Duncan McConnell and Frank H. Verhoek The Ohio State University
Columbus
I
I
Crystals, Minerals, and Chemistry
T h e intimate relationship between mineralogy and chemistry was established in the late eighteenth and early nineteenth centuries, when Hauy (1743-1822) and Mitscherlich (1794-1863) examined the relationship between crystal form and chemical constitution. Hauy was convinced that identity of crystal form meant identity of chemical constitution, and conversely, that difference of crystal form meant difference in chemical constitution ( I ) . The first of Hauy's convictions was controverted by Mitscherlich's work on the isomorphic character of the potassium acid phosphates and arsenates (2); of potassium sulfate, selenate and manganate (S), and of potassium permanganate and perchlorate (4). The conclusion from this work was formulated by Mitscherlich in his principle of isomorphism' which played a notable role in the determination of chemical formulas, valence, and atomic weights. The second of Hauy's convictions was shown to he erroneous when Rfitscherlich discovered the dimorphism of sulfur (5); and it was finally disproved for compounds, too, when chemists accepted the analytical data from samples of aragonite which contained no strontium. The Hauy school had claimed (6) that the strontium commonly found in aragonite structures forced the calcium carbonate to adopt the strontianite structure rather than the calcite structure; the existence of a strontium-free aragonite proved this hypothesis i n c o r r e ~ t . ~ Although the nineteenth century saw many descriptions of mineral substances, many measurements of angles, and elaborate classifications of minerals, the definitive study of crystals had to await the development of X-ray diffraction methods for crystal structure analysis. Of fundamental importance in connection with this new approach to crystal chemistry were the early structure determinations of W. H. and W. L. Bragg, the empirical ionic radii of V. M. Goldschmidt, and Pauling's "rules" for the determination of crystal structures. Today, additional techniques are available, such as neutron diffraction, nuclear magnetic resonance, differential thermal analysis, and infrared absorption Mitscherlich, E. (ref. (Z), p. 70): "Ett lika antul atomer, dd de ii70 pd 1tka S W forenade, frambringa like krystall former, och krystall formen bemr e j af atomernus nalur, utan af deras antnl och fdreningssdtt." (Equal numhers of atoms, combined in the same way, produce similar crystal forms, and the crystal form does not depend upon the nature of the atoms hut on their number and mode of combination.) a Mitscherlich had already suggested the conjugate of isomorphism in his 1821 paper before the Swedish Academy (ref. (2)): " ~ och n samma k$pp, som ar sammansatt af samma d a m n efter samma proportioner, kan antuga lvenne olika former." (The same body, composed of the same substances, in the same proportions, can take on two unlike forms.)
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Journal of Chemical Education
spectroscopy. All of these methods have contributed to a detailed knowledge of crystallography and mineralogy. Nevertheless, simple chemical analysis gives much information about minerals, and shows that the textbook concepts of stoichiometry must he abandoned when dealing with oxygenated systems in the solid state. Stoichiometry and Isomorphism
Most chemists are familiar with the two series of carhonates of divalent cations listed in Table 1. Not so well understood, however, is the fact that crystals of these substances often are not "pure" carhonates of a single cation, but contain more than one cation, as in the strontium-containing aragonite which confused Hauy and his adherents. The strontium is not there as a separate strontium carbonate phase. Only one phase is present, with the strontium ions substituted a t random for calcium ions in the aragonite structure. Table 1.
Two Isomor~hicSeries of Carbonate Minerals
Rhomhohedrel (R&) Calcite Rhadochrosite Siderite Smithsonite Magxsite ... ...
...
Forn~ula CeC03 MnCOa FeCOa ZnCOa MgCOs SrCOa PhCOa I3aCOa
Cation Radius Orthorhombic (A) (Pmm) 0.99 0.80 0.74 0.74 0.66
1.12 I .2fl 1.34
Aragonite
... ... ... ...
Stronbianite Cerussite Witherite
Some persons call such a substance an isonlorphic mixture, but it is not a mixture in the sense that more than one phase is present. Others n~ouldspeak of it as a solid solution, but the term solution is so familiarly used in connection with liquids as to imply a lack of spatial organization. To overcome these difficulties, the more general term isomorphic variant has been proposed. Isomorphic variants for both of the forms of Table 1 are common. I n the calcite group there are various compositions of iron-bearing smithsonite or zincbearing siderite, and crystals containing various amounts of manganese in addition to iron and zinc. I n addition to the strontium-calcium variants in the aragonite group, there exist barium-calcium and leadcalcium carbonates. For all these cases it must he emphasized that only a single phase is present. The factor which determines the crystal form of the carbonates is the cation radius, with 0.99 A representing the value common to both structures. When the cations are in about equal amounts, they tend to assume
specific positions in the crystal lattice, rather than appearing in a random arrangement. The appearance of two kinds of atoms in positions formerly occupied by calcium ions causes the crystal to lose some of its symmetry characteristics, and instead of the internal structure of calcite, the structure of dolomite, CaMg(C03)%, and ankerite, CaFe(C03)?,is observed. These minerals still belong to the rhombohedra1class although their internal (space group) symmetry is lower. To accommodate the larger barium ion, however, a differeut external form is also required, so that CaBa(CO& is monoclinic. Still more complex variants occur among the silicates. While orthoclase is clearly a monoclinic crystal closely approaching the formula KA1Si308, the triclinic plagioclase feldspars which make up the common igneous rocks have compositions intermediate between NaAISiaOs and CaA1&O8, so that a particular crystal might have an analysis represented by the formula Na.M Cao.ap Al1.n Si2.6808. Isomorphic Substitutions
The substitution of one ion for another without significant disturbance of the structural arrangement is called isomorphic substitution or diadochy. As has already been observed for the equi-atom calcium-barium carbonate, the tendency for this substitution to occur without change in structure depends upon the sizes of the ions or ionic groups involved. Thus sodium, which has about the same ionic radius as calcium, can replace the latter fairly readily and to a significant extent. The larger potassium ion, on the other hand, is either absent or is preseut only in very small amounts in structures for which the principal cation is calcium. Although it is frequently true that the substituting ion has the same charge as the substituted one, as in the isomorphic carbonate variants discussed above, the sodium-for-calciunl substitution in the feldspars indicates that this is not a rigorous requirement. Here the substitution of monovalent sodium for the divalent calcium of the unsubstituted CaAl?Si?Os has been accompanied by an iucrease in the silicon content and a decrease in the aluminum content. While the external form remains essentially uuchanged by this substitution and charge compensation, the X-ray patterns show that changes have occurred in the positions of ions in the crystal. The Al ion is larger than Si and the Ca ion is larger than Na, so changes in the unit-cell dimensions do occur as an accompaniment of compositional changes. I t must be emphasized, however, that the crystal lattice should not be looked upon as defective, in the sense of having vacant positions; merely minor rearrangements have occurred through substitution of sodium and silicon for calcium and aluminum. Another common occurrence is the addition of hydrogen to a structure, forming (OH) groupings of lower charge than that of the oxygens. The tiny proton cannot substitute for metallic cations in the structural positions previously occupied by them. If hydrogen is to enter the crystal structure, it must do so as hydroxyl, ammonium, or hydronium ions. whose radii are comparable to those of the ions they replace. It can, of course, also occur in the status of water molecules.
Coupled Substitution
Another way in which substitution of cations of dissimilar charge can occur is for the cation substitution to he coupled with an anion substitution. A striking example of this is offered by the isostructural minerals herlinite, an aluminum phosphate (AIPOJ, and the low-temperature form of quartz (SiSiOJ. Both of these substances show the same symmetry characteristics, and both form right-and left-handed crystals, although one can be considered to have a +3, -3 oxidation state and the other a +4, -4 oxidation state. For classification purposes, it is often more convenient to fix one's attention on the positive oxidation states alone, and look upon this as a "coupled diadochy" in whichA1P substitutes for SiSi. Thus this case can he considered to be similar to the substitution of CaAl for NaSi in plagioclase feldspar, or of CeNa for 2Ca in apatite (CaloF?(P04)s) to give britholite
Callrr,(CeNa).Fz(POa)~). Substitution of Anions
The disparity in sizes of silicon and phosphorus in one instance, and of silicon and aluminum in the other, preclude the formation of isomorphic variants between the two end members, herlinite and quartz. The hydrogarnets, on the other hand, are the variants connecting the two isostructural extremes represented by the mineral grossular, 3CaO.AI2O3.3SiO2,and tricalcinm aluminate hexahydrate, 3Ca0.A120,.GH,0. The Xray data demonstrate that both of these compounds and the hydrogarnets 3 x 0 . Yz03.(3-n)SiOz.2nHz0have 96 oxygen atoms in the unit cell, and that these oxygens occupy the same structurally equivalent positions in all three compounds (7). Since the silicate ions in grossular have the tetrahedral configuration characteristic of SiO+ it must be supposed that when the silicon atoms are replaced by hydrogen atoms in the "hydrated" compounds at the rate of 4 protons per Si4+ (to maintain electrical neutrality), the tetrahedral configuration of the oxygens is maintained. Because of their low scattering power for X-rays, the protons cannot be located by X-ray techniques, hut it can be assumed that they are closely associated with the oxygen atoms, a t the same time remaining as far removed as possible from each other and from the calcium and aluminum ions. The most symmetrical positions for the protons would be the centers of each of the four triangular faces of a tetrahedron which has an oxygen at each apex. I n any case the simplest formulas for grossular and the hydrogarnet variants should be written Ca.A1dSi04)a,Ap&(SiQ,)4H4O,)., A I B ~ H ~ O ~ ) ~ .
Synthetic compounds in which A is Ca or Sr and B is A1 or Fe have been investigated. In these formulas the HI04groups represent "tetrahedral hydroxyls." The group H,On can also substitute for phosphate and sulfate in the complex minerals listed in Table 2. In these cases the substitution of the anion must he coupled with cation substitution, because of the difference in the oxidation states of H40pand the other anions. The extent to which the simple anion substitutions observed by Mitscherlich in his studies of the isomorphism of phosphates and arsenates can be carried, in complex minerals, was first shown in 1937 in the study Volume 40, Number 70, October 7963
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of the mineral ellestadite (8). All the physical proper-
ties of ellestadite, a calcium sulfate-silicate Cal,(F,OH)2(S04)3(Si04)3, are similar to those of apatite, with which it is isostructural. Table 3 shows some of the wide range of apatite minerals, all of which may be considered as derivatives of, and all of which are essentially isostructural with, apatite. A predominant feature of all of these minerals is that they contain 24 oxygen atoms per unit cell (except where OH or 0 substitutes for F) and that the other atoms fit themselves to the pattern set by the oxygens. Table 2.
Mineral Examples of lsomorphic Substitution of Anions
Si01 PO, SO, Hydrogarnets Griphite Ettringite Cofinite Vis6item Montmorillanite Apatite Antigorite Crandallite ZrSi04-,(OH),, PO4 substituted fa7 SiO* Griphite, a phosphate garnet VisBite, a phnsphate zeolite (snalcime)' Berlinite, AIP04 with quart5 structure SiO, and SO4for PO4 Ellestadite. a sulfate-silicate a m t i t e C~,O(F,OH).(SO~).(S~O~), a Vis6ite has a framework struct,ure of the type A [X Y4&1.H*O (X is Al for analeime and Y is Si) in which case the tetrshedrel oxygens are linked to form (A10&, (SiOdo, (POz)+ and (HIOX)-, ao that the numher of protons sssoc~stedwltb the 4 shared oxygens is 3 rather t h ~ n4. Except montmorillonite and antigorite, other examples are orthosilicates or orthnphosphates.
Toble 3.
Isomorphic Variants a n d End Members of the Apatite Group, CaloFz(P0nh
Mineral
Ca
Substitutions inr F
POI
-
. A .
vu
PSI Fermorite llehrnite Lewistonite Manesnvoelkerite ~hukumalite Rritholite Frnncoliteh Ihhlliteb Synthetic Synthetic Synthetic Synt,lretic
-
...
... Cd" . .. Na
A1
...
COi
OH
CO:
... CI . .. ...
...
Cr04 $04
AIOI
The substitution is essentially complete (end members). & A distinction between dshllite, containing
