1. Pauling’s Rules GLY 4200 Fall, 2017
In crystal structures, the minimum size in the range for a particular structure class is actually the only size for an exact fit. Any larger size will force the anions apart, and any smaller size will “rattle” and is thus not permitted. Thus, is the size for an exact fit of octahedral or square planer, but sizes up to are acceptable.
Knowledge of the units (linear, trigonal, planar, tetrahedron, etc.) which go into a crystal structure is important but it is not enough to describe most crystal structures. Some crystal structures can be described by simply stating the type of array, such as Hexagonal Closest Packing (HCP) or Cubic Closest Packing (CCP), and stating what voids are occupied.

2. Planar Packing Hexagonal array of spheres
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Closest packing involves the tightest packing of spheres into a three-dimensional array. In a plane, spheres of equal size are most densely packed (with the least amount of empty space) when each sphere touches six other spheres arranged in the form of a regular hexagon.
Hexagonal array of spheres

3. Primitive Hexagonal Array
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If another layer of spheres is added directly over the first layer, a primitive hexagonal array results. This type of packing is called close-packing. It is not the densest possible form.
A type of close packing

4. A-B Layers Closest-packing
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Instead of stacking hexagonal closest packed planes directly above one another, they can be stacked such that atoms in successive planes nestle in the triangular "indentations" of the adjacent plane. (Note: There are six of these "indentations" surrounding each atom in the hexagonal plane, but only three of them can be covered by atoms in the adjacent plane).
Closest-packing

5. Hexagonal Closest Packing
This produces a structure with two types of layers, labeled A and B. The resulting structure is hexagonal closest packing (HCP), with a layer arrangement denoted ....ABABABAB...

6. A-B-C Layers Another form of closest-packing
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Suppose the first two layers of hexagonal closest packed planes are stacked in "AB" fashion but the third layer is positioned so that its atoms lie over the three grooves in the A layer which were not covered by the atoms in the B layer. Then the third layer is in a different orientation from either A or B and is labeled "C".
Another form of closest-packing

7. Cubic Closest Packing
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If a fourth layer then repeats the A layer orientation, and succeeding layers repeat the pattern ABCABCA... = (ABC), known as cubic closest packing.

8. Halite Structure A derivative of the CCP structure
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Other structures can be described by giving the exact locations of all the atoms or ions in a cell. This works for minerals with a simple structure and high degree of symmetry such as halite and fluorite. Complicated structures can’t be easily described in this manner.
A third possibility is to describe the structure in terms of the polyhedron that comprises it – this is done by describing how the polyhedra are linked together. For example, the simplest 3-D polyhedron is the tetrahedron. As we have seen, the tetrahedron possesses four sides and four vertices (corners). In a crystal, the tetrahedron is formed by a central cation surrounded by anions at the vertices. A very common example is SiO4.

9. Beryl Beryl is Be3Al2Si6O18 - unit cell shown above
The yellow Si tetrahedra are in the upper layer, the green ones in the lower layer
The purple tetrahedra contain Be
The solitary blue atoms are Al, in 6-fold coordination with the adjacent tetrahedral oxygens
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In the mineral beryl, we have both SiO4 and BeO4 tetrahedra present.

10. Corner Sharing Tetrahedra sharing one atom
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If two tetrahedron share an anion the tetrahedron are said to share a corner. With silica tetrahedra, this makes Si2O7.
Tetrahedra sharing one atom

11. Edge Sharing Two atoms shared
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If two tetrahedron share two anions the tetrahedron shares an edge. This would make Si2O6, or in reduced form SiO3.
Two atoms shared

12. Face Sharing Three atoms shared
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It is also possible to imagine that two tetrahedron could share three anions.
This would be called face sharing. However, for tetrahedron, this does not happen, because face sharing brings the cations too close together. Electrostatic repulsion is too large.
In octahedra or larger units, face sharing is possible.
Three atoms shared

13. One of four people who have been the recipient of two Nobel Prizes, the prize for chemistry in 1954 and the peace prize in 1960
During his long life, he was engaged in a broad range of interests within the sciences and, along with many of his colleagues in the scientific community, was actively involved in the antinuclear bomb movement after World War II
Photograph by Michael Collopy
Linus Pauling
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To date, four people have won a Nobel Prize twice.  Those include: Maria Sklodowska-Curie (1903 and 1911, for discovery of radioactivity (physics) and later for isolating pure radium (chemistry)); John Bardeen (1956 and 1972, for invention of the transistor (physics) and for coming up with the theory of superconductivity(physics)); Linus Pauling (1954 and 1962, for research into the chemical bond in terms of complex substances (chemistry) and for anti-nuclear activism (peace)); and Frederick Sanger (1958 and 1980, for discovering the structure of the insulin molecule (chemistry) and inventing a method to determine base sequences in DNA (chemistry)). (

14. Rule 1
A coordinated polyhedron of anions is formed about each cation, the cation-anion distance being determined by the radius sum, and the coordination number of the cation by the radius ratio

15. Rule 2 Sometimes called “The electrostatic valiancy principle”
In a stable ionic structure, the valence of each anion, with changed sign, is exactly or nearly equal to the sum of the strengths of the electrostatic bonds to it from the adjacent cations
Example – Na Cl – Each anion surrounded by six cations, each cation by six anions. One-sixth of the charge of the cation is assigned to each anion and vice-versa.

16. Rule 3
The existence of edges, and particularly of faces, common to two anion polyhedra in a coordinated structure decreases its stability; this effect is large for cations with high valency and small coordination number, and is especially large when the radius ratio approaches the lower limit of stability of the polyhedron

17. Rule 4
In a crystal containing different cations, those of high valency and small coordination number tend not to share polyhedron elements with each other

18. Rule 5 “The principle of parsimony”
The number of essentially different kinds of constituents in a crystal tends to be small
This last “rule” is simply an observation; some authors would not include it. However; it is a valid description, indicating that in complicated structures with several different types of cation, each distinct site may be occupied by more than one type of cation. All the different cations would be one constituent.

19. Isostructural Minerals
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Structure types in crystalline solutions
Sometimes one crystal structure type occurs in more than one mineral. Some are quite common. Example Na Cl, halite structure
Others MgO (periclase), KC1, (sylvite) PbS (galena) and many others.
When this has occurred, the minerals are said to be isostructural or to belong to the same structure type. If every ion in one mineral has an exact counterpart in the other the term is isotype.
Clockwise from upper left – halite (NaCl), Galena (PbS), Periclase (MgO), and Sylvite KCl)