Scon I. M o r r o w FRL Propellants Picatinny Arsenal Dover, N e w Jersey 07801
One Hundred and Fifty Years of Isomorphism
It is appropriate upon the advent of the 150th anniversary of the "discovery" of isomorphism to focus the attention of the chemical teaching community on this phenomenon. There is considerable evidence to suggest that this rather esoteric subject is generally overlooked or a t best mentioned briefly in the teaching of inorganic chemistry. That this should not be so will be apparent when one considers the story of isomorphism, past and present. Although the discovery of isomorphism is generally attributed to E. Wlitscherlich in 1819, it was actually revealed first by W. H. Wollaston in 1812. I n fact even as early as 1772 Rome De L'Isle ( 1 ) observed that "isomorphous" cubic alums formed mixed crystals or overgrowths of one crystal on another. 'This early work on "isomorphous" mixed crystals in advance of the actual elucidation of the true nature of the phenomenon was extended by Le Blanc in 1784, Vauquelin in 1797, and Gay Lussac in 1819. The fact that isomorphism was discovered as early as it was is due to the mechanical ingenuity of Wollaston. For in 1809 he invented the reflecting goniometer, the first highly accurate instrument for measuring the interfacial angles of crystals. An instrument believed to resemble his is shown in Figure 1.' By this means he discovered that crystals of different chemical compounds having the same external form actually had small differences in the corresponding interfacial angles. Except for giving a name to the phenomenon, as was done later by Mitscherlich, this constituted the discovery of isomorphism. Wollaston published the results of his investigations in 1812 (2). He found that the rhombohedra1 angle of calcite was 105" 5', the same angle for dolomite ~ v a s106' 15', and that of chalybite as 107" 0'. These measurements were sufficient,lyaccurate so that they are accepted today after repeated further measurements by later crysstallographers ( 2 ) . Differences in a specific angle of about 2", such as in the preceding case, are not uncommon in isomorphous crystal series. Wollaston's work remained in obscurity for seven years until Mitscherlich, evidently unaware of it, rediscovered isomorphism. Ironically when he did so, he was unable, as had Wollaston earlier, to distinguish between the interfacial angles of such apparently identical crystals as RHJ'OI, (NH4)H2P04,RH2As04, and (NHn)H,AsOa. However, he did learn of Wollaston's paper on the subThis paper was presented at the Division of Chemical E d u c e tion at the 156th Meeting of the American Chemical Society, Atlantic City, New Jersey, September 13, 1968. ' W e are indebted to St. Martin's Press, New York City, New York for permission to reproduce material from several of Macmillan and Co., Limited books cited here as references.
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Figure 1. Simple form of Studnet's goniometer. Reproduced from A. G. Tufton'. "Crystallography and Practical Cr/stol Mewuremenb" (31 of Macmillon ond Company, publishers. with
ject. Also, he had an extremely sophisticated reflecting goniometer constructed from Wollaston's original design. This goniometer had four vernier scales and could be read to ten seconds of arc (3). The significance of such accuracy can be appreciated when one considers that interfacial angular measurements found in the literature are only reported to the nearest minute of arc. Mitscherlich did not use this "super-delicate instrument" for its designed purpose of carrying out precise comparative angular measurements of isomorphous crystals. He became interested instead in measuring the change in interfacial angles a t elevated temperatures. However, he was very active in research on isomorphism, not all of the results of which were published. Whether he was the true discoverer of isomorphism or not, nilitscherlich did play a key role in developing an accurate concept of the phenomenon. Upon Berzelius' prompting that the phenomenon needed a name, Mitscherlich turned to the Greek words iobs, meaning "equal to," and pup&, "shape" or "form." Thus, the term he derived means "equally shaped" or "identically formed." As for a definition of the word, Mitscherlich went on to state in 1821 (4) that "The same number of atoms combined in the same manner produces the same crystalline form; and the same crystalline form is independent of the chemical nature of the atoms, and is only' determined by the number and relative position of the atoms." "The last definition of isomorphism which we have direct from Mitscherlich," according to Tutton (5), was "'Substances possessing an analogous composition, which crystallize in the same form (or in similar forms) and which are capable of mixing in all proportions, are isomorphous.' " This is a
remarkably good description of isomorphism, though it is a matter of debate as to whether the restriction "all proportions" should be applied. Isomorphism has played a distinguished role in the development of chemistry. Even though there may be less interest in it today from a purely chemical standpoint than there was in the nineteenth century, it is none the less a most important modern tool, particularly in structural analysis. The significance of isomorphism both from an historical and modem standpoint can be summarized as follows
Table 2.
enabled Berzelius to draw up the first fairly accurate table of atomic weights in 1826. became a principle method for deriving atomic weights from chemical analytical dsts. showed periodic relationships of the elements. stimulus to interest in and study of crystallographic relation~hips'and~properties of crystals. affords a powerful modern tool for solving problems in structural analysis. offers a guide to development of new materials.
Table 3.
Study of isomorphous relationships in a purely crystallographic sense reached a high-water mark in this century as the result of efforts of Bruni (6) and Tutton (1, 3). Tutton, in particular, carried on and extended the unfinished work of Mitscherlich on the two isomorphous series of salts: (1) the alkali sulfates and selenates, (2) the double sulfates and selenates. His work on the characterization of crystals (1, S), though long out of print, are classics in the field. As has been seen, similarities in the shapes of crystals led to the discovery of isomorphism. This is revealed in Figure 2, which shows the slight variation in crystal form characteristic of three isomorphous materials.
Table 1 . Comparative Table of Interfacial Anaular ~ a g n i k d e of s Orthorhombic Sulfates
-
Angle ap
= (lOO):(llO)
Angle PP' =(ll0):(130)
Angle p'b
= (130):(010)
Mean Refractive Indices of Orthorhombic Sulfates 'Ida B v)Ns
+ +
Coefficient of Linear Expansion of Orthorhombic Sulfates a t t o ar=a+2bt Substance Direction a X 10F 2b X 10K$O, Parallel Axis a 3.616 2.88 b 3.225 2.82 e 3.634 8.26 RblS01 Parallel Axis a 3.637 4.06 b 3.214 3.68 c 3.463 7.60 CdO, Pardel Axis a 3.385 4.28 b 3.195 3.64 c 3.590 3.28
difference in one angle is 2" 29'. Of course, in the cubic system which has the highest symmetry of all, the interfacial angles are invariant. Thus the extent of variation of corresponding interfacial angles is a reflection of structural symmetry of the crystal series. The manner in which such an important physical property as the refractive index varies in an isomorphous e r y d s r r k is of consiilr~xhlr sigi~ifir~~nre. T:~hle2 shvws the values of thr nimii refrwtivr in~lires of "isomorphous" crystalsz listed by Tutton (7) for sodium light. I n the case of the three particularly closely related elements, potassium, rubidium, and cesium, there is progression in the refractive indices according to the atomic weight. At the same time there is a progressive diminution of the double refraction (the difference between the two extreme indices of refraction, or and y) of the three salts from I&SOa to Cs2SOI. The values for the ammonium salt are characteristically slightly higher than, but close to, the corresponding rubidium salt. The effect of the relatively high atomic weight of thallium (TI 204.37 versus 132.905 for Cs, for instance) is evident. This illustrates a general^ phenomenon, that replacing a light atom by a heavy one tends to increase the refractive index of a salt. I n a series of three closely related salts, such as ILSOa, RbpSOa,and Cs2Sod, other physical properties, on the other hand, may show negligible variation. The coefficient of linear expansion of these salts shown in Table 3 varies but little. Table 4 shows the close crystallographic similarity of this same series of salts. However, as Table 5 ~
Figure 2.
Variation in c r y t d habit in o series of iromorphov* cryrtolr.
Some of the interfacial angles in Figure 2 are.listed in Table 1. I n this particular series of salts where there is a fair degree of symmetry, differences in the corresponding anglesarenotgreat. For the angleslisted, thedifferences are less than a degree. I n fact angle pp' varies only by a minute. I n a series where the symmetry is lower, as in the case of the monoclinic double sulfates and selenates, KzCu(SeO&.6H20 and CslCu(Se0&.6H~O,the
~
According to our subsequent definition of isomorphism, this is not a true isomorphous series because KBO, and Cs2SO*do not form mixed crystals. Volume 46, Number 9, September 1969
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Table 4.
Crystol Data of Orthorhombic Sulfates
cell----Unit dimensions, A A B C 7.46 KBO, RblSOl 7.81 CstSOc 8.22 (NH,)?SO, 7.79 TI260, 7.81
10.08 10.43 10.92 10.62 10.68
Average
~;$;n Pnam Pbnm
2.621 3.615 4.246 1.772 6.77
Effect of Lattice Parameters in Orthorhombic Sulfates
-Form
Mixed-
7.79 10.62 5.98
c
Pnam
--Specific-Gravity Meas. Cdc.
Table 5.
Crystals (NH,)$O, K$O, a b
5.78 5.97 6.24 5.98 6.02
Space Grouo
.. .
7.46 10.08 5.78
...
Don't Form Differ- Mixed Crystals ence 70 C d O , K 8 0 4
4.42 5.36 3.46 4.41
8.22 10.92 6.24
...
7.46 10.08 5.78
...
2.658
... . .. ... ...
Difference
yo
10.2 8.33
7.96 8.16
shows by a comparison of the lattice constants for two different pairs of salts from this series, mixed crystals mill not form if there is too great a difference in these values. The average differences in the lattice parameters of IizSOnand (iYHa)lSOnis only 4.41 per cent. For ILSOa and CszSOn,however, the average difference is 8.16 per cent. I n the latter case this difference is sufficiently great so that the pair do not form mixed crystals. Figure 3 is a renresentatiou of the Dehve Scherrer powder patterns of these orthorhombic sulfates. c,
Figure 3. X-ray diffraction ponernr for isomorphour rulfater
The patterns of C&SOaand TltSOh are quite similar. I t is interesting to note that the patterns of I@04and Cs2SOI, which do not form mixed crystals, resemble each other more than do those of 1%O1 and (NH&SOI, which do form mixed crystals. The "abnormal" pattern of ammonium sulfate is due to the fact that the ammonium ion is a polyatomic tetrahedral one, rather than a monoatomic spherical one like the metal ions. Also hydrogen bonding causes a shift in the "d" spacings of (NHp)2SOa. Although Tutton may well have been the only chemist in this century who spent the major part of his career studying isomorphism from a purely crystallographic standpoint, there is a substantial amount of inorganic research relevant to the subject being conducted today. Banks (8) for instance, has been concerned with the similarities in structure of CazCrOaCl and C&P04C1. 582
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He showed (9) that the structures are made up of discrete Cr04a- and POa3- tetrahedra, both of which are considerably distorted from theidealconfiguration. His spectral studies in the ultraviolet, infrared, and visible regions as well as electron spin resonance investigations on chlorospodiosite, Caz(Cr04),(P04)l-,C1, mixed crystals showed that the C r O P was more distorted than the P O P tetrahedra. An example of other current work related to isomorphism is that of Conroy and Park (10) on the electrical properties of the group IV disulfides. They found that an unexpected, wide range of electrical properties was exhibited in the series of isostructural a-type semiconductors: Ti&, Zr&, HfS2, and SnSz. (Particularly in the case of the hafnium and tin compounds one would expect that mixed crystals could be obtained since the atomic radius for Hf4+is 0.78 A and for Sn4+0.71or 0.74 A). From the outset isomorphism has been beset with a basic dilemma, as well as various other confusing overtones which may not even yet he fully apparent. This is due to the fact that two different phenomena are involved-congruency of crystal structure and mixed crystal formation. As was pointed out earlier, the phenomenon of mixed crystal formation (1772) was known long before isomorphism was enunciated explicitly by Mitscherlich in 1819. However, the Wollaston-Mitscherlich elucidation of isomorphism was based upon observation of similarity of external crystal form as revealed by interfacial angular measurements. Only later did the concept of formation of mixed crystals between isomorphs come full circle from the work of De L'Isle and become implicit in the definition of isomorphism. Tuttou appears to have been the last authority on isomorphism to have stated the case sufficiently clearly and in full enough detail to facilitate a modern definition of the term. I n fact it is necessary to refer to his original discussions of the subject to appreciate some of the fine points involved (3). Before arriving a t this definition, thereare three more or less synonymous terms that bear mention. The first and most important of these is isostructural. We believe this term should be used in a more limited sense than isomorphism, in that it should not necessarily connote mixed crystal formation. Two crystals can be essentially structurally equivalent, and yet sufficiently different so that they do not form mixed crystals. Another term is isotypism explained by Kotovich (11). As used by Goldschmidt in 1937, the term refers to similar crystal structures which have different ratios of building blocks, i.e., CaF2-YF,. Fersman in 1934 used the term in the same way and mentioned the formation of mixed crystals. Isogonism mentioned by Yannlov in 1959 (12) appears to be an essentially synonymous but obscure term. There are also four other terms that are relate'tohut not synonymous with isomorphism. The first, endocryptism, refers to the case in which a non-naturally occurring compound is masked in a compatible mineral structure. The term is used principally in mineralogy. Isodimorphism refers to non-structurally identical crystals which exhibit polymorphism only in the presence of each other in mixed crystals. For instance, hexagonal osmium and cubic iridium form mixed crystals. The structure of the mixed crystals is either hexagonal or cubic, depending upon which isomorphous
constituent is present. in the greatest concentration. Another illustration of the way in which the term isodimorphous is used is the case of certain divalent metal (i.e., Mg2+, ZnZ+,NiZ+,MnZ+) sulfate heptahydrates (3), the vitriols. These can be caused to crystallize in a second form, monoclinic, by seeding the supersaturated solution with a monoclinic vitriol (i.e., Fez+, Co2+). Kotovich also mentioned the case of anomalous inixed crystals, an example of which is FCC& with NHnCI. He said that one material is selectively deposited on certain crystal faces of the second component. This is due to a two-dimensional instead of three-dimensional similarity of the two crystals. There is also a new term, krypto-isomorphism which has been set forth by Wolten (19). Iirypto or "hidden" isomorphism is exemplified by the systems shown in Table 6. Table 6.
Krypto-lsomo~ .phous Crystals That Form Mixed Crystals
5rOz Tetraional 1100°C) agonal lloonC) ieonal
UOS Cubic Gd.Ol Cubic T h G Monoclinic
Me% Tetraeonal
I n these cases materials ~ ~ idifferent th but nevertheless somewhat similar crystal structures can be made to form mixed crystals a t elevated temperatures. Even though a pair of crystals do not have sufficiently compatible structures to form mixed crystals a t one temperature, it may be possible for them to form mixed crystals under other conditions. Conversely, it is conceivable that mixed crystals could revert to their individual constituents under conditions where their respective lattices are incompatible. Thus i t is necessary to be quite specific as to the environmental conditions when referring to an isomorphous relationship. I n arriving at a judgement as to whether materials are isomorphous or not, it is necessary to compare the structures in as much detail as possible. An all important factor for isomorphism to exist is that'the crystals should he of the same type and belong to the same class. Information on this is given in standard crystallographic reference worl
