Search NASA⌕ Search

SEARCH · Search NASA

Results for “growth law”

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 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

A buoyancy–shear–drag-based turbulence model for Rayleigh–Taylor, reshocked Richtmyer–Meshkov, and Kelvin–Helmholtz mixing

A phenomenological turbulence model for Rayleigh–Taylor, reshocked Richtmyer–Meshkov, and Kelvin–Helmholtz instability-induced mixing is developed using a general buoyancy–shear–drag model. Analytic solutions to the simplified model equations corresponding to each instability are derived separately, which are then used to calibrate the model coefficients to predict specific values of the mixing layer growth parameters and exponents. The buoyancy-shear–drag equations for the bubble and spike mixing layer widths are then solved numerically, and a turbulent diffusivity (or viscosity) is constructed dimensionally as the product of the mixing layer width, h, and its time-derivative, dh/dt. Surrogate turbulent fields are then constructed by multiplying a presumed, approximate self-similar spatial profile by appropriate functions of h and dh/dt. Using several simplifying approximations, the turbulent diffusion equations satisfied by the mean mass fraction and mean shear velocity are solved analytically in a reference frame moving with the mean advection velocity, and it is shown that the mean fields evolve in space and time as expected. The explicit modeling and solution of turbulent transport equations (e.g., for the turbulent kinetic energy and its dissipation rate or a lengthscale) are not required. By using separate equations for the bubble and spike evolution, the model naturally captures the asymmetry induced by an increasing density contrast between the heavy and light fluids. The model also includes molecular dissipation and diffusion, and therefore, can describe transition to fully-developed turbulence if the initial turbulent diffusivity/viscosity is much smaller than the molecular diffusivity/viscosity. This model is applied to constant-acceleration Rayleigh–Taylor, impulsively reshocked Richtmyer–Meshkov, and variable-density Kelvin–Helmholtz mixing layers to demonstrate its utility. It is shown that the numerical solutions of the model calibrated using specific values of the instability growth parameters and exponents: (1) produces mixing layer widths in agreement with the expected self-similar growth power laws; (2) gives spatiotemporal profiles of turbulent fields that are expected and consistent with previous results; (3) predicts the expected power-law growths and decays of the spatially-integrated turbulent fields, and; (4) gives spatiotemporal profiles of the mean fields that are expected and consistent with previous results. This relatively simple model can be implemented numerically, and is expected to be useful for fundamental as well as astrophysical and inertial confinement fusion applications.

42 ENGINEERING↗
DOE OSTI2022

Multilayer interface tracking model of pure tungsten oxidation

Here, we present a numerical model to predict oxide scale growth on tungsten surfaces under exposure to oxygen at high temperatures. The model captures the formation of four thermodynamically-compatible oxide sublayers, WO 2 , WO 2.72 , WO 2.9 , and WO 3 , on top of the metal substrate. Oxide layer growth is simulated by tracking the oxide/oxide and oxide/metal interfaces using a sharp-interface Stefan model coupled to diffusion kinetics. The model is parameterized using selected experimental measurements and electronic structure calculations of the diffusivities of all the oxide subphases involved. We simulate oxide growth at temperatures of 600°C and above, extracting the power law growth exponents in each case, which we find to deviate from classical parabolic growth in several cases. We conduct a comparison of the model predictions with an extensive experimental data set, with reasonable agreement at most temperatures. While many gaps in our understanding still exist, this work is a first attempt at embedding the thermodynamic and kinetic complexity of tungsten oxide growth into a comprehensive mesoscale kinetic model that attempts to capture the essential features of tungsten oxidation to fill existing knowledge gaps and guide and enhance future tungsten oxidation models.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Multi-material additive manufacturing of aluminum 6061-T6 alloy with stainless steel 304: Suppression of intermetallic compounds and interface growth mechanism

Fabricating integrated aluminum-steel structures is difficult because of metallurgical incompatibilities that promote intermetallic compound (IMC) formation at their interfaces. This work introduces a practical route for additively manufacturing 6061-T6 aluminum alloy (AA6061-T6) directly onto 304 stainless steel (SS304) using a high shear strain rate-assisted interfacial bonding mechanism. Through the friction extrusion deposition-based additive manufacturing method, both single- and multi-layer deposits of AA6061-T6 were successfully fabricated on SS304, yielding a robust hybrid multi-material structure. Comprehensive analyses of deposition quality, interface porosity, and bonding performance showed that the interface achieved a tensile strength exceeding 154 MPa under quasi-static loading. Microstructural observations revealed that the deposited aluminum layers experienced severe plastic deformation, resulting in pronounced grain refinement. Importantly, the interfacial zone was found to be free of brittle IMCs, instead containing a thin amorphous layer that evolved through a non-linear reaction-zone growth law. This solid-state additive strategy establishes a promising pathway for lightweight structural systems, nuclear energy component cladding, and multifunctional engineering components, redefining how dissimilar metals can be integrated for advanced applications.

Aluminum alloy↗
DOE OSTI2021

Stability of expanding accretion shocks for an arbitrary equation of state

We present a theoretical stability analysis for an expanding accretion shock that does not involve a rarefaction wave behind it. The dispersion equation that determines the eigenvalues of the problem and the explicit formulae for the corresponding eigenfunction profiles are presented for an arbitrary equation of state and finite-strength shocks. For spherically and cylindrically expanding steady shock waves, we demonstrate the possibility of instability in a literal sense, a power-law growth of shock-front perturbations with time, in the range of $h_c< h<1+2 {\mathcal {M}}_2$ , where $h$ is the D'yakov-Kontorovich parameter, $h_c$ is its critical value corresponding to the onset of the instability and ${\mathcal {M}}_2$ is the downstream Mach number. Shock divergence is a stabilizing factor and, therefore, instability is found for high angular mode numbers. As the parameter $h$ increases from $h_c$ to $1+2 {\mathcal {M}}_2$ , the instability power index grows from zero to infinity. This result contrasts with the classic theory applicable to planar isolated shocks, which predicts spontaneous acoustic emission associated with constant-amplitude oscillations of the perturbed shock in the range $h_c< h<1+2 {\mathcal {M}}_2$ . Examples are given for three different equations of state: ideal gas, van der Waals gas and three-terms constitutive equation for simple metals.

Huete, César (ORCID:0000000232278520)↗
DOE OSTI2020

Toward quantifying capacity losses due to solid electrolyte interphase evolution in silicon thin film batteries

To understand the origins of failure and limited cycle life in lithium-ion batteries (LIBs), it is imperative to quantitatively link capacity-fading mechanisms to electrochemical and chemical processes. This is extremely challenging in real systems where capacity is lost during each cycle to both active material loss and solid electrolyte interphase (SEI) evolution, two indistinguishable contributions in traditional electrochemical measurements. Here, we have used a model system in combination with (1) precision measurements of the overall Coulombic efficiency via electrochemical experiments and (2) x-ray reflectivity measurements of the active material losses. The model system consisted of a 515 Å thick amorphous silicon (a-Si) thin film on silicon carbide in half-cell geometry using a carbonate electrolyte with LiPF6 salt. This approach allowed us to quantify the capacity lost during each cycle due to SEI evolution. Combined with electrochemical analysis, we identify SEI growth as the major contribution to capacity fading. Specifically, the continued SEI growth results in increasing overpotentials due to increased SEI resistance, and this leads to lower extent of lithiation when the cutoff voltage is reached during lithiation. Our results suggest that SEI grows more with increased time spent at low voltages where electrolyte decomposition is favored. Finally, we extracted a proportionality constant for SEI growth following a parabolic growth law. Our methodology allows for the quantitative determination of lithium-ion loss mechanisms in LIBs by separately tracking lithium ions within the active materials and the SEI and offers a powerful method of quantitatively understanding LIB loss mechanisms.

25 ENERGY STORAGE↗
DOE OSTI2023

Mechanistic FCCI model for BISON

In this report, multi-scale simulations to develop a mechanistic model of fuel-cladding chemical interaction (FCCI) conducted under the auspices of the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program in FY23 are described. The model assumes that cladding wastage is dominated by the intermetallic phase (Fe,Cr)$_{17}$Nd$_2$, and calculates production and diffusion of Nd in the fuel, diffusion into the cladding, and formation and growth of the intermetallic wastage layer. Atomistic simulations are used to calculate diffusivity of Nd in the (Fe,Cr) system. Mesoscale simulations, informed by previous atomistic calculations, are used to determine the effective diffusivity of Nd through the fuel, accounting for empty and sodium-filled porosity within the fuel. The BISON model incorporates this data and calculates the wastage layer thickness as a function of time, assuming parabolic growth kinetics based on the best available data. The results of the new mechanistic BISON model are compared to existing assessment cases for the X447 experiment in EBR-II, and show good agreement with experimental data and the existing BISON empirical model. To improve predictions of kinetics for future work, a phase-field model that includes fuel, wastage, and cladding phases is developed. Preliminary testing indicates that the kinetics may differ significantly from the assumed parabolic growth law, suggesting direction for future improvement of the model that will allow it to be applied to other fuel designs with greater confidence.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2020

Damage and Failure in a Statistical Crack Model

In this paper I will take a close look at a statistical crack model (SCM) as is used in engineering computer codes to simulate fracture at high strain rates. My general goal is to understand the macroscopic behavior effected by the microphysical processes incorporated into an SCM. More specifically, I will assess the importance of including local interactions between cracks into the growth laws of an SCM. My strategy will be to construct a numerical laboratory that represents a single computational cell containing a realization of a statistical distribution of cracks. The cracks will evolve by the microphysical models of the SCM, leading to quantifiable damage and failure of the computational cell. I will use the numerical data generated by randomly generated ensembles of the fracture process to establish scaling laws that will modify and simplify the implementation of the SCM into large scale engineering codes.

42 ENGINEERING↗
DOE OSTI2022

Hierarchical microstructures: a potential route to enhanced stability in structural materials for advanced nuclear reactors

The drive to increase efficiency in nuclear energy systems is leading to the need for materials that operate at higher temperatures and stress levels for extended periods, while maintaining stable microstructures to ensure their performance is not compromised. A novel route to producing materials that can perform well in such environments is the creation of hierarchical microstructures. A hierarchical microstructure is a microstructure in which features are present at multiple length scales simultaneously. In this work, a hierarchical microstructure is fabricated in a nickel-base superalloy, featuring nanometer-size gamma precipitates inside larger gamma-prime particles, which are in turn embedded in the gamma matrix phase. The hierarchical features of the microstructure lead to enhanced stability of the gamma-prime precipitates during annealing; the particle size does not follow the expected t^(1/3) growth law predicted by the classic LSW theory. Phase-field simulations are used to understand the unexpected stability of the gamma-prime precipitates.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Hierarchical microstructures: a potential route to enhanced stability in structural materials for advanced nuclear reactors

The drive to increase efficiency in nuclear energy systems is leading to the need for materials that operate at higher temperatures and stress levels for extended periods, while maintaining stable microstructures to ensure their performance is not compromised. A novel route to producing materials that can perform well in such environments is the creation of hierarchical microstructures. A hierarchical microstructure is a microstructure in which features are present at multiple length scales simultaneously. In this work, a hierarchical microstructure is fabricated in a nickel-base superalloy, featuring nanometer-size gamma precipitates inside larger gamma-prime particles, which are in turn embedded in the gamma matrix phase. The hierarchical features of the microstructure lead to enhanced stability of the gamma-prime precipitates during annealing; the particle size does not follow the expected t^(1/3) growth law predicted by the classic LSW theory. Phase-field simulations are used to understand the unexpected stability of the gamma-prime precipitates.

36 - MATERIALS SCIENCE↗
DOE OSTI2021

Late Stage Domain Coarsening Dynamics of Lamellar Block Copolymers

Block copolymer (BCP) phase separation dynamics can be expected to differ significantly from that of the polymer blends due to the constraint of chain connectivity. BCP phase separation dynamics has been studied theoretically, but there has been little experimental evidence to confirm the BCP domain growth scaling laws put forward theoretically. Here, we investigate the dynamics of late-stage lamellar BCP domain coarsening and find that the scaling exponent for lamellar domain growth is ≈1/6 (0.17), irrespective of the annealing temperature, a value close to the scaling exponent of 0.2 predicted by theoretical studies. Furthermore, we show that the prefactors in the domain coarsening equation show Arrhenius dependence on temperature, indicating that the BCP domain growth dynamics is Arrhenius over the temperature range investigated.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Measurement-induced entanglement phase transitions in variational quantum circuits

Variational quantum algorithms (VQAs), which classically optimize a parametrized quantum circuit to solve a computational task, promise to advance our understanding of quantum many-body systems and improve machine learning algorithms using near-term quantum computers. Prominent challenges associated with this family of quantum-classical hybrid algorithms are the control of quantum entanglement and quantum gradients linked to their classical optimization. Known as the barren plateau phenomenon, these quantum gradients may rapidly vanish in the presence of volume-law entanglement growth, which poses a serious obstacle to the practical utility of VQAs. Inspired by recent studies of measurement-induced entanglement transition in random circuits, we investigate the entanglement transition in variational quantum circuits endowed with intermediate projective measurements. Considering the Hamiltonian Variational Ansatz (HVA) for the XXZ model and the Hardware Efficient Ansatz (HEA), we observe a measurement-induced entanglement transition from volume-law to area-law with increasing measurement rate. Moreover, we provide evidence that the transition belongs to the same universality class of random unitary circuits. Importantly, the transition coincides with a “landscape transition” from severe to mild/no barren plateaus in the classical optimization. Our work may provide an avenue for improving the trainability of quantum circuits by incorporating intermediate measurement protocols in currently available quantum hardware.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Impurity radiation seeding of neoclassical tearing mode growth

Abstract The physics of neoclassical tearing modes (NTMs) is of great concern to tokamak plasma stability and performance, especially in the burning plasma regime. Whereas in many situations the seed events can be clearly identified, such as sawteeth and edge localized modes, the potential seeding mechanism of NTMs due to the resistive tearing instability driven by the impurity radiation cooling still needs more study. Recent NIMROD simulations have demonstrated that local impurity radiation cooling can drive the seed island growth and trigger the subsequent onset of NTM instability. The seed island is mainly driven by the local helical perturbation of the diamagnetic current induced by the perturbed pressure gradient as a result of the impurity radiative cooling on the rational surface. A heuristic closure for the neoclassical viscosity is adopted, and the seed island is further driven by the perturbed bootstrap current induced from the neoclassical electron viscous stress in the extended Ohm’s law. The growth rate of the NTM in simulations is found proportional to the electron neoclassical viscosity, and a theoretical neoclassical driving term is adopted to account for the nonlinear neoclassical island growth in the simulations.

Zeng, Shiyong (ORCID:000000017098818X)↗
DOE OSTI2023

Scaling laws for two-dimensional dendritic crystal growth in a narrow channel

Here, we investigate analytically and computationally the dynamics of two-dimensional needle crystal growth from the melt in a narrow channel. Our analytical theory predicts that, in the low supersaturation limit, the growth velocity $\textit{V}$ decreases in time $\textit{t}$ as a power law $V ~t^{–2/3}$, which we validate by phase-field and dendritic-needle-network simulations. Simulations further reveal that, above a critical channel width $Λ ≈ 5l_D$, where $l_D$ is the diffusion length, needle crystals grow with a constant $V < V_s$, where $V_s$ is the free-growth needle crystal velocity, and approaches $V_s$ in the limit $Λ \gg l_D$.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Conceptualizing Biogeochemical Reactions With an Ohm's Law Analogy

Abstract In studying problems like plant‐soil‐microbe interactions in environmental biogeochemistry and ecology, one usually has to quantify and model how substrates control the growth of, and interaction among, biological organisms (and abiotic factors, e.g., adsorptive mineral soil surfaces). To address these substrate‐consumer relationships, many substrate kinetics and growth rules have been developed, including the famous Monod kinetics for single‐substrate‐based growth and Liebig's law of the minimum for multiple‐nutrient‐colimited growth. However, the mechanistic basis that leads to these various concepts and mathematical formulations and the implications of their parameters are often quite uncertain. Here, we show that an analogy based on Ohm's law in electric circuit theory is able to unify many of these different concepts and mathematical formulations. In this Ohm's law analogy, a resistor is defined by a combination of consumers’ and substrates’ kinetic traits. In particular, the resistance is equal to the mean first passage time that has been used to derive the Michaelis‐Menten kinetics under substrate replete conditions for a single substrate as well as the predation rate of individual organisms. We further show that this analogy leads to important insights on various biogeochemical problems, such as (a) multiple‐nutrient‐colimited biological growth, (b) denitrification, (c) fermentation under aerobic conditions, (d) metabolic temperature sensitivity, and (e) the legitimacy of Monod kinetics for describing bacterial growth. We expect that our approach will help both modelers and nonmodelers to better understand and formulate hypotheses when studying certain aspects of environmental biogeochemistry and ecology.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Growth and Properties of Vapor Diffused Nb3Sn Coating for Superconducting Radiofrequency Accelerator Cavity Applications

The desire to reduce construction and operating costs of future SRF accelerators motivates the search for higher-performing alternative materials. Nb3Sn (Tc ~ 18.3 K and Hsh ~ 425 mT) is the front runner. The tin vapor diffusion process is currently the technique of choice to produce promising Nb3Sn-coated cavities. Understanding Nb3Sn nucleation and growth in this process is essential to progress. Samples representing different stages of Nb3Sn formation have been produced and studied to elucidate the effects of nucleation, growth, process conditions, and impurities. Nb3Sn films with thickness from a few hundred nm up to ~15 µm were grown and characterized. The microscopic examination of samples suggests the mechanisms of thin film nucleation and growth. Broadly, nucleation deposits tin as a thin surface phase and, under some conditions, a few hundred nanometer sized particles as well. Conditions that impair nucleation promote the formation of defects, such as ?patches?, in subsequent coating growth. Analysis of coated samples is consistent with the model of Nb3Sn grown in which tin diffuses via grain boundaries to Nb3Sn-Nb interface, where the growth Nb3Sn into the niobium bulk takes place. Similar scaling laws are found for grain growth and layer thickness. Non-parabolic layer growth is consistent with significant grain growth, which reduces the number of Sn-transport channels. Examination of patchy region in Nb3Sn coating revealed it to be large single crystalline grains, pointing to impeded Nb3Sn layer growth due to low grain boundary density, resulting in a significantly thin coating in those areas. Examination of RF loss regions from a coated cavity, identified with a thermometry mapping system showed patchy regions and carbonus defects were associated with strong local field-dependent surface resistance. RF measurements of coated cavities were combined with material characterization of witness samples and coated-cavity cutouts to improve the coating process. Understanding obtained and applied to cavity coatings, resulted in single-cell Nb3Sn cavities with a quality factor of ~2 ×1010 up to 15 MV/m accelerating gradient at 4 K, without "Wuppertal" Q-slope. We have also produced Nb3Sn-coated CEBAF 5-cell cavities with accelerating gradients useful for accelerator cryomodules. This dissertation will discuss the genesis of the Nb3Sn coating in a typical tin vapor diffusion process, effects of different process parameters, and its consequences to the coating of single-cell and multi-cell SRF cavities.

Pudasaini, Uttar↗
DOE OSTI2022

Role of electronic energy loss on defect production and interface stability: Comparison between ceramic materials and high-entropy alloys

High-entropy alloys (HEAs) and some complex alloys exhibit desirable properties and significant structural stability in harsh environments, including possible applications in advanced reactors. Energetic ion irradiation is often used as a surrogate for neutron irradiation; however, the impact of ion electronic energy deposition and dissipation is often neglected. Moreover, differences in recoil energy spectrum and density of cascade events on damage evolution must also be considered. In many chemically complex alloys, the mean free path of electrons is reduced significantly, thus their decreased thermal conductivity and slow dissipation of localized radiation energy can have noticeable effects on displacement cascade evolution that is greatly different from metals with high thermal conductivity. In this work, nanocrystalline HEAs of Ni 20 Fe 20 Co 20 Cr 20 Cu 20 and nonequiatomic (NiFeCoCr) 97 Cu 3 , both having much lower room-temperature thermal conductivity than pure Ni or Fe, are chosen as model HEAs to reveal the role that electronic energy loss during ion irradiation has in complex alloys. The response of nanocrystalline HEAs is investigated under irradiation at room temperature using MeV Ni and Au ions that have different ratios of electronic energy to damage energy, which is the energy dissipated in displacing atoms. Different from previously reported amorphization of nanocrystalline SiC, experimental results on these HEAs show that, similar to the process in nanocrystalline oxide materials, both inelastic thermal spikes via electron–phonon coupling and elastic thermal spikes via collisions among atomic nuclei contribute to the overall grain growth. The growth follows a power law dependence with the total deposited ion energy, and the derived value of the power-exponent suggests that the irradiation-induced instability at and near grain boundaries leads to local rapid atomic rearrangements and consequently grain growth. The high power-exponent value can be attributed to the sluggish diffusion and delayed defect evolution arising from the chemical complexity intrinsic to HEAs. Here, this work calls attention to quantified fundamental understanding of radiation damage processes beyond that of simplified displacement events, especially in simulating neutron environments.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Effect of Charged Block Length Mismatch on Double Diblock Polyelectrolyte Complex Micelle Cores

Polyelectrolyte complex micelles are hydrophilic nanoparticles that self-assemble in aqueous environments due to associative microphase separation between oppositely charged blocky polyelectrolytes. In this work, we employ a suite of physical characterization tools to examine the effect of charged block length mismatch on the equilibrium structure of double diblock polyelectrolyte complex micelles (D-PCMs) by mixing a diverse library of peptide and synthetic charged-neutral block polyelectrolytes with a wide range of charged block lengths (25–200 units) and chemistries. Early work on D-PCMs suggested that this class of micelles can only be formed from blocky polyelectrolytes with identical charged block lengths, a phenomenon referred to as chain length recognition. Here, we use salt annealing to create PCMs at equilibrium, which shows that chain length recognition, a longstanding hurdle to repeatable self-assembly from mismatched polyelectrolytes, can be overcome. Interestingly, D-PCM structure–property relationships display a range of values that vary systematically with the charged block lengths and chemical identity of constituent polyelectrolyte pairings and cannot be described by generalizable scaling laws. We discuss the interdependent growth behavior of the radius, ionic pair aggregation number, and density in the micelle core for three chemically distinct diblock pairings and suggest a potential physical mechanism that leads to this unique behavior. By comparing the results of these D-PCMs to the scaling laws recently developed for single diblock polyelectrolyte complex micelles (S-PCMs: diblock + homopolymer), we observe that D-PCM design schemes reduce the size and aggregation number and restrict their growth to a function of charged block length relative to S-PCMs. Understanding these favorable attributes enables more predictive use of a wider array of charged molecular building blocks to anticipate and control macroscopic properties of micelles spanning countless storage and delivery applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Investigation of twin growth mechanisms in precipitate hardened AZ91

Here, in this work, an elasto-viscoplastic fast-Fourier-transform (EVP-FFT) model with a dislocation-density (DD) based hardening law is employed to study the growth of a {10$\bar{1}$2} tensile twin that is blocked by basal-precipitates in precipitate-hardened AZ91 magnesium alloy. It is frequently reported that twin growth is hindered in precipitate-hardened Mg alloys; however, thick twin domains are often observed experimentally in these material systems. Detailed numerical investigation of deformation twinning starting from an early propagation stage, before twin growth, reveals that the stress fields that result from two sequentially propagated twins co-impinging on a precipitate relaxes the twin back stress locally and promotes twin growth at the twin-precipitate junction. Based on these findings, a two-step growth mechanism is proposed for twins arrested by precipitates. In the first step, the interaction of a twin tip with a precipitate develops a stress concentration on the other side of the precipitate, prompting the formation of a second twin. Subsequently, the back stresses associated with the first twin are relaxed by the formation of the second twin, allowing the first twin to grow at the twin-precipitate junction and eventually engulf the precipitate. This mechanism suggests that twin growth can be achieved locally with minimal additional external forces, explaining how relatively large twin domains can develop even in the presence of arrays of precipitates.

36 MATERIALS SCIENCE↗