Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “PHASE VELOCITY”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,369 records · Page 76
All sourcesNASA NTRSDOE OSTI
DOE OSTI2014

Determining the refractive index of shocked [100] lithium fluoride to the limit of transmissibility

Lithium fluoride (LiF) is a common window material used in shock- and ramp-compression experiments because it displays a host of positive attributes in these applications. Most commonly, it is used to maintain stress at an interface and velocimetry techniques are used to record the particle velocity at that interface. In this application, LiF remains transparent to stresses up to 200 GPa. In this stress range, LiF has an elastic-plastic response with a very low (<0.5 GPa) elastic precursor and exhibits no known solid-solid phase transformations. However, because the density dependence of the refractive index of LiF does not follow the Gladstone-Dale relation, the measured particle velocity at this interface is not the true particle velocity and must be corrected. For that reason, the measured velocity is often referred to as the apparent velocity in these types of experiments. In this article, we describe a series of shock-compression experiments that have been performed to determine the refractive index of LiF at the two most commonly used wavelengths (532 nm and 1550 nm) between 35 and 200 GPa to high precision. A modified form of the Gladstone-Dale relation was found to work best to fit the determined values of refractive index. In addition, we provide a direct relationship between the apparent and true particle velocity to correct experimentally obtained wave profiles by others using these velocimetry techniques.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2014

(U) Equation of State and Compaction Modeling for CeO 2

Recent efforts have focused on developing a solid-liquid and three-phase equation of state (EOS) for CeO 2 , while parallel experimental efforts have focused on obtaining high-fidelity Hugoniot measurements on CeO 2 in the porous state. The current work examines the robustness of two CeO 2 SESAME equations of state, a solid-liquid EOS, 96170, and a three-phase EOS, 96171, by validating the EOS against a suite of high-pressure shock compression experiments on initially porous CeO 2 . At lower pressures compaction is considered by incorporating a two-term exponential form of the P-compaction model, using three separate definitions for α(P). Simulations are executed spanning the partially compacted and fully compacted EOS regimes over the pressure range 0.5 - 109 GPa. Comparison of calculated Hugoniot results with those obtained experimentally indicate good agreement for all definitions of α(P) with both the solid-liquid and three-phase EOS in the low-pressure compaction regime. At higher pressures the three-phase EOS does a better job at predicting the measured Hugoniot response, though at the highest pressures EOS 96171 predicts a less compliant response than is observed experimentally. Measured material velocity profiles of the shock-wave after it has transmitted through the powder are also compared with those simulated using with solid-liquid and three-phase EOS. Profiles lend insight into limits of the current experimental design, as well as the threshold conditions for the shock-induced phase transition in CeO 2 .

36 MATERIALS SCIENCE↗
DOE OSTI2011

Application of accelerometers for sensing combustion phasing of an advanced combustion engine

This paper evaluates the ability of accelerometers to detect combustion phasing of a single-cylinder air-cooled internal combustion engine undergoing homogeneous charge compression ignition. Metrics derived from the measured surface acceleration waveform, surface velocity, and the surface-specific kinetic energy were compared to the 50 per cent energy release location (CA50) on a cyclic basis for three different experimental test cases. The peak surface velocity location showed a robust ability to detect CA50 on a cyclic basis for short combustion durations. Finally, using a simple single-degree-of-freedom vibration model, it is shown the impulsive nature of the combustion load and the natural frequency of the engine structure governs when the peak velocity location will indeed robustly detect CA50 on a on a per-engine cycle basis.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2026

Numerical simulation of vortex-induced vibration response of a single IEA 10-MW wind turbine blade

Three-dimensional simulation of vortex-induced vibration (VIV) of a single International Energy Agency (IEA) 10-MW reference wind turbine blade with a length of 97.325 m is performed using the ExaWind stack, an open-source suite of codes. This study aims to illustrate the spanwise VIV response characteristics and cross-validate the results with an existing commercial framework. Five near-body meshes and three time steps are selected for the convergence study. To improve computational efficiency, several VIV triggering methods are also compared to shorten the VIV development period. The ExaWind-based VIV simulation strategy for a single IEA 10-MW blade is determined. First, the modal shape is validated against published results. Then, spanwise VIV responses of four blade configurations under a fixed and varied incoming flow velocity are analyzed. Results show that the VIV response is dominated by the first edgewise (second overall) mode. Little first-mode contributions appear near the second-mode node, producing a pi phase jump, and a higher harmonics response occurs near the blade root. Rotational degrees of freedom are minor compared with translational motion. The response versus reduced velocity is analyzed, showing a two-branch behavior similar to that of VIV for a bluff cylinder. Across all tested cases, the dominant frequency remains locked to the natural frequency of the second mode with no observed desynchronization. A mild deviation is observed for the case of 90-degree pitch and 310-degree azimuth rotation near a reduced velocity of 6, which will be examined with additional cases in future work. These findings indicate that severe VIV responses can arise under specific configurations and flow conditions, thereby increasing the potential for VIV fatigue damage and requiring greater attention during operation.

17 WIND ENERGY↗
DOE OSTI2014

Plasma rotation and NTM onset driven by central EC deposition in TCV tokamak

The effects of the central electron cyclotron heating (ECH) and current drive (ECCD) on the spontaneous plasma rotation and on the presence of Tearing Modes (TM), observed in the TCV tokamak[1], were recently investigated as an interplay between the toroidal velocity and NTM onset in absence of sawteeth, ELMs and error fields [2–3]. In a set of reproducible TCV discharges (I{sub p}∼ −150 kA, B{sub t}∼ −1.4 T, ne,{sub av∼} 1.5 10{sup 19} m{sup −3}, T{sub e}∼ 3 keV and T{sub i}∼0.25 keV, q{sub 95}∼5.8) with both pure EC heating and current drive the cnt-Ip toroidal velocity was observed to be reduced with subsequent co-Ip appearance of 3/2 and 2/1 modes during the ramp up EC phases. The understanding of the capability of the on-axis EC power to modify the rotation profiles before and after the TM onset and of the sudden disappearance of 3/2 mode when 2/1 starts is the main purpose of this work. The velocity profile modifications are due to a direct effect of the EC absorbed power and also related to some variation of the perpendicular diffusion of the toroidal momentum and to magnetic braking effects of the kind of neoclassical toroidal viscosity (NTV) due to the NTM resonant field perturbations associated to the presence of TM. Numerical investigations are performed using a 1D toroidal momentum balance equation including contributions by external sources, as EC power, and NTV torques. Furthermore, the combined evolution of the 3/2 and 2/1 modes requires considering also coupling effects included in a generalized Rutherford equation for the modelling of the TM time growth.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

The influence of δ-(Al,Fe)OOH on seismic heterogeneities in Earth’s lower mantle

The high-pressure phases of oxyhydroxides (δ-AlOOH, ε-FeOOH, and their solid solution), candidate components of subducted slabs, have wide stability fields, thus potentially influencing volatile circulation and dynamics in the Earth’s lower mantle. Here, we report the elastic wave velocities of δ-(Al,Fe)OOH (Fe/(Al + Fe) = 0.13, δ-Fe13) to 79 GPa, determined by nuclear resonant inelastic X-ray scattering. At pressures below 20 GPa, a softening of the phonon spectra is observed. With increasing pressure up to the Fe 3+ spin crossover (~ 45 GPa), the Debye sound velocity (vD) increases. At higher pressures, the low spin δ-Fe 13 is characterized by a pressure-invariant vD. Using the equation of state for the same sample, the shear-, compressional-, and bulk-velocities (v S , v P , and v Φ ) are calculated and extrapolated to deep mantle conditions. The obtained velocity data show that δ-(Al,Fe)OOH may cause low-v Φ and low-v P anomalies in the shallow lower mantle. At deeper depths, we find that this hydrous phase reproduces the anti-correlation between v S and v Φ reported for the large low seismic velocity provinces, thus serving as a potential seismic signature of hydrous circulation in the lower mantle.

58 GEOSCIENCES↗
DOE OSTI2013

OGLE-2011-BLG-0417: A RADIAL VELOCITY TESTBED FOR MICROLENSING

Microlensing experiments are returning increasingly detailed information about the planetary and binary systems that are being detected, far beyond what was originally expected. In several cases the lens mass and distance are measured, and a few very special cases have yielded complete eight-parameter Kepler solutions, i.e., the masses of both components, five Kepler invariants, and the phase. We identify one such case that is suitable for a precision test that could be carried out by comparing Doppler radial velocity (RV) measurements with the predictions from the microlensing solution. The lens primary is reasonably bright (I = 16.3, V = 18.2) and is expected to have a relatively large RV semi-amplitude (K {approx} 6.35 km s{sup -1}).

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

A frozen Gaussian approximation-based multi-level particle swarm optimization for seismic inversion

In this paper, we propose a frozen Gaussian approximation (FGA)-based multi-level particle swarm optimization (MLPSO) method for seismic inversion of high-frequency wave data. The method addresses two challenges in it: First, the optimization problem is highly non-convex, which makes hard for gradient-based methods to reach global minima. This is tackled by MLPSO which can escape from undesired local minima. Second, the character of high-frequency of seismic waves requires a large number of grid points in direct computational methods, and thus renders an extremely high computational demand on the simulation of each sample in MLPSO. We overcome this difficulty by three steps: First, we use FGA to compute high-frequency wave propagation based on asymptotic analysis on phase plane; Then we design a constrained full waveform inversion problem to prevent the optimization search getting into regions of velocity where FGA is not accurate; Last, we solve the constrained optimization problem by MLPSO that employs FGA solvers with different fidelity. The performance of the proposed method is demonstrated by a two-dimensional full-waveform inversion example of the smoothed Marmousi model.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Time-lens photon Doppler velocimetry (TL-PDV)

Here, we describe a time lens (TL) to expand the dynamic range of photon Doppler velocimetry (PDV) systems. The principle and preliminary design of a TL-PDV system are explained and shown to be feasible through simulations. In a PDV system, an interferometer is used for measuring frequency shifts due to the Doppler effect from the target motion. However, the sampling rate of the electronics could limit the velocity range of a PDV system. A four-wave-mixing (FWM) TL applies a quadratic temporal phase to an optical signal within a nonlinear FWM medium (such as an integrated photonic waveguide or a highly nonlinear optical fiber). By spectrally isolating the mixing product, termed the idler, and with appropriate lengths of dispersion prior to and after this FWM TL, a temporally magnified version of the input signal is generated. Therefore, the frequency shifts of PDV can be “slowed down” with the magnification factor M of the TL. M = 1 corresponds to a regular PDV system without a TL. M = 10 has been shown to be feasible for a TL-PDV system. The use of this effect for PDV can expand the velocity measurement range and allow for the use of lower bandwidth electronics. TL-PDV will open up new avenues for various dynamic material experiments.

47 OTHER INSTRUMENTATION↗
DOE OSTI2022

The dynamical state of RXCJ1230.7+3439: A multi-substructured merging galaxy cluster

We analyse the kinematical and dynamical state of the galaxy cluster RXCJ1230.7+3439 (RXCJ1230), at $z$ = 0.332 using 93 new spectroscopic redshifts of galaxies acquired at the Telescopio Nazionale Galileo and from SDSS DR16 public data. We study the density galaxy distribution retrieved from photometric SDSS multiband data and find that RXCJ1230 appears as a clearly isolated peak in the redshift space, with a global line-of-sight (LOS) velocity dispersion of $σ$ v = 1004 -122 +147 km s -1 . Several tests applied to the spatial and velocity distributions reveal that RXCJ1230 is a complex system with the presence of three subclusters, located to the southwest, east, and south with respect to the main body of the cluster, containing several bright galaxies (BGs) in their respective cores. Our analyses confirm that the three substructures are in a pre-merger phase, where the main interaction takes place with the southwest subclump, almost in the plane of the sky. We compute a velocity dispersion of $σ$ v ~ 1000 and $σ$ v ~ 800 km s -1 for the main cluster and the southwest substructure, respectively. The central main body and southwest substructure differ by ~870 km s -1 in the LOS velocity. From these data, we estimate a dynamical mass of $M$ 200 = 9.0 ± 1.5 × 1014 $M$ ⊙ and 4.4 ± 3.3 × 1014 $M$ ⊙ for the RXCJ1230 main body and southwest clump, respectively, which reveals that the cluster will undergo a merger characterised by a 2:1 mass ratio impact. We solve a two-body problem for this interaction and find that the most likely solution suggests that the merging axis lies ~17° from the plane of the sky and the subcluster will fully interact in ~0.3 Gyr. However, a slight excess in the X-ray temperature observed in the southwest clump confirms a certain degree of interaction already. The comparison between the dynamical masses and those derived from X-ray data reveals good agreement within errors (differences ~15%), which suggests that the innermost regions (< r 500 ) of the galaxy clumps are almost in hydrostatical equilibrium. In summary, RXCJ1230 is a young but also massive cluster in a pre-merging phase accreting other galaxy systems from its environment.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

Features of Relaxation of a Stress Tensor in the Microscopic Volume of Nematic Phase under the Action of a Strong Electric Field

A numerical study of new regimes of reorientation of director field n̂, velocity v, and components of stress tensor σ{sub ij} (ij = x, y, z) of nematic liquid crystal (LC) encapsulated in a rectangular channel under the action of a strong electric field E directed at angle α(∼(π/2)) to the horizontal surfaces bounding the LC channel is proposed. The numerical calculations performed in the framework of nonlinear generalization of the classical Eriksen-Leslie theory have shown that at certain relations between the torques and momenta affecting the unit LC volume and E ≫ E{sub th}, transition periodic structures can emerge during reorientation of n̂, if the corresponding distortion mode has the fastest response, and, thus, suppress all other modes. Rotating domains originating within this process decrease the energy dissipation rate and create more favorable regimes of the director field reorientation, as compared with the uniform rotational displacement.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Calibration and validation of the foundation for a multiphase strength model for tin

In this work, the Common Model of Multi-phase Strength and Equation of State (CMMP) model was applied to tin. Specifically, calibrations of the strength-specific elements of the CMMP foundation were developed with a combination of experiments and theory, and then the model was validated experimentally. The first element of the foundation is a multi-phase analytic treatment of the melt temperature and the shear modulus for the solid phases. These models were parameterized for each phase based on ab initio calculations using the software VASP (Vienna Ab initio Simulations Package) based on density functional theory. The shear modulus model for the ambient phase was validated with ultrasonic sound speed measurements as a function of pressure and temperature. The second element of the foundation is a viscoplastic strength model for the phase, upon which strength for inaccessible higher-pressure phases can be scaled as necessary. The stress–strain response of tin was measured at strain rates of 10 -3 to 3 x 10 3 s -1 and temperatures ranging from 87 to 373 K. The Preston–Tonks–Wallace (PTW) strength model was fit to that data using Bayesian model calibration. For validation, six forward and two reverse Taylor impact experiments were performed at different velocities to measure large plastic deformation of tin at strain rates up to ⁠10 5 s -1 . The PTW model accurately predicted the deformed shapes of the cylinders, with modest discrepancies attributed to the inability of PTW to capture the effects of twinning and dynamic recrystallization. Some material in the simulations of higher velocity Taylor cylinders reached the melting temperature, thus testing the multiphase model because of the presence of a second phase, the liquid. In simulations using a traditional modeling approach, the abrupt reduction of strength upon melt resulted in poor predictions of the deformed shape and non-physical temperatures. With CMMP, the most deformed material points evolved gradually to a mixed solid–liquid but never a fully liquid state, never fully lost strength, stayed at the melt temperature as the latent heat of fusion was absorbed, and predicted the deformed shape well.

36 MATERIALS SCIENCE↗
DOE OSTI2018

Formation of intermetallic structures at the interface of steel-to-aluminium explosive welds

Highlights: • The interface of Fe-Al explosive welds was characterised by SEM/EDS and EBSD. • The intermetallics formed at the weld interface are rich in Al (Fe{sub 4}Al{sub 13}, Fe{sub 2}Al{sub 5}). • The presence of intermetallic phases on the interface deeply affects the weldability. • Al-rich intermetallics increase the solidification time of the weld interface. - Abstract: The formation of intermetallic structures at the interface of carbon steel to 6082 aluminium alloy explosive welds and their influence on the weldability of these two materials were studied. The morphology, the microstructure, the chemical and phase compositions of the welds were characterised by several types of microscopy techniques. The interface characterisation proved that explosive mixtures with a lower detonation velocity were revealed as being more suitable for achieving consistent welds since jet entrapment was prevented and continuous molten layers were not formed at the weld interface. It was also found that the physical properties of the intermetallic phases generated at the weld interface have a strong influence on the weldability of steel-to-aluminium explosive welds. Specifically, it was shown that the formation of aluminium-rich intermetallic phases at the weld interface increases the solidification time of the interfacial molten material, decreasing the weldability of these two materials. The formation of these intermetallic compounds should be avoided by reducing the interaction between the flyer and the baseplate as well as by avoiding excessive molten layers.

36 MATERIALS SCIENCE↗
DOE OSTI2015

SN 2013ej IN M74: A LUMINOUS AND FAST-DECLINING TYPE II-P SUPERNOVA

We present extensive ultraviolet, optical, and near-infrared observations of the Type IIP supernova (SN IIP) 2013ej in the nearby spiral galaxy M74. The multicolor light curves, spanning from ∼8–185 days after explosion, show that it has a higher peak luminosity (i.e., M{sub V} ∼ −17.83 mag at maximum light), a faster post-peak decline, and a shorter plateau phase (i.e., ∼50 days) compared to the normal Type IIP SN 1999em. The mass of {sup 56}Ni is estimated as 0.02 ± 0.01 M{sub ⊙} from the radioactive tail of the bolometric light curve. The spectral evolution of SN 2013ej is similar to that of SN 2004et and SN 2007od, but shows a larger expansion velocity (i.e., v{sub Fe} {sub ii} ∼ 4600 km s{sup −1} at t ∼ 50 days) and broader line profiles. In the nebular phase, the emission of the Hα line displays a double-peak structure, perhaps due to the asymmetric distribution of {sup 56}Ni produced in the explosion. With the constraints from the main observables such as bolometric light curve, expansion velocity, and photospheric temperature of SN 2013ej, we performed hydrodynamical simulations of the explosion parameters, yielding the total explosion energy as ∼0.7× 10{sup 51} erg, the radius of the progenitor as ∼600 R{sub ⊙}, and the ejected mass as ∼10.6 M{sub ⊙}. These results suggest that SN 2013ej likely arose from a red supergiant with a mass of 12–13 M{sub ⊙} immediately before the explosion.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Microemulsions in the driven Widom-Rowlinson lattice gas

An investigation of the two-dimensional Widom-Rowlinson lattice gas under an applied drive uncovered a remarkable nonequilibrium steady state in which uniform stripes (reminiscent of an equilibrium lamellar phase) form perpendicular to the drive direction [R. Dickman and R. K. P. Zia, Phys. Rev. E 97, 062126 (2018)]. Here we study this model at low particle densities in two and three dimensions, where we find a disordered phase with a characteristic length scale (a “microemulsion”) along the drive direction. Further we develop a continuum theory of this disordered phase to derive a coarse-grained field-theoretic action for the nonequilibrium dynamics. The action has the form of two coupled driven diffusive systems with different characteristic velocities, generated by an interplay between the particle repulsion and the drive. We then show how fluctuation corrections in the field theory may generate the characteristic features of the microemulsion phase, including a peak in the static structure factor corresponding to the characteristic length scale. This work lays the foundation for understanding the stripe phenomenon more generally.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Planck intermediate results: XXVIII. Interstellar gas and dust in the Chamaeleon clouds as seen by Fermi LAT and Planck $\star$

The nearby Chamaeleon clouds have been observed in γ rays by the Fermi Large Area Telescope (LAT) and in thermal dust emission by Planck and IRAS. Cosmic rays and large dust grains, if smoothly mixed with gas, can jointly serve with the H i and 12 CO radio data to (i) map the hydrogen column densities, N H , in the different gas phases, in particular at the dark neutral medium (DNM) transition between the H i -bright and CO-bright media; (ii) constrain the CO-to-H 2 conversion factor, X CO ; and (iii) probe the dust properties per gas nucleon in each phase and map their spatial variations across the clouds. We have separated clouds at local, intermediate, and Galactic velocities in H i and 12 CO line emission to model in parallel the γ-ray intensity recorded between 0.4 and 100 GeV; the dust optical depth at 353 GHz, τ 353 ; the thermal radiance of the large grains; and an estimate of the dust extinction, A VQ , empirically corrected for the starlight intensity. Furthermore, the dust and γ-ray models have been coupled to account for the DNM gas. The consistent γ-ray emissivity spectra recorded in the different phases confirm that the GeV–TeV cosmic rays probed by the LAT uniformly permeate all gas phases up to the 12 CO cores. The dust and cosmic rays both reveal large amounts of DNM gas, with comparable spatial distributions and twice as much mass as in the CO-bright clouds. We give constraints on the H i -DNM-CO transitions for five separate clouds. CO-dark H 2 dominates the molecular columns up to AV ≃ 0.9 and its mass often exceeds the one-third of the molecular mass expected by theory. The corrected A VQ extinction largely provides the best fit to the total gas traced by the γ rays. Nevertheless, we find evidence for a marked rise in A VQ /N H with increasing N H and molecular fraction, and with decreasing dust temperature. The rise in τ 353 /NH is even steeper. Here, we observe variations of lesser amplitude and orderliness for the specific power of the grains, except for a coherent decline by half in the CO cores. This combined information suggests grain evolution. We also provide average values for the dust properties per gas nucleon in the different phases. The γ rays and dust radiance yield consistent X CO estimates near 0.7 × 10 20 cm -2 K -1 km -1 s. The A VQ and τ 353 tracers yield biased values because of the large rise in grain opacity in the CO clouds. These results clarify a recurrent disparity in the γ-ray versus dust calibration of X CO , but they confirm the factor of 2 difference found between the X CO estimates in nearby clouds and in the neighbouring spiral arms.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Calibration and validation of the foundation for a multiphase strength model for tin

In this work, the Common Model of Multi-phase Strength and Equation of State (CMMP) model was applied to tin. Specifically, calibrations of the strength-specific elements of the CMMP foundation were developed with a combination of experiments and theory, and then the model was validated experimentally. The first element of the foundation is a 10 multi-phase analytic treatment of the melt temperature and the shear modulus for the solid phases. These models were parameterized for each phase based on ab initio calculations using the software VASP (Vienna Ab initio Simulations Package) based on density functional theory (DFT). The shear modulus model for the ambient β phase was validated with ultrasonic sound speed measurements as a function of pressure and temperature. The second element of the foundation is a viscoplastic strength model for the β phase, upon which strength for inaccessible higher-pressure phases can be scaled as necessary. The stress-strain response of tin was measured at strain rates of 10 -3 to 3 x 10 3 s -1 and temperatures ranging from 87 to 373 K. The Preston-Tonks-Wallace (PTW) strength model was fit to that data using Bayesian model calibration. For validation, six forward and two reverse Taylor impact experiments were performed at different velocities to measure large plastic deformation of tin at strain rates up to 10 5 s -1 . The PTW model accurately predicted the deformed shapes of the cylinders, with modest discrepancies attributed to the inability 20 of PTW to capture the effects of twinning and dynamic recrystallization. Some material in the simulations of higher velocity Taylor cylinders reached the melting temperature, thus testing the multiphase model because of the presence of a second phase, the liquid. In simulations using a traditional modeling approach, the abrupt reduction of strength upon melt resulted in poor predictions of the deformed shape and non-physical temperatures. With CMMP, the most deformed material points evolved gradually to a mixed solid-liquid but never fully liquid state, never fully lost strength, 25 stayed at the melt temperature as the latent heat of fusion was absorbed, and predicted the deformed shape well.

36 MATERIALS SCIENCE↗