Crystal Morphology Prediction Models and Regulating Methods

Abstract

Growing high-quality crystals with ideal properties is of great importance. The morphology of crystal is one key factor reflecting product quality, as it can affect the performance of products and downstream operations. In this work, the current state of crystal morphology modification is reviewed from different perspectives. First, the most widely used crystal growth models are discussed. Then, a variety of crystal morphology control methods, which include adjustment of crystallization operation parameters, addition of foreign molecules, change of different solvents, membrane assistance, the addition of external physical fields and the use of ball milling are summarized. As for applications, the control of crystal morphology has application potential in pharmaceutical and material fields, for example, energetic materials and semiconductor materials. Finally, the future development direction of crystal morphology regulation is discussed.

1. Introduction

Crystal engineering is one of the fields of solid-state chemistry, which has been widely used in pharmaceutical, energy, chemical, military, high energy materials and many other fields [1,2,3]. Solid-state products with the desired properties, such as purity, polymorphism, crystal size distribution (CSD) and morphology, can be produced through crystal engineering [4,5]. Among those properties, crystal morphology is of significant importance in the pharmaceutical industry, since it can greatly affect not only the product performance (i.e., bulk density, mechanical strength, and wettability) but also downstream processing (i.e., filtration and drying) during the manufacture of drugs [6,7]. In terms of energetic materials, the mechanical sensitivities (i.e., impact sensitivity and friction sensitivity) of the material are also closely related to its crystal morphology [8,9].

The crystal morphology obtained during crystal formation is highly sensitive to the growth conditions [10]. Generally speaking, the final morphology of crystal products is the combined results of the internal structure of the compound and external growth environment conditions such as the cooling rate, solvent, and supersaturation [11,12]. The relative growth rates of different crystal facets in different orientations can determine its external morphology. The faster it grows in a given direction, the smaller the face perpendicular to it will be.

Crystals exhibit different morphologies, such as needles, acicular or dendritic shapes, platelets or flakes. In practice, needle-like and plate-like crystals are usually undesirable because they have poor fluidity and are easily broken, which might bring difficulties to filtration, drying, and handling in downstream processing [13]. At the same time, needle-like crystals typically exhibit lower bulk density and occupy a larger volume in storage equipment than particles with low aspect ratios. Thus, particles with good fluidity and compressibility are highly desired, as they can be compressed directly without further granulation [14]. In general, stout crystals with approximately similar length and width resulting from uniform three-dimensional growth are ideal with respect to morphology. However, specific application requirements also need to be considered. For example, needle-like crystals of a small size might be beneficial for improving drug dissolution rates [15,16]. To obtain crystals with ideal morphology, it is necessary to fully understand and precisely control the crystallization process, which is still very challenging nowadays.

In order to design the morphology of crystals scientifically, a great deal of efforts have been made in recent decades to understand the causes of the diversity in crystal morphology and to effectively model the underlying crystal growth mechanisms. Different growth models have been proposed and developed, which could provide useful guidance for experiments. In 2015, Li et al. [17] systematically reviewed various crystal shape prediction models proposed in previous literature, and proposed a theoretical framework for crystal shape prediction. This review has stimulated more work on crystal morphology prediction. However, in order to better simulate or predict crystal morphology, crystal growth models still need to be developed and improved.

This work mainly focuses on the modification of crystal morphology. First, the most widely used crystal growth models and molecular dynamics-based crystal morphology prediction methods are summarized and discussed. Then, a comprehensive overview of the state-of-the-art of crystal morphology modification methods is reviewed. In addition, the applications of crystal morphology control in pharmaceutical and material fields are also reviewed. Finally, prospectives and future outlooks of crystal morphology control are proposed.

2. Crystal Growth Models & Prediction

Understanding growth behavior is critical to accurately predicting the shape and size of the final crystal. In order to reflect the effects of different physicochemical factors on crystal growth, such as temperature, solvent, and supersaturation from a mechanistic base using the underlying growth physics, an applicable model should have high chemical fidelity.

Early crystallographers assumed that the shape of crystals was the result of the ordered arrangement of constituent atoms inside. In 1792, Hauy put forward the idea that polyhedral crystal shapes could be constructed by stacking cubes (unit cells) in various three-dimensional sequences, and Gibbs proposed in 1875 that the polyhedral shapes of crystals could minimize the total free energy [18]. Based on this, scientists have already proposed several theoretical models of crystal growth such as the Bravais–Friedel–Donnay–Harker (BFDH) model, the periodic bonded chain theory, the attachment energy model, the spiral growth model, and the 2D nucleation model [19], which are summarized in chronological order in

Table 1. Historical development of crystal growth theories and models.

Time	Theory/Model	Presenter
1866	Laws of Bravais	Bravais
1878	Gibbs–Wulff principle	Gibbs and Wulff
1901	Gibbs–Curie–Wulff principle	Gibbs, Curie, and Wulff
1927	Layer Growth theory	Kossel and Stranski
1937	BFDH	Bravais, Friedel, Donnay, and Harker
1951	BCF	Burton, Cabrera, and Frank
1952	Periodic Bond Chain theory	Hartman and Perdok
1952	BPS	Burton, Prim, and Slichter
1955	Hartman–Perdok theory	Hartman and Perdok
1959	Rough Interface model	Jackson
1966	Dispersion Interface model	Temkin
1966	2D nucleation model	Budevsky and Bostanov

. These models mainly concern four aspects: surface energy, adsorption layer, diffusion-reaction, and growth kinetics [20].

2.1. Gibbs–Curie–Wulff Principle

The Gibbs–Curie–Wulff principle is a fundamental principle of crystal growth and surface science, It was created in 1901 by Josiah Willard Gibbs, Pierre Curie, and Georg Wulff. The principle states that in the equilibrium state of isothermal and isobaric, the end geometry of the crystal will spontaneously form to obtain the minimum total surface energy, which is called the Wulff shape of the crystal. The Wulff structure determines the equilibrium state of the crystal by drawing outward from a certain point inside the crystal (Wulff point) a vector proportional to the surface energy of each crystal face.

Specifically, the content of the Gibbs–Curie–Wulff principle is that the distance from the Wulff point to the various crystal faces is proportional to the reciprocal of the specific surface free energy of these crystal faces, which can be described as Equations (1) and (2). This relationship ensures that during crystal growth, the individual crystal faces can expand at an appropriate rate, thus maintaining the overall minimum energy state.

$${\displaystyle \sum _{i=1}^{\infty }{S}_i}{\gamma }_i=\mathrm{Min}$$

(1)

$${\gamma }_1:{\gamma }_2:{\gamma }_3\cdots =n_1:n_2:n_3\cdots$$

(2)

where S_i refers to the area of the facet of No. i. γ_i is the surface energy of the facet of No. i and n_i is the length of normal from crystal center to the facet of No. i [21].

2.2. BFDH Model

The BFDH model, known as the Bravais–Friedel–Donnay–Harker model, was one of the first models used to predict crystal morphology. This model is based on the symmetry and lattice parameters of the crystal, using geometric calculations to predict the possible growth faces of the crystal and the growth rate of these crystal faces [22]. The BFDH method uses the lattice and symmetry of the crystal to generate a list of possible growth surfaces and infer the morphology of the crystal from the growth rates of these surfaces. The main contribution of Bravais and Friedel was to clarify the problem of the crystal face growth rate, and to propose the relationship between crystal face spacing and growth rate [23,24]. Donnay and Harker further developed this theory, suggesting that the growth rate of higher order crystal faces may be higher than that of lower order crystal faces, and taking into account the symmetry and shift symmetry operators of crystals [25,26].

According to the BFDH model, the crystal face growth rate G_hkl is inversely proportional to the crystal face spacing d_hkl, as illustrated in Equation (3). This means that the more spaced crystal faces (i.e., those with a smaller Miller index) will grow slower. The BFDH model takes into account the surface energy and growth dynamics of different crystal faces to predict the final morphology of crystals, and emphasizes the importance of crystal face stability during crystal growth.

$$G_{hkl}\propto \frac{1}{d_{hkl}}$$

(3)

When studying the re-growth of crystals after fracture, Bade et al. [27] used the BFDH model to predict the morphology of the model compound, paracetamol, under equilibrium conditions. The modeling result was consistent with the crystal morphology obtained by the slow evaporation of ethanol under experimental conditions. In order to predict the crystal morphology of indole analogs, Pisarek et al. [22] employed the BFDH model and found that all indole derivatives are affected by solvent polarity and tend to form plate crystals with maximum (002) faces. The BFDH crystal morphology predicted by Laue symmetry (6/mmm) in the study of synthesis of [(CH₃)₄N]₃Bi₂Cl₉ by Ouasri et al. [28] gives a high surface with two (hkl) face indices (a crystal face that grows preferentially during crystal growth due to its low surface energy), as well as its center-to-surface distance d_hkl and growth rate.

However, the BFDH model mainly focuses on the influence of the internal structure of the crystal on the crystal morphology, especially the relationship between the crystal face spacing and the growth rate. However, it does not fully consider the effects of intermolecular interactions and environmental factors (such as solvent, temperature, and pressure) on crystal morphology. To overcome the limitations of the BFDH model, researchers are exploring ways to incorporate intermolecular interactions and environmental factors into crystal form prediction models. This may involve the development of new theoretical models, improved computational methods, or corrections combined with experimental data.

2.3. AE & MAE Model

Hartman and Perdok took into account the direct effects of intermolecular interactions on crystal morphology when building attachment energy (AE) models. The AE model, which is based on the periodic bond chains (PBC) theory, is the most widely used model with the advantages of simple calculation steps and relatively reliable accuracy. Here also is a brief introduction to PBC theory, which predicts and explains the growth properties of crystals in specific directions by analyzing the arrangement and repeating patterns of interatomic bonds in the crystal structure. PBC theory holds that the periodic arrangement of strong and weak bonds in crystals can affect the growth rate and the shape of crystals. During the crystal growth process, atoms or molecules tend to develop along the direction of bond strength, thus forming crystals with specific orientations.

The AE model proposes that the growth rate of the crystal surface is proportional to its attachment energy. The attachment energy (E_att) is defined as the energy per mole molecule released when a slice layer with a thickness of interplanar distance (d_hkl) is added onto the corresponding crystal face (hkl), which can be calculated by Equations (4) and (5) [29,30].

$$E_{\mathrm{att}}=E_{\mathrm{latt}}-E_{\mathrm{slice}}$$

(4)

$$G_{hkl}\propto \left|E_{\mathrm{att}}\right|$$

(5)

where E_latt and E_slice represent the energy of the lattice and the growing layer, respectively, kJ/mol. In this model, the growth rate G_hkl of a crystal layer is proportional to the absolute value of E_att.

The AE model is proposed based on stoichiometry, while the stoichiometry-based energy correction term is usually different in a solution and a vacuum. The thickness of the growth slice in a vacuum is definite, while in a solution, the thickness of the solvent layer in the crystal–solvent interface is uncertain. Since the influence of the adsorption of solvent molecules at the crystal face on crystal growth is not considered in the AE model, the attachment energy is usually modified (E_mod), and the modified attachment energy (MAE) model is derived as Equation (6) [31,32,33].

$$E_{\mathrm{mod}}=E_{\mathrm{att}}-S{E}_{\mathrm{s}}$$

(6)

where S is the correction factor reflecting the roughness of the crystal face and is defined as Equation (7); E_s represents the effect of solvent adsorption on the energy term and can be calculated as Equation (8).

$$S=\frac{A_{\mathrm{acc}}}{A_{hkl}}$$

(7)

$$E_{\mathrm{s}}=\frac{A_{hkl}}{A_{\mathrm{box}}}{E}_{\mathrm{int}}$$

(8)

where A_acc, A_hkl and A_box represent the solvent-accessible area of the crystal, cross-sectional area, and cross-sectional area of the crystal face in the simulation box, respectively; E_int is defined as the difference between the total energy of the crystal–solvent interface and the isolated energy of the crystal face and solvent layer, as shown in Equation (9).

$$E_{\mathrm{int}}=E_{\mathrm{tot}}-(E_{\mathrm{cry}}+E_{\mathrm{sol}})$$

(9)

where E_tot refers to the sum of potential energy between the crystal layer and the solvent layer, kJ/mol; E_cry and E_sol represent the potential energies of the independent crystal layer and solvent layer respectively, kJ/mol.

In summary, the modified attachment energy can be described as Equation (10):

$$E_{\mathrm{mod}}=E_{\mathrm{att}}-[E_{\mathrm{tot}}-(E_{\mathrm{cry}}+E_{\mathrm{sol}})]\times \frac{A_{\mathrm{acc}}}{A_{\mathrm{box}}}$$

(10)

Although the AE and MAE models provide an important theoretical framework for understanding and predicting crystal growth, their limitations should not be ignored. Both the AE and MAE models assume that the crystal surface growth rate is constant, which limits the ability of the model to evaluate the influence of dynamic factors such as supersaturation, and cannot fully capture the complex dynamic changes in the crystal growth process, such as temperature fluctuations, solvent composition changes, impurity effects and pressure conditions. In addition, the accuracy and reliability of the AE and MAE models are highly dependent on the quality of experimental data and the accurate determination of model parameters. In practical applications, it may be necessary to adopt multi-scale simulation methods, combining micro- and macro-level models, to fully describe the dynamic process of crystal growth.

A new correction term S, which refers to crystal surface roughness, was applied by Duan et al. [34] in the MAE model through molecular dynamics modeling of the acetone solvent layer. The model was used to predict the effect of solvents on the morphology of octohydro-1,3,5,7-tetranitro-1,3,5,7-tetrazepine (HMX). Mao et al. [35] distinguished the different application scenarios of the AE and MAE models, and used the AE model to predict the crystal morphology of CL-20/TFAZ cocrystal in a vacuum. The crystal morphology of CL-20/TFAZ cocrystal in isopropyl alcohol (IPA)/acetone (AC), IPA/dimethyl sulfoxide (DMSO), IPA/ethyl acetate (EA), and IPA/water (H₂O) were predicted by the MAE model and the molecular dynamics (MD) method.

2.4. The Occupancy Model

The occupancy model is another essential extension of the MAE model. Compared with other AE-based models, this model considers not only the effects of solute and solvent, but also the influence of temperature [36]. Basically, crystal growth is dominated not only by the interactions between solute molecules, but also by the solvent molecules. The model takes into account the probability that atoms or molecules occupy lattice points, as well as their dynamic behavior during crystal growth, thereby helping scientists understand and control the formation of crystal defects, the distribution of impurities, and the final shape of the crystal. For example, crystal growth may be accelerated when solute molecules occupy the crystal surface, while it may be inhibited when solvent molecules occupy the crystal surface. The occupancy model can be described as Equation (11) [37].

$$E_{\mathrm{ocu}}=k{E}_{\mathrm{att}}$$

(11)

where k stands for relative occupancy, which can be calculated by Equation (12).

$$k=\frac{\Delta E_{\mathrm{solu}-\mathrm{surf}, \mathrm{m}}}{\Delta E_{\mathrm{solu}-\mathrm{surf}, \mathrm{m}}+\Delta E_{\mathrm{solv}-\mathrm{surf}, \mathrm{m}}}$$

(12)

where ΔE_solu-surf,m and ΔE_solv-surf,m represent the interaction energy of a solute molecule or a solvent and the crystal surface, respectively, which can be calculated by Equations (13) and (14).

$$\Delta E_{\mathrm{solu}-\mathrm{surf}, \mathrm{m}}=\frac{\Delta E_{\mathrm{solu}-\mathrm{surf}}}{N_{\mathrm{solu}}}$$

(13)

$$\Delta E_{\mathrm{solv}-\mathrm{surf}, \mathrm{m}}=\frac{\Delta E_{\mathrm{solv}-\mathrm{surf}}}{N_{\mathrm{solv}}}$$

(14)

where N_solu and N_solv are the number of solute or solvent molecules, respectively. N_solu and N_solv can be calculated by Equations (15) and (16).

$$N_{\mathrm{solu}}=\frac{V_{hkl}}{V_{\mathrm{solu}, \mathrm{m}}}=\frac{A_{\mathrm{surf}}{d}_{hkl}{\rho }_{\mathrm{solu}}{N}_{\mathrm{A}}}{M_{\mathrm{sol}}}$$

(15)

$$N_{\mathrm{solv}}=\frac{V_{hkl}}{V_{\mathrm{solv}, \mathrm{m}}}=\frac{A_{\mathrm{surf}}{d}_{hkl}{\rho }_{\mathrm{solv}}{N}_{\mathrm{A}}}{M_{\mathrm{sol}}}$$

(16)

where A_surf is the surface area of one solute or solvent molecule at set temperature; d_hkl is the distance between crystal faces; ρ_solu and ρ_solv are the densities of solute and solvent, respectively; N_A represents the Avogadro constant; M_sol is the molecular weight of solute.

In Equation (13), k actually reflects the competition power of solute molecules to occupy crystal surfaces: when k is larger than 0.5, the competition ability of solute molecules is stronger than that of solvent molecules.

In order to verify the occupancy model’s validity, Zhang et al. [36] applied it to a number of well-known nitroamine explosives, such as hexahydro-1,3,5-trinitro-1,3,5-triazine (RDX). The outcomes showed that the expected morphology and the experimental observations agree well. Wang et al. [38] studied the crystallization behavior of 1,3,5,7-tetanitro-1,3,5,7-tetrazazane (HMX) in acetone and DMSO/H₂O solvent systems by MAE model and the occupancy model, respectively. By comparing the calculation and experimental results, it was found that compared with the MAE model, the calculation results of occupancy model agreed better with the experimental results. It is not uncommon for the occupancy model to predict the results more accurately than the MAE model. Similarly, Liu et al. [37] also predicted the morphology of 1,1-Diamino-2,2-dinitroethene in H₂O/NMP and DMSO/AC solvent systems.

2.5. Spiral Crystal Growth Model

Although non-mechanical (thermodynamic) models, such as the BFDH model (as discussed in detail in Section 2.2), are the basis for crystal morphology prediction, they are considered system-specific and do not take into account the crystallization environment (such as solvents, additives, impurities, and supersaturation), which can significantly influence crystal morphology. The acquisition of high-quality crystals depends on a good understanding of the basic interaction between solvents and crystals. Therefore, mechanical (dynamic) models, such as the spiral growth model, are applied to predict crystal morphology when the crystal growth environment changes. Budevsky and Bostanov [39] developed the voltage pulse method to study two-dimensional nucleation dynamics of silver electrodes, an electrochemical technique that studies and controls two-dimensional nucleation dynamics during electrolysis by applying a series of precisely controlled voltage pulses to a disc-free (100) silver electrode. This allows scientists to precisely explore and optimize the early stages of crystal growth.

In 1951, Burton, Cabrera, and Frank (BCF) proposed the spiral growth theory based on dislocation in actual crystal structure defects [40]. Because of the high thermodynamic free energy barrier, this mechanism provides the basis for predicting the growth of organic molecular crystals in low-supersaturated solution [41]. In this growth mechanism, when internal forces accumulate in the lattice, the lattice can undergo shear slip and spiral dislocation. The helical dislocation forms a helical path inside the crystal, resulting in a step-like structure on the crystal surface. Crystals grow more rapidly on these steps than on flat crystal planes because the steps provide a lower energy nucleation site that facilitates the deposition of atoms or molecules. This theory not only explains some morphological characteristics during crystal growth, but also reveals how crystal defects affect crystal growth dynamics, which is of great significance for understanding and controlling crystal morphology and quality. The crystal growth process described by the spiral growth model is shown in Figure 1, and its contents can be described by Equations (17) and (18).

$$G_{hkl}=\frac{h_{hkl}}{\tau }=\frac{v{h}_{hkl}}{y}$$

(17)

where G_hkl is the growth rate of a crystal face; v is the perpendicular step velocity across the surface in the edge direction; h_hkl is the height of the step; τ is the spiral rotation time; y is the inter step distance.

$$\tau ={\displaystyle \sum _{i=1}^N\frac{l_{c,i+1}\sin ({\alpha }_{i,i+1})}{v_i}}$$

(18)

where l_c,i is the critical length of edge i, α_i,i+1 is the angle between edge i and i + 1, and the step velocity v_i is the rate of lateral advancement of steps.

The step velocity for edge i, v_i, is limited by kink attachment and detachment kinetics, which is given as Equation (19).

$$v_i=a_{\mathrm{p},i}{\rho }_i{u}_i$$

(19)

where a_p,i refers to the step propagation length, ρ_i means the kink density, and u_i is the kink rate for edge i.

To start growing, the length of an edge must reach a critical length l_c.

$$\begin{gathered} v=0, l\le l_c \\ v=v_{\infty }, l>l_c \end{gathered}$$

Due to the non-Kossel growth unit and intricate bonding network, the morphology prediction of hexahydro-1,3,5-trinitro-1,3,5-triazine (RDX) has been described as an exceedingly challenging problem. Shim et al. [43] predicted the crystal shape of RDX with the spiral crystal growth model successfully (as shown in Figure 2). The mechanical model not only expands the model selection range of crystal morphology prediction, but also plays an important role in accurately presenting the expression of crystal growth rate. Tilbury et al. [44] applied a mechanical model to layered crystal growth and introduced a framework to connect the different mechanisms of crystal growth under different supersaturation conditions, which successfully predicted the cross supersaturation on each face. When simulating the specific supersaturation of crystal growth, this helps to guarantee that the correct growth rate expression is applied on each face. Using the concepts of two-dimensional nucleation and spiral growth, Martins et al. [45] calculated the displacement velocity at each step of the solution and vapor growth process by different kinetic methods, and obtained generalized expressions between the crystal growth rate and major variables such as supersaturation, temperature, crystal size, surface topology, and interface properties. The crystallization kinetics of sucrose at 40 °C were verified.

2.6. Molecular Simulation

With the increase in computing power and the continuous advancement of simulation algorithms, molecular simulation has become a powerful tool to provide detailed information on crystal growth and morphological evolution at the microscopic level. By precisely calculating the interactions between crystals and solvent molecules, molecular simulations are able to predict the crystal structure and dynamic behavior of molecules during crystallization. With appropriate theoretical models and force fields, molecular simulation can simulate a variety of physical and chemical properties of the system, such as solubility, melting point, lattice energy and intermolecular forces, so as to predict the morphology and stability of the crystal. This method can not only reveal the microscopic mechanism of crystal growth, but also guide experimental design, optimize crystal growth conditions, and improve crystal quality. Compared with high-throughput screening experiments, molecular simulation has higher efficiency and lower cost, and can screen and analyze a large number of compounds in a short time, providing important theoretical support for the development of new materials and drug design. In addition, molecular simulation can also be combined with experimental data to verify and improve the theoretical model by comparing the simulation results and experimental observations, and further improve the accuracy and reliability of the simulation [46].

The diversity of crystal morphologies in the same material indicates that the macroscopic shape is highly sensitive to the growth condition and that the shape of most particles is actually controlled by the dynamics of the atomic growth process in which molecular assembly occurs. There are generally two approaches to growth modeling based on dynamics: kinetic Monte Carlo (KMC) and molecular dynamics (MD) [47]. In scientific research, the Monte Carlo algorithm has been applied more widely. For example, Piana et al. [48] studied the growth process of the urea–solvent interface through combining MD and KMC simulations, which described three-dimensional growth of urea crystals and predicted crystal morphology in different solvents. Shim et al. [49] used step energy calculation and KMC simulation for molecular modeling, which not only predicted the rod-like shape of DADNE crystals obtained from cooling crystallization, but also provided an understanding of the growth dynamics of the growing units on each crystal surface. In addition to the common environmental effects of solution, the influence of impurities on crystal morphology cannot be ignored, which can also be reasonably explained in KMC simulation. Mazal et al. [41] studied the effect of impurities on the morphology of step growth through KMC simulation, and examined the step growth mechanism mediated by impurities under different conditions.

Besides KMC, MD simulations were also investigated to reveal the crystal growth process and predict the crystal morphology. Mao et al. [50] explained the effect of additives on the crystal morphology of calcium sulfate whisker in HCl aqueous solution through MD simulation. In the presence of cetyltrimethylammonium bromide (CTAB), calcium sulfate whisker showed the phenomenon of small diameter and high aspect ratio, which was the result of the combined effect of surface adsorption of CTAB and inhibition of solute diffusion. Wang et al. [51] applied molecular dynamics simulation to the morphology prediction of low-sensitivity high-energy materials (LSHEMs), and found that the adhesion energy of LSHEMs crystal faces and the predicted crystal morphology in different solvents are determined by the HB site on the crystal faces, and are closely related to the solvent polarity, which provides an effective solvent selection method for the topography customization of LSHEMs.

Molecular simulation shows strong potential for crystal growth prediction, but there are still some limitations, such as the need for large computational resources, dependence on force fields and model accuracy, the challenge of finding global minimum energy structures in the face of large search Spaces, the difficulty of considering both kinetic and thermodynamic stability, and the difficulty of accurately describing solvent and grain boundary effects in simulations. In addition, the accurate simulation of experimental conditions, the guarantee of prediction accuracy, the difference of results between different simulation software and tools, and how to effectively combine simulation results with experimental research are all problems that molecular simulation is facing at present. However, it is undeniable that molecular simulation is still an important aid in crystal growth research, especially in cases where experimental conditions are difficult to achieve or difficult to study through traditional methods.

3. Methods of Modification

The primary idea behind manipulating crystal morphology is to manage the relative development rates of distinct crystal faces, because the slow-growing face will be retained in the eventual crystal while the fast-growing face will be removed. The crystal morphology can be affected by many external factors, for instance, supersaturation, solvent type, operating temperature, cooling rate, desired foreign molecules (additives), or unwanted foreign molecules (impurities). A change in any of these factors can result in a dramatic change in crystal morphology [52].

3.1. Temperature

The selection of an appropriate operating temperature range is necessary to control crystal growth, especially during the solution crystallization process, where reducing the temperature of the solvent and active pharmaceutical ingredient (API) mixture can generate a crystallization driving force. For example, Matsuura et al. [53] used the difference between the experimental crystal growth temperature and phase equilibrium temperature, ΔT_sub, as a driving force to characterize the thermodynamic conditions of hydrate formation. It was found that the crystal morphology was significantly dependent on ΔT_sub, and the crystal shape of hydrate would change from polygon to dendritic shape during the gradual increase of ΔT_sub. This is a more commonly used way of controlling crystal morphology in anti-solvent crystallization. It was found that the higher the operating temperature, the less the effect of supersaturation on the growth rate. This helps us to control crystal growth during the anti-solvent crystallization process. Generally, anti-solvent crystallization at higher temperatures is more conducive to crystal growth [54]. Altering the rate of temperature change and temperature cycling are also common methods to control crystal growth. Researchers managed to selectively grow large metastable crystals with uniform morphology while obtaining different crystal forms by adjusting the cooling rate by using glutamic acid as the model drug [55,56]. Zhang et al. [57] examined the temperature at which sodium sulfate crystallizes, as well as the changes in grain size and morphology, at various rates of stirring and cooling. Their findings suggest that the cooling rate is a major factor in the variations in the critical time and average crystallization grain size. Temperature cycling could eliminate fine particles and promote the growth and increase length–diameter ratio by cycling between positive and negative supersaturation [58]. Simone et al. [13] found that the shape of succinic acid changed significantly after several temperature cycles, from plate-like to diamond-like.

3.2. Supersaturation

Supersaturation is the basic driving force for crystal nucleation and growth. Supersaturation-dependent growth is a general way to control the exposed surface of crystals’ growth. In order to control supersaturation, process variables such as the temperature and the amount of anti-solvent could be manipulated [59]. According to the crystal growth mechanism, supersaturation-dependent crystal morphology is closely related to the two-dimensional nucleation rate. When the driving force is large enough to overcome the energy barrier of forming a step on the crystal surface, the two-dimensional nucleation rate would determine the relative growth rate of the crystal faces. Shim et al. [49] controlled the supersaturation rate by changing the cooling rate, and found that the 1,1-diamino-2,2-dinitroethylene (DADNE) crystal aspect ratio decreased with the increase of the solution cooling rate (as shown in Figure 3). This is because the reduction of the 2D nucleation free energy at high supersaturation reduces the aspect ratio of DADNE, thus blurring the distinctive features of DADNE in the anisotropic growth behavior.

3.3. Foreign Molecules

The crystallization process is often modified by foreign molecules including impurities and additives (summarized in

Table 2. Foreign molecules commonly used to affect crystal growth.

Types	Classic Examples	Advantages	Ref.
Tailor-made additives	Amino acids and inorganic salts.	Easy operation, small amount, allowing for careful design	[61]
Small-molecule additives	Coenzymes, inhibitors, metal ions and prosthetic groups.	Versatility, directionality, and stability	[62,63]
Large-molecule additives	Polymers, peptides and proteins.	Safe and have no impact on crystal structures	[64]
Surfactant	Sodium dodecyl sulfate, AES	Significant effect on hydrate crystallization	[65]
Micro-/nanobubbles	O2, CO2 and N2.	Low cost, no pollution	[66]

), which usually affects crystal morphology by selectively promoting/inhibiting the growth of crystal surfaces via the interaction with the crystals [60]. Generally speaking, the mechanism for foreign molecules of modifying the crystal morphology can be simply illustrated, as in Figure 4: foreign molecules are adsorbed to the crystal surface first and then affect the binding of solute molecules to the crystal surface.

Traditionally, additives are usually divided into three categories: tailor-made additives, small-molecule additives, and large-molecule additives. Tailor-made additives, a concept first proposed in 1985, refer to additives which possess similar geometric structure, charge distribution, and molecular volume as the solute molecules [67]. They can be selectively adsorbed on fixed crystal surfaces to obtain the desired crystal shape. Kaskiewicz et al. [68] combined molecular modeling and experimental techniques to screen multiple additives with similar structures. They successfully obtained customized additives which can interfere with the nucleation pathway of molecular preassembly and play a role in inhibiting nucleation. A desired change in crystal morphology can also be achieved by changing the properties and amounts of additives. Yu et al. [69] studied the effect of natural additives on the crystal morphology of anhydrous clozapine and found that the type of additives could affect the crystal morphology significantly, while the amount of additives had a greater effect on the average grain size of crystals. Liu et al. [70] found that the reason why the addition of Na₂CO₃ could affect NaHCO₃ crystal morphology in water was that there is a strong hydrogen bond between hydrogen atoms of NaHCO₃ (011) face and oxygen atoms of Na₂CO₃ surface, which would weaken the hydration between crystal surface and water molecules, and thus significantly change the adhesion energy and growth rate of the crystal surface.

For a long time, polymers were widely used as additives, as many polymers are generally considered to be safe (GRAS) compounds and, due to their large molecule size, they are not easy to incorporate into crystal structures as impurities. Madeja et al. [71] adjusted the growth mode of gypsum crystal with a polymer, revealed the interacting mode of a copolymer in the crystallization process, and proposed that the dynamic additive behavior at the growth front was the key to the morphology control of the calcium sulfate system. Wang et al. [72] found that adding SiO₂ nanoparticles (NPs) to paraffin wax could delay the crystallization rate of paraffin wax in crude oil, hinder the growth of heterogeneous core wax crystals, regulate the morphology of wax crystals, and inhibit the formation of large-size wax crystals. Wang et al. [73] used polymer additives to modify the morphology of methionine crystals from elongated leaf-like crystals to hexagonal plates or blocks with a reduced aspect ratio, which solved the problems of poor density, easy fragmentation, poor fluidity, and difficult transportation. Hatcher et al. [74] found that the hydrophobic additive poly(propylene glycol) (PPG) seems to restrict the growth of lovastatin along the long needle axis during recrystallization, helping to change the crystal habit from needle-like to plate-like. Reducing the aspect ratio of the crystal helps to enhance the crystal performance. Poly(di-n-octylfluorene) (PFO) is a semiconductor polymer with a variety of semi-crystalline forms. Controlling semiconductor crystal morphology can improve the charge transmission and help the electronic devices work as intended. Rosencrantz et al. [75] controlled the polymer form and its macroscopic shape and appearance by changing the concentration of Poly(vinylpyrrolidone-co-vinyl acetate) (PVPVA). While low concentrations of PVPVA produce mixed morphology spherulite particles, higher concentrations produce spherical particles with crystalline content via a regulated condensation–crystallization mechanism, as shown in Figure 5.

Surfactants—amphiphilic molecules which could reduce the interfacial tension (IFT) between the water and oil phases—are often used to promote the growth of hydrate crystals [65]. Sun et al. [76] studied the influence of surfactants on crystal growth after nucleation of HCFC-141b hydrate and reported that temperature had a great influence on the growth rate of the hydrate: the lower the temperature, the faster the growth of hydrate crystals. Mitarai et al. [77] studied the effect of surfactants on clathrate hydrate crystal growth at the interface of water and cyclopentane. They reported that the behavior of cyclopentane hydrate crystal growth varied with the type, the concentration of the surfactant, and the difference between the equilibrium temperature and the experimental temperature. The effects of surfactants consisted of two aspects: one was preventing hydrate agglomeration and the other was promoting hydrate production.

With the presence of additives, supersaturation is not the only factor affecting crystal growth any more. Additives can eliminate the negative effect of solvent on the surface diffusion of solute molecules through competition among solute, solvent, and additive molecules, and reduce the solubility and interfacial energy of solute molecules. Additives also have the effect of promoting nucleation and affecting the growth of molecules [78,79]. Their unusual behavior is due to the selective adsorption caused by the electrostatic interactions and hydrogen bonds between the solute and additive molecules. In particular, the exposure of anionic groups to the end of the additive could cause a special phenomenon wherein small changes in the charge density and hydrogen bonding ability can lead to significant differences in influencing the crystal growth [80]. The solvent condition will also affect the additive effect. The solvent mixture significantly enhances the interaction between the additive and the crystal, thus providing a powerful method to precisely adjust the blocking of the additive within the crystal and modify the crystal morphology [81].

The simultaneous use of more than one “crystallization modifier” has been proved to be a reliable method of modifying the crystal growth process [82]. The effects of combined modifiers could normally be classified as synergistic or antagonistic by comparing the effect of employing the modifier combination with that of only single modifier involved [83]. Ma et al. proposed an antagonistic synergistic mechanism between crystallization inhibitors (by studying the effects of modifiers on the two-dimensional nucleation rate) and propagation rate of new crystal layers, which emphasized the interaction of modifiers mediated by dynamics and structure at the crystal interface [84]. The study of the combination of modifiers can not only guide the search for suitable combinations of inhibitors to control the crystallization of pathological, biomimetic and synthetic materials, but also guide the morphology control of crystals in nature and industry.

Considering the adverse effects of conventional additives on product purity, researchers have developed “green additives” by taking advantage of micro-/nanobubbles [85]. Nanobubbles range in diameter from 50 to 1000 nm, while the category of micro-/nanobubbles belongs to all fine bubbles less than 100 μm in diameter, which act as an additive to affect crystal growth by changing the solid–liquid interfacial tension on the crystal surface and by solvent evaporation into the bubble [86]. Accordingly, Tagomori et al. [87] proposed a heterogeneous nucleation mechanism for calcite crystal growth: air nanobubbles may affect crystal growth by changing the solid–liquid interfacial tension on the crystal surface, reducing free growth sites, adsorbing Ca²⁺ ions, acting as bubble pads and thermal buffers on the crystal surface, or a combination of them (Figure 6). By comparing the effect of seeding and gas in succinic acid cooling crystallization, Kleetz et al. [88] found that compared with traditional cooling crystallization and seeding cooling crystallization, the gas crystallization method not only avoided the influence of impurities, but also had simple operation, improved reproducibility, and significantly shortened batch processing time. Generally speaking, gas volume flow, gas duration, and gas supersaturation can all be adjusted during the crystallization process.

3.4. Solvents

Solution crystallization is one of the most widely used crystallization methods in industry. Considering the non-negligible role of solvents in the regulation of crystal morphology, it is of great significance to choose the appropriate solvent system to produce APIs with desirable crystal habits. Jiang et al. [89] conducted a crystal regrowth experiment in methyl acetate and found that the broken aceclofenac crystal could be restored to its original form, as shown in Figure 7. Compared with the crystal obtained in acetone, it was found that the aceclofenac crystal in methyl acetate had a larger aspect ratio. Solvent composition and reagent ratio are the means to affect crystal shape [90], and its regulatory effect on crystal morphology is basically attributed to the interactions between the crystal surface and the solvent (including hydrogen bonding force, van der Waals force, and Coulomb force), which can change the relative growth rate of different faces and lead to the change of crystal morphology [91].

Crystal surface roughness has an important effect on the adsorption of solvent molecules. This usually involves the determination and structural analysis of important crystal faces, and S is a common value used for quantitative analysis of crystal face roughness (as described in detail in Section 2.3, Equation (9)). Cui et al. [92] studied the effects of water, methanol and ethanol on the crystal morphology of sucralose by combining experiment and simulation. The results are shown in Figure 8. It was found that the aspect ratio of crystal growth in the three solvents is determined by the relative growth rate of the morphologically important crystal faces (011) and (101). It is the difference in roughness that leads to the disappearance of the (002) and (100) crystal faces, and causes the (101) faces to have lower morphological importance than the (011) faces. Similarly, Cao et al. [93] studied the influence of different solvent systems on the morphology of risperidone (Form I) crystals. Through structural analysis of the main crystal faces, it was found that the huge U-shaped structure on the (11-1) and (01-1) crystal faces could prevent the adsorption of solute molecules, thus making the two crystal faces of great morphological importance. The diffusion ability of solvent on the crystal surface also has a non-negligible effect on the interaction. The rapid diffusion of solvent molecules can contribute to strong interaction between the solvent and the crystal surface, thus inhibiting the growth of the crystal surface [94]. In addition, the steric hindrance and polarity of solvent resistance should also be considered, indicating that the diffusion coefficient of solvent molecules is not positively correlated with the interaction energy [95]. Sun et al. [96] discovered that olanzapine exhibited different surrounding face families in different solvents with different polarity. The relative exposure of different crystal surfaces is also strongly influenced by the polarity of the solvent [97]. Pawar et al. [98] found that the crystal morphology of lactose changed between a polyhedron and curved needle shape with the change of anti-solvent addition, anti-solvent feed rate, and initial lactose concentration.

In recent years, the use of supercritical fluid (SCF) instead of traditional organic solvents has become increasingly popular [99]. Even if the system under study inevitably uses organic solvents, SCF greatly reduces the amount of them used compared to many industrial processes. As a result, it is generally considered to be environmentally friendly. As the most widely used one, supercritical carbon dioxide (scCO₂), with its low critical temperature (T_c = 304.21 K) and accessible critical pressure (P_c = 7.38 MPa), has provided a new choice for crystal morphology regulation of the heat-sensitive APIs. Compared with traditional separation processes, supercritical fluids-assisted technologies require fewer unit operations and reduce the possible evolution of crystals in successive steps, resulting in more controllable size, CSD, and habits. Different crystallization methods can be chosen depending on the role played by scCO₂ to the different system, which are summarized in

Table 3. Various crystallization methods can be used according to the role of scCO₂.

Types	Most Commonly Used Process	Scope of Application
Precipitation solvent	Rapid Expansion of a Supercritical Solution (RESS) process	Solutes having a solubility higher than about 10−3 g·g−1 of SCF
Precipitation anti-solvent	Supercritical Anti-Solvent (SAS) process	Polar drug molecule
Dispersing agent	Particles from Gas Saturated Solutions (PGSS) process	Polymers in which CO2 is sorbed in significant quantities

[99,100]. Since many APIs have relatively low solubility in carbon dioxide, anti-solvent crystallization is actually more widely used than decades ago. For instance, Field et al. [101] precipitated C60 from a saturated organic solution using supercritical carbon dioxide as anti-solvent. By allowing carbon dioxide to enter the C60 lattice during crystal growth, regular octahedral particles with high crystallinity were produced under moderate conditions, avoiding high temperature and high pressure.

With the emergence of confined space crystals crystallization, microemulsion has also been introduced into the crystallization process in recent years for morphology regulation. Basically, microemulsion is an isotropic mixture of oil, water, and surfactants, in which crystals will exhibit different properties compared with those in bulk solution. The existence of droplet interface and the controllable structure of microemulsion droplets could help to enrich the crystallization environment, and the interfacial mass transfer caused by droplet collision will have a great influence on the crystal morphology [102]. Liu et al. [103] used glycine as a model compound to crystallize in a microemulsion environment, and analyzed the structure and morphology of the crystals obtained by microemulsion crystallization, as shown in Figure 9. The results showed that the crystal structure and morphology could be controlled by microemulsion crystallization. In particular, by controlling the thermodynamics of microemulsion crystallization, it is possible to skip Ostwald’s phase rule and directly crystallize stable polycrystals. This was demonstrated by the work of Chen et al. [104] which succeeded in crystallizing nanoaggregates in microemulsions by exceeding Ostwald’s rules.

3.5. Membrane Assistance

With the rapid development of membrane technology, membrane-assisted crystallization has become a new method to accurately regulate crystal growth [105]. Compared with conventional crystallization, it creates efficient micro-mixing and mass transfer for the crystallization process by introducing membranes with nanometer or micron pores and high specific surface area, thus providing a more stable nucleation and growth environment [106]. The membranes used in current research for crystallization processes are usually made of polymers, summarized in

Table 4. Organic polymer membranes commonly used in crystallization.

Types	Advantages	Ref.
Polypropylene (PP)	High porosity and hydrophobicity	[107]
Polyvinylidene fluoride (PVDF)	High permeable flux, microporous structure, and hydrophobicity	[109]
Polytetrafluoroethylene (PTFE)	High mechanical strength, thermal stability, chemical resistance, and high hydrophobicity	[110]
Polyethersulfone (PES)	High alternative surface area	[111]

. Jiang et al. [107] reported the crystal morphology modification mechanism of classical industrial ternary solution (NaCl-EG-H₂O) treated by membrane-assisted crystallization, emphasizing and simulating various nucleation barriers, multinuclear growth and diffuse-controlled growth mechanisms during membrane-assisted crystallization (which have significant effects on crystal morphology and size distribution), and the resulting crystals have a specific form. The flexibility of membrane-assisted crystallization allows growth control of the crystallization process under different conditions, for instance, acidic or alkaline solutions [108], high temperature (such as membrane distillation), and vacuum.

The surface structure characteristics (such as roughness) of the membrane have an influence on the growth of crystals to different extents. The common methods to adjust the surface structure of the membrane include soft lithography and the addition of polymers [112,113]. The addition of different types of cross-linked agents can also affect the growth of crystals. The growth rate and size of crystals can be regulated by changing the mechanical stability or flexibility of the membrane so that its position is not subject to the change of crystal growth or its position can adapt to the growing crystals.

Besides the surface structure characteristics of the membrane, the set-up configuration of the membrane can also affect the morphology of crystals [105]. The configuration of the membrane is commonly divided into two types, as shown in Figure 10: 1. Tubular membranes: Usually a capillary/tubular/hollow fiber membrane is used, with the inner cavity of the membrane or the whole body in solution; 2. Flat membranes: The solution can be divided into two parts [111]. Generally speaking, laminar flows in hollow fiber membranes can provide opportunities for better arrangement of molecules, resulting in better crystal lattices, and ultimately producing better crystal shapes and purer products.

3.6. External Physical Fields

Physical field-assisted crystallization refers to the methods of enhancing the crystallization process by using different physical fields. It has become an increasingly popular method of modifying the crystal morphology due to advantages such as environmental friendliness, low cost, and no impurity introduced into the crystallization process. The physical fields that have been used in the crystallization process include light radiation, ultrasound waves, microwaves, magnetic fields, and electric fields.

Laser can play a role in morphology regulation, nucleation induction, and polycrystalline screening in crystallization [114,115,116]. The principle of laser crystallization may be attributed to the heat induced by the laser power, which can lead to reorganization within the particles and promote the aggregation and growth of the crystals. Laser basically exhibits higher device performance compared with traditional thermal annealing [117]. At the same time, cavitation occurs when laser irradiates the metastable region without nucleation. The cavitation bubbles generated by laser irradiation can briefly produce a local high concentration region in the solution and promote crystal formation [118]. According to the traditional crystal morphology theory, the uniformity of the concentration around the crystal surface is the key factor of determining the crystal morphology. Laser triggered crystal generation is easier at the air/solution interface, as both gradient and scattering forces contribute to the concentration increase. The number of clusters in the solution can change with the laser power. The high efficiency of cluster capture at high laser power can increase the concentration near the crystal, and stabilize the high concentration cluster domain which formed at the laser focus at the same time, as shown in Figure 11 [119]. Different kinds of beams may lead to differences in crystallinity, which mainly depends on the melting of non-single crystal regions along the laser scan direction. The concave-trailing profile produces larger grains and result in single crystals, while the convex-trailing profile results in smaller grains and polycrystals [120]. For example, by irradiating droplets on the photosensitive hydrophobic substrate with light beams, Li et al. [121] quickly converted the light energy into heat to facilitate the morphology control (Figure 12). Meanwhile, the resulting interface behavior, internal flow, and non-uniform concentration distribution were all jointly responsible for manipulating the morphology of three-dimensional crystals. Compared with traditional evaporative crystallization, the operation is more flexible and convenient for high flux screening.

Microwave-assisted crystallization process has the advantages of speed, simplicity of control, minimal thermal inertia, high reproducibility, and low heat loss [122]. The microwave heating used for microwave-assisted crystallization can be coupled directly to the solution molecules without the need for heat exchange surfaces or fluids, thus achieving precise heating control over the entire volume and avoiding temperature fluctuations. At the same time, microwave heating can speed up the crystallization process, significantly shorten the evaporative crystallization time, and produce high supersaturation, meaning that it is often used to degrade crystal size [123]. However, microwave-assisted crystal sizes can sometimes be made even larger. For example, metal-assisted and microwave-assisted evaporative crystallization (MA-MAEC), a combination of microwave heating and plasma nanostructures, not only accelerates the crystallization process, but also provides nucleation sites for crystal growth, resulting in the formation of larger, more organized crystals in the same amount of time [124,125,126].

Sonocrystallization, the use of ultrasound wave in crystallization processes, has grown in importance over the past few years as a way to more effectively control crystal growth [127]. Richards and Loomis published the first publication on the use of ultrasound waves in crystallization processes in 1927. By determining the correct ultrasonic crystallization control strategy, the crystal size can be reduced and the CSD can be controlled [128]. By generating air bubbles, the metastable zone widths (MZW) are reduced, the induction periods are shortened, and more uniform and smoother crystals can be formed [129,130]. Basically, ultrasonic crystallization can be carried out in an ultrasonic horn or a bathtub. At present, there are two mechanistic explanations for ultrasound waves to modify the crystal morphology: 1. In solution, cavitation bubbles collapse, leading to the thinning of the hydrodynamic boundary layer and microscopic turbulence around particles, which improves mass transfer and increases the possibility of solute molecules combining with each other. This could also compensate for the different growth rates of different crystal faces, consequently leading to more uniform crystals; 2. In metal-containing slurry, particles melt into spherical particles after the implosion of the cavitation bubble, and the collapsing cavitation bubble produces strong shock waves, which could result in the high-speed collision of particles. These collisions lead to extreme heating at the point of impact, resulting in particles melting together [131,132]. Ultrasound typically produces smaller crystals with a narrower CSD than the normal cooling crystallization process. Ramisetty et al. [133] used different ultrasonic strategies (continuous, single pulse, and multi-pulse) to control the CSD of piracetam, paracetamol, and ibuprofen, and obtained a narrower CSD.

The effect of magnetic fields on crystal growth has been studied for decades, and early scientists have proposed four possible mechanisms to explain the effect of magnetic fields on crystal growth in solution, including the thermodynamic effect, magnetohydrodynamic effect, magnetic dipole interaction, and magnetic field gradient [134]. Magnetic fields can cause a lag in nucleation temperature at higher supersaturation, thus resulting in a greater degree of supersaturation in the system, which could lead to more nucleation and smaller crystal size [135]. This is particularly significant in protein crystallization [136]. The competition between convective and diffusive transportation of molecules determines the properties and dynamics of crystal growth. The application of an external magnetic field during protein crystallization reduces natural convection by counteracting gravity, and increases the viscosity of the protein solution, thus orienting the growing crystals and contributing to crystal morphology regulation [137]. Magnetic fields with gradients can inhibit the convex surface and thus slow the growth of protein crystals [138]. Magnetic fields can also have an effect equivalent to an increase in the saturation temperature of the solution [139]. Considering the high cost of strong magnetic fields, some researchers chose the combination of a weak magnetic field and growth gel to improve crystal quality. The uniform field can affect the relative thermodynamic stability at small nuclei/crystallite sizes by influencing the structure and local supersaturation of the crystal surface [140].

Electric fields are also used to help modify crystal morphology because of their flexibility. Design variables such as electrode type, material, and space layout, as well as operating variables such as electric field intensity and frequency can be adjusted flexibly [141,142,143]. In addition to the common uniform electrodes, patterned electrodes provide opportunities for extremely flexible designs of potential energy landscapes. Such experiments are usually performed in microfluidic devices (MFD) made of polydimethylsiloxane (PDMS). Indium tin oxide (ITO) is commonly used as a nucleation template because of its advantages of optical transparency, high conductivity, and ease of fabrication by standard photolithography. The application of an electric field can result in higher secondary nucleation rates at lower supersaturation conditions, resulting in the formation of more crystals. The MFD can be integrated with other crystallization facilities downstream, using a large number of small crystals as seeds with large surface volume ratio for further growth in a dedicated growth chamber [144,145].

3.7. Ball Milling

Ball milling is a mechanical process that uses a ball to carry out strong impact and grinding in a container, which can produce local high temperature and high pressure, resulting in physical and chemical changes such as deformation, cold welding, fracture, and recrystallization of solid powder. In crystal growth, ball milling can refine the powder particles, increase the defect density of the particles, and improve the activity of the powder through the cyclic cutting and deformation of large grains, thus promoting the nucleation and growth of the crystals. In addition, ball milling can achieve solid-state reactions of different materials to prepare composite crystals or nanocrystals. Because of its advantages of simple operation, low cost, and strong controllability, ball milling technology has been widely used in the fields of material synthesis, nanotechnology, solid state chemistry, and powder metallurgy. By optimizing milling parameters, such as milling time, ball material and ball material ratio, the crystal growth process can be controlled and crystal material with specific morphology and properties can be obtained.

Ball milling will affect the internal defects of the crystal. Yang et al. [146] synthesized Y₃Al₅O₁₂:Eu³⁺ powder with a high energy ball mill (HEB) and the traditional solid state reaction method (SSR). The particles produced by high-energy ball milling are smaller than the solid-state reaction method, and smaller particles are less likely to produce internal defects and are more difficult to break. Ball milling also affects the size of the crystal. Li et al. [147] found that when calcium sulfate dihydrate (DH) was used to prepare calcium sulfate whisker by ball milling, a large amount of Ca²⁺ and SO₄²⁻ ions were released during the whisker growth process, and the formation of new crystal nuclei led to a decrease in the overall length of whisker, which was smaller than that of non-ball milling whisker. Ball milling can also affect the growth shape of crystals. Ahmad et al. [148] used ball milling technology to synthesize plasma Al-Li-graphene nanosheets (Al-Li-GNSs) with anisotropic morphology. Structural analysis by SEM and TEM showed that Al-Li-GNSs nanoparticles were hexagonal flake single crystals, as shown in Figure 13.

Ball milling is also a common method for the preparation of pharmaceutical cocrystal. Active pharmaceutical ingredients (APIs) are mixed with cocrystal ligands (such as organic acids, bases, or salts) by a ball mill and high energy ball milling, so that the raw material in the solid state occurs uniform mixing, local melting or ion exchange, resulting in the formation of cocrystal with a specific stoichiometric ratio. The particle size, morphology, and purity of drug cocrystal can be controlled by precisely controlling milling parameters (such as material, size, speed, and time of milling medium) and experimental conditions (such as temperature and solvent). Xiao et al. [149] successfully prepared Azilsartan-nicotinamide cocrystal with a molar ratio of 1:2 by the mechanical ball milling method. By comparing the SEM images of Azilsartan, nicotinamide, Azilsartan-nicotinamide cocrystal, and the physical mixture of Azilsartan and nicotinamide (Figure 14), it can be seen that the microstructure of Azilsartan is mainly a regular cuboid structure, while that of nicotinamide is a long, rod-like structure. The crystal morphology of typical Azilsartan blocks and long niacinamide rods can be clearly observed in the images of physical mixing, indicating that Azilsartan cannot interact with niacinamide by physical mixing alone. In the Azilsartan-nicotinamide cocrystal image, there are loose block-broken crystals of varying sizes that are completely different from Azilsartan and nicotinamide, which further indicates that ball milling produces new crystal morphology.

4. Summary and Outlook

Crystal morphology has a great influence on crystal product performance and downstream processes. This work provides a systematic and comprehensive review of crystal morphology regulation. In the future, crystal morphology control will continue to be an important issue in the field of crystalline materials.

Researchers are still trying to develop new techniques to regulate crystal morphology and optimize process parameters to obtain a more ideal crystal morphology. With the proposals of limiting carbon dioxide emissions and becoming carbon neutral, a more environmentally friendly crystallization process is also a major direction of future development. From the perspective of crystal morphology regulation, it is worth considering the development of some low energy-consuming methods, such as designing more effective tailor-made additives [150]. However, a thorough understanding of crystal growth theory and the accurate construction of the growth model is a long-standing challenge. The rise of model prediction has profoundly changed people’s understanding of crystals. Compared with high-throughput screening experiments, simulation is a more convenient way to provide molecular and micro-scale interpretation of experimental results. However, existing models have their limitations under different conditions. In the past 30 years, it seems that crystallographers have preliminarily established the relationship between micro-structure and macroscopic mechanical properties, while many interactions are often neglected in classical MD simulations due to the real complex crystal growth environment and unclear effects of various reaction reagents.

In summary, although crystal morphology control is an important subject in the area of crystal engineering and great progress has been made in past years, comprehensive and precise crystal morphology control is still quite challenging and much more research work needs to be carried out to better understand the crystal growth process and to develop better technology.