Order–disorder transformations
Many polymorphs differ from one another only in terms of the degree of regularity in the distribution of certain ions within their respective crystal structures. Their structures can range from perfectly ordered to a random distribution of ions within structural sites (Figure 4.38). The potassium feldspar minerals (KAlSi3O8) provide many examples of such variation in regularity or order in the distribution of aluminum ions within the structure. In the feldspar structure, one in every four tetrahedral sites is occupied by aluminum (Al+3), whereas the other three are occupied by silicon (Si+4). In the potassium feldspar high sanidine, the distribution of aluminum cations is completely random (high disorder); the probability of finding an aluminum cation in any one of the four sites is equal. Crystal structures with such random distributions of cations are highly disordered and are favored by high temperatures and low pressures of formation. On the other hand, in the potassium feldspar low microcline, the distribution of aluminum cations is highly ordered (low disorder), with the aluminum distributed regularly in every fourth tetrahedral site. The probability of finding an aluminum cation in these sites approaches 100%, and the probability of finding one in the other three sites approaches zero. Crystal structures with such regular distributions of cations possess very low disorder, and their formation is favored by low temperatures and/or high pressures of formation. Intermediate degrees of order exist within the potassium feldspar group. High sanidine, with its high degree of disorder, crystallizes in the monoclinic system, and is common in volcanic rocks formed at high temperatures and low near surface pressures, whereas low microcline, with its low degree of disorder, crystallizes in the triclinic system, and is common in rocks formed at higher pressures, and in some cases lower temperatures, below the surface.
Figure 4.38 Variations in the order of minerals.
Source: Klein and Hurlbut (1985). © John Wiley & Sons.
4.9.2 Pseudomorphs
Minerals that take the crystal form of another, pre‐existing mineral are called pseudomorphs and are said to be pseudomorphic after the earlier mineral (Figure 4.39). Pseudomorphs can be produced in many ways. All require that the original crystal possessed a significant number of crystal faces (was euhedral or subhedral) at the time it formed. Some pseudomorphs are produced by replacement in which the atoms in a pre‐existing mineral are replaced by the atoms of a new mineral that retains the external crystal form of the original crystal. A common example is the replacement of pyrite (FeS2) crystals by goethite (FeOOH) to produce goethite pseudomorphs after pyrite. Another common example is quartz (SiO2) pseudomorphs after fluorite (CaF2). Some pseudomorphs are casts produced by dissolution of the old mineral followed by precipitation of the pseudomorph to fill the cavity left behind. Other pseudomorphs are produced by the loss of a constituent from the original crystals. For example, the dissolution of carbonate ion from crystals of the copper carbonate mineral azurite [Cu3(CO3)2(OH)2] can produce native copper (Cu) pseudomorphs after azurite. Still other pseudomorphs are produced when the new mineral forms a thin layer or crust over the original crystal. The encrustation of the original mineral by the new mineral allows the new mineral to mimic the crystal form of the original mineral. Still other pseudomorphs form by inversion as when β quartz crystals are transformed into α quartz, as described in the preceding section.
Figure 4.39 (a) Hematite replacing pyrite; (b) chalcedony encrusting aragonite; (c) quartz cast filling an aragonite solution cavity.
Source: Photo courtesy of Stan Celestian, Maricopa Community College.
The properties of minerals and other crystalline materials are strongly influenced by their crystal structures and chemical compositions. These properties and the minerals that possess them are the subjects of Chapter 5.
CONTENT ASSESSMENT
1 Discuss the difference between a motif and a node and explain why both are important in illustrating and understanding how long‐range patterns of atoms/ions can be generated by symmetry operations.
2 What are symmetry operations and how are they related to crystal structures? How do simple and compound symmetry operations differ?
3 Carefully define the following symmetry operations and the symbols used to denote each one.translation and unit translation vectorrotation and axis of rotationreflection and mirror planeinversion and centerglide reflectionrotoinversionscrew rotation
4 Discuss the properties and differences between the following types of plane meshes or nets.squarerectanglediamondhexagonal (rhombic)oblique
5 Define the essential properties of each of the seven (if hexagonal and trigonal are separated) crystal systems in terms of the properties of their Bravais lattices and their crystallographic axes (lengths and intersection angles).
6 6 In Weiss parameters and Miller indices, what do the three sequential parameters or indices represent? Convert the following Weiss parameters into the equivalent Miller indices.2, ∞, 1½, 1, 22, ∞, 2, 2, 11/3, , 1
7 Explain the meaning of the following Miller indices in terms of crystallographic axial intercepts with respect to axial ratios(111){111}(1 2){hkl}(hh )
8 What are twinned crystals and what are their chief defining characteristics? What is the essential difference between contact and penetration twins? Give a couple of good examples of each.
9 What are polymorphs? What is the difference between reconstructive and displacive polymorphs? Give an example or two of each. Which is most likely to produce long term metastable polymorphs?
REFERENCES
1 Davis, G.H., Reynolds, S.J., and Kluth, C.F. (2011). Structural Geology of Rocks and Regions, 3e. New York: Wiley 864 pp.
2 Hobbs, B.E., Means, W.D., and Williams, P.E. (1976). An outline of structural geology. New York: Wiley 571 pp.
3 Klein, C. and Dutrow, B. (2007). Manual of Mineral Science (Manual of Mineralogy), 23e. New York: Wiley 704 pp.
4 Klein, C. and Hurlbut, C.S. Jr. (1985). Manual of Mineralogy, 20e. New York: Wiley 644 pp.
5 Nesse, W.D. (2016). Introduction to Mineralogy, 3e. New York: Oxford University Press 512 pp.
6 van der Pluijm, B.A. and Marshak, S. (2004). Earth Structure: An Introduction to Structural Geology, 2e. New York: W.W. Norton 672 pp.
7 Wenk, H.‐R. and Bulakh, A. (2016). Minerals: Their Constitution and Origin, 3e. Cambridge, UK:
