Abstract. Neutron diffraction data suitable for Rietveld refinements were collected on a powder sample of synthetic Mg(OH)2 by the Polaris time-of-flight spectrometer (ISIS spallation source, U.K.) at 10 -4, 7.8(3) and 10.9(6) GPa. The Paris-Edinburgh high-pressure cell with WC anvils was used. Pressure calibration and equation-ofstate results were attained by separate runs with an NaC1 internal standard. Interpolation of p(V) data by the fourth-order Birch-Murnagban e.o.s, yields K0=41(2 ) GPa, K0=4(2 ) and Ko'= 1.1(9) GPa -1. The bulk modulus obtained is smaller than previously reported results. Rietveld refinements (Rprof= 1.45% and 2.02% at 10 .4 and 10.9 GPa) show that H lies on the threefold axis (1/3, 2/3, z) up to 10.9 GPa, where a model with H disordered in (x, 2x, z) can be refined. In the latter case, a hydrogen bond with O-H=0.902 (7), H..O =2.026(8) A and

Brief outline 2 1.2 Hierarchical classification of structures 3 1.3 Short recapitulation of non-modular categories of similarity 5 1.4 Elements of modular description. Types of homologous/ polysomatic series 9 1.5 Polysomatism 35 1.6 Chemical composition series 41 1.7 Variable-fit homologous series and series with a combined character 42 1.8 Merotype and plesiotype series 57 1.9 Ordered derivatives of solid solutions as modular structures 110 1.10 Principles of prediction of modular structures 113 2 OD structures 127

The crystalline State and isometric Operations 1 Symmetry elements 3 Axes of rotational symmetry 3 Axes of rototranslation or screw axes 5 Axes of inversion 5 Axes of rotorefiection 5 Refiection planes with translational component (glide planes) 6 Lattices 6 The rational properties of lattices 7 Crystallographic directions 7 Crystallographic planes 8 Symmetry restrictions due to the lattice periodicity and vice versa 9 Point groups and symmetry classes 11 Point groups in one and two dimensions 16 The Laue classes 17 The seven crystal Systems 17 The Bravais lattices 18 Plane lattices 18 Space lattices 19 The space groups 22 The plane and line groups 30 On the matrix representation of symmetry Operators 32 Appendices: LA The isometric transformations 35 l.B Some combinations of movements 37 l.C Wigner-Seitz cells 41 l.D The space-group rotation matrices l.E Symmetry groups l.F Symmetry generalization References Crystallographic Computing Carmelo Giacovazzo

The introduction of a fifth amphibole group, the Na-Ca-Mg-Fe-Mn-Li group, defined by 0.50 < B(Mg,Fe2+,Mn2+,Li) < 1.50 and 0.50 ≤ B(Ca,Na) ≤ 1.50 a.f.p.u. (atoms per formula unit), with members whittakerite and ottoliniite, has been required by recent discoveries of B(LiNa) amphiboles. This, and other new discoveries, such as sodicpedrizite (which, here, is changed slightly, but significantly, from the original idealized formula), necessitate amendments to the IMA 1997 definitions of the Mg-Fe-Mn-Li, calcic, sodic-calcic and sodic groups. The discovery of obertiite and the finding of an incompatibility in the IMA 1997 subdivision of the sodic group, requires further amendments within the sodic group. All these changes, which have IMA approval, are summarized.

A simplified definition of a mineral group is given on the basis of structural and compositional aspects. Then a hierarchical scheme for group nomenclature and mineral classification is introduced and applied to recent nomenclature proposals. A new procedure has been put in place in order to facilitate the future proposal and naming of new mineral groups within the IMA-CNMNC framework.