Reference State Research Articles

Solid-liquid phase boundary of oxide solid solutions using neural network potentials

We propose a cost-effective computational approach for predicting the phase boundary of oxide solid solutions, i.e., melting point, by identifying the point where the free energies of the solid and liquid phases are equivalent. To evaluate the melting point, we computed the temperature-dependent free energies of both phases using the thermodynamic integration (TI) method. This was combined with the reverse-scaling technique, employing the Einstein model for the solid and the scaled Uhlenbeck–Ford model for the liquid as the reference systems. The change in free energy between the real and reference states in the present TI method was calculated as the ensemble average of the configurations sampled from molecular dynamics (MD) simulations using neural network potentials (NNPs) trained on first-principles density functional theory (DFT) data. Initially, we benchmarked copper (Cu) as a typical metal. Tungsten (W) and magnesium oxide (MgO) were then tested as typical high melting-point metals and oxides, respectively, achieving good agreement with both ab initio MD (AIMD) results and experimental data. We then applied our established approach to a BaO–CaO oxide solid solution, observing that the computed phase boundary aligns well with Calphad predictions from previous studies. The integration of NNPs into phase boundary prediction is essential for reducing computational costs while ensuring accuracy, compared with AIMD-based approaches.

Fourth-Order Algebraic Diagrammatic Construction for Electron Detachment and Attachment: The IP- and EA-ADC(4) Methods.

We present a non-Dyson fourth-order algebraic diagrammatic construction formulation of the electron propagator, featuring the distinct IP- and EA-ADC(4) schemes for the treatment of ionization and electron attachment processes. The algebraic expressions have been derived automatically using the intermediate state representation approach and implemented in the Q-Chem quantum-chemical program package. The performance of the novel methods is assessed with respect to high-level reference data for ionization potentials and electron affinities of closed- and open-shell systems. While only minor improvements over the corresponding third-order methods are observed for one-hole ionization and one-particle electron attachment processes from closed-shell systems (MAEIP-ADC(4) = 0.27 eV and MAEEA-ADC(4) = 0.05 eV), a significantly enhanced performance is found in case of open-shell reference states (MAEIP-ADC(4) = 0.11 eV and MAEEA-ADC(4) = 0.02 eV). A particularly appealing feature of the novel methods is their accurate treatment of satellite transitions. For closed-shell reference states, we obtain accuracies of MAEIP-ADC(4) = 0.81 eV and MAEEA-ADC(4) = 0.27 eV, while in case of open-shell reference states, mean absolute errors of MAEIP-ADC(4) = 0.15 eV and MAEEA-ADC(4) = 0.27 eV are found.

Theory and experiment on distributed output formation tracking of unmanned aerial and ground vehicle swarm systems over jointly connected digraphs

This paper studies the distributed output formation tracking control problem of the unmanned aerial vehicle (UAV) and unmanned ground vehicle (UGV) swarm systems, where the UAV swarm cooperatively tracks the output trajectory of the UGV in a formation under directed jointly connected communication networks. A three-layer formation tracking protocol is proposed. Firstly, a novel distributed observer using neighbor interactions is designed for each UAV to estimate the states of the UGV with parameterized inputs over periodic jointly connected digraphs. Next, based on the observation result and output regulation theory, a virtual reference system that tracks the trajectory of the UGV in the desired formation is constructed to generate reference states for each UAV. Then based on the differential flatness of UAVs, a geometric controller is utilized for UAVs to track the reference states and form the formation. An algorithm to determine the gain matrices of the protocol is also presented while the convergence of the system is analyzed. Finally, an experiment platform with three quadrotor UAVs and one UGV is built. The effectiveness of the proposed protocol is validated both by the simulation and experiment.

Quantum multi-anomaly detection

A source assumed to prepare a specified reference state sometimes prepares an anomalous one. We address the task of identifying these anomalous states in a series of n preparations with k anomalies. We analyze the minimum-error protocol and the zero-error (unambiguous) protocol and obtain closed expressions for the success probability when both reference and anomalous states are known to the observer and anomalies can appear equally likely in any position of the preparation series. We find the solution using results from association schemes theory, thus establishing a connection between graph theory and quantum hypothesis testing. In particular, we use the Johnson association scheme which arises naturally from the Gram matrix of this problem. We also study the regime of large n and obtain the expression of the success probability that is non-vanishing. Finally, we address the case in which the observer is blind to the reference and the anomalous states. This scenario requires a universal protocol for which we prove that in the asymptotic limit, the success probability corresponds to the average of the known state scenario.

Grassland restoration on linear landscape elements – comparing the effects of topsoil removal and topsoil transfer

Artificial linear landscape elements, including roads, pipelines, and drainage channels, are main sources of global habitat fragmentation. Restoration of natural habitats on unused linear landscape elements can increase habitat quality and connectivity without interfering with agricultural or industrial development. Despite that topsoil removal and transfer are widely applied methods in restoration projects, up to our knowledge these were previously not compared in the same study system. To address this knowledge gap, we compared spontaneous vegetation recovery after the elimination of positive (embankments) and negative landscape scars (drainage channels) in lowland alkaline landscapes in South Hungary. The novelty of our study is that we compared the fine-scale and landscape-scale results of both methods. At the fine scale, we monitored the spontaneous vegetation development on the created open surfaces in the first, second and fourth year after restoration in 160 permanent plots per year. For characterizing the habitat changes on the landscape scale, we prepared habitat maps and assigned naturalness scores to each patch before and after the restoration activities. Both restoration methods resulted in a rapid vegetation recovery at the fine scale, progressing toward the reference state. In the topsoil removal treatment, a large part of the soil seed bank was removed; therefore, the colonization of the bare surface was a slower process. Seeds of halophytes, including the endemic and protected Suaeda pannonica, were probably present in the deeper soil layers, and these species became established in the restored surfaces, despite being absent in the surrounding vegetation. For restoring vegetation cover, topsoil transfer was a more rapid option; however, vegetation closure and competition by generalist species and weeds hampered the establishment of target species. The removal of the landscape scars by both methods made the sites accessible for grazing. At the landscape scale, the two methods had different effects: there was a slight increase in the habitat naturalness in the topsoil removal site, and a slight decrease in the topsoil transfer site because of weed encroachment. Spreading an upper layer of nutrient-poor soil with low amounts of weed seeds, direct propagule transfer, and targeted grazing regimes could enhance restoration success.

Towards 2050: Evaluating the Role of Energy Transformation for Sustainable Energy Growth in Serbia

This paper aims to investigate the outlook of energy generation by means of transformation within the context of sustainable energy development. An analysis is conducted to assess the stability of energy systems so to implement cutting-edge energy production models at the national level, with a focus on a contemporary approach to energy modeling. Considering the energy transition and the existing constraints within the energy industry, the model assesses the feasibility of the practical advancement of renewable energy sources. The bottom-up energy model was used to determine how the components of energy development sustainability can be applied until the year 2050. To perform comparison testing with the reference state scenario, the LEAP energy model was used. This instrument was selected because of its ability to provide flexible and advanced options for selecting suitable parameters for energy transformation prediction. A progressive reduction in environmental pollution can be achieved by the deployment of current methods of energy generation by transformation until the year 2050 in Serbia, as indicated by the findings. The research highlights the significance of utilizing green energy sources for the continuing development of energy and the gradual reduction in environmental pollution through value co-creation.

Computation of rate coefficients in solutions based on transition state theory combined with a heuristically corrected polarizable continuum model: intermolecular Diels-Alder reactions as case studies.

Transition state theory (TST) based on activation parameters computed using quantum mechanics calculations combined with the polarizable continuum model (QM/PCM) is a fundamental tool for investigating reaction rates in the liquid phase. In conventional QM/PCM methods, thermodynamic data and partition functions for a solute are often derived from a quasi-ideal gas treatment (IGT) widely implemented in commercially available computation packages. This approach tends to overestimate entropy because calculations of thermodynamic parameters in the liquid phase ignore hindered translational and rotational modes in real solutions. The present work formulated partition functions for more realistic solutes hindered by surrounding solvent molecules in conjunction with the basic QM/PCM concept. In addition, a configuration partition function for solute molecules at a standard concentration of 1 mol dm-3 was incorporated using a simple lattice model. The canonical partition function and thermodynamic functions were derived based on statistical thermodynamics for localized systems. Expressions for rate coefficients within TST were also derived with a consistent formalism based on the standard state selected in partition function calculations. The performance of the proposed method was assessed by predicting rate coefficients for three different Diels-Alder reactions and comparing these with experimental results. QM/PCM calculations at the G4//ωB97X-D/6-311++G(d,p)/IEF-PCM level of theory with corrections for the dispersion and repulsion energies were performed to obtain the electronic structures of stationary points on potential energy surfaces as a means of finding activation enthalpy, entropy and Gibbs energy values based on revised partition functions as well as predicting rate coefficients. The activation Gibbs energies obtained from our proposed method were lower than those obtained from the IGT method due to reasonable entropy computations. The proposed method overestimated the rate coefficients by one to two orders of magnitude compared to the experimental values, whereas the IGT method underestimated them by the same amount. This discrepancy arises because the proposed method calculates the partition function from the viewpoint of a localized system, whereas the IGT method calculates it from the viewpoint of a non-localized system. Given that actual liquids exist in a state between non-localized and localized systems, it is essential to formulate the partition function in a way that more accurately represents the liquid state.

Electron Binding Energies of Open-Shell Species from Diagonal Electron-Propagator Self-Energies with Unrestricted Hartree-Fock Spin-Orbitals.

For closed-shell molecules, valence electron binding energies may be calculated accurately and efficiently with ab initio electron-propagator methods that have surpassed their predecessors. Advantageous combinations of accuracy and efficiency range from cubically scaling methods with mean errors of 0.2 eV to quintically scaling methods with mean errors of 0.1 eV or less. The diagonal self-energy approximation in the canonical Hartree-Fock basis is responsible for the enhanced efficiency of several methods. This work examines the predictive capabilities of diagonal self-energy approximations when they are generalized to the canonical spin-orbital basis of unrestricted Hartree-Fock (UHF) theory. Experimental data on atomic electron binding energies and high-level, correlated calculations in a fixed basis for a set of open-shell molecules constitute standards of comparison. A review of the underlying theory and analysis of numerical errors lead to several recommendations for the calculation of electron binding energies: (1) In calculations that employ the diagonal self-energy approximation, Koopmans's identity for UHF must be qualitatively correct. (2) Closed-shell reference states are preferable to open-shell reference states in calculations of molecular ionization energies and electron affinities. (3) For molecular electron binding energies between doublets and triplets, calculations of electron detachment energies are more accurate and efficient than calculations of electron attachment energies. When these recommendations are followed, mean absolute errors increase by approximately 0.05 eV with respect to their counterparts obtained with closed-shell reference orbitals.

Impact of temperature and relative humidity variations on coda waves in concrete

The microstructure of concrete can be affected by many factors, from non-destructive environmental factors through to destructive damage induced by transient stresses. Coda wave interferometry is a technique that is sensitive enough to detect weak changes within concrete by evaluating the ultrasonic signal perturbation compared to a reference state. As concrete microstructure is sensitive to many factors, it is important to separate their contributions to the observables. In this study, we characterize the relationships between the concrete elastic and inelastic properties, and temperature and relative humidity. We confirm previous theoretical studies that found a linear relationship between temperature changes and velocity variation of the ultrasonic waves for a given concrete mix, and provide scaling factors per Kelvin for multiple settings. We also confirm an anti-correlation with relative humidity using long-term conditioning. Furthermore, we explore beyond the existing studies to establish the relationship linking humidity and temperature changes to ultrasonic wave attenuation.

МУГАЛИМДЕРДИН КОММУНИКАТИВДИК КОМПЕТЕНТТҮҮЛҮГҮНҮН СОЦИАЛДЫК-ПСИХОЛОГИЯЛЫК АСПЕКТИЛЕРИ

In addition to instilling general and specialized knowledge on the basis of a competent attitude, along with the psychological aspects of professional competence required by state standards, the qualities necessary for the growth and development of society are developed (communication, initiative, independence, preparation at a creative level, responsibility, determination, ability to implement set goals, etc.). The reports of scientists on the problem of communicative skills, communicative abilities, and their formation, considered as components of the psychological aspects of communicative competence, are presented, and five different types of teacher activities and a scheme of socio-psychological competence of a teacher are presented. The processes taking place in the economic life of our country, Kyrgyzstan's entry into developed world cooperation create conditions for the development of the organization of new forms of production in the economy. This is a reduction in the cycle of technical updates, the widespread use of information technology, computer technology, complex electronic equipment.

Entanglement and Generalized Berry Geometrical Phases in Quantum Gravity

A new formalism is introduced that makes it possible to elucidate the physical and geometric content of quantum space–time. It is based on the Minimum Group Representation Principle (MGRP). Within this framework, new results for entanglement and geometrical/topological phases are found and implemented in cosmological and black hole space–times. Our main results here are as follows: (i) We find the Berry phases for inflation and for the cosmological perturbations and express them in terms of the observables, such as the spectral scalar and tensor indices, nS and nT, and the tensor-to-scalar ratio r. The Berry phase for de Sitter inflation is imaginary with the sign describing the exponential acceleration. (ii) The pure entangled states in the minimum group (metaplectic) Mp(n) representation for quantum de Sitter space–time and black holes are found. (iii) For entanglement, the relation between the Schmidt type representation and the physical states of the Mp(n) group is found: This is a new non-diagonal coherent state representation complementary to the known Sudarshan diagonal one. (iv) Mean value generators of Mp(2) are related to the adiabatic invariant and topological charge of the space–time, (matrix element of the transition −∞<t<∞). (v) The basic even and odd n-sectors of the Hilbert space are intrinsic to the quantum space–time and its discrete levels (in particular, continuum for n→∞), they do not require any extrinsic generation process such as the standard Schrodinger cat states, and are entangled. (vi) The gravity or cosmological on one side and another of the Planck scale are entangled. Examples: The quantum primordial trans-Planckian de Sitter vacuum and the classical late de Sitter vacuum today; the central quantum gravity region and the external classical gravity region of black holes. The classical and quantum dual gravity regions of the space–time are entangled. (vii) The general classical-quantum gravity duality is associated with the Metaplectic Mp(n) group symmetry which provides the complete full covering of the phase space and of the quantum space–time mapped from it.

The effects of heat treatment on the mechanical properties of 450 HB wear resistant steel

The effects of heat treatment on the mechanical properties of 450 HB wear resistant steel produced by Usiminas steelworks in the form of heavy plates were investigated. The results showed that when tempering temperature is lower than 200°C, there are no significant changes in hardness, tensile properties and absorbed energy in Charpy V-notch test. With further increase in temperature up to 400°C, hardness, tensile strength, total elongation and impact toughness exhibited a slight downward trend. For heating carried out from 400°C to 600°C, a very significant drop in hardness and tensile strength and an increase in total elongation and absorbed energy values were observed. The abrasive wear resistance, evaluated by dry-sand rubber wheel test, increased with the heating up to 500°C. With the additional rise in temperature to 600°C, the abrasive wear resistance decreased, reaching a similar level to the reference state (steel in as-delivered condition).

Применение конопляного урбеча и нутовой муки в составе комбинированных творожных десертов

Purpose. Determination of the functional and technological compatibility of whipped food systems of combined curd desserts with neoprotein ingredients. Materials and Мethods. Experimental research and development of samples were carried out in the conditions of the Department of Food Production Technologies of Volgograd State Technical University and Complex Analytical Laboratory of VRIMMP (Volgograd). The object of the study was combined curd desserts with neoprotein ingredients: urbech from peeled hemp seeds in the curd part and chickpea flour in the biscuit part. All studies within the framework of this work were carried out in accordance with regulatory documents of state standards of the Russian Federation: assessment of organoleptic indicators – according to GOST R ISO 22935-2-2011 and GOST 31986-2012; whipped of the curd part was determined according to GOST R 52175-2003, mass fraction of moisture – according to GOST 3626-73, titratable acidity – titrimetrically (GOST 3624-92), mass fraction of moisture in the biscuit – according to GOST 5900-2014. Results. Sample of curd part No. 2 with the addition of 6% urbech from purified hemp kernels and sample of biscuit No. 2 using chickpea flour after frying demonstrated the best organoleptic characteristics. The results of physicochemical and rheological tests showed that the addition of urbech increases whipped of the curd part by 2 times, reduces acidity by 11.1% and increases mass fraction of moisture by 5.5%, and frying chickpea flour helps to increase the mass fraction of moisture in the biscuit, which slows down staling. The use of neoprotein components enriches the combined whipped curd product with plant protein, dietary fiber, macro- and microelements. Conclusion. Production of combined whipped curd products using neoprotein components - hemp urbech and fried chickpea flour, is advisable due to the improvement of the organoleptic, physico-chemical and rheological properties of both the curd and biscuit parts of the product, as well as increasing their nutritional and biological value.

High performance ultrasonic vibration assisted Wire-arc directed energy deposition of Invar alloy

As the utilization of composite materials flourishes in commercial aircraft, the use of Invar alloy with low coefficient of thermal expansion (CTE) for fabricating composite molds has gained prominence. The large-size composite molds can be fabricated by Wire-arc Directed Energy Deposition (Wire-arc DED), due to its high deposition efficiency and ability to form optimized topologies. However, the Wire-arc DED Invar components still exhibit heterogeneous microstructure, low strength and non-tunable CTE. To address these challenges, this study explores the integration of an ultrasonic energy field during the deposition process to systematically investigate its effects on microstructural evolution, mechanical properties and CTE of Invar alloy. The results reveal that the ultrasonic vibration-assisted deposition significantly refines the grain structure, resulting in a decrease of 81.04 % in grain size compared to the reference state. Moreover, the components fabricated by ultrasonic vibration assisted Wire-arc DED exhibit exceptional properties, with a yield strength (YS) of 408 ± 11.37 MPa, ultimate tensile strength (UTS) of 645 ± 7.61 MPa, and elongation (EL) of 31.3 %. Additionally, the correlation between grain size and CTE was established. The effectiveness of introducing an ultrasonic energy field in improving the mechanical properties and modulating the CTE of the components is further validated by rigorous theoretical calculations. This research provides a promising way to fabricate high performance Invar alloy composite molds.

Shifting baselines clarify the impact of contemporary logging on forest‐dependent threatened species

AbstractDespite the importance of protecting forests and woodlands to achieve global climate and biodiversity goals, logging impacts persist worldwide. Forestry advocates often downplay these impacts but rarely consider the cumulative threat deforestation and degradation has had, and continues to have, on biodiversity. Using New South Wales (Australia) as a case study, we quantify the extent of deforestation and degradation from 1788 (pre‐European colonization) to 2021. We used historical loss as a baseline to evaluate recent logging (2000–2022) and the condition of the remaining native forest and woodland. Condition was quantified by measuring the similarity of a current ecosystem to a historical reference state with high ecological integrity. Using these data, we measured the impacts on 269 threatened terrestrial species. We show that possibly over half (29 million ha) of pre‐1788 native forest and woodland vegetation in NSW has been lost. Of the remaining 25 million ha, 9 million ha is estimated to be degraded. We found recent logging potentially impacted 150 species that had already been affected by this historical deforestation and degradation, but the impacts varied across species. Forty‐three species that were identified as impacted by historical deforestation and degradation and continue to be impacted by logging, now have ≤50% of their pre‐1788 extent remaining that is intact and nine species now have ≤30%. Our research contextualizes the impact of current logging against historical deforestation and highlights deficiencies in environmental assessments that ignore historical baselines. Future land management must consider both the extent and condition of remaining habitat based on pre‐1788 extents.

Dynamics and control for spacecraft tracking a displaced orbit around an asteroid exploiting solar sail

This study investigates the displaced orbit around a near-Earth asteroid for spacecraft achieved via a realistic solar sail with a performance based on the existing technology in a low distance. Using the realistic solar sail to achieve the displaced orbit with a short displaced distance is more difficult compared with using a traditional thruster under two main limitations: The force limitation and the position limitation. Firstly, the solar radiation pressure (SRP) force generated by the solar sail is limited by the solar sail’s property and the sunlight direction. Therefore, the feasibility of maintaining a displaced orbit at an equilibrium point around the asteroid at a low distance using a solar sail with realistic performance is investigated analytically. The results demonstrate that the equilibrium point of the displaced orbit can be achieved. Secondly, the usage of the solar sail is also limited by the position of the spacecraft. The SRP force cannot be generated in the eclipse region wherein sunlight is absent; specifically, in a displaced orbit with a low displaced distance, the position limitation is more notable. To address this challenge, spacecraft dynamics and control using a solar sail are investigated to achieve the displaced orbit, and a method of orbit transfer outside the eclipse region is proposed. Numerical simulations reveal that the spacecraft can maintain the displaced orbit using the solar sail without entering the eclipse region. Moreover, spacecraft can achieve orbit transfer between two equilibrium points without entering the eclipse region by using the solar sail. The impact of non-spherical shape of the primary asteroid is also investigated. Results show that the proposed method can maintain a displaced orbit with errors from the reference state less than 10 % during a limited time span when the primary asteroid has a non-spherical shape.

THE PROBLEM OF BUILDING DIAGNOSTIC EQUIPMENT FOR RADIO-ELECTRONIC EQUIPMENT IN THE RUSSIAN FEDERATION

The reasons leading to the lack of proper diagnostic support for electronic equipment (REE), which is necessary to ensure their proper quality and reliability, are disclosed. Ignoring the issues of creating proper diagnostic support has a negative effect on the organization of production processes, further operation and repair of REE. The reasons for the lack of proper diagnostic support for REA are largely determined by the imperfection of the regulatory and technical base in the form of outdated state standards, the lack of domestic modern hardware and software diagnostic complexes on the Russian market and the availability of opportunities to circumvent the issues of building proper diagnostic support when developing REE. The reasons can be eliminated by creating a set of regulatory and technical documents that take into account the modern development of electronic, computing and measuring technology.

PENGEMBANGAN MODEL PEMBELAJARAN METODE KASUS BERBASIS PROYEK PADA MATA KULIAH SISTEM INFORMASI MANAJEMEN

Participatory and cooperative classes are part of the key performance indicators that are mandatory for universities in their fulfillment. National higher education standards state that case studies and project-based learning can both be used for teaching. However, students at the Nobel Institute of Technology and Business Indonesia have not been given knowledge about how to think at a higher level and solve cases that occur in the world of work. Using the project-based case method, this study aims to create a learning model for the Management Information System (MIS) course in an effort to support the application of the learning outcomes-based curriculum (OBE). Research & Development (R&D) research methodology uses the ADDIE model (Analysis, Design, Development, Implementation, Evaluation). Instructional analysis of learning outcomes; Semester Learning Plan (RPS); Lecture Event Unit (SAP); Learning Implementation Plan (RPP); and textbooks are some of the outputs of this research through the project-based Case Method Learning Model (CMT).

Theoretical analysis to optimize heat extraction from a solar pond integrated with a carbon dioxide heat pump

Heat pumps integrated with renewable energy sources represent an efficient approach to residential heating and cooling, with minimal environmental impact and reduced carbon emissions. While these systems have been extensively researched, there is a necessity to broaden their scope by investigating novel approaches to energy capture and storage that are adopted to the specific characteristics of the region. This study analyzes the effects of different operating parameters on heat extraction from a solar pond integrated with a heat pump using carbon dioxide under transcritical conditions. Subsequently, an optimization examination is conducted to assess and determine the conditions required to achieve the maximum heat extraction rate and the minimum pumping power. The outcomes of this investigation demonstrate that the carbon dioxide mass flux and operating pressure exert a greater influence on the responses compared to the inlet temperature of carbon dioxide and the lower convective zone temperature of the solar pond. Additionally, within the investigated range of mass flux, the highest level of heat extraction occurs at operating pressures near the critical point of carbon dioxide, approximately 7.5 MPa. To meet the demand for maximum heat extraction from the solar pond, the optimal conditions result in an overall performance improvement of 2.61 times compared to the reference state. Furthermore, optimizing the system to maximize heat extraction from the solar pond while using the minimum pumping power results in a total performance enhancement of 4.13 times.

Ab initio study of surfaces of lead and tin based metal halide perovskite structures

Abstract Hybrid perovskite materials, known for their potential in cost-effective optoelectronic applications, face a knowledge gap in crucial areas, particularly the atomic-level properties of the surface. This study addresses this challenge by refining ab initio methods for characterizing surface structures of cubic methylammonium lead bromide and methylammonium tin bromide (MAMeBr3 with Me = Sn, Pb), avoiding superficial restrictions in atomic movement during geometry optimization. The resulting structures confirmed nearly random MA+ molecule alignment, comparable to real-world experimental conditions. Calculating surface energies for these structures with crystal orientations {100} and {110}, each with different terminations, provides valuable insights into structural properties. Using a carefully chosen thermodynamic reference state, mimicking experimental conditions enables a thermodynamic discussion and facilitates the modulation of the MeBr2 component’s chemical potential. This modulation, in turn, allows for the prediction of crystal morphologies, as illustrated by Wulff’s construction. This approach establishes a crucial link between theoretical predictions and experimental conditions, shedding light on the complexities of hybrid perovskite materials.