis force dominated regime. Results of 3D calculations are presented for two thermal configurations of the crystal growth cell: top heated and bottom heated with respect to the centrifugal acceleration. In the top heated configuration, a substantial reduction in the convection intensity within the melt can be attained by centrifuge operations, and close to steady diffusion-limited thermal conditions can be achieved over a narrow range of the imposed microgravity level. In the bottom heated configuration the Coriolis force has a stabilizing effect on fluid motion by delaying the onset of unsteady convection.
Ramachandran, N.↗
Analysis of Experimental Ice Accretion Data and Assessment of a Thermodynamic Model During Ice Crystal Icing
This paper evaluates a thermodynamic ice crystal icing model that has been previously presented to describe the possible mechanisms of icing within the core of a turbofan jet engine. The model functions between two distinct ice accretions based on a surface energy balance: freeze-dominated icing and melt-dominated icing. Freeze-dominated icing occurs when liquid water (from melted ice crystals) freezes and accretes on a surface along with the existing ice of the impinging water and ice mass. This freeze-dominated icing is characterized as having strong adhesion to the surface. The amount of ice accretion is partially dictated by a freeze fraction, which is the fraction of impinging liquid water that freezes. Melt-dominated icing occurs as unmelted ice on a surface accumulates. This melt-dominated icing is characterized by weakly bonded surface adhesion. The amount of ice accumulation is partially dictated by a melt fraction, which is the fraction of impinging ice crystals that melts. Experimentally observed ice growth rates suggest that only a small fraction of the impinging ice remains on the surface, implying a mass loss mechanism such as splash, runback, bounce, or erosion. The fraction of mass loss must be determined in conjunction with the fraction of freezing liquid water or fraction of melting ice on an icing surface for a given ice growth rate. This mass loss parameter, however, along with the freeze fraction and melt fraction, are the only experimental parameters that are currently not measured directly. Using icing growth rates from ice crystal icing experiments, a methodology that has been previously proposed is used to determine these unknown parameters. This work takes ice accretion data from tests conducted by the National Aeronautics and Space Administration (NASA) at the Glenn Research Center in 2018 that examined the fundamental physics of ice crystal icing. This paper continues evaluation of the thermodynamic model from a previous effort, with additions to the model that account for sub-freezing temperatures that have been observed at the leading edge of the airfoil during icing. The predicted temperatures were generally in good agreement with measured temperatures. Other key findings include the total wet-bulb temperature being a good first order indicator of whether icing is freeze-dominated (sub-freezing values) or melt-dominated (above freezing). Maximum sticking efficiency values, the fraction of impinging mass that adheres to a surface, was calculated to be about 0.2, and retained this maximum value for a range of melt ratios (0.3 to 0.65 and possibly higher), which is defined as the ratio of liquid water content to total water content. Higher air velocities reduced the maximum sticking efficiency and shifted the icing regime to higher melt ratio values. Finally, the leading edge ice accretion angle was found to be related to ice growth (lower growth rates for smaller angles) and melt ratio (smaller melt ratios resulted in smaller angles, likely due to erosion effects).
Ice-Crystal Icing↗
Orthopyroxenes as recorders of diogenite petrogenesis: Trace element systematics
Eucrite, howardite, and diogenite members of the achondrites are considered, by many, to be genetically related. Therefore, each provide a piece of the puzzle for reconstructing magmatic processes on the eucrite parent body (EPB). The relationship between eucrites and diogenites can be viewed within the context of two distinctly different models: (1) fractional crystallization; and (2) partial melting. In fractional crystallization models, eucrites and diogenites represent a complementary continuum of planetary fractional crystallization products in which the diogenites represent crystal accumulations during the crystallization of eucritic magmas at shallow to deep levels in the EPB. Alternatively, experimental studies may be interpreted as indicating eucrites represent peritectic partial melts of a primitive, chondritic EPB mantle. Within this type of model, the diogenites are also generally considered to be cumulates; however, their petrogenetic relationship to the eucrites is less clear. Sack et al. proposed that the olivine diogenites represent residua from the partial melting events that produced eucritic liquids. Initial trace element studies of orthopyroxene (OPX) are consistent with this model. However, this trace element modeling of the olivine diogenites is nonunique. As a further test of these models, we did the following three things: (1) analyzed OPX from cumulate diogenites to compare with the olibine diogenite data; (2) improved ion microprobe analytical techniques for the analysis of elements critical to our interpretations; and (3) selected more relevant Kd's for OPX-eucritic melt.
Shearer, C. K.↗
Modeling the Crystallization of Martian Igneous Compositions
The martian crust is dominated by basalts and ultramafic rocks [1]. Understanding the crystallization sequence of martian igneous rocks is critical for constraining the petrologic and geochemical evolution of the crust and mantle. Experimental studies have investigated the parental liquid compositions and crystallization behavior using martian meteorite compositions [2-7], as well as compositions measured by rovers on the martian surface [8,9]. While experiments deliver crucial results, they are often limited by time and resources. Therefore, modeling approaches are an ideal tool to complement experimental results. The application of the MELTS software package [10, 11], to calculate the crystallization of martian compositions, reproduces important compositional details of magma crystallization but significant uncertainties regarding the pressure of the olivine-pyroxene multiple saturation point have been reported [12], and in the temperatures of initial crystallization [12, 13]. Recently, a new melting model, MAGMARS, has been shown to reproduce martian primary melts more accurately [14]. Here, we constrain the applicability of Gibbs free energy minimization software Perple_X [15] for martian compositions by comparing our modeled results to experimentally derived crystallization paths for two martian compositions.
J Semprich↗
Controls on Highly Siderophile Element Concentrations in Martian Basalt: Sulfide Saturation and Under-Saturation
Highly siderophile elements (HSE; Re, Au and the platinum group elements) in shergottites exhibit a wide range from very high, similar to the terrestrial mantle, to very low, similar to sulfide saturated mid ocean ridge basalt (e.g., [1]). This large range has been difficult to explain without good constraints on sulfide saturation or under-saturation [2]. A new model for prediction of sulfide saturation places new constraints on this problem [3]. Shergottite data: For primitive shergottites, pressure and temperature estimates are between 1.2-1.5 GPa, and 1350-1470 C [4]. The range of oxygen fugacities is from FMQ-2 to IW, where the amount of Fe2O3 is low and thus does not have a significant effect on the S saturation values. Finally, the bulk compositions of shergottites have been reported in many recent studies (e.g., [5]). All of this information will be used to test whether shergottites are sulfide saturated [3]. Modeling values and results: The database for HSE partition coefficients has been growing with many new data for silicates and oxides [6-8] to complement a large sulfide database [9- 11]. Combining these data with simple batch melting models allows HSE contents of mantle melts to be estimated for sulfide-bearing vs. sulfide-free mantle. Combining such models with fractional crystallization modeling (e.g., [12]) allows HSE contents of more evolved liquids to be modeled. Most primitive shergottites have high HSE contents (and low S contents) that can be explained by sulfide under-saturated melting of the mantle. An exception is Dhofar 019 which has high S contents and very low HSE contents suggesting sulfide saturation. Most evolved basaltic shergottites have lower S contents than saturation, and intermediate HSE contents that can be explained by olivine, pyroxene, and chromite fractionation. An exception is EET A79001 lithology B, which has very low HSE contents and S contents higher than sulfide saturation values . evidence for sulfide saturation during late fractional crystallization. These results show that shergottite HSE contents are controlled by silicates, oxides, and sulfides. In addition, the mantle producing the most primitive shergottites did not contain near chondritic relative ratios of the HSEs like the terrestrial mantle, and did not experience a late chondritic veneer.
Righter, Kevin↗
Numerical Modeling of Crystal of ZnSe by Physical Vapor Transport - Towards a more Comprehensive Formulations
Crystal growth from the vapor phase has various advantages over melt growth. The main advantage is from a lower processing temperature which makes the process more amenable in instances where the melting temperature of the crystal is high. Other benefits stem from the inherent purification mechanism in the process due to differences in the vapor pressures of the native elements and impurities, and the enhanced interfacial morphological stability during the growth process. Further, the implementation of PVT growth in closed ampoules affords experimental simplicity with minimal needs for complex process control which makes it an ideal candidate for space investigations in systems where gravity tends to have undesirable effects on the growth process. Bulk growth of wide band gap II-VI semiconductors by physical vapor transport has been developed and refined over the past several years at NASA MSFC. Results from a modeling study of PVT crystal growth of ZnSe are reported in this paper. The PVT process is numerically investigated using both two-dimensional and fully three-dimensional formulation of the governing equations and associated boundary conditions. Both the incompressible Boussinesq approximation and the compressible model are tested to determine the influence of gravity on the process and to discern the differences between the two approaches. The influence of a residual gas is included in the models. The results show that both the incompressible and compressible approximations provide comparable results and the presence of a residual gas tends to measurably reduce the mass flux in the system. Detailed flow, thermal and concentration profiles will be provided in the final manuscript along with computed heat and mass transfer rates. Comparisons with the 1-D model will also be provided. The effect of gravity on the process from numerical computations shows subtle effects although experimental evidence from vertically and horizontally grown samples show dramatic evidence of gravitational effects. The shortcomings of the problem formulation will be discussed and a framework will be provided leading up towards a more comprehensive model of PVT systems.
Ramachandran, N.↗
Are Ferroan Anorthosites Direct Products of the Lunar Magma Ocean?
According to Lunar Magma Ocean (LMO) theory, lunar samples that fall into the ferroan anorthosite (FAN) category represent the only samples we have of of the primordial crust of the Moon. Modeling indicates that plagioclase crystallizes after >70% LMO crystallization and formed a flotation crust, depending upon starting composition. The FAN group of highlands materials has been subdivided into mafic-magnesian, mafic-ferroan, anorthositic- sodic, and anorthositic-ferroan, although it is not clear how these subgroups are related. Recent radiogenic isotope work has suggested the range in FAN ages and isotopic systematics are inconsistent with formation of all FANs from the LMO. While an insulating lid could have theoretically extend the life of the LMO to explain the range of the published ages, are the FAN compositions consistent with crystallization from the LMO? As part of a funded Emerging Worlds proposal (NNX15AH76G), we examine this question through analysis of FAN samples. We compare the results with various LMO crystallization models, including those that incorporate the influence of garnet.
Neal, C. R.↗