2.1. Neutron powder diffraction at high pressure

Ambient-temperature, high-pressure neutron powder diffraction data were collected by the time-of-flight technique at the PEARL beamline high-pressure facility (HiPr) at ISIS. Approximately 50 mm³ of L-serine-d₇ was gently ground into a fine powder and loaded into a Paris-Edinburgh (P-E) high-pressure cell. The P-E cell ram pressure was monitored and controlled by means of a computer-controlled hydraulic system. The sample was loaded into a null-scattering Ti-Zr alloy capsule gasket (Marshall & Francis, 2002). A pellet of lead was included as a pressure marker.

Time-of-flight neutron powder diffraction data suitable for structure refinement were obtained by electronically focusing the 1080 individual detector element spectra of the main PEARL/HiPr 2 = 90° detector bank. The summed pattern was then normalized with respect to the incident beam monitor and the scattering from a standard vanadium calibration sample. Lastly, the diffraction pattern intensities were corrected for the wavelength and scattering-angle dependence of the neutron attenuation by the P-E cell anvil (WC) and gasket (TiZr) materials.

In order to ensure that the pressure applied to a crystal held in a pressure cell is uniform, it is necessary to immerse the sample in a medium which displays hydrostatic behaviour throughout the pressure range of interest. A 4:1 mixture of methanol and ethanol is commonly used in high-pressure work, although L-serine has some solubility in this mixture. A 1:1 mixture of deuterated pentane and 2-propanol was therefore used for an initial survey. Data were collected in approximately 0.7 GPa steps from 0.1 GPa to a final pressure of 4.3 GPa. Peak broadening occurred above 4.3 GPa, suggesting that conditions became non-hydrostatic at high pressures.

Based on our previous work on crystal growth from solutions at high pressure, the solubility of L-serine was expected to decrease at elevated pressures (Fabbiani et al., 2005). In order to extend the pressure range for this study a second sample of L-serine was loaded with a 4:1 mixture of MeOD:EtOD as the hydrostatic medium. Diffraction data were collected in approximately 1 GPa steps from 4.6 GPa to a final pressure of 8.1 GPa. On increasing pressure to 5.2 GPa, the phase transition from L-serine-I to L-serine-II was observed, a transition which we have observed previously in a single-crystal high-pressure X-ray diffraction experiment on a non-deuterated sample of L-serine-I (Moggach, Allan, Morrison, Parsons & Sawyer, 2005). On increasing pressure further to 8.1 GPa, another phase transition was observed to a hitherto uncharacterized phase of L-serine which we have designated L-serine-III.

2.2. Structure solution and refinement

Powder-pattern indexing, structure solution and Rietveld refinements were carried out using TOPAS-A (Coelho, 2005). Rietveld refinement of phases I and II was carried out starting from the 4.8 and 5.4 GPa coordinates of Moggach, Allan, Morrison, Parsons & Sawyer (2005) for L-serine-I and L-serine-II, respectively.

The structure of the new phase (L-serine-III) was indexed on an orthorhombic unit cell, a = 6.5574, b = 9.5397, c = 5.6101 Å, in the space group P2₁2₁2₁ using the method of Coelho (2003). The structure was then solved by simulated annealing. The crystal structure of phase III could be re-solved to yield the same structure in repeated simulated annealing runs. The same solution was also obtained by the refinement of phase II coordinates: the difference between the phases largely lies in the orientation of the hydroxyl group and the two structures are similar enough that one can be refined into the other. During refinement the serine molecules were treated as variable metric rigid groups using the Z-matrix formalism available in TOPAS.

Lead (included in the sample as a pressure marker), tungsten carbide and nickel were also included in the refinement models. The weak tungsten carbide and nickel peaks both arise from the P-E cell anvil cores which consist of cemented WC with a Ni binder. The refined cell dimensions of lead were used to calculate the applied pressure using a Birch-Murnaghan equation-of-state (Birch, 1947) using V_o = 30.3128 Å³, B_o = 41.92 GPa, B' = 5.72. These parameters were derived by Fortes (2004) as averages of the values in Kuznetsov et al. (2002), Miller & Schuele (1969) and Waldorf & Alers (1962).

All intramolecular bond distances and angles were constrained to their ambient pressure values for all but the hydroxyl group, whose O-D distance and C-O-D angle were refined. All torsion angles were also refined. All N-D and C-D distances were constrained to 1.009 and 1.083 Å, respectively. All non-H atoms were refined with a common isotropic displacement parameter; the displacement parameters of the D atoms were equal to 1.5 times this value. The final Rietveld fits are shown in Fig. 1. Unit-cell dimensions and refinement parameters for L-serine-I at 4.6 GPa, L-serine-II at 5.2 and 7.3 GPa, and L-serine-III at 8.1 GPa are included in Table 1.¹ Fourier difference maps calculated after the removal of some atoms returned the positions of the same atoms again; the success of this test attests to the quality of the data measured.

Crystal structures were visualized using the programs MERCURY (Bruno et al., 2002) and DIAMOND (Crystal Impact, 2004). Analyses were carried out using PLATON (Spek, 2003), as incorporated in the WIN-GX suite (Farrugia, 1999). Hirshfeld surface analysis was performed using the program CrystalExplorer (Wolff et al., 2005).

3.1. The response of L-serine-I-d₇ to 4.5 GPa

We have previously investigated the response of L-serine-I to pressure using single-crystal X-ray diffraction (Moggach, Allan, Morrison, Parsons & Sawyer, 2005). Boldyreva et al. (2005) also studied L-serine-I to 4.4 GPa, obtaining similar results. While deuterated materials can sometimes display different phase behaviour to their perhydrogenated analogues, the response of deuterated L-serine-d₇-I is essentially the same as that of L-serine-h₇-I up to 4.6 GPa. On increasing pressure to 5.2 GPa, the sample underwent a phase transition to L-serine-II. The phase transition from L-serine-I to L-serine-II is marked by a sudden decrease in volume (Fig. 2).

3.2. Description of phases I and II

We have discussed the structures of L-serine-I and II in detail in Moggach, Allan, Morrison, Parsons & Sawyer (2005), and our motive for including a summary here is to highlight hydrogen-bonded motifs relevant to the development of L-serine-III, described below.

C(5) chains are formed in both L-serine-I and II along c by N1D5O2 hydrogen bonds (Figs. 3a and b). A second C(5) chain, generated from the first via a 2₁ operation, is linked to the first through N1D6O1 hydrogen bonds, and together the N1D5O2 and N1D6O1 interactions form ribbons containing successive R₃³(11) ring motifs. The CD₂OD side chains are distributed along the outside edges of these ribbons. In L-serine-I these link the ribbons into a layer via ODODOD interactions (Fig. 3a). In L-serine-II the ribbons are connected into a layer by O3D7O2 hydrogen bonds formed between the alcohol and carboxyl moieties (Fig. 3b). The graph-sets thus-formed are R³₃(13) and R²₃(13), and the layers are stacked along the a axis in both phases.

The layers are linked together in both phases I and II by N1D4O2 interactions, which build another primary-level C(5) chain. The combination of the N1D5O2 and N1D4O2 C(5) chains along a and c builds a third set of secondary-level ring motifs, those having the descriptor (Figs. 4a and b). In fact, these chains can be viewed as building up another layer, which is parallel to the ac plane. Overall, the structure consists of two sets of layers: one stacks along a and contains R³₃(11) and R³₃(13) ring motifs, the other stacks along b and contains R³₄(14) rings. In Moggach, Allan, Morrison, Parsons & Sawyer (2005) we referred to these as the A and B layers, respectively.

3.3. Comparison of L-serine-I at 4.5 GPa and L-serine-II at 5.2 GPa

One difference between L-serine-I and -II is the position of the hydroxyl H atom. In our original X-ray study the position of this H atom was rather imprecisely determined, but our conclusions are confirmed by the present neutron study. The OO and DO distances in the O3D7O2 hydroxyl-carboxyl hydrogen bonds in phase II are substantially shorter than the O3D7O3 hydroxyl-hydroxyl hydrogen bonds in phase I (Table 2).

The conformations of the rings in L-serine-I and -II represent a second difference between the crystal structures of the two phases. Voids observed in L-serine-I-d₇ at 4.6 GPa at the centres of the ring motifs are closed-up on undergoing the transition (Figs. 5a and b). This is accomplished by:

(i) a displacement along the +c and -c directions by successive C(5) chains formed by N1D5O2 hydrogen bonds, and (ii) a shortening of the distance between the chains along the a direction (Figs. 6a and b).

The opposite directions of displacement of the C(5) chains break the O3D7O3 hydroxyl-hydroxyl hydrogen bonds which are replaced by O3D7O2 hydroxyl-carboxylate hydrogen bonds in phase II.

CDO contacts are also more numerous in L-serine-II than in L-serine-I. All C-H bonds act as donors in two hydrogen-bonding interactions which span the R²₃(13) and rings (Table 2, Figs. 3b and 4b).

3.4. L-Serine-II between 5.2 and 7.3 GPa

As the pressure on L-serine-II is increased from 5.2 to 7.3 GPa, the largest compression occurs along the a direction, with the a axis decreasing in length by 2.7%; the b and c axes reduce by only 0.6 and 0.8%, respectively. The relative displacement of the N1D5O2 C(5) chains and the reduction in the distance between the chains both continue up to 7.3 GPa, leading to further compression of the voids within ring motifs (Figs. 6a and b, and 5c).

In the most compressible NDO hydrogen bond, N1D5O1, the DO distance decreases by 0.075 (11) Å between 5.2 and 7.3 GPa. This hydrogen bond is the longest of its type at 5.2 GPa, and its shortening increases the bifurcation in the interaction N1D5O1/O2. N1D6O1, which is short anyway at 5.2 GPa, remains relatively unchanged. The largest change occurs for O3D7O2, which was formed in the transition from phase I to phase II: by 7.3 GPa the OO distance in this contact measures only 2.516 (17) Å, which is very short. Although it is short, O3D7O2 is unsymmetrical, with O3-D7 and D7O2 measuring 0.97 (2) and 1.56 (3) Å, respectively.

The shortest OHO hydrogen bond found under ambient pressure conditions [2.474 (2) Å] occurs in the CSD refcode AMHACY (Leban, 1974). This, however, corresponds to a symmetrical hydrogen bond where the H atom is shared equally between adjacent carboxyl groups from neighbouring molecules. Strong hydrogen bonds of this type are common when formed between acids and complementary bases (Steiner, 2002). If this search is limited to hydrogen-bonding interactions between a free hydroxyl group donor (bonded to an alkyl CH₂) and carboxyl group acceptor, the shortest interaction observed under ambient conditions measures 2.584 (2) Å for GOLWIN (Tusvik et al., 1999). The O3D7O2 hydrogen bond therefore appears to be pushed to below this lower limit observed under ambient pressure conditions, and on increasing pressure further the structure undergoes another phase transition to a second high-pressure phase, L-serine-III.

3.5. Structure of L-serine-III at 8.1 GPa

The phase transition from L-serine-II to L-serine-III, unlike that from phase I to II, occurs with only a modest decrease in volume (Fig. 2d); the volume per non-H atom at 8.1 GPa is only 12.5 Å³. Overall the structure is closely related to the structures of phases I and II (Figs. 3c and 4c), and the structure can again be considered in terms of layers which stack along the a and b directions.

The ring motifs in the B layers appear longer and thinner than they do in L-serine-I and -II (Figs. 4b and c), and over the course of the II-to-III phase transition the relative displacement of neighbouring N1D5O2 C(5) chains in the +c and -c directions continues (Fig. 6a). The associated compression along the a direction also continues (Fig. 6b) and at 8.1 GPa there are no visible voids within the rings (Fig. 5d). Small voids present at the centre of R²₃(13) ring motifs of the A layers remain essentially unchanged through the transition, while no observable voids can be observed at the centres of R³₃(11) ring motifs in phase II or III.

The phase transition from L-serine-I to L-serine-II was, in part, characterized by a change in the hydrogen bonds formed by the hydroxyl group, O3D7. A further change in hydrogen bonding in this region of the structure also occurs in the transition from phase II to phase III. In phase II the hydrogen bonding from O3D7 was confined to one A layer, but in phase III the hydrogen bonding from D7 becomes bifurcated between the same O3D7O2 interaction that was present in phase II, and a new O3D7O1 hydrogen bond which connects different A layers together. This change in the hydrogen-bonding environment of the O3D7 group may explain the findings of Kolesnik et al. (2005), who observed that the largest changes in the Raman spectra of L-serine on undergoing the transition from phase II to III occurred in bands at 1250 (HOC bend) and 1430 cm^-1 (CO₂ sym. str). When viewed in projection the A and B layers seem very similar in phases II and III: the difference lies in the way they are connected together and this is clearer in the c-axis projection illustrated in Fig. 7.

The O3O2 distance within the O3D7O2 hydrogen bonds in phase II is very short [2.516 (17) Å] at 7.3 GPa and the structure presumably experiences significant strain in this region. It seems reasonable to suggest that the II-to-III transition is driven by the need to alleviate close contacts about O3 in L-serine-II as pressure is increased beyond 7.3 GPa.

In general, at elevated pressures the influence of hydrogen bonds as structure-directing interactions is expected to diminish relative to the need to pack molecules more efficiently and several of the NDO and ODO hydrogen bonds in phase III at 8.1 GPa are longer than those in phase II at 7.3 GPa. In L-serine-II the hydrogen-bonding capacity of the C-D bonds is saturated and so the transition from phase II to III does not result in an increase in number of CDO interactions, with the six interactions present in L-serine-II, still observed in L-serine-III.

3.6. Changes in CDO and DD interactions: Hirshfeld fingerprint plot analysis

McKinnon et al. (2004) have recently described how a Hirshfeld surface analysis can assist in the interpretation of differences between related crystal structures. Hirshfeld surfaces are created by partitioning space within a crystal structure into regions where the electron density from a sum of spherical atoms (the promolecule) dominates over the sum of the electron density of the crystal (the procrystal). The surfaces surround each molecule in a crystal structure, enabling various properties relating to packing to be calculated. Two such properties are d_e (the distance from the surface to the nearest atom in another molecule) and d_i (the distance from the surface to the nearest atom in the molecule itself). Plots of d_e against d_i are referred to as fingerprint plots and they encode information on the overall three-dimensional packing characteristics in a two-dimensional diagram. Fingerprint plots for the structures obtained in this study are shown in Fig. 8.

On increasing the pressure in L-serine-I to between 0.1 to 4.6 GPa, the drive to compress the hydrogen-bonding interactions is represented clearly on the fingerprint plots with d_e values driven to shorter distances (Figs. 8a and b). In particular, the two long spikes present in all fingerprint plots represent NDO and ODO hydrogen-bonding interactions, which can clearly be observed moving toward smaller values of d_e in L-serine-I (Figs. 8a and b). The number of points at larger values of d_e and d_i also decrease on increasing pressure, giving a more compact plot at 4.6 GPa; the fingerprint plot is still more compact at 5.2 GPa (Fig. 8c). This illustrates the compression of voids within R³₃(11) and ring motifs within A and B layers, respectively. A `hump' appears between the spikes at 4.5 GPa, becoming more prominent at 5.2 GPa. This corresponds to close DD contacts. The shortest of these contacts at 4.6 GPa, D3D6, forms between A layers between D atoms from CD₂ and ammonium groups of adjacent molecules, respectively. DD contacts become more numerous at 5.2 GPa, for example a D3D6 distance formed along the a direction decreases from 2.19 to 2.08 Å.

On increasing the pressure further to 7.3 GPa, the fingerprint plots look much the same, although a slight movement of the NHO/ODO spikes toward the lower values of d_e can be observed (Figs. 8c and d). The `hump' between the spikes at 7.3 GPa also appears to sharpen and move to larger values of d<sub>e</sub>. This is accounted for by the movement of the hydroxyl OD group, which at 5.2 GPa forms the shortest DD contact (D7D3, 1.91 Å). On increasing the pressure to 7.3 GPa, this close contact is actually relieved by the hydroxyl group, which twists, making the O3D7O2 hydrogen bond more linear, while increasing the D7D3 distance (1.98 Å). This movement of the hydroxyl group can be quantified by comparing the D7-O3-C3-C2 torsion angle at 5.2 GPa (-178.5°) and 7.3 GPa (+172.3°). Nevertheless, on increasing pressure to 7.3 GPa, the number of close DD contacts does increase, represented in Fig. 8(d) as an increase in the green colour within the `hump' region of the plot.

At 8.1 GPa the spikes corresponding to NDO hydrogen bonds appear at larger values of d_e; this is caused by the increased lengths of NDO and ODO contacts in phase III referred to above (Figs. 8d and e). We have suggested above that the II-to-III transition is driven by the need to relieve short intermolecular contacts, and the similarity of the volumes of phases II and III suggests that the transition does not result in markedly more efficient packing. However, there is a pronounced increase in the number of close DD contacts between the spikes in the fingerprint plot shown in Figs. 8(d) and (e). Close contacts between H atoms are characteristic of the fingerprint plots obtained for alkanes (McKinnon et al., 2004) and in serine their gradually increasing prominence illustrates much more graphically than tables of data the tendency for efficient packing to compete with hydrogen bonding as structure-directing phenomena.