Four-circle diffractometer with three-axis energy analysis

The structure of the cage compound 5-hydroxy-7,10-dimethyltetracyclo[,9.O4,8]decan-2-one (C12H16O2) at 30K

R.H. Fenn, M.S. Lehmann, O.S. Mills, C.I.F. Watt and S. Whitworth, Acta Cryst. C45 (1989) 423-428.

The use of crystallographic data to map reaction pathways is well established for interactions of nitrogen and oxygen nucleophiles with carbonyl, both in bond formation and cleavage. Could a similar analysis by structural correlation be applied to the reduction of ketonic carbonyl by hydride addition?

A number of polycylic hydroxyketones, containing sterically constrained 4-hydroxycyclohexanone or 4-hydroxycycloheptanone substructures which rearrange by a 1,4 hydride shift on treatment with base (Fig. 2), were prepared. Rates of rearrangement of the derived alkoxides had been determined, as had the X-ray crystal structures of derivatives of some of the hydroxyketones. Crucial to the analysis of the correlations were the positions of the potentially hydridic hydrogens at the alcohol methine, and should ideally be determined by neutron diffraction. This experiment was the first such determination of the structure of a reactive hydroxyketone.

4466 Bragg reflections were scanned in six days to give 3196 unique reflections that were used for refinement of the positions and anisotropic thermal displacement parameters of the 30 independent atoms (271 parameters).

The asymmetric unit contains two molecules, and each molecule is one half of a dimer generated by a centre of symmetry. The refinement showed that corresponding bond lengths and angles within the two independent molecules are nearly identical except for the opposing torsional rotations of H(12) and H(26) about C(1)-O(12) and C(15)-O(26) respectively (Fig. 3).

This analysis gave clear evidence of steric compression of the potential hydride donor and accepting carbonyl. Somewhat surprisingly there was no evidence of any adjustment in molecular geometry to show coupling between the functional groups, a result attributed to the weaker hydridic character of this alcohol compared to its salts.

I. Fehst, M. Paasch, S.L. Hutton, M. Braune, R. Böhner, A. Loidl, M. Dörffel, Th. Narz, S. Haussühl, and G.J. McIntyre, Ferroelectrics 138 (1993) 1; G.J. McIntyre, M. Paasch and A. Loidl, Acta Cryst. B, Submitted.

Mixed crystals of betaine phosphate, (CH3)3NCH2COO.H3PO4 (BP), and betaine phosphite, (CH3)3NCH2COO.H3PO3 (BPI), exhibit a disordered polar state over a wide concentration range. These are hydrogen-bonded structures where for the two end members the hydrogen bonds order along linear chains at sufficiently low temperatures, and weak interactions across the chains determine whether the ordered state is ferroelectric (BP) or antiferroelectric (BPI). Dielectric and specific heat experiments on mixed crystals, (BP)1-x(BPI)x, show that for 0.2 < x < 0.8 the electric phase transitions are suppressed to give frustrated polar states at low temperature.

The first stage in the study of this complex system is the determination of the high-temperature disordered and low-temperature ordered structures of the end members, and characterisation of the transitions. Diffraction measurements were made on non-deuterated samples of volume 30-40 mm3 at a wavelength of 1.26Å. 1500 to 3000 reflections were needed to solve the structure of each phase, which contains ~27 to ~54 unique atoms. In both compounds the polar states arise by ordering of hydrogen atoms within bonds linking the phosphate or phosphite groups, accompanied by sizeable structural changes in these groups. Only two atoms of the 28 (BP) or 27 (BPI) in the asymmetric unit are directly involved in the phase transition (Fig. 4).

Fig. 3. The high-temperature disordered structure of betaine phosphite at 295 K, with the ordering hydrogen atoms marked

In betaine phosphite the space group symmetry is lowered from P21/c to P21 with no change in the unit cell, and only small contributions to the few new reflections h 0 l, l = 2n+1. Indeed, confirmation of the true low-temperature structure was only possible by Fourier techniques (Fig. 5). The solution was slightly easier for betaine phosphate since a doubling of the unit cell along the a-axis occurs.

Fig. 4. Fobs Fourier maps for betaine phosphite at 10K with phases from refinements with, a) H(13) and H(15) attached to different PO3 groups, b) H(13) and H(15) attached to the same PO3 group. There is a clear preference for structure a).

S. Bates, C. Patterson, G.J. McIntyre, S.B. Palmer, A. Mayer, R.A. Cowley & R. Melville, J. Phys. C: Solid State Phys. 21 (1988) 4125; R.A. Cowley, D.A. Jehan, D.F. McMorrow & G.J. McIntyre, Phys. Rev. Lett. 11 (1991) 1521; D.A. Jehan, D.F. McMorrow, R.A. Cowley & G.J. McIntyre, Europhys. Lett. 17 (1992) 553.

The discovery in the mid-eighties of long-period commensurate magnetic structures in holmium rekindled intense interest in the magnetic structures of the heavy rare-earth metals. Most of the neutron studies on holmium have been made on D10, first with no field applied, later with fields applied along the propagation vector of the high-temperature incommensurate phase or along the easy axis.

Fig. 6 is a plot of linear scans along 1 0 l as a function of temperature in zero field. The intensity scale is logarithmic and spans nearly four orders of magnitude! 1 0 0 and 1 0 1 are nuclear reflections, 0+ denotes the fundamental satellites of the basal-plane helix that propagates along c, and +1+ and +2+ are effectively satellites of the fundamental satellites and are due to spin slips in the otherwise continuous helix (Fig. 7). 2q and 3q are higher-order harmonics of the fundamental satellites and are attributed in part to asphericity in the magnetisation distribution. A marked feature of Fig. 6 is the occurrence of a number of temperatures at which the different peaks cross one another, and which correspond to long-period commensurate structures.

Fig. 6. The model for the spin-slip structure with q = (1/5)c*

The complex magnetic structure of holmium is due to competition between the exchange interaction which favours simple (sinusoidal) incommensurate ordering and the crystal-field interaction which favours formation of commensurable structures. Application of a magnetic field alters the balance between these interactions producing modifications of the zero-field structures, and even completely new types of magnetic order, such as the helifan, predicted by Jensen and Mackintosh and observed in holmium when the field is applied along the easy b axis (Fig. 8).

Fig. 5 The helifan (3/2) structure in holmium ??

Existence of two length scales in magnetic critical scattering in CeAl2

T. Chattopadhyay & G.J. McIntyre, Physica B 234-236 (1997) 682-684.

M. Vergnat, S. Houssaini, C. Dufour, A. Bruson, G. Marchal, P. Mangin, R. Erwin, J.J. Rhyne & C. Vettier, Europhys. Lett.14 (1991) 457.

Traditional techniques for the determination of hydrogen and deuterium profiles in amorphous silicon have a resolution of 100 Å at best, and are thus limited to studies of long-range diffusion. In the first experiment of its kind the hydrogen motion over very short distances was studied on D10 by taking advantage of the greatly different coherent scattering amplitudes of the H and D isotopes to observe the variation with time of H and D concentrations in multilayer Si:H/Si:D/Si:H/Si:D... samples with 45 Å thick layers.

A periodic modulation of the scattering amplitude density can be expanded in a Fourier series, each term of which gives rise to a pair of satellites of Bragg reflections in a crystalline material. In an amorphous material, only the 000 forward scattering peak and its satellites are observed. A typical scan measured in the high-resolution triple-axis configuration set to zero-energy transfer is shown in Fig. 9. In the kinematical approximation the diffusion coefficient can be obtained from the decay rate of the first-order satellite. The integrated intensity of this satellite was measured during isothermal annealing at various temperatures as a function of time (Fig. 10).

The measured diffusion coefficients are much smaller than the values usually quoted and confirm that microvoids due to H-related configurations (Si-H, Si-H2 or Si-H3) play an important role. The non-linearity of the observations (Fig. 10) could be accounted for by dispersion of the diffusion with the attempt frequency.

S.Lefebvre, F. Bley, M. Fayard & M. Roth, Acta Metall. 29 (1981) 749.

Ni3Fe is a fcc alloy which, like Cu3Au, forms a L12 ordered structure below Tc ~ 500° C. Above Tc there is only local compositional ordering of Ni and Fe which gives rise to temperature-dependent diffuse scattering extended throughout the entire Brillouin zone, due mainly to a modulation of the Laue diffuse scattering by an interference function I(k). I(k) is a sum of the short-range-order intensity ISRO and of static displacement intensities I1 and I2. ISRO remains unchanged from zone to zone, while I1 and I2 increase linearly and quadratically in reciprocal space, which allows the three terms to be separated experimentally. The high-temperature disordered states are retained on quenching which allows them to be studied at lower, more convenient, temperatures where the thermal displacement factors are smaller. Neutrons are necessary because of the very similar X-ray scattering factors of Ni and Fe. The contrast for neutrons is further improved if the isotope 62Ni is used.

The diffuse scattering was measured in steps of 0.1 in the reciprocal cell indices in the low-resolution triple-axis configuration in the complete minimum volume for separation of ISRO, I1 and I2 (100 to 203) for samples quenched at 385°C and 535°C., and over the minimum volume for ISRO alone for several other temperatures. The intensity distribution at each temperature could be Fourier transformed to obtain the Warren-Cowley short-range order parameters almn or fitted by least-squares to a theoretical model (Fig. 11).

The signs of the Warren-Cowley parameters of successive shells are the same as in the long-range ordered state; the local order thus weakens without discontinuity (Fig.12). The static displacements due to local order are negligibly small, as expected for the very similar electronic structures of Ni and Fe.

J.L. Baudour & M. Sanquer, Acta Cryst. B39 (1983) 75; C. Zeyen, Physica 120B (1983) 283.

Biphenyl (C12H10) consists of two phenyl rings connected by a single C-C bond (Fig. 13). At low temperature the molecules become non-planar with a torsion angle ~10°, as a result of competition between ortho-hydrogen intramolecular repulsions and intermolecular packing forces. The modifications in the low-temperature phases are in fact incommensurate with the high-temperature planar structure, and are modulated in the amplitude of the torsion, in the angular phase between the planes of successive molecules, and in the relative translations of successive molecules.
A model for the modulation in the simpler phase III, where the modulation is purely along b*, was derived from analysis of the integrated intensities of the main and satellite reflections measured in the 'conventional' diffraction configuration (Fig. 14).

Excitations in the modulation of an incommensurate phase were expected, specifically wave-like thermal fluctuations in the phase (phasons) and in the amplitude (amplitudons) of the modulation. The technique of choice to detect these is inelastic scattering, but certain observation is difficult. D10 is occasionally used for preliminary inelastic experiments, particularly when 3-D access in reciprocal-space is necessary to find the scattering plane of interest. One such experiment, on biphenyl, revealed for the first time the propagating phase waves in the incommensurate phase III, which together with the amplitude waves were later investigated in more detail on conventional triple-axis spectrometers.

B.Roessli , J.Schefer , G.Petrakovskii, B.Ouladdiaf , M.Böhm , U.Staub, A. Vorotinov and L.Bezmaternikh.
Phys. Rev. Letter, (2001).

Magnetostatic measurements such as specific heat and susceptibility have revealed two phases transitions in CuB2O4 at TN=21K and T*=10K. CuB2O4 crystallises in space group I-4 2d( D2h). The chemical contains 12 formula units. The Cu2+ ions occupy two non-equivalent sites namely Cu(A) at 4b site (local symmetry ) and Cu(B) at 8d site (local symmetry 2). The neutron diffraction on single crystal measurements were carried out using the four-circle diffractometer D10 with lamda=2.36Å. Below TN =21K, the intensity of some nuclear Bragg peaks and specially the forbidden reflections (110) and (0 0 2) increase with decreasing the temperature, which indicates that CuB2O4 orders antiferromagnetically with a propagation vector k =0. The magnetic structure for this commensurate phase was determined with the help of group theory.
The relevant irreducible representations of the magnetic structure ( k=0) are those of the point group . There are five irreducible representations. Four of them are one-dimensional (G1, G2, G3, G4) and one labelled G5 is two-dimensional. The reduction of the induction representation gives G4b = G3 + G4 +2 G5 and G8d = G1 + 2G2 +G5 +2G4+ 3G5 for Cu at site 4b and 8d respectively.
The magnetic modes of G3 and G4 of the 4b site correspond to a collinear ferromagnetic and antiferromagnetic ordering along the z-axis respectively. The modes associated with G5 describe a 90° configuration in the basal plane. Similar magnetic modes for 8d site can be deduced. A set of 25 pure magnetic reflections was used in the refinement at T=12K. The magnetic structure, which is obtained from these calculations, can be described as a non-collinear arrangement of both the Cu(A) and Cu(B) spins along the diagonals of the tetragonal plane (Fig. 1).

The value of the magnetic moment is 1mB for the Cu(A) with a small component along the c-axis m=0.25mB. The Cu(B) spins are confined within the ab-plane and have a small magnetic moment m=0.25mB. The magnetic moments do not compensate and therefore a small spontaneous ferromagnetic component arises in the basal plane.
Below T*, new magnetic satellites appear at symmetrical points with respect to the commensurate reciprocal lattice points. The corresponding propagation vector is =(0,0,0.15) at T=1.8K. This indicates that the magnetic structure becomes incommensurate along the c-axis. Figure 2 shows the thermal dependence of the 0 0 2 reflection and the corresponding satellites. The refinement of the neutron data shows that the magnetic structure of CuB2O4 below T*=10K consist of an helix with a constant amplitude and phase shifts between different spins in the unit cell.
At the incommensurate-commensurate transition, the propagation vector (T) goes smoothly to zero. The transition is of second order. Therefore it is not likely that competing interactions are at the origin of the helical structure. In such case a first order phase transition and a jump in the wave vector is produced.

Symmetry analysis of the chemical structure of CuB2O4 shows that the DM-interaction is allowed between two Cu(A)- nearest-neighbour spins, with a DM-vector parallel to the tetragonal c-axes. The role of this interaction in forming the magnetic ground state in copper metaborate is confirmed by the 90° configuration of the magnetic moments in the commensurate phase as the DM- interaction favours a non-collinear spin arrangement.
According to Dzyalloshinskii's theory the presence of an additional crystal anisotropy distorts the regular helical arrangement of the spins along the helical axis. In order to minimise the free energy, the spins acquire a phase dependence j(z) of the helix which is given by a solution of the non-linear sine-Gordon differential-equation. The solution of this equation describes a situation where the phase of the spins along z will stay almost constant over a given length L but changes abruptly over a short period x (Fig. 3). Changing the temperature changes the anisotropy term, which causes on the other hand an increase of L. Close to the phase transition T*, the magnetic structure can be represented as a periodic structure of domains which are separated by domain walls or equivalently solitons.

The soliton lattice is further confirmed by the appearance of higher order harmonics and considerable diffuse scattering near the central peaks in agreement with the calculation of Izyumov.