Mineralogy. Coordination numbers.

The coordination number of the given atom in mineral structure terms number of the next atoms nearest from it. So, in a halite a sodium coordination number - 6 ((round it the chlorine coordination number also is located on six atoms of chlorine), - 6 (each atom of chlorine adjoins to six atoms of sodium).

In ideal close packings the coordination number depends on a relation of the sizes of its atoms: if one view of atoms composes packing depends on the size of other atoms in what cavity (tetrahedral or octahedral) they can be located. The sizes of cavities depend on the sizes of the atoms ("balls") formativing a close packing, and an optimum relation of radiuses of these atoms and atom radius in cavity always same. For octahedral coordination it is equal 0.41, for tetrahedral - 0.22. Also it is densely possible to dispose atom between three, eight, twelve next. For such structures coordination numbers 3, 4, 6, 8, 12 are possible.

Ideal close packings of atoms are possible only in structures of minerals with the nondirectional, i.e. completely the ionic or metal chemical bonds between atoms. In minerals with with covalent bindings linking of atoms in crystalline construction is carried out at the expense of nationalisation of electrons on orbitals p, d, f. In native sulphur atoms S are united in molecule S8, thus electrons of exterior orbitals p (at their sulphur six) unite so, that each atom has an inconvertible eight-electronic exterior shell. Also at the expense of nationalisation of electrons of an exterior orbital p atoms of carbon in diamond structure are joined, thanks to it each atom completes the exterior shell to 8-electronic, i.e. the most inconvertible. It is essential, that the shape of orbitals p not globe, and more difficult and with strictly certain orientation in space of directions on which the next atoms can be related. Therefore in minerals with a covalent binding the coordination number depends on two factors: relations of the sizes of atoms; character of a location in space of the valence orbitals p, d, f - electrons. The greatest possible number of adjoining atoms is spotted by a relation of their sizes, and the real number can appear other depending on number and a standing of the valence orbitals. Different coordination numbers - 2, 3, 4, 5, 6, 7, 8, 9 are admissible.

Nuclear and ionic radiuses. The true sizes of atoms and ions to measure it is impossible. For mineralogy radiuses of ions in their real crystalline constructions are important, but observationally (X-ray and other methods) are spotted only between central distances of spatial lattices. Distance centre to centre the nearest atoms of silicon and oxygen in monoxide silicon - quartz equally 0.161 nanometers. As to radiuses of ions and atoms in crystals this question at various times and different researchers was solved differently therefore various systems which can be broken on two groups were generated: in the first radiuses of ions of the pivotal in earth crust of chemical elements (Si, Fe, Ca, Mg, Na, etc.) there is less than radius of an ion of oxygen; in second these relations are return.

The first system of radiuses is gobed up A.Lande's by operations. In 1920 he has calculated radiuses Mg2 +, S2 - Se2 - on the basis of measuring of following internuclear distances (in nanometer) in some selenides and sulphides: Mg-Se (0.273), Mg-S (0.260), Mn-S (0.259). Having accepted idea about a close packing of atoms in crystals ("balls" of anions and cations concern each other and are cramped by the close fashion), it on the basis of the elementary calculations has given such values of radiuses (in nanometer): for S2 - 0.183, for Se2 - 0.193, for Mg2 + 0.076.

In 1923 the Vasasherna, proceeding from exponents of a refractive of some fluorides and oxides and using theoretical dependence of radiuses of molecules and ions, on the one hand, and exponents of a refractive of substances, with another, has calculated for radius of an anion of fluorine value of 0.133 nanometers, and for oxygen - 0.132 nanometers. These values have been taken as a principle V.M.Goldshmidtom's further calculations. Having accepted idea of a close packing of ions and cations and consistently dilating a circle of substances with between central in distances, V.M.Goldshmidt has created on the basis of an additivity principle (simple summation of radiuses) system of radiuses for ions of all chemical elements. In it ions of the most widespread chemical elements have following radiuses (in nanometer): Si - 0.039, Al - 0.057, Fe (II) - 0.082, Fe (III) - 0.067, Ca - 0.106, Na - 0.098, Mg - 0.078, Ti (IV) - 0.064, they of less ions of oxygen and only kalium and oxygen have the identical sizes.

Second, absolutely other, the system of radiuses is gobed up V.Bregga's by roentgenometric operations. In 1920 on the basis of the observational definition of internuclear distance S-S in pyrite (0.205 nanometers) it has accepted for radius S2 - value of 0.103 nanometers. On measured distances Zn-S (0.235 nanometers in sphalerite and Zn-O (0.197 nanometers) in V.Bregg's zincite has gained for radiuses Zn2 + 0.132 nanometers and for О2-0.065 nanometers.

Cation radiuses have appeared more radius of oxygen. Unlike V.M.Goldshmidta's system the oxygen radius here has been spotted on the basis of the elementary measurings, instead of indirect calculations of the Vasasherna.

Measurings and the calculations begun by V.Breggom have not been prolonged, and general popularity was gained by well developed and complete system of radiuses of V.M.Goldshmidta. Only considerably later were the complete systems of radiuses of ions in which Bragg relation Rk> Ro is held out are developed. They are offered in A.Slejterom, A.S.ShChukarevym, V.I.Lebedevym's different updatings. On V.I.Lebedevu, for example, radius О2-makes 0.045 nanometers, radius Mg2 + - 0.160 nanometers. Thus it is supposed, that in the majority of crystalline substances the close packing is formed by cations, and in cavities between them ions of oxygen and other anions settle down.

Now there is the active revaluation of different representations about the sizes of ions in crystalline constructions of minerals. For example, A.S.Povarennyh considered, that in chemical combinations different in the nature atoms of the same device should have various radiuses. The size of ion Fe3 + in sulphides makes 0.111 nanometers, in fluorides - 0.086 nanometers, in oxides - 0.094. These representations prove to be true many operations on elektronno - and radiographic analyses of minerals. So for Na oscillations of radius from 0.109 to 0.131 nanometers, for example, are erected. Representations about the unequal sizes of ions in different substances, obviously, are most progressive, but they yet do not send due development, further values of radiuses on V.M.Goldshmidtu therefore will be used.