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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Freeze-in, glaciation, and UV sensitivity from light mediators

Dark matter (DM) freeze-in through a light mediator is an appealing model with excellent detection prospects at current and future experiments. Light mediator freeze-in is UV-insensitive insofar as most DM is produced at late times, and thus the DM abundance does not depend on the unknown early evolution of our universe. However the final DM yield retains a dependence on the initial DM population, which is usually assumed to be exactly zero. We point out that in models with light mediators, the final DM yield will also depend on the initial conditions assumed for the light mediator population. We describe a class of scenarios we call “glaciation” where DM freezing in from the SM encounters a pre-existing thermal bath of mediators, and study the dependence of the final DM yield on the initial temperature of this dark radiation bath. To compute DM scattering rates in this cosmology, we derive for the first time an exact integral expression for the Boltzmann collision term describing interactions between two species at different temperatures. We quantify the dependence of the DM yield on the initial dark temperature and find that it can be sizeable in regions near the traditional (zero initial abundance) freeze-in curve. We generalize the freeze-in curve to a glaciation band, which can extend as much as an order of magnitude below the traditional freeze-in direct detection target, and point out that the DM phase space distribution as well as the yield can be strongly dependent on initial conditions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

NEUTRON STAR MASS–RADIUS CONSTRAINTS USING EVOLUTIONARY OPTIMIZATION

The equation of state of cold supra-nuclear-density matter, such as in neutron stars, is an open question in astrophysics. A promising method for constraining the neutron star equation of state is modeling pulse profiles of thermonuclear X-ray burst oscillations from hot spots on accreting neutron stars. The pulse profiles, constructed using spherical and oblate neutron star models, are comparable to what would be observed by a next-generation X-ray timing instrument like ASTROSAT , NICER , or a mission similar to LOFT . In this paper, we showcase the use of an evolutionary optimization algorithm to fit pulse profiles to determine the best-fit masses and radii. By fitting synthetic data, we assess how well the optimization algorithm can recover the input parameters. Multiple Poisson realizations of the synthetic pulse profiles, constructed with 1.6 million counts and no background, were fitted with the Ferret algorithm to analyze both statistical and degeneracy-related uncertainty and to explore how the goodness of fit depends on the input parameters. For the regions of parameter space sampled by our tests, the best-determined parameter is the projected velocity of the spot along the observer’s line of sight, with an accuracy of ≤3% compared to the true value and with ≤5% statistical uncertainty. The next best determined are the mass and radius; for a neutron star with a spin frequency of 600 Hz, the best-fit mass and radius are accurate to ≤5%, with respective uncertainties of ≤7% and ≤10%. The accuracy and precision depend on the observer inclination and spot colatitude, with values of ∼1% achievable in mass and radius if both the inclination and colatitude are ≳60°.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Renormalization of the Standard Model Effective Field Theory from geometry

S-matrix elements are invariant under field redefinitions of the Lagrangian. They are determined by geometric quantities such as the curvature of the field-space manifold of scalar and gauge fields. We present a formalism where scalar and gauge fields are treated together, with a metric on the combined space of both types of fields. Scalar and gauge scattering amplitudes are given by the Riemann curvature Rijkl of this combined space, with indices i, j, k, l chosen to be scalar or gauge indices depending on the type of external particle. One-loop divergences can also be computed in terms of geometric invariants of the combined space, which greatly simplifies the computation of renormalization group equations. We apply our formalism to the Standard Model Effective Field Theory (SMEFT), and compute the renormalization group equations for even-parity bosonic operators to mass dimension eight.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2019

Real time time-dependent density functional theory using higher order finite-element methods

We present a computationally efficient approach to solve the time-dependent Kohn-Sham equations in real time using higher order finite-element spatial discretization, applicable to both pseudopotential and all-electron calculations. To this end, we develop an a priori mesh adaption technique, based on the semidiscrete (discrete in space but continuous in time) error estimate on the time-dependent Kohn-Sham orbitals, to construct an efficient finite-element discretization. Subsequently, we obtain the full-discrete error estimate to guide our choice of the time step. We employ spectral finite elements along with special reduced order quadrature to render the overlap matrix diagonal, thereby simplifying the inversion of the overlap matrix that features in the evaluation of the discrete time-evolution operator. We use the second-order Magnus operator as the time-evolution operator, wherein the action of the discrete Magnus operator, expressed as exponential of a matrix, on the Kohn-Sham orbitals is obtained efficiently through an adaptive Lanczos iteration. We observe close to optimal rates of convergence of the dipole moment with respect to spatial and temporal discretization, for both pseudopotential and all-electron calculations. We demonstrate a staggering 100-fold reduction in the computational time afforded by higher order finite elements over linear finite elements, for both pseudopotential and all-electron calculations. Further, for similar level of accuracy, we obtain significant computational savings by our approach as compared to state-of-the-art finite-difference methods. Here, we also demonstrate the competence of higher order finite elements for all-electron benchmark systems. Lastly, we observe good parallel scalability of the proposed method on many hundreds of processors.

36 MATERIALS SCIENCE↗
NASA NTRS1994

The role of structural dynamics in the design and operations of space systems: The history, the lessons, the technical challenges of the future

Structural dynamics and its auxiliary fields are the most progressive and challenging areas space system engineering design and operations face. Aerospace systems are dependent on structural dynamicists for their success. Past experiences (history) are colored with many dynamic issues, some producing ground or flight test failures. The innovation and creativity that was brought to these issues and problems are the aura from the past that lights the path to the future. Using this illumination to guide understanding of the dynamic phenomena and designing for its potential occurrence are the keys to successful space systems. Our great paradox, or challenge, is how we remain in depth specialists, yet become generalists to the degree that we make good team members and set the right priorities. This paper will deal with how we performed with acclaim in the past, the basic characteristics of structural dynamics (loads cycle, for example), and the challenges of the future.

Ryan, Robert S.↗
DOE OSTI2022

Effects of Horizontal Resolution, Domain Size, Boundary Conditions, and Surface Heterogeneity on Coarse LES of a Convective Boundary Layer

Atmospheric properties in a convective boundary layer vary over a wide range of spatial scales and are commonly studied using large-eddy simulations (LES) in various configurations. We examine how the boundary layer depth and distribution of variability across scales are affected by LES grid spacing, domain size, inhomogeneity of surface properties, and external forcing. Two different setups of the Weather Research and Forecasting (WRF) model are analyzed. A semi-idealized configuration uses a periodic domain, flat surface, prescribed homogeneous surface heat fluxes, and horizontally uniform profiles of large-scale advective tendencies. A nested LES setup employs a larger domain and realistic initial and boundary conditions, including an interactive land surface model with representative topography and vegetation and soil types. Subdomains of identical size are analyzed for all simulations. Characteristic structure sizes are quantified using the variability scales L 50 and L 95 , defined such that features smaller than that contain 50% and 95% of the total variance, respectively. Progressive increase in L 50 from vertical velocity to temperature and moisture structures is systematically reproduced in all simulation configurations. This dependence of L 50 on the considered variable complicates the development of scale-aware parameterizations for models with grid spacing in the “terra incognita”. In simulations using a larger domain with heterogeneous surface properties, the development of internal mesoscale patterns significantly affects variance distributions inside analyzed subdomains. Sizes of boundary layer structures also strongly depend on the LES grid spacing and, in case of heterogeneous surface and topography, on location of the subdomain inside a larger computational domain.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

An experimental comparison of a space-time multigrid method with PFASST for a reaction-diffusion problem

We consider two parallel-in-time approaches applied to a (reaction) diffusion problem, possibly non-linear. In particular, we consider PFASST (Parallel Full Approximation Scheme in Space and Time) and space-time multigrid strategies. For both approaches, we start from an integral formulation of the continuous time dependent problem. Then, a collocation form for PFASST and a discontinuous Galerkin discretization in time for the space-time multi-grid are employed, resulting in the same discrete solution at the time nodes. Strong and weak scaling of both multilevel strategies are compared for varying orders of the temporal discretization. Moreover, we investigate the respective convergence behavior for non-linear problems and highlight quantitative differences in execution times

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

A Gaussian graphical model approach to climate networks

Distinguishing between direct and indirect connections is essential when interpreting network structures in terms of dynamical interactions and stability. When constructing networks from climate data the nodes are usually defined on a spatial grid. The edges are usually derived from a bivariate dependency measure, such as Pearson correlation coefficients or mutual information. Thus, the edges indistinguishably represent direct and indirect dependencies. Interpreting climate data fields as realizations of Gaussian Random Fields (GRFs), we have constructed networks according to the Gaussian Graphical Model (GGM) approach. In contrast to the widely used method, the edges of GGM networks are based on partial correlations denoting direct dependencies. Furthermore, GRFs can be represented not only on points in space, but also by expansion coefficients of orthogonal basis functions, such as spherical harmonics. This leads to a modified definition of network nodes and edges in spectral space, which is motivated from an atmospheric dynamics perspective. We construct and analyze networks from climate data in grid point space as well as in spectral space, and derive the edges from both Pearson and partial correlations. Network characteristics, such as mean degree, average shortest path length, and clustering coefficient, reveal that the networks posses an ordered and strongly locally interconnected structure rather than small-world properties. Despite this, the network structures differ strongly depending on the construction method. Straightforward approaches to infer networks from climate data while not regarding any physical processes may contain too strong simplifications to describe the dynamics of the climate system appropriately.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Structural, magnetic and electrical properties of samarium substituted multiferroic bismuth ferrite

Polycrystalline Bi{sub 0.8}Sm{sub 0.2}FeO{sub 3} was synthesized by a simple co – precipitation route. Single phase of the prepared sample was confirmed by X-ray diffraction analysis which further reveals that it crystalizes as mixed crystal structure of rhombohedral with R3c space group and orthorhombic with Pnma space group. A considerable increase in magnetization was observed at room temperature VSM analysis and temperature dependent dielectric analysis shows an anomaly at the vicinity of Neel temperature (T{sub N}). Room temperature ferroelectric study explicitly authenticates the formation of a better loop due to the reduced leakage current and the suppression of oxygen deficiencies.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Fast Computational Algorithms for Partial Differential Equations and Uncertainty Quantifications

This project concerned the construction, testing and analysis of computational algorithms for solving parameterized and stochastic partial differential equations. The study and understanding of equations of this type is of fundamental importance in numerous engineering and scientific applications. Examples include simulation of plasma dynamics in models of electric propulsion and nuclear fusion, simulation of multiphase flows, such as the flow of water, gas and oil in reservoirs, and structural analysis of the dependence of structures on materials. Parametrization is used in such settings when properties of the models such as viscosity of fluids or electric resistivity of materials are not precisely understood and instead are treated as random variables. The resulting solutions are themselves random, and having such solutions will enable engineers to use probabilistic methods to assess the likelihood of events, for example, whether a pollutant in a liquid will exceed a limit, and to use such analyses to develop ways to ensure positive outcomes. Construction of accurate (high resolution) computational solutions is expensive, requiring significant computer time and computational resources, and there is need to reduce computational cost to make simulation useful and effective. The aim of the project was to construct algorithms to efficiently compute surrogate solutions to parameterized problems to allow for efficient and accurate simulation. The technical approach used focused on two related strategies, based on rank-reduction methods and reduced-order models. These methods construct surrogate solutions of parameter-dependent models by projection or interpolation into low-dimensional approximation spaces. Cost savings are achieved if the low-dimensional spaces can be identified and constructed efficiently and if the resulting low-dimensional algebraic systems can be solved cheaply. Accomplishments include: Theoretical and empirical demonstration of the effectiveness of fast multigrid solution strategies for computing low-rank representations of parameter-dependent solutions to discrete partial differential equations, including the first proof establishing so-called textbook convergence properties for low-rank methods. Development of efficient solution algorithms for solving nonlinear parameter-dependent partial differential equations used in models of fluid dynamics. Developent of efficient algorithms for low-rank representation of solutions of time-dependent simulations of fluid dynamics using multi-dimensional tensor representations of solutions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Cu-doped CdS and its application in CdTe thin film solar cell

Cu is widely used in the back contact formation of CdTe thin film solar cells. However, Cu is easily to diffuse from the back contact into the CdTe absorber layer and even to the cell junction interface CdS/CdTe. This phenomenon is generally believed to be the main factor affecting the CdTe solar cell stability. In this study Cu was intentionally doped in CdS thin film to study its effect on the microstructural, optical and electrical properties of the CdS material. Upon Cu doping, the V{sub Cd{sup −}} and the surface-state-related photoluminescence emissions were dramatically decreased/quenched. The presence of Cu atom hindered the recrystallization/coalescence of the nano-sized grains in the as-deposited CdS film during the air and the CdCl{sub 2} annealing. CdTe thin film solar cell fabricated with Cu-doped CdS window layers demonstrated much decreased fill factor, which was induced by the increased space-charge recombination near the p-n junction and the worsened junction crystalline quality. Temperature dependent current-voltage curve measurement indicated that the doped Cu in the CdS window layer was not stable at both room and higher temperatures.

36 MATERIALS SCIENCE↗
DOE OSTI2018

Anisotropic nano-scale resolution in 3D Bragg coherent diffraction imaging

We demonstrate that the resolution of three-dimensional (3D) real-space images obtained from Bragg coherent x-ray diffraction measurements is direction dependent. We propose and demonstrate the effectiveness of a metric to determine the spatial resolution of images that accounts for the directional dependence. The measured direction dependent resolution of ~4-9 nm is higher than the best previously obtained 3D measurements. Lastly, we quantify the relationship between the resolution of recovered real-space images and dosage and discuss its implications in the light of next generation synchrotrons.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1986

Chaotic instability in the three-body problem

The existence of global exponential instability leading to chaos in plane (nonrigid) motions of the three-body system is demonstrated. In the presence of Newtonian attracting forces the trajectories of the three-body system in the configuration space will no longer be geodesic, and their convergence will depend on the geodesic curvature in addition to the Gaussian curvature. It is noted that the global exponential instability occurs in the n-body problem for n greater than 3 if at least two angular coordinates are disturbed, and that the chaotic instability is not necessarily accompanied by an exponential increase of the distance between the mass-points, but is associated with the exponential divergence of trajectories in the configuration space.

Zak, M.↗
DOE OSTI2011

Synthesis, structural characterization and magnetic properties of RE{sub 2}MgGe{sub 2} (RE=rare-earth metal)

A series of rare-earth metal-magnesium-germanides RE{sub 2}MgGe{sub 2} (RE=Y, Nd, Sm, Gd-Tm, Lu) has been synthesized by reactions of the corresponding elements at high temperature. Their structures have been established by single-crystal and powder X-ray diffraction and belong to the Mo{sub 2}FeB{sub 2} structure type (space group P4/mbm (No. 127), Z=2; Pearson symbol tP10). Temperature dependent DC magnetization measurements indicate Curie-Weiss paramagnetism in the high-temperature regime for all members of the family, excluding Y{sub 2}MgGe{sub 2}, Sm{sub 2}MgGe{sub 2}, and Lu{sub 2}MgGe{sub 2}. At cryogenic temperatures (ca. 60 K and below), most RE{sub 2}MgGe{sub 2} phases enter into an antiferromagnetic ground-state, except for Er{sub 2}MgGe{sub 2} and Tm{sub 2}MgGe{sub 2}, which do not undergo magnetic ordering down to 5 K. The structural variations as a function of the decreasing size of the rare-earth metals, following the lanthanide contraction, and the changes in the magnetic properties across the series are discussed as well. - Graphical Abstract: The structure of RE{sub 2}MgGe{sub 2} (RE=Y, Nd, Sm, Gd-Tm, Lu) can be best viewed as 2-dimensional slabs of Mg and Ge atoms (anionic sub-lattice), and layers of rare-earth metal atoms (cationic sub-lattice) between them. Within this description, one should consider the Ge-Ge dumbbells (formally Ge{sup 6-}{sub 2}), interconnected with square-planar Mg atom as forming flat [MgGe{sub 2}] layers (z=0), stacked along the c-axis with the layers at z=1/2, made of rare-earth metal cations (formally RE{sup 3+}). Highlights: > RE{sub 2}MgGe{sub 2} (RE=Y, Nd, Sm, Gd-Tm, Lu) are new ternary germanides. > Their structures can be recognized as a 1:1 intergrowth of CsCl- and AlB{sub 2}-like slabs. > Ge atoms are covalently bound into Ge{sub 2} dumbbells. > Most RE{sub 2}MgGe{sub 2} phases are antiferromagnetically ordered at cryogenic temperatures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2001

Tortuosity measurement and the effects of finite pulse widths on xenon gas diffusion NMR studies of porous media

We have extended the utility of NMR as a technique to probe porous media structure over length scales of approximately 100-2000 microm by using the spin 1/2 noble gas 129Xe imbibed into the system's pore space. Such length scales are much greater than can be probed with NMR diffusion studies of water-saturated porous media. We utilized Pulsed Gradient Spin Echo NMR measurements of the time-dependent diffusion coefficient, D(t), of the xenon gas filling the pore space to study further the measurements of both the pore surface-area-to-volume ratio, S/V(p), and the tortuosity (pore connectivity) of the medium. In uniform-size glass bead packs, we observed D(t) decreasing with increasing t, reaching an observed asymptote of approximately 0.62-0.65D(0), that could be measured over diffusion distances extending over multiple bead diameters. Measurements of D(t)/D(0) at differing gas pressures showed this tortuosity limit was not affected by changing the characteristic diffusion length of the spins during the diffusion encoding gradient pulse. This was not the case at the short time limit, where D(t)/D(0) was noticeably affected by the gas pressure in the sample. Increasing the gas pressure, and hence reducing D(0) and the diffusion during the gradient pulse served to reduce the previously observed deviation of D(t)/D(0) from the S/V(p) relation. The Pade approximation is used to interpolate between the long and short time limits in D(t). While the short time D(t) points lay above the interpolation line in the case of small beads, due to diffusion during the gradient pulse on the order of the pore size, it was also noted that the experimental D(t) data fell below the Pade line in the case of large beads, most likely due to finite size effects.

Non-NASA Center↗
NASA NTRS1993

Knowledge Engineering for Temporal Dependency Networks as Operations Procedures

This paper presents a case study of the knowledge engineering process employed to support the Link Monitor & Control Operator Assistant (LMCOA). The LMCOA is a prototype system which automates equipment used to support space-ground communication with deep space spacecraft in NASA's Deep Space Network (DSN). The primary knowledge base in the LMCOA is the Temporal Dependency Network (TDN). The paper provides a brief background on the DSN, and describes the evolution of the TDN and supporting knowledge bases, the process used for knowledge engineering, and an analysis of the successes--and problems--of the knowledge engineering effort.

operations↗
DOE OSTI2015

Superoxide produced in the matrix of mitochondria enhances methylmercury toxicity in human neuroblastoma cells

The mechanism of intracellular metabolism of methylmercury (MeHg) is not fully known. It has been shown that superoxide (O{sub 2}·{sup −}), the proximal reactive oxygen species (ROS) generated by mitochondria, is responsible for MeHg demethylation. Here, we investigated the impact of different mitochondrial respiratory inhibitors, namely rotenone and antimycin A, on the O{sub 2}·{sup −} mediated degradation of MeHg in human neuroblastoma cells SH-K-SN. We also utilized paraquat (PQ) which generates O{sub 2}·{sup −} in the mitochondrial matrix. We found that the cleavage of the carbon-metal bond in MeHg was highly dependent on the topology of O{sub 2}·{sup −} production by mitochondria. Both rotenone and PQ, which increase O{sub 2}·{sup −} in the mitochondrial matrix at a dose-dependent manner, enhanced the conversion of MeHg to inorganic mercury (iHg). Surprisingly, antimycin A, which prompts emission of O{sub 2}·{sup −} into the intermembrane space, did not have the same effect even though antimycin A induced a dose dependent increase in O{sub 2}·{sup −} emission. Rotenone and PQ also enhanced the toxicity of sub-toxic doses (0.1 μM) MeHg which correlated with the accumulation of iHg in mitochondria and depletion of mitochondrial protein thiols. Taken together, our results demonstrate that MeHg degradation is mediated by mitochondrial O{sub 2}·{sup −}, specifically within the matrix of mitochondria when O{sub 2}·{sup −} is in adequate supply. Our results also show that O{sub 2}·{sup −} amplifies MeHg toxicity specifically through its conversion to iHg and subsequent interaction with protein cysteine thiols (R-SH). The implications of our findings in mercury neurotoxicity are discussed herein. - Highlights: • Superoxide produced in the matrix of mitochondria degrades MeHg. • Superoxide produced in intermembrane space does not degrade MeHg. • Matrix-generated superoxide enhances Hg toxicity by converting MeHg to iHg.

60 APPLIED LIFE SCIENCES↗
NASA NTRS1999

Effects of Melt Processing on Evolution of Structure in PEEK

We report on the effects of melt processing temperature on structure formation in Poly(ether-ether-ketone), PEEK. Real time Small Angle X-ray Scattering, SAXS, and thermal analysis are used to follow the melting behavior after various stages of processing. Assignment of peaks to structural entities within the material, the relative perfection of the crystals, and the possibility of their reorganization, are all influenced by the melt processing history. With the advent of high intensity synchrotron sources of X-radiation, polymer scientists gain a research tool which, when used along with thermal analysis, provides additional structural information about the crystals during growth and subsequent melting. PEEK is an engineering thermoplastic polymer with a very high glass transition temperature (145 C) and crystal melting point (337 C). PEEK has been the subject of recent studies by X-ray scattering in which melt and cold crystallization were followed in real-time. X-ray scattering and thermal studies have been used to address the formation of dual endothermic response which has been variously ascribed to lamellar insertion, dual crystal populations, or melting followed by re-crystallization. Another important issue is whether all of the amorphous phase is located in interlamellar regions, or alternatively whether some is located in "pockets" away from the crystalline lamellar stacks. The interpretation of scattering from lamellar stacks varies depending upon whether such amorphous pockets are formed. Some groups believe all of the amorphous phase is interlamellar. This leads to selection of a smaller thickness for the crystals. Other groups suggest that most amorphous phase is not interlamellar, and this leads to the suggestion that the crystal thickness is larger than the amorphous layer within the stacks. To investigate these ideas, we used SAXS and Differential Scanning Calorimetry to compare results of single and dual stage melt crystallization of PEEK using a treatment scheme involving annealing/crystallization at T(sub a1) followed by annealing at T(sub a2) where either T(sub a1) < T(sub a2) or T(sub a1) > T(sub a2). We proposed a model to explain multiple melting endotherms in PPS, treated according to one or two-stage melt or cold crystallization. Key features of this model are that multiple endotherms: (1) are due to reorganization/recrystallization after cold crystallization; and, (2) are dominated by crystal morphology after melt crystallization at high T. In other words, multiple distinct crystal populations are formed by the latter treatment, leading to observation of multiple melting. PEEK 45OG pellets (ICI Americas) were the starting material for this study. Films were compression molded at 400 C, then quenched to ice water. Samples were heated to 375 C in a Mettler FP80 hot stage and held for three min. to erase crystal seeds before cooling them to T(sub a1) = 280 C . Samples were held at T(sub a2) for a period of time, then immediately heated to 360 C. In the second treatment samples were held at T(sub a1) = 31 C for different crystallization times t(sub c) then cooled to 295 C and held 15 min. In situ (SAXS) experiments were performed at the Brookhaven National Synchrotron Light Source with the sample located inside the Mettler hot stage. The system was equipped with a two-dimensional position sensitive detector. The sample to detector distance was 172.7 cm and the X-ray wavelength was 1.54 Angstroms. SAXS data were taken continuously during the isothermal periods and during the heating to 360 C at 5 C/min. Each SAXS scan was collected for 30 sec. Since the samples were isotropic, circular integration was used to increase the signal to noise ratio. After dual stage melt crystallization with T(sub a1) < T(sub a2) the lower melting endotherm arises from holding at T(sub a1). During cooling a broad distribution of crystals forms, and the low-melting tail is perfected during T(sub al). Heating to T(sub a2) melts these imperfect crystals and allows others with greater average long spacing to form in their place. After dual stage crystallization with T(sub a1) > T(sub a2), the amount of space remaining for additional growth at T(sub a2) depends upon the holding time at T(sub a1). The long period of crystals formed at T(sub a2) is smaller than that formed at T(sub a1) due to growth in a now-restricted geometry. Perfection of crystals is seen as an increase of the intensity of the population scattering at higher s, while the intensity of the population scattering at lower s stays constant. During heating from below to above the minor endotherm, we see rapid decrease of the intensity of the X-ray scattering corresponding to the population of crystals scattering in the shoulder. Another important observation is that after the sample is annealed at 295 C, the shoulder intensity is restored once again. The population scattering at higher s remains longer before it disappears in the sample treated to the second stage of melt crystallization, compared to the sample crystallized with a single stage. This could be interpreted as an effect of continued perfection of the less perfect population, which is also reflected in the increased melting temperature of the smaller endotherm as the holding time at 295 C increases. In the corresponding DSC scans we see a shift in the area and the peak temperature of the lower melting endotherm with an increase of the annealing time.

Georgiev, Georgi↗