research papers Acta Crystallographica Section B

Structural Science, Crystal Engineering and Materials ISSN 2052-5206

E. J. Chan,a* Q. Gaob and M. Dabrosb a

Solid State Modelling and Simulation, Materials Science, Drug Product Science and Technology, Bristol-Myers Squibb, 1 Squibb Drive, New Brunswick, NJ 08903, USA, and bSolid State Chemistry, Materials Science, Drug Product Science and Technology, Bristol-Myers Squibb, 1 Squibb Drive, New Brunswick, NJ 08903, USA

Correspondence e-mail: [email protected]

Understanding the structure details when drying hydrate crystals of pharmaceuticals – interpretations from diffuse scattering and inter-modulation satellites of a partially dehydrated crystal Simplified models for the crystal lattice of the sesquihydrate form of the hemi-sulfate salt of (5S,6S,9R)-5-amino-6-(2,3difluorophenyl)-6,7,8,9-tetrahydro-5H-cyclohepta[b]pyridin9-yl 4-(2-oxo-2,3-dihydro-1H-imidazol[4,5b]pyridin-1-yl)-1piperidine carboxylate (BMS-927711, C28H29F2N6O3+) are used to calculate diffuse diffraction features in order to develop a mechanistic understanding of the dehydration process with respect to disruption of the lattice, since a Bragg model cannot be established. The model demonstrates that what we observe when the water leaves the crystal is partial transformation from the parent form to a child form (a new form, less hydrated and structurally related to the parent). Yet this ‘dried’ structure is not a pure phase. It consists of semirandom layers of both child, parent and an interfacial layer which has a modulated structure that represents a transitory phase. Understanding the fact that a single ‘dried’ crystal can have the disordered layer structure described as well as understanding mechanistic relationships between the phases involved can have implications in understanding the effect of common large scale bulk drying procedures. During the development of BMS-927711, difficulties did arise during characterization of the dried bulk when using only routine solid-state analysis. The material is now better understood from this diffraction study. The diffraction experiments also reveal intermodulation satellites, which upon interpretation yield even more structural information about the crystal transformation. The model suggests the mechanism of transformation is laminar in which layers of the crystal are driven to approach a stable B-centered supercell phase of lower water content.

Received 16 January 2014 Accepted 6 March 2014

1. Introduction

# 2014 International Union of Crystallography

Acta Cryst. (2014). B70, 555–567

The hydration behavior of crystalline active pharmaceutical ingredients (APIs) is of high importance in the pharmaceutical industry. This is due to the fact that the state of hydration affects the physical properties of the API, in turn having a great impact on drug processability (e.g. scale-up considerations) and drug product performance (i.e. stability, solubility and bioavailability). Characterization of bulk materials during drying is often performed using powder X-ray diffraction (PXRD), whereby a reference standard representative of different stages of the drying procedure can be constructed. The expected PXRD of any known phase can be obtained from a well characterized and phase-pure bulk or it can be calculated from knowledge of a crystal structure using a single-crystal diffraction experiment, the latter being more favorable. Challenges exist when the analytical references do not match pre-conceived expectations. For example, one can be faced with a situation where doi:10.1107/S2052520614005125

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research papers the bulk is incompletely dry and varying degrees of both anhydrate and hydrate phases can be identified. Certain ambiguities arise where the bulk can be considered to have phases classed as non-stoichiometric hydrates (Authelin, 2005). Quite often real structural information about the nature of these dehydrated phases is elusive as the parent hydrate can have a propensity to form any number of partially hydrated phases that can be difficult to characterize (Kang et al., 2011). Ideally, drying of single crystals prior to elucidation by singlecrystal X-ray Bragg diffraction experiments (SXD) can be performed (Day et al., 2005). Understanding the hydration of organic crystalline solids has a vast scientific background comprising a variety of thermodynamic, kinetic and structural understandings (Petit & Coquerel, 1996; Renou et al., 2009; Galwey, 2000; Authelin, 2005). In addition to calorimetric studies (e.g. differential scanning calorimetry, DSC), solid-state nuclear magnetic resonance (SSNMR) and vibrational spectroscopy are widely accepted as methods to examine the behavior of variable hydration and associated structure disorder (Chakravarty et al., 2010; Byard et al., 2012). In the following report we demonstrate a novel supplementary analysis to complement the above-mentioned methods for the structural characterization of dehydrated phases. In order to gain this further insight we perform a

single-crystal diffraction experiment with the intention of identifying and interpreting non-Bragg diffraction features. We are able to reproduce these diffraction features from computer models that represent differing degrees of lattice disorder and modulation. Thus we can identify mechanistic relationships between changes in the lattice structure that occur as a result of the drying process. Our methodology is conceptually similar to a study by Welberry (Welberry et al., 2011) whereby an interpretation for the lattice disorder in a protein structure is made without any knowledge of the Bragg structure. Generally, the interpretation of diffuse or non-Bragg scattering features from dehydrating crystalline materials is not an entirely new idea, yet within the scope of molecular systems the literature is limited to the studies of the diffuse component from PXRD (Bates et al., 2007). This report is the first of its kind combining the study of dehydration and non-Bragg scattering features from a single API crystal. To demonstrate the usefulness of this analytical technique as applied to industry, we base our report on diffraction images uncovered during investigations into the dehydration behavior for the hemi-sulfate form of BMS-927711 (described further below) which has a parent form that is a sesquihydrate. From the results we envisage that the mechanism of the dehydration process for this compound involves layers of the crystal drying in an ordered fashion to form a new child phase (a lower hydrate). The bulk is envisaged to comprise of crystallites which have disordered layers of these different phases and the interfacial region between parent and child layers can be described by layers of a modulated phase.

1.1. Description of API parent structure

Figure 1 Packing diagrams depicting the BMS-927711 hemi-sulfate sesquihydrate structure. Blue and green circles highlight the positions of water and sulfate, respectively. (a) View down the c axis, water molecules lying on the twofold axis are superimposed on the sulfate and not highlighted for the purpose of clarity. (b) View down the a axis. Disorder in the fluorinated pendant ring is visible in the latter and highlighted using black arrows.

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The crystalline material of present interest is the sesquihydrate form of the hemi-sulfate salt of (5S,6S,9R)-5-amino-6(2,3-difluorophenyl)-6,7,8,9-tetrahydro-5H-cyclohepta[b]pyridin-9-yl 4-(2-oxo-2,3-dihydro-1H-imidazo[4,5-b]pyridin-1yl)-1-piperidinecarboxylate (BMS-927711, Scheme 1). This API molecule was a candidate as a calcitonin gene-related peptide (CGRP) agonist for use in the treatment of migranes. The crystal structure of the parent was derived from a routine Bragg scattering experiment (details described in x2). In this structure the molecules are found to pack in the space group P21 21 2, with the sulfate units positioned on twofold axes. The API molecules in the structure do not hydrogen bond with Acta Cryst. (2014). B70, 555–567

research papers each other; rather, sulfate-(O) atoms interact primarily as hydrogen-bond acceptors via protonated amine-(N) groups of the molecule and, also, intercalated lattice water molecules. Packing diagrams depicting prominent hydrogen bonding and the relevant positions of water and counterions are shown in Fig. 1. The water molecules in the lattice are positioned such that one sits at a special position on the twofold axis parallel to c (above or below the sulfate) and another occupies an equivalent position close to the sulfate, the water and sulfate thus constituting channels along the c axis. It is difficult to predict which water is most likely to leave the structure during dehydration from geometrical interpretations because of the fact that all the water molecules are seen to be in close proximity with the API and sulfate species, and, also, displacement parameters for the two water sites are very similar. Preliminary molecular mechanics (MM) and DFT calculations examining lattice-energy differences against modified structures with and without selected water sites suggest that neither water is bound appreciably more strongly than the other. The structure does suggest that the likely path which the water molecules would enter/exit the crystal is through the {001} surfaces. 1.2. Background for interpretation of diffuse scattering and inter-modulation satellites

The diffraction of X-rays by crystals can be split into two components: (i) the Bragg component which contains long-range order information is a result of the average of the structure-factor components, and (ii) the diffuse component (short-range order) which results from the difference between the structure-factor components (Welberry, 2004; Bu¨rgi et al., 2005). When discussed in this manner the totality of the diffraction has often been described as ‘total scattering’ (Proffen et al., 2001; Billinge et al., 2010). To truly understand the background of these specific diffraction components goes beyond the scope of this report. Nowadays recent developments in computing power and software tools (Proffen & Neder, 1997; Goossens et al., 2011) enables users with only a basic understanding of the fundamental underlying concepts to be adept at making the required practical interpretations of these lesscommon diffraction features. However, this rather intuitive process is not currently automated and often requires some creative input from the interpreter (e.g. in a report by Bond, 2012, such features had been identified yet detailed interpretations were not made). The reader should also keep in mind that in the context of diffuse scattering it is synchrotron data that is primarily used to make interpretations; however, for this study standard laboratory data was used. Most conventional crystal structure descriptors (e.g. atom parameters for the asymmetric unit) are based on long-range order models derived from the Bragg diffraction components. In these models the calculated Bragg intensities are usually refined against observed data by an analytical procedure incorporating the least-squares method. In order to calculate Acta Cryst. (2014). B70, 555–567

diffuse features a short-range order model, or at least a model that qualitatively describes the disorder that is causing these features, needs to be implemented (i.e. a Bragg structure is not always a prerequisite to obtaining useful information from the diffuse component; Welberry et al., 2011). Classical methods involve mathematical descriptions of the structure in reciprocal space (Welberry, 2004; Withers et al., 2008). Descriptions in real space can be more difficult and require more computing effort to interpret (Chan & Welberry, 2010; Chan & Goossens, 2012; Chan, Welberry, Heerdegen & Goossens, 2010). In some cases a solution to the diffuse scattering features can be obtained and also refined quantitatively (Welberry et al., 1998; Chan, Welberry, Goossens & Heerdegen, 2010). Inter-modulation satellites occur as the parent structure becomes modulated with different degrees of complexity (van Smaalen, 2007; Jansen et al., 2007), and more specifically, the structure can also be considered as quasi-periodic. These lattice modulations are long-range ordered and usually represent a wavevector in the crystal, such that the satellites are also considered as Bragg components. A very common example of a modulation is the phenomenon observed when distortion of the parent lattice occurs that can cause a break in translational symmetry and multiplication of the corresponding lattice parameter. This is usually termed commensurate if the wavelength of the modulation is commensurate with the parent lattice, otherwise incommensurate. In the latter case a higher-dimensional symmetry is often used to recover the loss of periodicity with respect to the parent structure. Another typical example of a lattice modulation is a phonon (Born & Huang, 1954). If a parent structure can be derived from the non-satellite Bragg diffraction (i.e. non-satellite reflections), and correct indexing and integration of inter-modulation satellites is performed, then the method of least squares can also be used to quantitatively refine the extended parameters for the modulation in the parent structure, which often involves describing the modulation parameters with the terms of a Fourier series (Wagner & Scho¨nleber, 2009). This approach is not always possible due to: (i) the data being inadequate for such an investigation, and (ii) the lack of an initial solution for the non-satellite structure, both of which apply to the situation in the case described here, but we could have chosen to describe the modulation by mathematical representation in reciprocal space. Instead we report on how to achieve this non-mathematically by constructing a real-space model which can describe the structural features for both the diffuse and inter-modulation components, without knowledge of the Bragg structure of the child phase (lower hydrate).

2. Experimental The experiment comprises several sections where a major component of the investigation involves the interpretation of the non-Bragg diffraction features. In this report we provide a brief overview followed by a description of the details for each of the different components of the experimental work. We Chan, Gao and Dabros



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research papers Table 1 Relevant parameters for the Bragg structure of BMS-927711 hemi-sulfate dihydrate at room temperature (300 K). Crystal data Chemical formula Mr Crystal system, space group Temperature (K) ˚) a, b, c (A ˚ 3) V (A Z Radiation type  (mm1) Crystal size (mm)

C28H29F2N6O3+0.5SO421.5H2O 610.63 Orthorhombic, P21212 296 10.9169 (9), 33.039 (3), 7.9038 (6) 2850.8 (4) 4 Cu K 1.27 0.26  0.22  0.18

Data collection Diffractometer Absorption correction

Bruker APEX-II CCD Multi-scan SADABS (Sheldrick, 2008) 0.755, 0.796 18 471, 3509, 3235

Tmin, Tmax No. of measured, independent and observed [I > 2(I)] reflections Rint max ( ) ˚ 1) (sin /)max (A

0.035 55.1 0.532

Refinement R[F 2 > 2(F 2)], wR(F 2), S No. of reflections No. of parameters No. of restraints H-atom treatment

0.038, 0.100, 1.04 3509 399 5 H atoms treated by a mixture of independent and constrained refinement 0.39, 0.18 Flack (1983) 0.01 (3)

˚ 3) max, min (e A Absolute structure Absolute structure parameter

describe the growth of the single crystal for the Bragg and diffuse diffraction experiments, followed by details of the single-crystal drying experiments. A detailed description of the construction of disorder models and computational methods is provided. 2.1. Overview

The details for the workflow of the experiments are as follows: (i) A modified single-crystal diffraction experiment is performed to obtain the frames required for precession reconstructions revealing the diffraction pattern of the parent. (ii) The crystal is dried while on the diffractometer and a further set of data frames is recollected. Interesting diffraction features from the single-crystal experiment are observed. (iii) Interpretation of these diffraction features is made through the use of computational methods.

2.2. Procedural details 2.2.1. Crystal growth and Bragg diffraction experiment. Single crystals of BMS-927711 suitable for either Bragg or diffuse scattering experiments were grown from aqueous alcoholic solutions. The crystals grow as well formed rectangular plates. Both the Bragg and diffuse data collection experiments were performed using a Bruker-AXS APEX2

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CCD system with Microstar-H Rotating anode generator (Cu ˚ ). The Bragg data were collected K radiation,  = 1.54184 A separately from the diffuse with the intention of obtaining the structure for the parent phase (see x2.2.2). The reader should note a diffuse data collection may also contain so-called Bragg intensities, but most diffuse data collections are not intended to derive the average crystal structure. Indexing and processing of the measured intensity data were carried out with the APEX2 software program suite (Bruker AXS, 2005). The structures were solved by direct methods and refined on the basis of all measured reflections using the SHELXTL suite (Bruker AXS, 2005). The derived atomic parameters (coordinates and displacement parameters) were refined through full-matrix least-squares. Data collection and selected refinement parameters are shown in Table 1. The structure coordinates are available in the supporting information.1 As depicted in Fig. 1 the 2,3-difluorophenyl substituent of the molecule is disordered in the structure over two orientations by non-crystallographic twofold rotation about the phenyl(C)—cyclohepta-(C) bond, site occupancies being 0.817 (5) and 0.183 (5). A CIF file and Bragg reflection data are also given in the supporting information. 2.2.2. Diffuse scattering/drying experiment. Data were collected as two 180 ’-scans offset by 90 in !. Exposure times were 15 s per frame at a detector distance of 55 mm. ˚ angular Precession images are generated with a cutoff of 2.0 A resolution using the precession image tool as part of the APEX2 software suite (Bruker AXS, 2005). A large crystal of BMS-927711 (dimensions > 1.0 mm), mounted on a glass fiber with epoxy was heated from 293 to 363 K over a period of 7 h and then allowed to cool to room temperature for a further 4 h. We note that moisture re-adsorption was not deemed an issue due to a sufficient dry nitrogen flow from the cryostream still present at room temperature. Preliminary thermogravimetric analysis of the sesquihydrate reveals a broad dehydration endotherm between room temperature and 373 K associated with 3.2% weight loss. Since the theoretical weight loss for the sesquihydrate is 4.4%, the applied heating protocol was therefore expected to produce some composition intermediate between a monohydrate and a hemihydrate. ’scans were collected prior to and after the heating procedure. All precession reconstructions were performed using an orientation matrix that was calculated from Bragg peaks present in the data frames collected prior to the heating. 2.2.3. Description of observed diffraction features and the child phase. The observed precession reconstructions with

appropriate zoom boxes highlighting the important scattering features are shown in Figs. 2 and 3. Inspection of the h0l section after heating reveals an intense peak offset at {h þ 0:5; 0; k þ 0:5} with respect to the parent Bragg spots. Diffuse rods exist along b in 0.5kl (Figs. 3c and e) confirming disordering of lattice layers perpendicular to the b-axis. Given that diffuse streaking occurs in 0.5kl and hk0.5 and not in the 0kl section (Fig. 2c), a stacking fault is ruled out and the crystal 1 Supporting information for this paper is available from the IUCr electronic archives (Reference: WF5109).

Acta Cryst. (2014). B70, 555–567

research papers space models that describe the positions of the atoms for an extended three-dimensional array of unit cells (Welberry, 2004; Proffen et al., 2001). Many-atom models of this type are then used to calculate scattered intensities based on the atomic form factor (Bu¨rgi et al., 2005). Models of this kind have been shown to be successful in the calculation of thermal diffuse scattering (TDS) and short-range order (SRO) diffuse scattering for disordered molecular crystal systems such as benzocaine, aspirin and paracetamol (Chan et al., 2009; Chan & Goossens, 2012; Chan, Welberry, Heerdegen & Goossens, 2010). In our work similar real-space models representative of the disordered and modulated BMS-927711 crystal are constructed so that the diffraction features can be calculated and compared with our observed precession reconstructions. The software used for construction of these models is ZMC (Goossens et al., 2011). Many trials were required to correctly account for all the significant features so that a single final model could reproduce all the important individual features. 2.3.1. Generation of inter-modulation satellites. In order to generate inter-modulation satellites a freshly written subroutine within the available FORTRAN90 program ZMC (Goossens et al., 2011) was created that allows input of the wavevector q components. The original Monte Carlo (MC) 2.3. Computational details engine of the program is not utilized; rather the workings of the program were used to construct the list of atom coordiPrevious accounts of the calculation of diffraction features nates for the crystal which are required for calculation of the for reciprocal space scattered X-ray intensities rely on real diffraction patterns. Once the q vector is input into the subroutine, knowledge of this vector and parameters associated with the specifics of the actual type of modulation can be implemented within the model crystal, e.g. changes in atom coordinates. The reciprocal q coordinate represents the direction and wavelength for the actual real space modulation. The procedure by which any modulation can be created within a real space model of any crystal using standard Cartesian coordinates, given its q is a component of the reciprocal lattice vectors {a ,b ,c } for a triclinic unit cell, is elaborated further here in a straightforward manner. Given that Cartesian coordinate lattice vectors for reciprocal space (with dimensions denoted by i; j; k) can be derived from the real-space Cartesian coordinate vectors, then Figure 2 unit-vector components of these Reciprocal space reconstructions of the observed single-crystal data before (a, b) then after (c, d) heating normalized vectors can act as (dehydration) the API sesquihydrate. (a) 0kl section, (b) h0l section. Zoom boxes are shown to the right of the h0l section to highlight the observed diffraction changes. Extra spots can clearly be seen at the direction cosines for magnitudes {h þ 0:5; 0; l þ 0:5} Bragg positions indicating a transformation from the parent structure, with weaker {A ,B ,C } of which the wavevector intensity inter-modulation satellites (white arrows) orbiting these new spots. Given that two wavevector q components of each can be used modulations exist, the satellite indicated by the white arrow in the zoom box would be at position (2 0 1 0 to represent the Q components as a 1), see text. is considered to be an intermediate phase between the parent and a child phase which is B-centered with respect to the parent. This was also shown to be the case by using the computational methods which will be described in later sections along with a more detailed dissection of these diffuse scattering features. Inter-modulation satellites about the parent diffuse streaks at 0:5a and 0:5c in h0l at the outset describe a further modulation in the a c direction, i.e. related to the B-centered phase. Modulation features are only present about those streaks which are B-centered, thus indicating that the modulation is closely related to the child phase. The satellites have been postulated as diffuse rods propagating in the b -direction alongside the parent streaks. This is attributed by observation of these features in the h0.5l section (Fig. 3d) which, prior to heating, shows no scattering features. We note that the domain sizes of the child and intermediate phases would have to be sufficiently large enough in the a and c directions to be observable in the diffraction pattern as longrange ordered layers, i.e. the diffuse rods along b , project as Bragg spots when viewed down b , at least as far as the inspection of basal sections are concerned.

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research papers Cartesian vector. Thus we obtain normalized values for the reciprocal lattice vectors ðb  cÞ ; jjb  cjj ðc  aÞ ; b^ ¼ jjc  ajj ða  bÞ : c^ ¼ jja  bjj a^ ¼

ð1Þ

Thus deriving magnitudes A ¼ fa a^i ; a a^j ; a a^k g; B ¼ fb b^i ; b b^j ; b b^k g; C ¼ fc c^i ; c c^j ; c c^k g;

projection down the b-axis, keeping in mind that this component of our model is really just four atoms. The atom coordinates from the parent structure represent the wet component of our layer, shown schematically using a blue square (Fig. 4c). A simple distortion of the atom coordinates is made to represent the dry component (i.e. red square, Fig. 4c). The basis for this is that since we do not have to understand the true nature of the structural distortion upon drying, we just need to be able to represent a structural distortion that reproduces certain aspects of the lattice transformation. After consecutive trials it was found that a displacement of atom

ð2Þ

where a^i represents the normalized Cartesian coordinate components of the reciprocal space vector a , corresponding to all such components. Then, given the reciprocal space wavevector (q) q ¼ fqi ; qj ; qk g:

ð3Þ

the wavevector expressed as Cartesian coordinate components (Q) will be Q ¼ fqi Ai ; qi Aj ; qi Ak g þ fqj Bi ; qj Bj ; qj Bk g þ fqk Ci ; qk Cj ; qk Ck g:

ð4Þ

Then given a displacement modulation the atom positions can be derived from the usual formal expressions (Jansen et al., 2007; van Smaalen, 2007), e.g. the atom displacement U can be described by U ¼ E þ Aðcosð2R  QÞÞ:

ð5Þ

This will displace atoms in the E direction with a magnitude of A in accordance with a cosine modulation with wavelength ð2=qÞ, in the q direction, where R is the Cartesian coordinates for the position of an atom in the real space parent crystal lattice. 2.3.2. Building the models. The main problem is that we do not have a structure for the B-centered child phase and we need to be able to represent this phase and the intermediate modulated phase in a single model. To account for this, firstly a model is constructed using single atoms to represent the position of the API molecules in the lattice, and secondly it is assummed that our model is composed of both ‘wet’ and ‘dry’ components. Single atoms representative of molecular positions are also appropriate for representing the desired modifications of the lattice because we do not need accurate structure-factor intensities and the speed of calculations will be much faster. The construction of the model is best appreciated with reference to Fig. 4. An O atom is used to represent the position of the API molecules in the unit cell, of which there are four units (individually colored) in the parent cell as can be clearly seen in the view down the c-axis (Fig. 4a). Because we are interested in the construction of the ac layers, we represent pictorially (Fig. 4b) the same four units, now in

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Figure 3 Reciprocal space reconstructions for the 0.5kl and h0.5l sections prior-to (a, b) and after (c, d) heating. For the sections prior to drying there are no scattering features. It is clear that the diffuse streaks are occurring at {h þ 0:5; k; l þ 0:5} coincident with the new spots at the B-centered positions in the h0.5l section. The diffuse streaking indicates disordered layer stacking perpendicular to the b-axis. A zoom box (e) better depicts the diffuse streaks that are visible in the 0.5kl section, i.e. corresponding to the B-centered phase. Clustered lumps of diffuse components match Bragg positions for the spacing (black lines) of the b-axis in the parent structure. Since inter-modulation satellites occur in the h0.5l section and they are closely linked to the phase transformation, it is postulated that these features are also streaks along the b direction. Bragg intensities in h0.5l not associated with streaking are not ascribed as streaks but rather attributed to the high degree of mosaicity about the c-axis that occurs from the drying (see Fig. 10 and the supporting information). Acta Cryst. (2014). B70, 555–567

research papers ˚ in the c direction coordinates in the dry component by +0.5 A is sufficient to reproduce the required diffraction features for our interpretations. Varieties of different layers are then

constructed in the model by using a supercell building block comprised of the wet and dry components. This supercell is simply an extension of the parent cell in the a and c directions ˚. with dimensions a = 21.8338, b = 33.0390, c = 15.8076 A Various atom locations of this supercell can comprise either the wet or dry components. The supercell representative of the B-centered child phase is depicted in Fig. 4(d). Each model crystal generated is comprised of arrays. When constructing layers of the modulated phase using the algorithm described in x2.3.1 a so-called ‘crenel’ modulation (Jansen et al., 2007; van Smaalen, 2007) is used to govern which type of atom components will be placed into the molecular locations of each layer. Instead of directly using a square wave, a variation of equation (5) is used such that a specific site-occupation factor (C) of dry components (e.g. C = 0.3, thus 30% dry and 70% wet) can be specified and then the displacement magnitude U is calibrated so that its values lie between 0.0 and 1.0. A conditional statement then assigns the wet or dry components based on this criterion and layers with different modulated structure (Fig. 5) can be generated. Note that a site occupation of 50% dry components does not imply the transition from a 1.5 hydrate to a 0.75 hydrate. To investigate the relationship between the child phase, intermediate phase and disordering of the ac layers, individual preliminary models needed to be constructed which are composed of either all modulated phase or just layers of parent and child phase. The final model of the crystal is actually a 20  20  20 supercell assembly of different layers of both child and modulated phases (Fig. 5). 2.3.3. Disorder in one dimension. A simple Markov chain formalism is used to generate the desired layer sequence required for the investigation. The implementation of such theory in investigating disorder of crystals is well presented pedagogically by Welberry (2004). For the purpose of this report, our crystal model can be described as being composed of two different layers, A and B, represented by x (using binary variables 1 or 0). Adding a layer type to site i can be represented by the conditional probability

Figure 4 Schematic diagrams for the building blocks are used to construct a model for the crystal. The view of the four API molecules in the parent cell is shown (a) down c and (b) down b. An O atom for each molecule is shown in black. The actual model is made up of these atoms which are used to represent locations of the molecules in the unit cell. (c) Unit cells are of two types, ‘wet’ (blue) or ‘dry’ (red), and these cell types are further designated into (d) different combinations of supercells. It is these supercells that are used to construct the model crystal used to perform the calculations (i.e. a larger 20  20  20 supercell array). Acta Cryst. (2014). B70, 555–567

Figure 5 Schematic diagram for the layers comprising the model crystal used. Different individual layers are comprised of the supercells depicted in Fig. 4(d). Chan, Gao and Dabros



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research papers Pðxi jxi1 Þ ¼  þ xi1 :

ð6Þ

Here  and are coefficients such that the total proportion mA of layer A is  ð7Þ mA ¼ 1 and the nearest-neighbor correlation CAA between layers is CAA ¼

PAA  m2A ¼ : mA ð1  mA Þ

ð8Þ

The probabilities ðPAA ; PAB ; PBA ; PBB Þ used for constructing the crystal can then be generated given any value of mA and CAA thus PAA ¼ m2A þ CAA mA ð1  mA Þ; PAB ¼ PBA ¼ mA ð1  mA Þ  ðCAA mA ð1  mA ÞÞ; PBB ¼ ð1  mA Þ2 þ CAA mA ð1  mA Þ:

ð9Þ

The above probabilities are implemented in a FORTRAN90 program which constructs the input files that represent the different layers (phases) in the crystal as variables that are readable by the ZMC software. The layer structure schematic used to represent differing degrees of layer disorder for the calculations of diffuse intensities is shown in Fig. 5. Given this formalism, negative correlation values will give alternating layers, e.g. ABAB, and positive correlations will give ordered stacks, e.g. AAAABBBB. A correlation of zero will give a disordered stack of layers. 2.3.4. Calculation of diffraction features from the models. All calculated diffraction projections from the models were performed using the program DIFFUSE (Butler & Welberry, 1992). In the case of the parent Bragg spot and inter-modulation satellite calculations, the total scattering for both the Bragg and non-Bragg intensities are calculated using a single lot comprising the entire representative crystal. In calculating diffuse intensities the Bragg component is removed and 64

random lots of size 5  15  5 supercells are sampled from the model and intensities averaged.

3. Results and discussion The discussion is divided into sections whereby statements concerning the interpretation of inter-modulation satellites and diffuse scattering are made. In the interest of clarity, smaller cutout sections (instead of the complete projections) of the calculated diffraction patterns are shown in the figures. The complete reconstructions for all of these cutouts which correspond to the observed patterns shown in Figs. 2 and 3 are provided as supporting information (this includes all relevant reciprocal-space reconstructions such as the h1l and h0.5l sections, i.e. confirming the diffuse scattering is not related to a simple stacking fault). The reader should note that for the intermodulation satellite interpretations, the cutout box is chosen to be offset by (h  1; 0; l þ 1) in the plane of the calculated projection with respect to the corresponding observed zoom-box section which is shown in Fig. 2 (the exact details of this are figuratively outlined in the supporting information). The reason for this is because since our model cannot perfectly reproduce relative intensities, we opted to choose a section of the calculation that best represents the effect of the lattice modulation on the first Brillouin zone. 3.1. Structural interpretations from inter-modulation satellites

Assuming water exits the crystal through [001] channels at the {001} surfaces we can begin our interpretation by considering the drying only from the perspective of a single ac layer (Fig. 6). Fig. 6 provides some description of how water at the {001} surfaces may escape through the channel and also aids in conceptualizing the structure of both wet and dry components (described in x2.3.2). Note that Fig. 6 depicts only half of the unit-cell contents of the parent building block. We must also envisage that water must diffuse from the internal core of each layer in some fashion so it can eventually exit from the {001} surfaces as depicted in Fig. 6. As a result of this loss of water, structural rearrangements will occur at various stages to eventually form the proposed Bcentered layer that was described in x2.2.3. How the intermodulation satellites provide insight into the transformation of parent to child phases for an individual layer is depicted in Fig. 7. For the purposes of an Figure 6 explanation, representations of a Molecular slices of the structure shown down b depicting how water might leave the crystal through [001] single q vector are used, yet later channels via the {001} surfaces. Water molecules are highlighted by blue dashed circles. The core of the we discuss the fact that the actual crystal will still be wet, so the distribution of water must be rearranged thus inducing the onset of the structural transformations on the path towards finally becoming the drier B-centered phase. modulation occurs as two ortho-

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research papers gonal q vectors. In this figure real-space models of individual modulated phases are represented by a red/blue schematic and the effect of the modulation on reciprocal space is shown as a corresponding cutout box of the calculated h0l diffraction pattern which can be compared with the observed h0l pattern (zoom-box) in Fig. 2. We begin with the parent form (Fig. 7a), which has a wavevector with q = (0, 0, 0) and no dry component (C = 0.0), i.e. no modulation. The onset of drying can be depicted by the model shown in Fig. 7(b), here with q = (0.3, 0, 0.3) and C = 0.1. According to our overall model for the phase transformation this represents a short-lived unstable phase which is unlikely to be observed. As the crystal continues to dry, Fig. 7(c) depicts the layer for an intermediate phase when q = (0.4, 0.0, 0.4) with C = 0.3. This is the phase that accounts for the intermodulation satellites that were observed and could likely arise from a metastable phase or be present at the boundary between parent and child phases. Fig. 7(d) represents another short-lived phase which then becomes the child phase such that the crenel function is set at q = (0.5, 0.0, 0.5) (Fig. 7e) and the site-occupation factor C must be 0.5. Hence, our structural transformation as a result of dehydration can be conceptually represented by the path of the crenel modulation from q = (0, 0, 0) ) q = (0.5, 0.0, 0.5) and the site occupation of dry components C from 0.0 ) 0.5. With reference to the layers depicted in Fig. 6(a) we can envisage the diffusion of water along the c-axis channels to create these modulated dry component regions with the necessary structural rearrangements occurring dynamically. To further elaborate, the model suggests that as the water leaves the channels there are structural forces continuously at play during the dehydration process which rearrange the molecules of the crystal, driving the creation of the child phase layers, such that the intermodulation satellite features represent an intermediate or boundary phase. It is evident that the observed diffraction pattern is actually a combination of both the child and intermediate phases. Thus,

a preliminary layer stacking model as depicted in Fig. 5 is constructed using a disordered stack sequence generated as described in x2.3.3 with an equal (50%) proportion of both of the intermediate (Fig. 7c) and child (Fig. 4d) layers in order to calculate the diffraction pattern in Fig. 8(a). It is important to realise how this combination of layers satisfies the absence conditions for where the inter-modulation satellites occur (i.e. they only originate from the parent Bragg positions). Since only a single q direction is used in the model for Fig. 7 the satellites will only be generated in one direction, yet the observation (Figs. 3e and f) shows satellites in two directions orthogonal to each other with respect to the reciprocal space cell. The most likely explanation is that there are two simultaneous and orthogonal wavevector modulations occurring (Fig. 8c) which will result in the final calculated diffraction pattern as shown in Fig. 8(b). This gives the best match to the observation. However, another possible cause for this observation is that the dried crystal is composed of twin domains rotated about the c-axis, which is justified by very high rotational smearing and mosaic spread in the (hk0) section (discussed further in x3.3). This twinning could also account for the observed satellites and it can often be difficult to differentiate between either of the two causes. The main argument in support of the former (two orthogonal q vectors) is that the vector magnitudes are always noticeably equal and consistently orthogonal, meaning that if it were twin domains which occur as a result of this drying process, then we could expect the domains to be somewhat heterogeneous so the corresponding magnitudes and orthogonality of the intermodulation satellites would not be as perfect. In order to investigate the possibility that the intermediate layer structure was comprised entirely of B-centered building blocks such as the supercell represented in Fig. 4(d), models can be assembled where the dry component of the modulated phase is constrained to such supercells (Fig. 8d) to explore whether there would be a better agreement with the obser-

Figure 7 Representation of the stages of transformation (a)–(e) from a ‘wet’ to a dehydrated phase for layers corresponding to a modulated phase with a single qvector setting (see text for further details). At the bottom of each figure is the schematic plot of the model used in the calculation and above is the cutout section of reciprocal space which was actually calculated and should be compared to the observed cutout section in Fig. 2(d). The respective values for q and concentration (C) used to construct the crenel functions are: (a) 0.0, 0.0; (b) 0.3, 0.1; (c) 0.4, 0.3; (d) 0.45, 0.3; (e) 0.5, 0.5. Given that one wavevector modulation exists, the satellite indicated by the black arrow would be at position (2 0 1 1). Acta Cryst. (2014). B70, 555–567

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research papers Table 2 Parameters required for modeling the calculated diffuse scattering shown in Fig. 9. Figure



mA

PAA

PAB

9(a) 9(b) 9(c)

0.3 0.0 0.3

0.5 0.5 0.5

0.325 0.25 0.175

0.175 0.25 0.325

vations (i.e. the two components of the crenel function are supercells which represent either parent or child phases, not the wet/dry components). Two such one-dimensional disordered layer stack models are tested where such intermediate phase layers are constrained as described (50%) also containing layers which are either: (i) all child phase or (ii) all parent phase. The corresponding diffraction patterns calculated from the models are shown as Figs. 8(e)–(f), and it is clear that the models break the required absence conditions with respect to the positions of the satellites. It is worth noting that the diffraction pattern from the second model (Fig. 8f) also still shows the effect of the B-centered supercells in the diffraction pattern even though there are no layers that are composed entirely of these B-centered cells (i.e. it is the Bcentered component of the domain brought about by the modulation that reproduces the break in the absence condition). It is clear a model for the modulated phase is in better

agreement with the former model (Fig. 8b) when the two components are the representative wet and dry unit cells. This means that a model envisaged as being made up of dry and wet components is not invalidated by the fact that we still do not know what the structure of the child phase actually is, in terms of either how much water is removed from the B-centered cell or exactly what the structural distortion of the molecules is to compensate the loss of water. 3.2. Diffuse scattering features

Calculated diffuse scattering cutouts of the 0.5kl section which correspond to the observed scattering (Fig. 3e) are shown as Figs. 9(a)–(c). Also shown in the figure is a real-space representation for the ordering of layers generated by the onedimensional Markov chain model as described in x2.3.3. Table 2 shows correlation values and probability terms required to generate the models used to calculate the Fig. 9 sections. With reference to Fig. 3(e) we notice that the diffuse streaking features are not continuous and have intensities clustered about Bragg positions. Black lines are used to indicate the spacing between this clustering of diffuse scattering and we note that the repeat along k is the same as that for the parent cell (see the 0kl section before and after drying in Fig. 2). The positional dependence of calculated diffuse intensities consequent on the different layered stacking models is an important consideration and from this we can infer the behavior of the layer fault during the drying transition. We can also infer from the clustered intensities that the layer fault is not likely to be random and we can confirm this by comparison to Fig. 9(b). The best representation is from a model with a layer stacking that is driven to be positively correlated such that layers of the same type will more likely stack next to each other (Fig. 9a). Layer types are less likely to be alternating because for this to be the case we would have expected to observe intensities to occur for Bragg positions at 0:5 k, as well as at the parent positions, depicted by the black arrows in Fig. 9c. Figure 8 Even though models have been In the current model the wet and dry components in the crenel-modulated layers are not restricted to used which represent one-dimenbeing comprised of B-centered supercells. A calculated reciprocal space section (a) occurs when the sional disorder it is highly unlikely model contains layers of both the modulated phase depicted in (Fig. 7c) and the B-centered phase. Given that one wavevector modulation exists, the satellite indicated by the black arrow would be at the position that in the real crystal such infinite (3 0 2 1). (b) Shows the output resulting from same model with two simultaneous orthogonal q taken two-dimensional layers exist. The into account. Given that two wavevector modulations exist, the satellite indicated by the black arrow purpose of the one-dimensional would be at position (2 0 2 0 1). This is the final layer model chosen that best reproduces our diffraction disorder model is for qualitative patterns with its model schematic shown in (c). Two further cases are described to test if the domains in the crenel-modulated layers are restricted to B-centered supercells. A schematic for the restricted layer interpretation. Our models calcumodel is shown as (d) and can be compared with Fig. 7(c). This model is identical to that shown in (a) only late spot sizes with a dependence that crenel-modulated domains are restricted to the B-centered supercells, the calculated reciprocal space on the given lot size for the calcusection being shown as (e). For the calculation shown in (f), modulated domains are still restricted, with no layers entirely comprised of the child phase; rather, layers of the parent phase are used. lation so the relation between

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research papers correlation length and domain size can be related to the overall two-dimensional size of the model for the crystal. Since the area of the calculated Bragg-centered diffuse features reproduced are roughly larger than those observed, this suggests that the two-dimensional layer domain sizes should be no smaller than the 20  20 supercells in a  c dimensions ( 50 nm). From the analysis it can be inferred that the real sizes are probably larger given that in the projection of the h0l section we can see that the diffuse rods will resemble Bragg

features (at least in the basal sections) without corrections for other factors such as the mosaic spread and those of the instrument. So we can conjecture that the layer size could be at the micro scale (> 1 mm or a similar scale to typical microscopic twin domains), noting that the diffuse features of the 0.5kl section are not entirely sharp along c . We could make the same inference about the size of the disordered layer domains. Given the model is 20 layer units in the b-direction ( 60 nm), clustered domains can be approximated to be no greater than half this size ( 33 nm). However, this would be even more of a rough estimate (in comparison to the former) for reasons that go beyond the scope of this report (Butler & Welberry, 1992; Proffen & Neder, 1997). To be able to perform further quantitative analysis of the diffuse scattering a highly detailed statistical model likely supported by knowledge of both Bragg structure for the child phase and X-ray diffraction data from a higher energy source (e.g. synchrotron) is suggested (Chan, Welberry, Heerdegen & Goossens, 2010). This would require computational resources that go beyond the scope of the current rapid, yet insightful, analysis as may be applicable to industry and performed on a modern day laptop. 3.3. Further interpretation

Figure 9 Results of modeling different layer stacking sequences. The bottom representation shows the schematic for the disorder in each model along b as shown in Fig. 5. The corresponding cutout of the calculated diffuse scattering for the 0.5kl section is shown above each schematic and should be compared to Fig. 3(e). The calculated features visibly show the relationship for layer stacks where there is (a) positive correlation, (b) no correlation and (c) anti-correlation. The black lines represent the repeat along k for the parent cell, with the black arrows at 0.5k. Acta Cryst. (2014). B70, 555–567

We note that reciprocal space reconstructions were also made from data acquired by breaking up the larger dried crystal into smaller fragments. One such fragment that was indexed on the diffractometer displayed no diffuse or satellite features and had a unit cell that matched the parent form (for projections and cell parameters, see the supporting information). This may suggest either that the large crystal contains substantial domains of the parent form or that the child phase can readily rehydrate back to the parent. Since the drying experiment was only performed with one crystal the question still remains as to how representative the dehydration of this crystal would be in comparison to a different crystal dried under different conditions. To further investigate this, the rest of the dried crystal was then crushed up and a suitable PXRD data collection performed. The PXRD from the dried crystal was then compared with PXRD obtained from several drying (vacuum oven) experiments so that structural inferences of the dried bulks could be made. Important similarities in the comparison of these PXRD patterns obtained by this manner were identified implying that the dried bulks of this material could be composed of crystals containing the disordered layer structure described in this article. However, since questions still remain concerning the sensitivity of the material towards rehydration under ambient conditions, such inferences remain the topic of a future study (e.g. moisture sorption kinetics). The observed rotational smearing along c represents crystallites that must be cleaved and rotated about the c-axis (Fig. 10). This suggests that the laminar ac-layer disorder occurs within crystallite components and the crystallites themselves have a higher positional variance in terms of degree of rotation from the c-axis. Since the parent structure contains a twofold axis along c then crystallites (or crystal domains) Chan, Gao and Dabros



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research papers related by this operation would be structurally invariant. Yet crystallites modulated by our previous description of a single q and then related by the twofold rotational operation would not be invariant and can represent twin domains. It can be

argued that these twin domains also represent modulation of the parent structure with orthogonal q as depicted in Fig. 8. We postulate that it is very unlikely that drying actually occurs as a single q and is always manifested as the two orthogonal vectors described due to the even magnitude of the opposing modulations (i.e. position of observable relative intensities). Also, given that the child phase is B-centered and that the water is most likely to exit via {001} surfaces through [001] channels, there is a strong geometric argument that it is unlikely the two single modulation components in the [101] direction would be separated by twin domains. This may have been more likely if the water was layered (or sitting in channels) along the [101] direction.

4. Conclusions This report has outlined the description of a novel interpretation of diffuse and satellite scattering features observed from the dehydration of a molecular crystal. The calculations can be performed using software that can operate on a single conventional laptop or desktop computer. This work provides a new structural interpretation of the solid material in question and may provide insight into better characterization of the dried bulk material which can be linked to a reference PXRD. The diffraction interpretations act as a guide which suggest that dried crystallites may have a laminar structure consisting of a disordered stack of three (structurally related) layer phases corresponding to the parent, a child (B-centered) and an intermediate (modulated) phase. The degree of disordering of the layer stacks was determined from the shape of the diffuse scattering to be correlated, meaning that the layer phases are aggregated. Our belief is that in the bulk the crystallites may be comprised of less of this parent phase and more of these other transformed layer phases which have lower degrees of hydration. Now that the nature of our structure is better understood in terms of diffraction, further drying experiments could be made in the hope of obtaining a solution to the Bragg structure of the child phase. Investigations can then be made to determine if these disorder models can be used to extract quantitative information concerning the length of the layer domains, no doubt involving more computationally intensive calculations and the use of synchrotron radiation.

Figure 10 (a) Observed reciprocal space reconstruction of hk0 section showing rotational smearing after heating the crystal. (b) Real-space representation viewed down c depicting misaligned crystallite blocks related by rotation about c with the corresponding twofold operation shown as a black ellipse. The mosaic blocks are proposed to be layers in the ac plane.

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The corresponding author would like to sincerely dedicate this work to the Professors, Mark Hollingsworth, Richard Welberry and Allan White. The hope was that the work builds upon their combined crystallography teachings in a modern and comprehensible fashion. Beth Sarsfield and Venkatramana Rao are thanked for helpful discussions. We acknowledge our ongoing affiliation with other members of the disordered materials group at the Research School of Chemistry (ANU) to which we are indebted for use of the DIFFUSE and ZMC software codes. We thank BMS for funding and use of the diffraction apparatus. Acta Cryst. (2014). B70, 555–567

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