Modeling Olanzapine Solution Growth Morphologies

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Modeling Olanzapine Solution Growth Morphologies yuanyuan sun, Carl J. Tilbury, Susan M. Reutzel-Edens, Rajni M. Bhardwaj, Jinjin Li, and Michael F. Doherty Cryst. Growth Des., Just Accepted Manuscript • DOI: 10.1021/acs.cgd.7b01389 • Publication Date (Web): 12 Dec 2017 Downloaded from http://pubs.acs.org on December 14, 2017

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Crystal Growth & Design

Modeling Olanzapine Solution Growth Morphologies Yuanyuan Sun1,2, Carl J. Tilbury2, Susan M. Reutzel-Edens3, Rajni M. Bhardwaj3, Jinjin Li1,*, & Michael F. Doherty 2,* 1

National Key Laboratory of Science and Technology on Micro/Nano Fabrication, Department of

Micro/Nano Electronics, Shanghai Jiao Tong University, Shanghai 200240, China. 2

Department of Chemical Engineering, University of California, Santa Barbara, CA 93106, United States.

3

Small Molecule Design & Development, Eli Lilly and Company, Indianapolis, Indiana 46285, United

States.

Correspondence

and

requests

for

materials

should

be

addressed

to

J.L.

([email protected]) or to M. F. D. (mfd@ ucsb.edu)

Abstract The ability to predict crystal growth habits is an important component of drug design, enabling a targeted sweep of optimal growth conditions that confer desirable properties. This article presents an investigation into the shape of olanzapine crystals grown from various solvents, exemplifying how mechanistic models of spiral growth can be applied to small molecule therapeutics. Olanzapine is recognized as the most effective treatment for schizophrenia, but a mechanistic treatment of the underlying crystal growth has yet to be established. We model spiral growth of olanzapine form I from five solvents (acetone, ethyl acetate, toluene, methyl isobutyl ketone and n-butyl acetate), considering a dimeric growth unit and periodic bond chains

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consisting of inter-dimer bonds. The centrosymmetric dimers are stabilized by multiple C-H… contacts. The {1 0 0} face family dominates the predicted crystal habits, in agreement with our experiments; this morphology stems from the in-plane hydrogen bonds that are exposed on the {1 0 0} surface. The close agreement between predicted morphologies and experimental determinations lends support to the hypothesis that olanzapine grows as a dimer from these solvents. This mechanistic treatment can be readily applied to other compounds.

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Introduction Schizophrenia is a severe chronic psychotic disorder that causes significant functional impairment and a severe reduction in the quality of life.1-3 Both pharmacologic and psychological treatments are employed to address these symptoms, and the former is typically viewed as more effective, with antipsychotic medications as the mainstay.4,5 After much exploration, olanzapine has emerged as the therapeutic of choice for treating schizophrenia, due to its demonstrated efficacy.6 Although olanzapine represents the state-of-the-art, its growth mechanism and crystallization behavior are not fully understood, in part due to the complexity of its molecular structure. Olanzapine

(2-methyl-4-(4-methyl-l-piperazinyl)-10H-thieno-[2,3b][1,5]benzo-

diazepine) can form polymorphs, hydrates and solvates, resulting in a complicated manufacturing process and diverse solid-state forms.7

The building block of all known

olanzapine crystals is a molecular dimer stabilized by multiple weak C–H…π contacts.8-10 There are three fused rings (diazepine, phenyl and thiophene) and one additional piperazine ring in the olanzapine molecule as shown in Fig. 1, with the middle seven membered diazepine ring adopting a distorted boat conformation.11 The dispersion-bound dimer is rather compact, its packing leaves exposed H-bonding groups (donor NH and acceptor N) and void spaces which can accommodate many different small organic solvent molecules, leading to solvate solid forms. Olanzapine crystallizes in three polymorphic anhydrates (I, II, III), three polymorphic hydrates, a higher hydrate and many pure and mixed solvates.12 Among the anhydrous forms, form I is monotropically the most stable and can be obtained by direct crystallization from suitable anhydrous solvents that are less amenable to solvate formation, such as ethyl acetate, acetone, toluene, n-butyl acetate and methyl isobutyl ketone. Metastable forms II and III have 3 ACS Paragon Plus Environment


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been concomitantly produced by desolvation of solvates, as well as by sublimation; pure samples of form II and III have not been produced to date. The solubility of olanzapine in water is very low, which is why an organic solvent is used in the manufacturing process. Since form I is most stable, it is the preferred pharmaceutical solid form. The crystallization process influences many fundamental properties of the resultant drug, including chemical purity and composition, polymorphic state, crystal size and shape distribution, etc. Size and shape distributions in turn influence many solid properties, such as end-use efficacy, e.g., bioavailability for pharmaceuticals,13 reactivity for catalysts,14 flowability, wettability,15-17 and adhesion.18 As a consequence of the impact of crystal morphology on a material’s properties, control of crystallization is essential for effective downstream blending and compaction of drug particles. In order to scientifically engineer the shape of crystalline solids, significant efforts have been undertaken in recent decades to understand and effectively model the underlying crystal growth mechanisms.19-24,26-28 For the controlled production of pharmaceutical compounds from solution, the 2D nucleation and spiral growth mechanisms are most relevant. For organic molecular crystals, these models provide useful insight to design materials and guide experiments. Our group at UCSB has contributed to the development of a general mechanistic model to predict the crystal morphologies of organic molecules (for both centrosymmetric and non-centrosymmetric growth units) grown from different environments (including vapor or solutions), via the surface growth mechanisms of spirals and twodimensional nucleation.19-25 These models capture the effect of factors such as temperature, solvent and supersaturation by accounting for the fundamental surface growth physics and interfacial chemistry. These models have furthermore been successfully applied by Koo and coworkers for many crystalline explosives.26-28 The Small Molecule Design and Development 4 ACS Paragon Plus Environment

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team at Eli Lilly and Co. has extensive experience crystallizing olanzapine from solution, where olanzapine form I is grown commercially by cooling crystallization from ethyl acetate.29 Our two teams have joined in this collaboration to crystallize olanzapine from several solvents, to predict its morphology from those same solvents, and to compare the results. Although the technological processes for olanzapine are relatively mature, from the perspective of fundamental understanding, fewer reports exist on experimental morphologies or the growth mechanism; correspondingly, to our knowledge there are no crystal habit predictions of olanzapine grown from solution. Crystal growth happens at the interface between the crystal surface and the solution or vapor. During the process of crystallization, the building blocks can be a single molecule (i.e., monomer) or several molecules stabilized by e.g. intermolecular bonds (a molecular cluster, typically existing as a dimer). The propensity to crystallize as a monomer or dimer can depend on both polymorph and solution environment. For example, as evidenced by solution diffusion data and surface diffraction, the crystallization of α-glycine from aqueous solution proceeds via incorporation of cyclic, hydrogen-bonded dimers,30-31 while the γ-form in acid or base solutions crystallizes as a monomer. For benzoic acid and tetrolic acid, FTIR spectroscopy also supports the conclusion that nucleation of a dimer is favored kinetically as a result of the preexistence of dimers in solution.32 The aforementioned dimers are hydrogenbonded with strong intermolecular (intra-dimer) interactions stabilizing the molecular pair and rendering it as the most favorable lattice building block. According to theoretical calculations, the binding energy of the olanzapine dimer is 8.68 kcal/mol,8 which indicates a similarly strong intermolecular interaction, although it is not formed from hydrogen bonds. Furthermore, PIXEL calculations indicate that this dispersive-interactionstabilized dimer could be the growth unit in olanzapine crystallization.7 Based on the strong 5 ACS Paragon Plus Environment


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intermolecular binding interaction, we consider this dimeric growth unit in modeling both the vapor crystallization and solution crystallization of olanzapine form I from acetone, ethyl acetate, toluene, methyl isobutyl ketone and n-butyl acetate. Due to its complicated molecular structure and ability to form various solvates and hydrates, it presents an interesting, industrially relevant system to study and benchmark the predictive utility of these mechanistic models. Of particular interest is accounting for dimeric growth, which we expect given the strength of the intra-dimer interactions and propensity for dimers to exist in solution. Thus, the application of mechanistic models and periodic bond chains (PBCs) consisting of dimeric growth units is a principal focus of this article. The following sections describe the experimental morphologies and the morphological predictions using the spiral growth model for dimeric olanzapine form I.

Experimental Morphologies Form I single crystals were grown by slow evaporation from a short list of solvents that have yet to form solvates with olanzapine:7 ethyl acetate, n-butyl acetate, acetone (dry), methyl isobutyl ketone, and toluene. Olanzapine solutions were freshly prepared, filtered through 0.45 micron Millex PTFE filters, then stored in covered petri dishes in a dark refrigerator at 5 °C (to minimize chemical decomposition) to allow for slow solvent evaporation. Depending on the solvent, single crystals grew in hours to days, in some cases to mm dimensions, from the solutions. The morphology of the form I crystals was captured, in the mother liquors when possible, by polarized light microscopy using an Olympus SZH Zoom stereo microscope, equipped with an Olympus SZH-D.F. Plan 0.75X objective and interfaced with a PaxCAM2 digital camera and PC. In all cases, the crystals of form I were rhombic and the {1 0 0} faces dominant. 6 ACS Paragon Plus Environment

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X-ray powder diffraction (XRPD) data were collected for samples (5-10 mg) placed on Si based low background sample holders, using a Bruker D8 Advance reflection diffractometer, equipped with a CuKa source (λ=1.54056 Å) and a Lynxeye detector, and operating at 40 kV and 40 mA, with a 0.2 mm divergence slit and an auto-changer. Data were collected in the range 240° with a 0.02° 2θ step size and 0.2 s step-1 count time. Experimental data were processed using MDI Jade 2010 (vs. 3.5.7). The XRPD patterns for crystals grown from these five solvents are reported in Fig. 2, together with the reference pattern for form I. The similarity of these patterns to the reference indicates that form I was grown from each solvent.

Predicted Morphologies Olanzapine form I crystallizes in the space group P21/c with four molecules in the unit cell. The cell parameters are a = 10.38 Å, b = 14.83 Å, c = 10.56 Å, β = 100.62° (UNOGIN01).9 We first calculated the intermolecular interactions within the lattice, using ADDICT (Advanced Design and Development of Industrial Crystallization Technology)22 and applying the AMBER force field33,34 as implemented by our group at UC Santa Barbara. The partial charges for each atom were obtained using GAUSSIAN0335 with the restrained electrostatic potential (RESP) model.36 The centrosymmetric olanzapine dimers with mass centers located at (0.5, 0.5, 0.5) and (0.5, 0, 1) were selected for the unit cell, as shown in Fig. 3.9 We then calculated interactions between olanzapine dimers in the solid state in order to determine periodic bond chains representing the strongest directional repeated interactions. The calculated lattice energy for dimer growth units is -26.73 kcal/mol (per mol of monomers), while it is -35.28 kcal/mol for a monomeric growth unit. The difference between these two lattice energies provides the binding energy for olanzapine dimers: -8.54 kcal/mol. Wawrzycka-Gorczyca et al. calculated the intra7 ACS Paragon Plus Environment


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dimer binding energies as -8.68 kcal/mol, at MP2 level of theory;8 the close agreement indicates that the applied AMBER force field is accurate enough for the present system. In order to predict the crystal shape for olanzapine, normalized step velocities on each Fface in the solid state were calculated and used to form expressions for spiral rotation times. The rotation times were used to calculate relative growth rates between various face families and determine the steady-state crystal shape via the Frank-Chernov condition (see eq. S13-S14).37,38 F-faces are crystal faces with two or more periodic bond chains. To determine periodic bond chains, we first calculated the inter-dimer solid-state interactions. Calculating aggregate interdimer interactions requires summation of four intermolecular interactions (each molecule in dimer 1 interacts with each molecule in dimer 2). For solution growth, the interfacial energy is calculated to account for the presence of solvent molecules. This treatment considers both pure solute and solvent cohesive energy penalties, in addition to the favorable contribution from the work of adhesion at the interface.19,39 The internal crystalline and solvent bonds must be broken to form a surface, which explains the cohesive energy penalty, and new crystal-solvent bonds form and deliver the adhesive energy reward (see eqs. S16-S18). The pure surface energies are divided into dispersive and acid-base components in order to quantify the degree to which matching interactions can exist at the surface. This division uses the force field components for the solid-state interactions and solubility parameters for the solvent-side interactions (see eq. S15, and values of solubility parameters in Table 1).40 As shown in eq. S17-S18, the interfacial energy between solid and solvent is calculated as the cohesive energy of each phase minus the interfacial work of adhesion. After obtaining bond energies in solution, periodic bond chains (PBCs) constructed from the strong repeating inter-dimer bonds were generated, and F-faces with two or more PBCs were found. We only include bond chains for which | | ≥ 8 ACS Paragon Plus Environment

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0.3 / (≈ ⁄2, ≈ 0.5 per bond), because edges with lower bond energy do not form identifiable steps on the crystal surface. There are seven F-face families with two or more PBCs:{1 0 0}, {1 1 1}, {0 1 1}, {1 1 0}, {1 2 0}, {0 2 0}, and {1 0 2}. Among these F-face families, {1 0 0}, {1 1 1} and {0 1 1} are the three slowest growing. The PBC bond energies for these faces are listed in Table 2 (the force field components for the PBC bonds are reported in Table S1), and the bonding structures for them are shown in Fig. 4. The corresponding results for the other faces can be seen in Fig. S1. As shown in Table 2, compared with the base solid-state bond energies (which correspond to vapor growth), the values for most PBCs are reduced for each solvent, indicating the stabilizing influence of solvent on crystal growth. The work of adhesion can be large if either significant dispersive interaction matching between the solid and solvent exists across the interface, or if there is potential for favorable crystal-solvent hydrogen bonding. From Table 2, it can also be seen that the [011] edge family ([011], [011], [01 1], [011]) typically represents the most stable edges (strongest kinkdirection interactions) under all solvents. The strength of the [011] edge family stems from the solid-state hydrogen-bonding interactions that exist between dimers (this distribution of hydrogen bonds is illustrated in Fig. 5 for the {100} face). Table 2 also indicates which edges remain on the steady-state spiral shapes predicted for each face, under each solvent. Eqs. S1-S2 were used to obtain kink densities and step velocities resulting from these solid-state interactions that form PBCs of centrosymmetric olanzapine dimers; these simple expressions are applicable due to the symmetric interaction environments present. Relative growth rates of F-faces are then calculated using eqs. S10-S14. Kink energies, kink densities, critical lengths, and face growth rates (relative to the {100} family) for the {1 0 0}, {1 1 1} and {0 1 1} faces are presented in Table 3, with intermediate data and corresponding results for the other faces reported in the SI. 9 ACS Paragon Plus Environment


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In vapor and all solvents studied, the {1 0 0} face family represents the slowest growing faces with greatest expression on the predicted steady-state morphologies. The surrounding faces in vapor growth are predicted to be the {0 1 1} family, generating a regular platelet crystal habit (shown in Fig. 6). For solution growth, however, the surrounding faces are instead predicted to be the {1 1 1} and {0 1 1} face families, except in toluene; this still produces rhombic crystals with the {1 0 0} faces dominant (see Fig. 7). For toluene, the only existing surrounding face family is {1 1 1}, due to different solvent effects. The predicted spiral shapes for vapor growth are shown in the SI. For all studied growth conditions, the remaining F-face families ({1 1 0}, {1 2 0}, {0 2 0} and {1 0 2 }) are predicted to grow out of the steady-state shape. These morphologically unimportant faces have high relative growth rates because of the generally lower values of kink energies within the slice, which produce high kink densities and low critical lengths, both of which lead to relatively short spiral rotation times, and thus larger normal growth rates. According to a recent article,41 crystals of olanzapine form I grown from ethyl acetate solution were indexed. The experimental crystal shape was observed to be rhombic with dominant {1 0 0} faces, and surrounding faces belonging to the {1 1 1} and {0 1 1} families. Therefore, our predictions agree well with the experiments. From the spiral growth rate expression there are three natural groupings of mechanistic parameters that primarily depend on solvent, crystal face, and supersaturation, respectively (see eq. S22). All quantities can be readily calculated except for (a solvent dependent parameter). To compare predicted growth rates between solvents we report ⁄ for the dominant face family (see Table 4). The detachment work anisotropy (i.e., differences in ∆ between solvents, or equivalently, differences in solubility between solvents) is the primary cause of differences


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between these predicted normalized growth rates. Table 4 indicates that on the basis of values of ⁄ , the (100) face grows fastest in toluene and slowest in acetone. Absolute growth rates will depend on the individual values of in each solvent (note, is related to the exponential of the free energy barrier for attachment of growth units at kink sites). Thus, we also report relative attachment rate constant values ( , arbitrarily assigning in toluene as unity) that would

make the (100) face grow equally fast in each solvent. In acetone, for example, would need to be ~ 106 times larger than for toluene in order for both solvents to produce similar absolute growth rates for the (100) face. Until such time as can be routinely calculated, Table 4 is the best estimate of relative growth rates for olanzapine crystals in different solvents. To test the accuracy of our predicted steady-state crystal habits, we grew olanzapine form I from five different solvents—acetone, ethyl acetate, toluene, methyl isobutyl ketone and nbutyl acetate by slow evaporation. These morphologies are shown in Fig. 7, alongside the theoretical predictions under spiral growth. For each solvent, the model predictions align well with the experimentally observed rhombic platelets.

Conclusion The successful prediction of olanzapine form I crystal habits grown from solution lends support to the hypothesis of a dimeric growth unit and operation of a spiral growth mechanism. This strongly bonded dimer is stabilized by multiple C—H…π contacts. The {100} face family dominates predicted shapes for all solvents. For solvents with larger polar and hydrogen bonding solubility parameters, the surrounding face families belong to {0 1 1} and {1 1 1}, while for nonpolar toluene, there is only surrounding face family {1 1 1}. Solvent modified bond energies



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are highest in acetone and smallest in toluene, suggesting the rate of crystallization may be faster for toluene (though anisotropic desolvation kinetics could still reverse that trend). The {100} face family exposes solid-state hydrogen-bonds, offering a mechanistic explanation for its morphological dominance. Ultimately, mechanistic modeling offers a powerful tool for engineering pharmaceutical compounds, providing insight into potential shape modification through fundamental theoretical understanding.

Supporting Information Mechanistic growth model and parameters used to predict the crystal shapes in vapor growth and all five solvents, bonding structures for all the F-faces, predicted spirals in vapor and additional illustrations of the crystal shape grown from all five solvents.

Acknowledgements The authors are grateful for the financial support provided by Eli Lilly and Company, Pfizer, Novartis, the National Natural Science Foundation of China (No. 51672176) and the Intergovernmental International Scientific and Technological Cooperation of Shanghai (No. 17520710200). We thank an anonymous reviewer for very helpful suggestions.

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Ternary Amino Acid Solutions. J. Cryst. Growth 1991, 110, 26-33. 31. Gidalevitz, D.; Feidenhans’l, R.; Matlis, S.; Smilgies, D.-M.; Christensen, M. J.; Leiserowitz, L. Monitoring In Situ Growth and Dissolution of Molecular Crystals: Towards Determination of the Growth Units. Angew. Chem., Int. Ed. Engl. 1997, 36, 955959. 32. Davey, R. J.; Dent, G.; Mughal, R. K.; Parveen, S. Concerning the Relationship between Structural and Growth Synthons in Crystal Nucleation: Solution and Crystal Chemistry of Carboxylic Acids As Revealed through IR Spectroscopy. Cryst. Growth. Des. 2006, 6, 1788-1796. 33. Case, D. A. AMBER 10; University of California: San Francisco, 2008. 34. Cornell, W. D., Cieplak, P., Bayly, C. I., Gould, I. R., Merz, K. M., Ferguson, D. M., Spellmeyer, D. C., Fox, T., Caldwell, J. W., Kollman, P. A. J. Am. Chem. Soc. 1995, 117, 5179-5197. 35. Frisch, M. J. Gaussian 03, Revision C.02. 2003. 36. Bayly, C. I.; Cieplak, P.; Cornell, W.; Kollman, P. A. A Well-Behaved Electrostatic Potential Based Method Using Charge Restraints for Deriving Atomic Charges: The RESP Model. J. Phys. Chem. 1993, 97, 10269-10280. 37. Chernov, A. A. Crystal Growth Forms and Their Kinetic Stability. Sov. Phys. Cryst. 1963, 7, 728-730. 38. Frank, F. C. In: Growth and Perfection of Crystals; Doremus, R. H.; Roberts, B. W.; Turnbull, D. Eds.; Wiley: New York, 1958. 39. Tilbury, C. J., Green, D. A., Marshall, W. J., Doherty, M. F. Predicting the Effect of Solvent on the Crystal Habit of Small Organic Molecules. Cryst. Growth Des. 2016, 16, 16 ACS Paragon Plus Environment

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2590-2604. 40. Barton, A. F. M. Solubility Parameters. Chem. Rev. 1975, 75, 731-753. 41. Warzecha, M; Guo, R.; Bhardwaj, R. M.; Reutzel-Edens, S. M.; Price, S. L.; Lamprou, D. A.; Florence, A. J. Direct observation of templated two-step nucleation mechanism during olanzapine hydrate formation. Cryst. Growth Des. DOI: 10.1021/acs.cgd.7b01060



Page 18 of 28

Figure 1. Molecular structure of olanzapine.


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Figure 2. XRPD data for olanzapine form I grown from toluene, n-butyl acetate, methyl isobutyl ketone, ethyl acetate, and acetone. (Form I-reference means the calculated XRPD pattern using the form I crystal structure (UNOGIN03) taken from the CSD)



Page 20 of 28

Figure 3. The olanzapine unit cell containing two centrosymmetric dimers.

Figure 4. Bonding structures of different F-faces for olanzapine dimers (a) {1 0 0} face, (b) {1 11} face, (c) {0 1 1} face (with graphic axes shown in the picture). 20 ACS Paragon Plus Environment

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Figure 5. The distribution of hydrogen bonds between olanzapine dimers within the {1 0 0} face.



Page 22 of 28

Figure 6. Crystal habit prediction for sublimation growth of olanzapine form I. ({1 0 0} face family in yellow; and {0 1 1} face family in pink)


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Figure 7. Comparison between predicted and experimentally observed morphologies of olanzapine form I grown from (a) acetone, (b) ethyl acetate, (c) toluene, (d) methyl isobutyl ketone and (e) n-butyl acetate. ({100} face family in yellow, {1 11} face family in blue, and {0 1 1} face family in pink)



Page 24 of 28

Table 1. Solvent information: molar volume (V" , cc/mol), dispersion solubility parameter (δ) , (cal/ mol)-/. ), polar solubility parameter ( δ/0 , (cal/mol)-/. ), hydrogen bonding solubility parameter (

δ1 , (cal/mol)-/.

),

scale

factor

(f),

and

surface

energies

(

2303 , erg⁄cm.). Solvent

V"

δ)

δ789

δ1

f

2303

Acetone

74.0

7.6

5.1

3.4

0.10

20.39

Methyl isobutyl ketone

125.8

7.5

3.0

2.0

0.10

17.52

Ethyl acetate

98.5

7.7

2.6

3.5

0.12

22.74

n-butyl acetate

132.5

7.7

1.8

3.1

0.12

21.90

Toluene

106.8

8.8

0.7

1.0

0.153

28.49


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Table 2. Energetic interactions for olanzapine, organized by face and edge. Solid-state (vapor growth) interaction strengths are listed, in addition to solvent-modified interactions. Bond energies refer to interdimer interactions and each PBC edge is responsible for two opposing edges of the resulting spiral surface structures (i.e., positive and negative directions). Bold typeface indicates the edges that remain in the steady-state spiral surface structures. Total PBC bond energy (kcal/mol) Face

{1 0 0}

{1 1 1}

{0 1 1}

Edge Vapor

Acetone

Ethyl acetate

Toluene

n-butyl acetate

Methyl isobutyl ketone

[001]

-5.76

-3.42

-2.34

-1.41

-1.85

-1.41

[011]

-14.60

-5.50

-4.61

-4.70

-4.37

-5.00

[01 1]

-14.60

-5.50

-4.61

-4.70

-4.37

-5.00

[101]

-3.02

-2.81

-2.23

-2.08

-1.94

-1.35

[211]

-2.80

-1.42

-0.92

-0.39

-0.70

-0.58

[011]

-14.60

-5.50

-4.61

-4.70

-4.37

-5.00

[100]

-7.70

-3.04

-1.92

-0.20

-1.47

-1.75

[211]

-2.80

-1.42

-0.92

-0.39

-0.70

-0.58

[011]

-14.60

-5.50

-4.61

-4.70

-4.37

-5.00



Page 26 of 28

Table 3. Predicted relative growth rates of olanzapine form I grown from ethyl acetate, acetone, toluene, n-butyl

acetate

and

methyl

isobutyl

ketone.

(h

is

the

step

height

in

Å;

Φ< is the kink energy in kcal/mol; ρ is the kink density; lc is the critical length in Å; R is growth rate of

each face relative to the {100} family under the same solvent) Faces

{1 0 0}

{1 1 1}

{0 1 1}

h

10.21

7.08

8.50

Edges

Vapor

[001]

[011]

[01 1]

[101]

[211]

[011]

[100]

[211]

[011]

Φ

Modeling Olanzapine Solution Growth Morphologies

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