Engineering of the XY Magnetic Layered System with Adeninium Cations: Monocrystalline Angle-Resolved Studies of Nonlinear Magnetic Susceptibility

An original example of modular crystal engineering involving molecular magnetic {CuII[WV(CN)8]}− bilayers and adeninium cations (AdeH+) toward the new layered molecular magnet (AdeH){CuII[WV(CN)8]}·2H2O (1) is presented. 1 crystallizes within the monoclinic C2 space group (a = 41.3174(12), b = 7.0727(3), c = 7.3180(2) Å, β = 93.119(3)°, and V = 2135 Å3). The bilayer topology is based on a stereochemical matching between the square pyramidal shape of CuII moiety and the bicapped trigonal prismatic shape of [WV(μ-CN)5(CN)3], and the separation between bilayers is significantly increased (by ∼50%; from ca. 9.5 to ca. 14.5 Å) compared to several former analogues in this family. This was achieved via a unique combination of (i) a 1D ribbonlike hydrogen bond system {AdeH+···H2O···AdeH+···}∞ exploiting planar water-assisted Hoogsteen···Sugar synthons with (ii) parallel 1D π–π stacks {AdeH+···AdeH+}∞. In-plane 2D XY magnetism is characterized by a Tc close to 33 K, Hc,in-plane = 60 Oe, and Hc,out-of-plane = 750 Oe, high values of in-plane γ critical exponents (γb = 2.34(6) for H||b and γc = 2.16(5) for H||c), and a Berezinskii–Kosterlitz–Thouless (BKT) topological phase transition, deduced from crystal-orientation-dependent scaling analysis. The obtained values of in-plane ν critical exponents, νb = 0.48(5) for H||b and νc = 0.49(3) for H||c, confirm the BKT transition (νBKT = 0.5). Full-range angle-resolved monocrystalline magnetic measurements supported by dedicated calculations indicated the occurrence of nonlinear susceptibility performance within the easy plane in a magnetically ordered state. We refer the occurrence of this phenomenon to spontaneous resolution in the C2 space group, a tandem not observed in studies on previous analogues and rarely reported in the field of molecular materials. The above magneto-supramolecular strategy may provide a novel means for the design of 2D molecular magnetic networks and help to uncover the inherent phenomena.


■ INTRODUCTION
Layered inorganic materials, e.g., magnetic, conducting, semiconducting, and so on, has gained interest owing to its high potential in construction of spintronic composites, e.g., multilayered spin valves exploiting giant magneto-resistance. In reference to and parallel to the first-choice components toward practical applications (graphene, metals, metalloids, their oxides or chalcogenides, and alloys), modern molecular and coordination chemistry quickly created a parallel extensive research field. 1,2 Very recently, various aspects of formation, flexibility, properties and application perspectives of 2D coordination polymers were very thoroughly reviewed by Vittal and co-workers. 3 Indeed, offering optical transparency, soft matter character, and generally environmentally friendly mild synthesis conditions, layered coordination networks opened a relatively easy access path toward a combination of magnetic and optical features, together with their external control. 4 Some layered coordination motifs appear systematically under particular synthesis conditions, and their functionality can be tuned using the variety of accompanying species (anions, cations, and neutral species). Thus, from the viewpoint of crystal engineering, they could be considered secondary building units (SBUs), with structural and functional properties tunable by crystallizing or cocrystallizing agents. Such an approach has been widely employed to achieve a diversity of spin-crossover (SCO) transitions in Hofmanntype M[M′ (CN) 4 ] (M = Fe II ; M′ = Ni II , Pd II , and Pt II ) clathrates, 5 19,20 tuning of LRMO in thiocyanato-bridged solid solutions [Co x Ni 1−x (NCS) 2 (ligand) 2 ] n , 21 or the very recent electrochemical modification of interlayer nanospace in newly established Cr(pyrazine) family. 22,23 A significant contribution to the field is provided by cyanide-bridged networks with recurrent modular 2D bimetallic backbones MM′·ligand·guest involving exchangeable [M′ (CN) 8 ] 3−/4− (M′ = Mo, W, Re, and Nb) and di-or trivalent 3d metal ions (Mn, Fe, Co, Ni, and Cu), or trivalent 4f ions, M. 24 Various combinations of components did operate within a limited number of topologies to shape LRMO and its anisotropy, 25−27 which was frequently accompanied by externally controlled change in solvate/guest composition, 28,29 charge transfer and spin transition phenomena, 30−34 and charge carrier injection/ extraction 35,36 (CN) 8 ]} − (M = Cu and Mn; M′ = Mo and W) bilayers constitute a good example of a systematically recurrent molecular module. The double-decker topological Prussian Blue Analogue (PBA) fragment is achieved due to a stereochemical matching between the square pyramidal (SPY-5) shape of Cu II moiety or octahedral shape of Mn II moiety, and the bicapped trigonal prism (BTRP-8) [W V (μ-CN) 5 (CN) 3 ] unit ( Figure 1). 39−47 Such double-decker fragments were previously put together by various cationic species: tetrenH 5 5+ (CuM′), 39 dienH 3 3+ (CuM′), 40 Cs + (CuW, CuMo), 41 guanidinium (guaH + ) (CuM′), 42 single Cu 2+ (CuMo,CuW), 43,44 and Mn 2+ (MnMo) 45 complexes or polymeric 1D {Cu(μ-pyz)} 2+ chains (CuM′). 46 The average interlayer distances varied between ca. 8 and 11 Å, which resulted in LRMO below T c between 27 and 43 K and coercive field H c between ca. 2500 Oe and ca. 80 Oe, both parameters decreasing with the increasing interlayer distance in the case of CuM′. The in-plane XY magnetism of a single CuW bilayer was recently exploited in the studies of inverse magnetocaloric effect (MCE) and rotational MCE (RMCE), 48 whereas the MnMo bilayers served as platforms for reversible cation (Li + ,Na + )-electron pairs injections/extractions processes, essential from the viewpoint of the fabrication of lithium batteries. 45 In this work, we make a step toward crystal engineering of coordination layered magnets using topologically advanced components. This inspiration came from the field of biochemistry: the purine-and pyrimidine-type nucleic bases offer the unique side double or triple hydrogen bond patterns owing to the specific distribution of N-heteroatoms and N−H, CO, and NH 2 functions. 49−52 Considering the above, and driven also by simple curiosity, we carried out self-assembly tests toward the formation of new solid phases involving {Cu II [M V (CN) 8 ]} − , using acidic aqueous solutions as a medium. As a result, we present the crystal structure and complete angle-resolved magnetic studies of (AdeH)-{Cu II [W V (CN) 8 ]}·2H 2 O (1) (AdeH + , adeninium cations). The new solution provides significantly enlarged interbilayer separation, possible chirality, and the occurrence of nonlinear susceptibility performance in the magnetically ordered state; the last envisaged by full-range angle-resolved monocrystalline magnetic measurements were supported by dedicated calculations.

■ EXPERIMENTAL SECTION
Precursors were purchased from commercial sources (Sigma-Aldrich, Idalia, Alfa Aesar) or synthesized using literature methods. 53 SC XRD (model 1) data were collected on BESSY II synchrotron BL14−3 beamline (Helmholtz Zentrum Berlin, Bessy II) 54 and processed with xdsapp 55,56 and CrysAlis Pro 57 (absorption correction), SHELXS and SHELX 2018/1 58 (solution and refinement), and WinGx/ROTAX 59 (solution of twinning) softwares. PXRD data (model 1p) were processed using EXPO2014 60 (indexing and preliminary structure model), FOX 61 (structure determination and optimization), and JANA2006 62 (refinement) software, considering the previous bilayer structural model 39 and CSD entries containing AdeH + cations. 63 All structural figures were prepared in Mercury. 64 Continuous shape measure analysis of coordination spheres was carried out using SHAPE 2.1. 47 The crystal structures are deposited in the CCDC database, with the deposition numbers 2058785 (model 1) and  Table S2). Such a diversity of intermolecular {AdeH + ···AdeH + } synthons and their tendency to form stacked arrangement offers the perspective of using the related infinite cationic blocklike synthons for molecular crystal engineering.
Structural Studies. The crystal structure of 1 was determined after a thorough analysis of SC XRD data obtained using synchrotron radiation (model 1). The crystal data and structure refinement parameters are presented in Table S3. Detailed information on the intralayer distances, bond lengths, angles, and types of coordination polyhedra are presented in the upper section of Table 1 and in Figure S7 and Tables S4 and S5. The topological motif of the 2D cyanidobridged network {Cu II [W V (CN) 8 ] − } n with four equatorial and one axial cyanido-bridged linkage was reproduced (Figure 4a). AdeH + cations based on CSD data (2020.1) together with their counts, including the synthon observed in 1 (e). Protonation at the N 1 atom was assumed on the basis of literature data. 65−70 The detailed constrains and the full list of structures (CSD refcodes) are presented in Figure S5 and Table S1.  Table 1. All examined parameters, the closest Cu···Cu, Cu···W, and W···W separations, together with the closest distances between the planes formed by Cu atoms (or W atoms) belonging to the neighboring layers (W planes and Figure 3. Dimeric parallel or offset parallel synthons between the adeninium cations based on CSD data (2020.1) together with their counts (a−c). The synthon observed in 1 was not observed in database until now (d). The distance between the neighboring AdeH + planes is not higher than 3.7 Å. The detailed constraints and a full list of the related CSD reference codes are presented in Figure S6 and Table S2. The average distance between the central atom and 8 adjacent atoms. c The average distance between the central atom of one bilayer and the nearest atoms from the neighboring layer. d The distance between two planes determined by positions of corresponding atoms from the first layer and from the neighboring layer. Inorganic Chemistry pubs.acs.org/IC Article Cu planes , respectively), indicate a significant increase of the interlayer separation of ca. 50% compared to the former analogues in this family. This was achieved owing to the specific molecular 2D arrangement of the adeninium AdeH + cations combining the in-plane contacts and stacking contacts, as illustrated in Figure 5 and It also confirmed a crucial role of the latter components in shaping of the interbilayer separation in 1 (for more detail, see the Supporting Information).
Chirality that could occur in the space group C2 is canceled by a 4-component twinning involving inversion operation necessary to model the crystal structure in SC XRD data analysis; however, the specific bilayer arrangement observed for the single primary grain will have substantial impact on magnetic properties. The twinning is dominated by the component obtained through the inversion operation of the original grain structure (47.5%) and completed by other minor components issued by the C 2 rotation with respect to the [100] direction (2.27%, see the description of TWIN command in the CCDC file), and by a combination of this rotation with the inversion operation (3.26%). Considering the fact that magnetization is a pseudovector (it does not change under the inversion operation), such twinning composition should not influence the magnetic properties.
Magnetic Properties. Magnetic measurements for a batch of single crystals were carried out along three orthogonal directions, H||a*, H||b, and H||c, indicated by indexing procedure and in accordance with solution model 1 ( Figure  S12). Figure 6 shows the temperature dependences of χT products with an applied field of 500 Oe. In the case of H||b and H||c orientations, a sharp increase of χT values start below 40 K, whereas for the direction perpendicular to the layer (H|| a*), a noticeable growth can be observed below 35 K. For all orientations, the maximum values were recorded at T peak = 28.0 K, reaching 1130 cm 3 mol −1 K for H||b, 1202 cm 3 mol −1 K for H||c, and 84 cm 3 mol −1 K for H||a*. It is clear that the magnetization prefers to align within the double-layer (within the bc plane), while the perpendicular direction, with the response more than 1 order of magnitude smaller, is the hard axis. However, much smaller but still noticeable differences can be observed between the two in-plane orientations. These dissimilarities are more evident in low field (50 Oe) ZFC/FC measurements (Figure 7 and S13), which show stronger difference between field-cooled and zero-field-cooled curves for H||c orientation than for those H||b. This suggests a more   Figure  S13), while the T c temperature, determined from the first derivative of ZFC susceptibility ( Figure S14), is slightly higher: T C = 32.8(2) K for H||a*, T c = 33.2(2) K for H||b, and T c = 33.0(2) K for H||c. Isothermal magnetization measurements at 2.0 K (Figure 8) indicate that 1 saturates for H||b and H||c for fields above 10 kOe at 2.0 μ B /f.u., which agrees with the expected value for the parallel alignment of the Cu II (S Cu = 1/2, g Cu = 2.0) and W V (S W = 1/2, g W = 2.0) magnetic moments per {Cu II [W V (CN) 8 ]} − unit. In contrast, the applied field in the perpendicular direction, even at 70 kOe, is too weak to reach saturation, which points to a significant magnetic anisotropy. Within a double-layer, 1 displays a rather soft magnetic behavior with the small coercive field of 60 Oe, whereas coercivity for H||a* is 1 order of magnitude higher reaching 750 Oe.
Both the isothermal magnetization and the temperature dependence of magnetic susceptibility points to a ferromagnetic behavior with significant intramolecular interactions within the bc plane. Since the interbilayer separation is substantial (about 14.5 Å) and there is no direct linkage between the planes, the most obvious candidate for interbilayer interaction is the dipole−dipole coupling.
Angle-Resolved Susceptibilities. The magnetic susceptibility was measured within three independent planes, i.e., the plane perpendicular to the a* crystallographic axis, the plane perpendicular to the b crystallographic axis, and the plane perpendicular to the c crystallographic axis, with the angle step of 5°in the applied field of 1 kOe at 2 K, using a Quantum Design Horizontal Sample Rotator and Quantum Design MPMS XL magnetometer. The raw data were corrected for diamagnetic contribution using the orientation averaged value of χ 0 ≈ −0.015 cm 3 mol −1 per formula unit (see Figures S15 and S16). The measurement results shown in Figure 9 confirm that the a* crystallographic axis corresponds to the hard magnetization direction, while the bc crystallographic plane constitutes the easy magnetization plane.
There is, however, one additional striking feature of angleresolved measurements: A rotation within the easy plane (bc) indicates the presence of a 4-fold axis, which contrasts with 2fold symmetry indicated by rotations within the planes parallel to the hard axis (a*b and ca*). This feature cannot be explained within the linear paradigm, where only the secondrank susceptibility tensor χ αβ is employed. To check if a 4-fold axis is a common feature of the Cu II −W V double-decker topological Prussian blue analogues family, angle-resolved measurement of (tetrenH 5 (Figure 10) was carried out within the ac   Inorganic Chemistry pubs.acs.org/IC Article easy plane, with respect to the direction b, and perpendicular to crystal plane. Although the crystal structures of 1 and 2 are very similar to each other, the latter compound shows only a 2fold axis. It could be that in the case of 2 the applied field is too weak to reveal the nonlinear behavior; however, this issue will be analyzed in more detail in further studies. In what follows, we will show within a simplified model that the 4-fold symmetry in 1 can be roughly reproduced assuming a higherorder contribution to the susceptibility which is nonlinear in the applied field. Let us expand the magnetization pseudovector in a series of the applied magnetic field:  with H 0 = 1 kOe and the rotation angle θ ∈ [0, 360°). We assume that the susceptibility linear tensor χ αβ is symmetric, i.e., χ αβ = χ βα , while the only nonvanishing components of the nonlinear tensor κ αβμν are those with indices bbcc and all different permutations thereof. Moreover, we assume that they are all equal as being of the same symmetry, i.e., κ bbcc = κ bccb = κ ccbb = κ cbbc = κ bcbc = κ cbcb ≠ 0. Then, a straightforward calculation using eqs 2 and 3 yields where κ = H 0 2 κ bbcc . Equations 4−6 have been simultaneously fitted to the experimental angle-resolved susceptibility data using the following test function (agreement quotient) where Ω = {a*, b, c} is the set of the rotation axes. The best fit yielded Q χ = 2.02 × 10 −2 and the set of parameter values listed in Table 3. The solid lines in Figure 8 show the best-fit curves.
One can see that the agreement with the experimental data is satisfactory but by no means perfect. The main feature of the data, i.e., the fact that rotations within the planes parallel to the hard axis (a*b and ca*, red and green, respectively, in Figure  9) reveal the presence of a 2-fold axis, while a rotation within the easy plane (bc, blue in Figure 9) indicates the presence of a 4-fold axis and is duly reproduced. However, the present model fails to reproduce the low-value kinks observed for rotations around the b axis (green in Figure 9) and c axis (red in Figure  9). This may be understandable due to the fact that the model in its present shape is crucially simplified, neglecting 75 out of 81 components of the nonlinear susceptibility tensor κ αβμν . However, the exceptionally large relative error for χ bc together with its relatively small absolute value make it practically redundant, showing that the model may be even further simplified. It is worth noting that the component χ bc would automatically vanish if one assumed that the system is composed of two sublattices transformed one into another by the 90°rotation around the hard axis (a* crystallographic axis). Then, the components κ bbcc = κ bccb = κ ccbb = κ cbbc = κ bcbc = κ cbcb ≠ 0 of the nonlinear susceptibility tensor of the fourth rank give the first nonzero contribution in its place. The {···N3− Cu−N5C5−W-C3···} ∞ and {···N2−Cu−N4C4−W-C2···} ∞ linear chains forming square grid arrangement in the bottom deck of the bilayer are also perpendicular to those in the top deck and this feature is repeated in each bilayer.
In the above model, the nonzero components of the nonlinear susceptibility tensor κ αβμν are crucial to reproduce the 4-fold symmetry axis for a rotation around the hard magnetization direction (a* crystallographic axis). At the same time, they give rise to an interesting feature of the total susceptibility tensor χ a*αβ associated with that rotation: where θ ⃗ * H ( ) a is given by the first row in eq 3. It is apparent from eq 8 that due to the nonlinear susceptibility term the total susceptibility tensor χ a*αβ becomes dependent on the orientation of the applied magnetic field expressed in terms of the rotation angle θ. Hence its eigenvalues and eigenvectors will also depend on the applied field orientation. Figures 11   and 12 show this dependence. It can be seen that the eigenvectors corresponding to the largest and the second largest eigenvalues lie in the bc easy plane and rotate in an anticlockwise sense around the a* axis with a rotation of the applied field θ ⃗ * H ( ) a . In this way, the direction of the external magnetic field coincides with the direction of the easy axis (red arrows in Figure 11) four times for angles θ roughly equal to 45,135,225, and 315°, which correspond to the local maxima of the largest eigenvalue (red symbols in Figure 12).
The quality of fit of the angle-resolved susceptibility data may be improved by adding to the present model other components of the four-rank tensor κ αβμν as well as by  Figure 11. Rotation of eigenvectors of χ a*αβ corresponding to the largest (red) and the second largest (green) eigenvalue as a function the orientation angle of the applied magnetic field θ ⃗ * H ( ) a . Figure 12. Dependence of the eigenvalues of χ a*αβ on the orientation angle of the applied magnetic field Inorganic Chemistry pubs.acs.org/IC Article extending the magnetization expansion in eq 1 to even higher orders. This is corroborated by the trigonometric polynomial approximation (see the Supporting Information). Scaling Analysis. The ordering process in 1 was analyzed with the static critical scaling of the magnetic susceptibility. To unambiguously obtain the values of γ and T C , we have used the approach described in a series of papers. 72−75 Figure 13 shows the temperature dependence of the d(ln(T))/d(ln(χT)). Linear fits above the phase transition were used to determine γ (the inverse value of the intersection point with the ordinate axis) and T C (the intersection with the abscissa axis). The fitting of critical exponents were done between ≈T c and ≈1.2T c (about 33−40 K) in case of in-plane orientations and between ≈T c and ≈1.1T c for the hard axis. Both in-plane fits points to high value of the critical exponents γ b = 2.34(6) (for H||b) and γ c = 2.16(5) (for H||c) with similar temperatures of the phase transition T C-b = 30.8(2) K (for H||b) and T C-c = 31.1(2) K (for H||c). The data for the out-of-plane orientation show a similar value of T C-a* = 32.4(2) K; however, the critical exponent for the H||a* γ a* = 0.23(2) is 1 order of magnitude lower than for the in-plane orientation. The low value of γ a* points to a very weak temperature dependence of the susceptibility for the hard axis below T C , which underlines the dominant role of the ordering within the bc plane and is symptomatic for 2D magnetism. 71 The scaling analysis in both in-plane directions (H||b and H|| c) has revealed high values of γ pointing to 2D ordering process like 2D XY (γ = 1.82) 76 or 2D XXZ (γ = 2.17(5)) 77 instead of 3D ones, which are characterized with much lower value of γ (3D Heisenberg γ = 1.385, 3D Ising γ ≈ 1.24 or 3D XY γ = 1.32). 78 The 2D character of the magnetic phase transition can be related to the Berezinskii−Kosterlitz− Thouless topological phase transition in which the bonding of vortex−antivortex pairs occurs below T BKT critical temperature. 79−81 In this case, the magnetic susceptibility follows χT = a χ e b χ (T−T BKT ) −ν with the critical exponent ν = 0.5. The above equation was used to analyze the susceptibility in both in-plane directions (Figure 14 and S19; the fitting ranges were the same as in the case of γ scaling) revealing: ν b = 0.48 (5) Ferromagnetic 2D ordering within the double-layer and the BKT-type phase transition were also recognized in our previous study of the {(tetrenH 5 ) 0. 8 71 2 reveals an LRMO below T C ≈ 33 K and the BKT phase transition with T BKT = 30.3 K and ν = 0.56 (11). The similarity between both compounds is striking: the intrabilayer separation in 1 is ca. 14.0 Å, while in 2 it is only ca. 9.0 Å. Both cases indicate that the significant anisotropy and interactions within the bilayer play the crucial roles and are responsible for the 2D ordering. However, the dipolar interactions have a minor influence on LRMO because even the sizable difference in the separation between the bilayers does not change the basic ordering parameters of both compounds.

■ CONCLUSIONS
The adeninium AdeH + monocations were successfully used in tuning of interlayer separation between the magnetic coordination {Cu II [W V (CN) 8 ] − } ∞ bilayers in 1. The cationic layers are composed of 1D infinite hydrogen-bonded ribbons engaging the Hoogsteen face and the sugar face of AdeH + together with the crystallization of H 2 O molecules; one of the topological hydrogen bond synthons existing in the structural database was reproduced in this way. These ribbons are further connected into 2D architecture by orthogonal π−π stacking, to be finally glued to the bimetallic coordination backbone via hydrogen bonds with the terminal CN − bridges. The implementation of such a blocklike arrangement led to the s i g n i fi c a n t i n c r e a s e o f s e p a r a t i o n b e t w e e n {Cu II [W V (CN) 8 ] − } ∞ bilayers, from ca. 9 to ca. 14 Å, compared to the congeners reported previously. Such combinations of polycationic blocks with polynuclear coordination complexes are relatively rare: Some examples are from the chemistry of polyoxometalates, 82,83 whereas for the first time it is observed in magnetochemistry of polycyanidometalate-based networks.
The complete angle-resolved magnetic measurements confirmed 2D character of magnetic ordering due to a strong magnetic exchange coupling between Cu(II) and W(V) spins within layers, in line with general features observed in the   First, non-negligible magnetic anisotropy was detected within the easy plane, which was not shown experimentally until now. Second, we acquired the nonlinear magnetic susceptibility in a relatively small magnetic field, which was manifested by rare 4fold symmetry of magnetization detected during the rotation within the easy plane. The observation was rationalized by the calculations using the dedicated model. The nonlinear magnetic response in a molecular magnet was also investigated by Mito et al. In their research, the [Cr (CN) 6 ][Mn(R)-pnH(H 2 O)](H 2 O) compound was measured with means of alternating current susceptibility and higher harmonics. Authors underlined the role of magnetic softness and chirality for the nonlinear response. 84 In our case, 1 does not reveal chirality; however, the soft magnetic degrees of freedom in the bc plane may play the key role in the observed magnetic nonlinear behavior.
Finally, the magnetic {Cu II [W V (CN) 8 ] − } ∞ backbone was incorporated in the crystal of the C2 space group, although the total chirality was canceled due to twinning dominated by the component reproduced by inversion symmetry. Nevertheless, further advances toward the general organization of coordination layers in the solid state can be achieved using organic components with diverse distribution of noncovalent interaction generators. The possible coexistence of BKT topological phase transition (within the regime of controlled XY magnetism) with chirality (if successfully acquired within the whole crystal) and nonlinear magnetic susceptibility offers the perspectives for systematic research on the magneto-chiral effects on the "colored" coordination backbones of the related type. 85,86 ■ ASSOCIATED CONTENT
Synthesis and basic characterization (materials and syntheses, physical techniques, AdeH + as a supramolecular tecton, SC XRD studies, PXRD studies); magnetic studies (description of all measurement; estimation of the diamagnetic corrections; trigonometric polynomial expansion for the angle-resolved data; scaling analysis); references (PDF) Accession Codes CCDC 2058785 and 2058786 contain the supplementary crystallographic data for this paper. These data can be obtained free of charge via www.ccdc.cam.ac.uk/data_request/cif, or by emailing data_request@ccdc.cam.ac.uk, or by contacting The Cambridge Crystallographic Data Centre, 12 Union Road, Cambridge CB2 1EZ, UK; fax: +44 1223 336033.