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At least 127 records · Page 7

Ultradynamic Isoreticularly Expanded Porous Organic Crystals

Porous organic materials showcasing large framework dynamics present new paths for adsorption and separation with enhanced capacity and selectivity beyond the size-sieving limits, which is attributed to their guest-responsive sorption behaviors. Porous hydrogen-bonded crosslinked organic frameworks (H C OFs) are attractive for their remarkable ability to undergo guest-triggered expansion and contraction facilitated by their flexible covalent crosslinkages. However, the voids of H C OFs remain limited, which restrains the extent of the framework dynamics. Here in this work, we synthesized a series of H C OFs characterized by unprecedented size expansion capabilities induced by solvents. These H C OFs were constructed by isoreticularly co-crystallizing two complementary sets of hydrogen bonding building blocks to generate porous molecular crystals, which were crosslinked through thiol–ene/yne single-crystal-to-single-crystal transformations. The generated H C OFs exhibit enhanced chemical durability, high crystallinity, and extraordinary framework dynamics. For instance, H C OF-104 crystals featuring a pore diameter of 13.6 Å expanded in DMF to 300 ± 10% of their original lengths within just 1 min. This expansion allows the HCOFs to adsorb guest molecules that are significantly larger than the pore sizes of their crystalline states. Through methanol-induced contraction, these large guests were encapsulated in the fast-contracted H C OFs. These advancements in porous framework dynamics pave the way for new methods of encapsulating guests for targeted delivery.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Investigation of Americium-Containing Phosphates, Silicates, Borates, Molybdates, and Fluorides Synthesized via High-Temperature Flux Crystal Growth

The crystal chemistry of americium-containing extended structures was investigated, and several classes of americium-containing solid-state oxide materials were obtained in single-crystal form via high-temperature flux crystal growth. This enabled the structural characterization of rare examples of ternary, quaternary, and penternary americium-containing silicates K 3 Am (Si 2 O 7 ) and Cs 6 Am 2 Si 21 O 48 , phosphates Na 3 Am (PO 4 ) 2 and K 3 Am (PO 4 ) 2 , borates Ba 3 Am 2 (BO 3 ) 4 and AmBO 3 , borate halides Ca 5 Am(BO 3 ) 4 Cl, molybdates Li 0.5 Am 0.5 MoO 4 , and fluorides CsAm 2 F 7 . Using these crystallographic data, the ionic radii of Am 3+ with coordination numbers of six (0.975 Å), seven (1.052 Å), and nine (1.162 Å) were established. A maximum entropy method (MEM) analysis was performed on the single-crystal X-ray diffraction data that were collected for K 3 Nd(PO 4 ) 2 /K 3 Am(PO 4 ) 2 , K 3 NdSi 2 O 7 /K 3 AmSi 2 O 7 , and NdBO 3 /AmBO 3 , to qualitatively compare the ionicities of the Nd–O and Am–O bonds. In conclusion, Raman spectroscopy data were collected on single crystals of K 3 Am(PO 4 ) 2 and compared to the calculated Raman spectrum of K 3 Am(PO 4 ) 2 obtained from DFT calculations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

An exciton crystal in a moiré excitonic insulator

Strong Coulomb interactions can drive electrons to crystallize into a Wigner lattice. Achieving the bosonic analogue—a crystal of excitons—has remained challenging owing to their short lifetimes and weaker interactions. Here we report the observation of a thermodynamically stable exciton crystal in an excitonic insulator coupled to a moiré potential. Using an electron–hole bilayer composed of a monolayer MoSe 2 and a WS 2 /WSe 2 moiré superlattice, we constructed a tunable extended Bose–Hubbard system with electrical control over exciton and charge doping in thermal equilibrium. Optical spectroscopy revealed spontaneous crystallization of long-lived excitons at one exciton filling per three moiré sites, manifested as strong Umklapp scattering peaks. Exciton transport measurements further showed a pronounced exciton resistance peak at the same filling. When doped away from net charge neutrality, this moiré electron–hole bilayer can host correlated insulating phases in which dipolar excitonic insulators form on top of the background of a hole Mott insulator or generalized Wigner crystals. In conclusion, these findings establish moiré electron–hole bilayers as a versatile platform for realizing correlated crystalline phases of bosons and fermions.

Qi, Ruishi [University of California, Berkeley, CA↗

Facets control charge separation during photoelectrochemical water oxidation with strontium titanate (SrTiO 3 ) single crystals

The photocatalytic overall water splitting reaction provides a pathway to hydrogen fuel from sunlight. Photocatalysts must achieve the reaction without the application of an external bias, which requires an effective charge separation mechanism. Photolabeling studies and electrostatic simulations for the well-known CoOOH/Al:SrTiO 3 /Rh/Cr 2 O 3 photocatalyst suggest that charge separation is driven by work function differences at the (100) and (110) facets of SrTiO 3 , which are electron and hole selective, respectively. Here we use hydrogen annealed SrTiO 3–x single crystals to obtain the first quantitative assessment of the charge separation ability of the (100), or (110), or (111) facets during oxygen evolution. Under UV illumination (60 mW cm –2 ), the crystals exhibit variable water oxidation photocurrents (0.34, 0.82, 1.36 mA cm –2 at 1.23 V versus RHE) and photovoltage values of 1.40, 1.52 and 1.52 V for (100), (110), and (111) SrTiO 3–x , respectively. A surface photovoltage increase in that same order (0.31 V < 0.57 V < 0.67 V) is confirmed independently with vibrating Kelvin probe surface photovoltage spectroscopy (VKP-SPV) under 375 nm (1.91 mW cm –2 ) illumination. Mott Schottky measurements in aqueous K 3/4 [Fe(CN) 6 ] reveal facet-dependent flatband positions of –0.58, –0.71, and –0.74 V RHE for the (100), (110), and (111) crystals respectively. This confirms that the photoelectrochemical water oxidation performance of SrTiO 3–x crystals is controlled by the work function of each facet, which determines the electron transfer barrier height of the respective solid–liquid junctions. After correcting for differences in electron donor concentrations, barriers are found to increase in the order (100) < (111) < (110) and differ by as much as 0.16 eV, similar to an earlier prediction. Altogehter, these results explain the charge separation mechanism in SrTiO 3 photocatalysts and highlight the need for faceted semiconductor crystals as light absorbers in particle-based photocatalysts.

08 HYDROGEN↗

Crystallization of nanopore-confined imidazolium ionic liquids probed by temperature-resolved in situ grazing-incidence wide angle X-ray scattering (GIWAXS)

The crystallization behavior of ionic liquids (ILs) 1-butyl-3-methylimidazolium [BMIM] hexafluorophosphate [PF 6 ] and chloride [Cl] is investigated upon confinement in 2.3 or 8.2 nm diameter silica nanopore arrays, along with the effects of covalently modifying the pore walls with 1-(3-trimethoxysilylpropyl)3-methylimidazolium [TMS-MIM] + groups. In situ grazing-incidence wide angle x-ray scattering (GIWAXS) is performed during heating from as low as -110 °C to room temperature. Partially ordered “nanodomains” are observed in both ILs in the bulk molten state, but they are disrupted by nanoconfinement. Melting point depression consistent with capillary effects is observed for [BMIM][PF 6 ] in 2.3 nm pores. However, the melting point is elevated for [BMIM][PF 6 ] in 8.2 nm pores, which provide sufficient space to stabilize the crystalline phase. For [BMIM][Cl], crystallization is observed only in 8.2 nm bare silica pores, but the melting point is severely depressed. Tethering with IL-like [TMS-MIM + ] also promotes the crystallization of [BMIM][PF 6 ], resulting in elevated melting points. The combined effects of a larger pore size and pore surface tethering on [BMIM][PF 6 ] result in a single stable crystal phase that persists from -140 °C to 25 °C (vs. the bulk melting point of -11 °C). These results show that when ILs are used in confined systems, complex crystallization behavior can emerge depending on the counterion, pore size, and surface modification that require consideration of ion layering in the confined space in addition to surface free energy effects.

He, Yuxin [University of Kentucky, Lexington, KY (↗

350 ps Ultrafast room-temperature scintillation realized on CsPbBr 3 -based single crystals via Br 2 over-doping

Ultrafast scintillators are essential for next-generation radiation detection, positron emission tomography, and high-speed medical imaging. All-inorganic CsPbBr 3 perovskites are attractive candidates because of their high stopping power, and excellent optical quality, yet their long carrier lifetimes result in slow scintillation responses on the order of hundreds of nanoseconds. Here, we demonstrate that controlled over-doping with Br 2 produces CsPbBr 3.03 single crystals with sub-nanosecond scintillation at room temperature while preserving crystal quality. Single crystals grown by the Bridgman method exhibit high transparency and maintain the orthorhombic perovskite structure. Br 2 over-doping induces a slight lattice expansion (about 0.42% increase in unit-cell volume) while maintaining the orthorhombic perovskite phase and high optical transparency. Optical absorption reveals a slight redshift of the absorption edge after Br 2 introduction, indicating a modified defect landscape. Time-resolved photoluminescence and radioluminescence measurements show that Br 2 doping creates dense and efficient recombination centers that reduce the scintillation decay time from more than 100 ns in undoped crystals to 350 ps under 5.486 MeV α-particle excitation, and the scintillation decay time decreases by two orders of magnitude. The doped crystals also achieve a spatial resolution of 12 lp mm −1 in X-ray imaging. These results reveal a defect-engineering route for achieving ultrafast scintillation in halide perovskites and highlight the potential of Br 2 -modified CsPbBr 3 for fast timing applications.

Li, Zongxiao [Chinese Academy of Sciences (CAS), N↗

Data Science Shows that Entropy Correlates with Accelerated Zeolite Crystallization in Monte Carlo Simulations

We have performed a data science study of Monte Carlo simulation trajectories to understand factors that can accelerate formation of zeolite nanoporous crystals, a process that can take days or even weeks. In previous work, Monte Carlo simulations predicted and experiments confirmed that using a secondary organic structure-directing agent (OSDA) accelerates crystallization of all-silica LTA zeolite, with experiments finding a three-fold speedup [PCCP 24, 142-148 (2022)]. However, it remains unclear what physical factors cause the speed-up. Here, we apply data science to analyze the simulation trajectories to discover what drives accelerated zeolite crystallization in Monte Carlo going from a one-OSDA synthesis (1OSDA) to a two-OSDA version (2OSDA). We encoded simulation snapshots using the Smooth Overlap of Atomic Positions approach, which represents all 2- and 3-body correlations within a given cutoff distance. Principal component analyses failed to discriminate datasets of structures from 1OSDA and 2OSDA simulations, while the Support Vector Machine (SVM) approach succeeded at classifying such structures with an area-under-curve (AUC) score of 0.99 (where AUC = 1 is a perfect classification) with all 3-body correlations, and as high as 0.94 with only 2-body correlations. SVM decision functions reveal relatively broad / narrow histograms for 1OSDA / 2OSDA datasets, suggesting that the two simulations differ strongly in information heterogeneity. Informed by these results, we performed pair (2-body) entropy calculations during crystallization, resulting in entropy differences that semi-quantitatively account for the speedup observed in the previous Monte Carlo simulations. We conclude that altering synthesis conditions in ways that substantially changes the entropy of labile silica networks may accelerate zeolite crystallization, and we discuss possible approaches for achieving such acceleration.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

Understanding vortex dynamics in CaK(Fe,Ni) 4 As 4 and Ba(Fe,Co) 2 As 2 single crystals under the influence of random point disorder

We report on the influence of doping on vortex dynamics in 3 MeV proton-irradiated single crystals of CaK(Fe 1–x Ni x ) 4 As 4 (1144, x = 0.015, 0.025, and 0.03) and Ba(Fe 1–x Co x ) 2 As 2 (x = 0.04, 0.062, 0.066 and 0.074). Non-irradiated crystals of the 1144 system display superconducting critical temperatures ranging from 31 K for x = 0.015–20.5 K, as doping increases to 0.03. On the other hand, pristine crystals of the 122 system show T c values between 14.6 and 23.6 K, with the maximum T c occurring at intermediate doping levels. The fluence was set at 3 × 10 16 p cm –2 , resulting in a decrease in the T c by around 1.5 K for all samples and significantly affecting the vortex dynamics by reducing the flux creep relaxation compared to previously reported values for unirradiated crystals. Parameters such as vortex pinning energy U 0 and the glassy exponent μ dependencies on doping and magnetic field strength are identified. For the 1144 system, U 0 reaches values approaching 500 K for small fields in samples with T c = 29.3 K (x = 0.015), systematically decreasing to around 200 K as T c falls below 20 K. Furthermore, U 0 decreases as the field increases to 3 T for the same sample, varying from approximately 250 K to 100 K as T c decreases. These changes are typically accompanied by modifications in μ, gradually increasing from values around 1 towards 1.5, corresponding to small bundle relaxation in the collective creep theory. Despite differences in the substitutional disorder and magnetic phase diagram with respect to the 1144 system, the results for 122 single crystals follow a similar tendency in which U 0 usually reduces and μ increase rise as the applied magnetic field is increased. Due to moderate U 0 in these systems (few hundreds of kelvins), the resulting decay of persistent current at liquid helium temperatures is primarily determined by a balance between U 0 and bundle size contribution. Furthermore, these findings provide valuable insights for potential applications of these systems, particularly in the context of intrinsic superconducting parameters and the resulting pinning landscape.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Random Forest Prediction of Crystal Structure from Electron Diffraction Patterns

Transmission electron microscopy (TEM) diffraction patterns are regularly used to determine the structure of crystalline materials. Electron diffraction is the most common method to solve for unknown or partially known crystal structures, as it provides direct and interpretable feedback on the orientation of crystal grains under the beam [1]. However, it remains a challenge to determine the crystal structure of a new material or even a new phase of an existing material. Analysis of such materials commonly requires manual exploration and comparison with simulated diffraction patterns. This is often a time consuming process with no obvious start point when many similar structures are possible, and this method cannot be used to determine crystal structure or orientation from structures not included in the diffraction libraries. Therefore, we have developed a machine learning model to determine the crystal structure of a material from its electron diffraction pattern.

36 MATERIALS SCIENCE↗

Fast ground-state-to-ground-state separation of small ion crystals

Rapid separation of linear crystals of trapped ions into different subsets is critical for realizing trapped ion quantum computing architectures where ions are rearranged in trap arrays to achieve all-to-all connectivity between qubits. Here we introduce a general theoretical framework that can be used to describe the separation of same-species and mixed-species crystals into smaller subsets. The framework relies on an efficient description of the evolution of Gaussian motional states under quadratic Hamiltonians that only requires a special solution of the classical equations of motion of the ions to describe their quantum evolution under the influence of a time-dependent applied potential and the ions' mutual Coulomb repulsion. We provide time-dependent applied potentials suitable for separation of a mixed-species three-ion crystal on timescales similar to that of free expansion driven by Coulomb repulsion, with all modes along the crystal axis starting and ending close to their ground states. Three separately confined mixed-species ions can be combined into a crystal held in a single well without energy gain by time-reversal of this separation process.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Crystal nucleation rates in one-component Yukawa systems

Nucleation in the supercooled Yukawa system is relevant for addressing current challenges in understanding a range of crystallizing systems including white dwarf (WD) stars. We use both brute force and seeded molecular dynamics simulations to study homogeneous nucleation of crystals from supercooled Yukawa liquids. With our improved approach to seeded simulations, we obtain quantitative predictions of the crystal nucleation rate and cluster size distributions as a function of temperature and screening length. These quantitative results show trends towards fast nucleation with short-ranged potentials. They also indicate that for temperatures T > 0.9⁢T m , where T m is the melt temperature, classical homogeneous nucleation is too slow to initiate crystallization but transient clusters of ~100 particles should be common. As a result, we apply these general results to a typical WD model and obtain a delay of ~0.6 Gyr in the onset of crystallization that may be observable.

36 MATERIALS SCIENCE↗

Construction of hopfion crystals

Hopfions, three-dimensional topological solitons characterized by nontrivial Hopf indices, represent a fundamental class of field configurations that emerge across diverse areas of physics. Despite extensive studies of isolated hopfions, a framework for constructing spatially ordered arrays of hopfions, i.e., hopfion crystals, has been lacking. Here, we present a systematic approach for generating hopfion crystals with cubic symmetry by combining the Hopf map with rational mapping techniques. By superposing helical waves in ℝ 4 , we construct hopfion crystals with tunable Hopf indices and controllable topology. We demonstrate simple cubic, face-centered cubic, and body-centered cubic hopfion crystals and extend our framework to create crystals of more complex topological structures, including axially symmetric tori, torus links, and torus knots with higher Hopf indices. Our results provide a foundation for searching hopfions in real materials and studying their collective phenomena.

3-dimensional systems↗

X-ray crystal structure of a designed rigidified imaging scaffold in the ligand-free conformation

Imaging scaffolds composed of designed protein cages fused to designed ankyrin repeat proteins (DARPins) have enabled the structure determination of small proteins by cryogenic electron microscopy (cryo-EM). One particularly well characterized scaffold type is a symmetric tetrahedral assembly composed of 24 subunits, 12 A and 12 B, which has three cargo-binding DARPins positioned on each vertex. Here, the X-ray crystal structure of a representative tetrahedral scaffold in the apo state is reported at 3.8 Å resolution. The X-ray crystal structure complements recent cryo-EM findings on a closely related scaffold, while also suggesting potential utility for crystallographic investigations. As observed in this crystal structure, one of the three DARPins, which serve as modular adaptors for binding diverse `cargo' proteins, present on each of the vertices is oriented towards a large solvent channel. The crystal lattice is unusually porous, suggesting that it may be possible to soak crystals of the scaffold with small (≤30 kDa) protein cargo ligands and subsequently determine cage–cargo structures via X-ray crystallography. The results suggest the possibility that cryo-EM scaffolds may be repurposed for structure determination by X-ray crystallography, thus extending the utility of electron-microscopy scaffold designs for alternative structural biology applications.

59 BASIC BIOLOGICAL SCIENCES↗

Imaging extended single crystal lattice distortion fields with multi-peak Bragg ptychography

Recent advances in phase-retrieval-based x-ray imaging methods have demonstrated the ability to reconstruct 3D distortion vector fields within a nanocrystal by using coherent diffraction information from multiple crystal Bragg reflections. However, these works do not provide a solution to the challenges encountered in imaging lattice distortions in crystals with significant defect content that result in phase wrapping. Moreover, these methods only apply to isolated crystals smaller than the x-ray illumination, and therefore cannot be used for imaging of distortions in extended crystals. We introduce multi-peak Bragg ptychography which addresses both challenges via an optimization framework that combines stochastic gradient descent and phase unwrapping methods for robust image reconstruction of lattice distortions and defects in extended crystals. Our work uses modern automatic differentiation toolsets so that the method is easy to extend to other settings and easy to implement in high-performance computers. This work is particularly timely given the broad interest in using the increased coherent flux in fourth-generation synchrotrons for innovative material research.

36 MATERIALS SCIENCE↗

Unraveling fundamental mechanisms of silicon nitride crystallization in microelectronics manufacturing

This research project investigates the fundamental mechanisms of silicon nitride (SiN) crystallization, aiming to enhance the understanding of this critical material in microelectronics manufacturing. Through a collaborative effort between Sandia National Laboratories, the University of Tennessee, and the University of Florida, we developed a comprehensive framework that integrates experimental techniques, atomistic modeling, meso-scale simulations, and an integrated multi-scale model to capture this physical phenomenon on multiple time and length scales . The project developed a new machine learning based atomistic potential and utilized advanced phase field modeling to capture the complexities of polycrystalline growth and the influence of mechanical stresses on crystallization dynamics. By employing a grain tracker algorithm, the meso-scale model effectively identified and tracked individual crystal grains, enabling the simulation of anisotropic growth behaviors reflective of SiN’s physical properties. The integration of atomistic simulations with meso-scale modeling created a powerful multi-scale framework that validated atomistic inputs and enhanced predictive accuracy for crystallization dynamics at larger scales, validated experimentally. This adaptable modeling capability not only accelerates development times by informing manufacturing processes but also serves as a valuable starting point for understanding crystallization physics in similar materials. The insights gained from this research unlock new opportunities for the development of advanced materials tailored for future microelectronics and photonics applications. Overall, this project represents a significant advancement in understanding of fundamental physics of SiN and establishes a foundation for future research in material science, bridging the gap between atomic-level phenomena and macroscopic material behaviors for practical applications.

36 MATERIALS SCIENCE↗

Beyond Magic Barrels: Digital manufacturing for crystallization, process development and optimization of explosive materials: Part II Resveratrol Exemplar

This SAND report summarizes work supported by an Engineering Sciences Research Foundation (ESRF) Lab Directed Research and Development (LDRD) project entitled “Beyond Magic Barrels: Digital manufacturing for crystallization, process development and optimization of explosive materials.” This SAND report is written in two parts with Part 1 discusses recrystallization of our explosive exemplar and Part 2 summarizing our work with recrystallization of resveratrol. We have studied resveratrol recrystallization with a multiscale approach combining experiments, modeling and simulation. At the single crystal scale, microscopy experiments illuminate crystal time-dependent growth rates using advanced image analysis. Bench scale experiments were carried out to look at growth of multiple particles in a small reactor creating thousands of particles and analyzing the results with microscopy and μCT. For the modeling we combine kinetic Monte Carlo (kMC) models with subscale information from density functional theory (DFT) or molecular dynamics. This work is discussed in Part 1 and can also be found in a paper from the project discussing a coarse-grained kMC model specifically developed for resveratrol. For well-mixed systems, we have population balance equations (PBE) linked with species mass conservation forming a set of ordinary differential equations that can be solved quickly. For more complicated geometries, such as the vat crystallization used throughout the complex, a coupled computational fluid dynamic (CFD)/PBE method was developed to account for gradients in temperature and concentration and differences in crystallization rates throughout the domain. These simulations are more complex and require high performance computing. We present results for two cases: 5% seed fast cool with parameters fit to the well-mixed case and 5% seed slow cool using the same parameters. We show reasonable agreement with experiments though are particles are significantly larger than the experiments.

36 MATERIALS SCIENCE↗

Bent Crystal Channeling for Optimized Beam Shadowing and Proton Extraction at Mu2e

The Mu2e experiment is designed to investigate the CLFV through the observation of a neutrinoless muon-to-electron conversion in the field of an Al nucleus. The observation of such a process would be clear evidence of physics beyond the standard model. Due to the rarity of this process, a cutting-edge, intense muon beam is required to achieve an improvement of the current single-event sensitivity by 4 orders of magnitude. To achieve this goal, a primary proton beam with 8 GeV is extracted from the Fermilab Delivery Ring using the slow resonant extraction technique. Mu2e requires ~3.6x10$^{20}$ protons-on-target to meet its goal; hence, it is crucial to minimize the extraction losses. An important source of such losses are the particles impacting on the electrostatic septum blade. A very promising solution to the problem lies in the beam shadowing scheme tested at CERN SPS. In this approach, a bent crystal is strategically placed upstream of the septum, deflecting particles from the blade at a precise angle via the phenomenon of channeling. As a result, a zone with reduced particle flux is created downstream of the crystal, safeguarding the septum anode by minimizing interactions with the beam. This work explores the optimization of beam shadowing design and the process in the manufacturing and characterization of the bent crystal sample. It emphasizes the promising role of channeling in bent crystals, and it underscores the significant potential of channeling in bent crystals to assist the Mu2e experiment.

Fedeli, Pierluigi [Ferrara U.; INFN, Ferrara] (ORC↗

Correlative analysis of CsPbBr2Hal (Hal = Cl, Br, I) meltcrystallization paramete

Abstract — Metal halide perovskites (MHPs) are an exciting research topic as they have the potential to make solar cells that are both more efficient than current siliconbased designs and have a wider range of applications. In this work the crystallization of CsPbBr2Hal (Hal = Cl, Br, I) halide perovskite melts were studied by the differential thermal analysis method. It was established that the crystallization of CsPbBr2Hal (Hal = Cl, Br, I) melts can be “hot” (i.e., at temperatures above the point of the alloy’s start-melting temperature) or with supercooling. The replacement of the bromine atom with another halogen atom leads to a shift of the dwell temperature range, at which “hot” crystallization takes place, from 830-846 K for CsPbBr3 to 807-832 K for CsPbBr2Cl and 741-768 K for CsPbBr2I. The activation energy of “hot” crystallization decreases in the same order. A linear dependence between the pre-exponential factor (ln(𝑽𝑽𝒄𝒄𝒄𝒄𝒄𝒄𝒔𝒔𝒕𝒕 𝟎𝟎 )) and the activation energy (Ea) of the crystallization process is revealed from the experimental data, proving the compensation effect.

Kopach, O.↗