Polyhedron chains

Nefedovite, Na5Ca4(P04)4F, consists of [8]-coordinated Ca and both [7]- and [10]-coordinated Na. The (Na([)io) polyhedra share apical corners to form chains that extend in the c-direction (Fig. 65a) with (PO4) tetrahedra linked to half of the meridional vertices. The (NaO ) polyhedra share apical corners to form chains extending in the c-direction, and the individual polyhedra share comers with the (Nact)io) polyhedra, each bridging adjacent polyhedra along each chain (Fig. 65a). These chains are linked in the (001) plane by (Ca(t)8) polyhedra. The decorated (Nact)io)-polyhedron chains have a square pinwheel appearance when viewed down [001] (Fig. 65b), and they are surrounded by a dense edge-sharing array of (NaOy) and (Cact)8) polyhedra. 

Residual Valence at an Anion Termination and at a Surface Polyhedron Chain. .. 169... 

A strongly bonded polyhedron chain which occurs on a crystal face contains ligands which bond either to cations of the chain or both to cations of the chain and to species in the adjacent aqueous solution. Any anion on such a chain and the cations to which it is bonded form a termination. Polyhedron chains are generally linear and have a small number of cation-cp (anion) terminations per unit length. In general, it is the incident bond-valence at the anion of the (bare) termination that controls the reactivity of that termination. If the incident bond-valence at the anion already satisfies the valence-sum rule, pZa = 0 in Eq. (1) and there is no driving force for that anion to react with any component of the adjacent aqueous solution. Conversely, if the incident bond-valence at the anion is less than that required by the valence-sum rule, the anion will react with some component of the adjacent aqueous solution to accord with the valence-sum rule. 

Consider a polyhedron chain with b and c different types of anion termination along its repeat length. The pATa value of an acid-base reaction involving this... 

The right-hand side of Eq. (6) is the O-atom residual valence for a polyhedron chain and correlates with the average pATa-value and the free energy of the acid-base reactions along a polyhedron chain, indicating the affinity of the constituent O-atoms for hydrogen bonds or O-H bonds [31]. 

Fig. 5 Polyhedron representation of the uranyl-oxide hydroxy-hydrate sheet in schoepite, [(U02)g02(0H)i2](H20)i2, showing polyhedron chains parallel to [1 0 0], [0 1 0], [1 2 0], [110] and [2 10], respectively equatorial 0 anions of the uranyl-polyhedra are shown as orangelgray circles, equatorial edges are shown as heavy black lines from [31]...

Fig. 8 Polyhedron and ball-and-stick representations of the [0 1 0] polyhedron chain exposed at the (0 0 1) surface in fabianite. The bonds (and corresponding bond-valences required) involving surface anions and constituents of the aqueous solution are shown as lines [bond valence donated from the (aquated) cations of the aqueous solution] and as arrows (bond valence draiated from H atoms of protonated surface anions to anions of the aqueous solutirm). Note that there are not many protonated anions that can participate in redox reactions with the aqueous solution...

For minerals crystaUizing from low-temperature aqueous solutions, the primary controls on their stability should be (a) the activity of the species in solution and G ) protonation reactions between solid and solution at the edges of polyhedron chains deprotonation of edge anions promotes attachment of aqueous cation species (i.e., crystallization), whereas protonation of edge anions weakens their bonds to the bulk structure and promotes dissolution. With regard to crystallization, the character and activity of the aqueous species is of interest as these provide groups of atoms that may attach to the solid during crystallization. 

Crystallization occurs via attachment of clusters at activated sites at anion terminations on the edge of polyhedron chains. Attachment produces one additional (H2O) or (OH) group per common comer between cluster and anion terminatirHi (Figs. 10d,e). Thus at an activated site involved in crystal growth, there are strong hydrogen bonds from anion terminations to a polyhedron cluster in solution. The other anions of the cluster and the (former) activated site stay activated until the anions do not require additional bond-valence from aqueous species (Fig. lOf). 

The surface of a crystal grows primarily by attaching species (usually polyhedra) to the dominant edges on that surface. The orientations of these edges are controlled by the orientation of the strongly braided polyhedron chains on that surface. There are two important factors to be considered here (1) polyhedron chains that... 

Fig. 14 The left and right chain terminations for different conformations of the polyhedron chain parallel to the [10 0] edge in the uranyl sheet of schoepite the positions of 0 anions are indicated by circles. For left terminations, the bulk structure continues to the right, and the surface occurs to the left, and vice versa...

Fig. 15 The calculated residual valence per unit length (v.u./A) of the polyhedron chains parallel to the [1 0 0], [0 1 0], [1 2 0], [1 1 0], and [2 1 0] edges on the (0 0 1) face for both left and right terminations the numbers along the abscissa denote the different conformations of each chain, and the corresponding values of the residual valence per repeat are shown on the ordinate...

Fig. 17 (a, b) Photographs of nobleite and tunellite crystals (from [50]) (c) sheet of polymerized polyhedra in the structures of nobleite and tunellite (d) sketch of the basal surface of the crystals of nobleite and tunellite and calculated residual valence of the polyhedron chains parallel to the [0 0 1], [0 1 0], and [0 1 1] edges... 

Periodic bond-chains are strongly related to the occurrence of faces on a crystal (and, in turn, the major growth directions of a crystal) [21-23]. We refer to periodic bond-chains as polyhedron chains. 

The residual valence of a polyhedron chain controls the growth or dissolution rate at the crystal face associated with that chain and may be calculated as the net residual valence of the terminations along the repeat length of the polyhedron chain. 

The bond-valence of an anion termination on a terminating polyhedron chain correlates with the intrinsic acidity constant, pA a, and with the free energy, AGat> of the corresponding acid-base reaction. 

The relative morphology of prominent basal faces of crystals will be controlled by the relative magnitudes of the residual valence of polyhedron chains parallel to specific edges. Faces should elongate in the direction of chains with low residual valence and should not be defined by edges parallel to chains with high residual valence. 

---