Measurement of the sign of the spectroscopic quadrupole moment for the 2(1)+ state in 70Se: no evidence for oblate shape.

Using a method whereby molecular and atomic ions are independently selected, an isobarically pure beam of 70Se ions was postaccelerated to an energy of 206 MeV using REX-ISOLDE. Coulomb-excitation yields for states in the beam and target nuclei were deduced by recording deexcitation gamma rays in the highly segmented MINIBALL gamma-ray spectrometer in coincidence with scattered particles in a silicon detector. At these energies, the Coulomb-excitation yield for the first 2+ state is expected to be strongly sensitive to the sign of the spectroscopic quadrupole moment through the nuclear reorientation effect. Experimental evidence is presented here for a prolate shape for the first 2+ state in 70Se, reopening the question over whether there are, as reported earlier, deformed oblate shapes near to the ground state in the light selenium isotopes.

Effective charges in the fp shell.

Following the heavy-ion fusion-evaporation reaction 32S+24Mg at 95 MeV beam energy the lifetimes of analogue states in the T(z)=+/-1/2 A=51 mirror nuclei 51Fe and 51Mn have been measured using the Cologne plunger device coupled to the GASP gamma-ray spectrometer. The deduced B(E2;27/2(-)-->23/2(-)) values afford a unique opportunity to probe isoscalar and isovector polarization charges and to derive effective proton and neutron charges, epsilon(p) and epsilon(n), in the fp shell. A comparison between the experimental results and several different large-scale shell-model calculations yields epsilon(p) approximately 1.15e and epsilon(n) approximately 0.80e.

Charge distribution as a tool to investigate structural details. II. Extension to hydrogen bonds, distorted and hetero-ligand polyhedra.

It is shown that one of the main reasons for most failures of the methods for calculating distance-dependent bond strengths is related to the distortion of the coordination polyhedra. The charge distribution (CD) method which depends on only one universal empirical parameter (contraction parameter) is modified to include: (i) an iterative calculation of the effective coordination number (ECoN), to deal with structures containing very distorted coordination polyhedra; (ii) a specific contraction parameter to treat structures containing any type of hydrogen bond; (iii) scale factors for coordination subshells, to treat structures with hetero-ligand polyhedra. The contraction parameter for the hydrogen bonds was obtained from 119 well refined structures based on neutron diffraction data. Examples of the application of the iterative charge distribution (CD-IT) are presented to show the efficiency of the new method in dealing with distorted (including hydrogen bonding) and hetero-ligand polyhedra. In particular, analysis of a series of 74 structures with pentacoordinated cations shows that deviations from overall trends are related to structure instability. The possible failure of the method with polyionic structures and 'dynamic' structures is discussed.

Crystal structure and charge distribution of YbFeMnO4.

The structure of synthetic YbFeMnO(4) has been refined by single-crystal X-ray diffraction. Space group R3m, a = 3.4580 (1), c = 25.647 (3) A, V = 265.59 (3) A(3), Z = 3. Yb is in octahedral coordination, whereas Fe and Mn are disordered on a single crystallographic type of trigonal bipyramid, in which the cation is off-centred from the basal plane. Assuming perfect stoichiometry, R(1) = 0.0195, but the charge distribution (CD) analysis suggests incomplete occupation of the Yb site. Refinement of the occupancy lowers R(1) to 0.0175, resulting in s.o.f.(Yb) = 0. 963 (3), with a significant improvement of the Fourier difference. The electroneutrality is likely preserved through incomplete occupancy of one of the two oxygen sites: the compound is thus non-stoichiometric, with the formula Yb(0.963)FeMnO(3.945). Another mechanism for preserving the electroneutrality is the oxidation of a small amount of Mn(2+) to Mn(3+), which is, however, less probable because of the reduction conditions in which the sample was synthesized. Both models give a satisfactorily CD result, but they cannot be definitively distinguished by X-ray data.

Identification of two allotwins of mica polytypes in reciprocal space through the minimal rhombus unit.

The X-ray investigation (precession method) of the Ruiz Peak oxybiotite, which is well known for the occurrence of a large number of polytypes and twins, revealed two complex diffraction patterns, which cannot be identified as long-period polytypes. These patterns are analysed in terms of the minimal rhombus, a geometrical asymmetric unit in reciprocal space which permits the decomposition of the composite reciprocal lattice of a twin or allotwin into the reciprocal lattices of the individuals. Both the recorded patterns correspond to a 1M-2M(1) allotwin: the relative rotation between the individuals is 120 degrees in one case and 60 degrees in the other. The geometrical criteria for evaluating the presence of twinning or allotwinning are analysed through these two natural examples.

Twins and allotwins of basic mica polytypes: theoretical derivation and identification in the reciprocal space

The geometry of the diffraction pattern from twins and allotwins of the four basic mica polytypes (1M, 2M1, 3T, 2M2) is analysed in terms of the 'minimal rhombus', a geometrical asymmetric unit in reciprocal space defined by nine translationally independent reciprocal-lattice rows. The minimal rhombus contains the necessary information to decompose the reciprocal lattice of twins or allotwins into the reciprocal lattices of the individuals. The nine translationally independent reciprocal-lattice rows are divided into three types (S, D and X): rows of different type are not overlapped by the n x 60 degrees rotations about c*, which correspond to the relative rotations between pairs of twinned or allotwinned individuals. A symbolic representation of the absolute orientation of the individuals, similar to that used for layers in polytypes, is introduced. The polytypes 1M and 2M1 undergo twinning by reticular pseudo-merohedry with five pairs of twin laws: they produce twelve independent twins, of which nine can be distinguished by the minimal rhombus analysis. The 2M2 polytype has two pairs of twin laws by pseudo-merohedry, which give a single diffraction pattern geometrically indistinguishable from that of the single crystal, and three pairs of twin laws by reticular pseudo-merohedry, which give a single diffraction pattern different from that of the single crystal. The 3T polytype has three twin laws: one corresponds to complete merohedry and the other two to selective merohedry. Selective merohedry produces only partial restoration of the weighted reciprocal lattice built on the family rows and the presence of twinning can be recognized from the geometry of the diffraction pattern.

Periodic intensity distribution (PID) of mica polytypes: symbolism, structural model orientation and axial settings.

Following a preliminary revisitation of the nomenclatures in use for mica polytypes, the properties of the periodic intensity distribution (PID) function, which represents the Fourier transform of the stacking sequence, are analysed. On the basis of the relative rotations of neighbouring layers, mica polytypes are classified into three types; for each type, the PID exists in different subspaces of the reciprocal space. A revised procedure to compute the PID, in which further restrictions on the structural model orientation are introduced, is presented. A unifying terminology based upon the most common symbols used to describe mica polytypes (RTW, Z and TS) is derived; these symbols represent the geometrical basis for the computation of the PID. Results are presented for up to four layer polytypes and are compared with the reflection conditions derived by means of Zvyagin's functions. Both the PID values and the reflection conditions are expressed in suitable axial settings and compared with previous partial reports, revealing some errors in previous analyses. A computer program to compute PID from the stacking symbols is available.

A TEM study of long-period mica polytypes: determination of the stacking sequence of oxybiotite by means of atomic resolution images and Periodic Intensity Distribution (PID).

In this study it is shown that the stacking sequences in long-period mica polytypes (including a rare example of a mixed-rotation polytype, with a 36-layer long periodicity) can be unambiguously determined using atomic resolution images recorded down two zone axes separated by 30 degrees (e.g. [100] and [31;0]) at the same area. Uniformity of these stacking sequences in a large area is further confirmed by the correspondence between computed and observed Periodic Intensity Distributions (PIDs) in electron diffraction patterns. The appearance of long-period polytypes containing layers with different orientation parity may be explained by the coalescence of two small crystals during crystal growth.

Charge distribution as a tool to investigate structural details: meaning and application to pyroxenes.

The charge distribution (CD) method, previously introduced as a development of the bond-valence (BV) approach, is applied for the first time to mineral structures, and specifically to pyroxenes. CD essentially involves the distribution of the Effective Coordination Number (ECoN) of a cation among all the neighboring anions. This distribution is then interpreted in terms of distribution of 'charges', where 'charge' represents the formal oxidation state. Differently from BV, the CD description depends upon the geometry of each coordination polyhedron, which is characterized through ECoN (a non-integer number). The contribution of each cation-oxygen bond to ECoN, labelled 'bond weight', corresponds to the bond strength in the BV method, but it is defined in terms of bond-length ratio in each polyhedron and not as a function of the cation-oxygen pair. The ratio q/Q of the formal oxidation number to the computed charge can be interpreted as a measure of the correctness of the structure (cation ratio) and of the degree of over- or under-bonding (anion ratio). A similar interpretation is not possible for the analogous quantities obtained through the BV approach. The analysis in terms of CD of the pyroxene chains (from 101 structures) shows different trends as a function of composition, temperature and pressure; in particular it shows a different behaviour of the two crystallographically independent chains of orthopyroxenes and of P2(1)/c clinopyroxenes.