The renormalization prescription of t'Hooft and Veltman is used to construct crossover scaling functions for the susceptibility and free energy in an isotropic n vector model. Some dilliculties in interpreting the E expansion in this context are discussed, and the formalism is illustrated by a calculation of the expansion factor a ' of a polymer in dilute solution.

The crystal structure of chloroxiphite, Pb 3 CuO 2 (OH) 2 Cl 2 , from Merehead Quarry (monoclinic, P2 1 /m, a = 6.6972(8), b = 5.7538(5), c = 10.4686(14) Å , b = 97.747(10)º, V = 399.72(8) Å 3 ) has been refined to R 1 = 0.041. The structure contains three symmetrically unique Pb sites and one Cu site. The strong distortion of the Pb 2+ coordination polyhedra is due to the stereoactivity of the s 2 lone electron pairs on the Pb 2+ cations. The Cu-site is coordinated by four OH À groups to form an almost planar Cu(OH) 4 square that is complemented by two apical Cl À anions, forming an elongated [Cu(OH) 4 Cl 2 ] octahedron. Because of the large size and variability of coordination polyhedra around Pb 2+ cations and the strength of the MeÀO bonds in comparison to the MeÀCl bonds (Me = metal), it is convenient to describe the structure of chloroxiphite in terms of oxocentred OPb 4 tetrahedra. The O1 atom is tetrahedrally coordinated by four Pb 2+ cations forming relatively short and strong OÀPb bonds. The OPb 4 tetrahedra link together via common edges to form [O 2 Pb 3 ] 2+ double chains. The difference between chloroxiphite and other natural oxyhalides is the presence of Cu 2+ cations which form an independent structural unit that links to units formed by OPb 4 tetrahedra. In this sense, chloroxiphite can be considered as a modular structure consisting of both strong cation-and anion-centred units.

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Yeomanite, Pb2O(OH)Cl, is a new Pb-oxychloride found in the manganese pod mineral assemblage at Merehead (Torr Works) Quarry, near Cranmore, Somerset, England. Yeomanite is named in joint recognition of Mrs Angela Yeoman (1931–) and her company, Foster Yeoman, who operated Merehead Quarry for aggregate until 2006. The mineral is normally white, occasionally grey, with a white streak and a vitreous to transparent lustre. Invariably intimately associated with mendipite, yeomanite appears to be formed of small, twisted, rope-like fibres growing from the end of columnar mendipite masses, forming loose mats and strands resembling asbestos. Individual fibres are generally <8 mm long, but exceptionally may reach up to 15 mm. There is a perfect cleavage parallel to the long axis of the fibres but this is masked by the fibrous nature, especially as individual fibres break easily. The Dcalc for the ideal formula is 7.303 g/cm3. The mean RI in air at 589 nm is 2.27. The eight strongest reflections in the powder X-ray diffraction pattern [(d in Å) (Intensity) (hkl)] are: 2.880(100)(113); 2.802(78)(006); 3.293(61)(200); 3.770(32)(011); 2.166(22)(206); 1.662(19)(119); 2.050(18)(303); 3.054(17)(105) Yeomanite is orthorhombic, Pnma, a = 6.585(10), b = 3.855(6), c = 17.26(1) Å, V = 438(1) Å3, Z = 4. Yeomanite is a new example of the growing family of lead oxychloride minerals that have a structure based upon oxocentred OPb4 tetrahedra, which, in this mineral, jointly with OHPb3 triangles, form [O(OH)Pb2]+ chains similar to those observed in synthetic Pb2O(OH)I. Yeomanite is structurally related to sidpietersite, penfieldite and laurionite.

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Analysis of polymorphic systems shows that extended patterns are conserved between polymorphic forms for 75% of cases studied. a) b) Figure 1. a) An 'R4 sheet' motif. b) An R2R6 sheet motif. Dots represent molecules, lines represent inter-molecular hydrogen bonds. The arrows indicate that these patterns are infinitely repeating in 2D.

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