Polymorf - Knowhwere- Minerals

The forgoing list is meant to be illustrative not exhaustive. Only the most common

elements or minerals possessing structural types that can be modeled with Polymorf

are included.

The fact that many of these mineral groups are isostructural indicates that their

underlying structural framework is as important in determining the group's physical

and chemical properties as is their individual chemical composition. The topological

approach and the compositional approach to describing matter therefore should be

seen as both sides of the same coin. The one cannot be fully appreciated without the

other.

Topological classification system

Another classification scheme emphasizes the internal structure of minerals and

the coordination of its constituent atom species. It arranges minerals by the type and

percent occupation of interstitial voids present in their crystal structures, that is by the

way that the atoms pack together.

Factors that affect how atoms of different species pack together include their

relative sizes, the direction and strength of the bonding forces of each atom type, and

the necessity for electronic neutrality of the structure.

Atoms that pack together as the result of ionic or metallic bonds between them

tend to generate structures that are closely packed together. Covalently bonded

atoms are oriented in specific directions relative to each other which affects how they

pack together to form solids.

There are a few compounds formed from different elements with nearly equal

atomic volumes, and therefore can be modeled like the pure elements as one type of

close packing or another. But the constituent atomic species of most compounds

have different volumes and therefore pack together according to the ratio of the

different atoms' volumes. Given the wide range of atomic radii exhibited by the

elements and the thousands of different combinations they can achieve with each

other, compounds can exhibit a wide range in the radius ratios of their constituent

atom species.

However, certain specific ratios of atomic radii give rise to general types of

mineral structures based on how the different sized atoms pack together. Typically

the relatively larger non-metallic atoms, or anions (X), in a compound pack together

so as to provide interstitial voids between them which can accommodate the

relatively smaller metal ions, or cations (A). In the following figure the largest size

sphere represents the anion with a radius of one and the smaller spheres are cations

of the various critical sizes. The smaller A atoms can be accommodated in holes

.
		Figure 56 - Critical radius ratio values for
		cubic, octahedral, and tetrahedral
		coordination of interstitial atoms

formed by packing the largest X atom with a radius of 1.0 in the shape of a cube (void

size .732), an octahedron (void size .414), and a tetrahedron (void size .225).

.

			Figure 57 - Cubic,
			tetrahedral and
			octahedral voids
			click image to enlarge

cubic (AX₈)	octahedral (AX₆)	tetrahedral (AX₄)
.

Thus these ratios result in eight large X atoms being coordinated around the

smaller A atom in the cubic arrangement, six X atoms in the octahedral arrangement,

and four X atoms in the tetrahedral arrangement. Other, less common coordinations

are trigonal prismatic with coordination six and a radius ratio of .528, square anti-

prismatic with coordination eight and a radius ratio of .645, and triangular with

coordination three and a radius ratio of .155 . And as already demonstrated for the

elements, compounds with radius ratios approaching one, that is with equal radius

atoms, usually pack with coordination twelve. Simply put, the coordination number,

or ligancy, increases with an increase in the radius ratio.

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Page 39 - Structure matters - Interstitial voids