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ELONGATED TWINS OF SODALITE AND OTHER ISOMETRIC MINERALS.

Sodalite family minerals frequently form pseudo-hexagonal twins elongated parallel to their [111] twin axes. This habit, which is almost unique to these minerals, is caused by (a) the predominance of dodecahedral faces on their crystals and (b) their propensity to twin by rotation about a three-fold axis.

INTRODUCTION

Tens of thousands of mineralogists reading the various editions of Dana's System or Textbook have seen the drawing of a sodalite twin reproduced here (Fig. 1). The projection used in the drawing does not make it clear that such twins are almost invariably elongated along the pseudo-hexagonal axis of the twin. The twins are elongated because of the predominance of dodecahedron faces in these species, and the special geometric properties of a dodecahedron twinned about a three-fold [111] axis.

CRYSTAL MORPHOLOGY OF SODALITE FAMILY MINERALS

The sodalite family is composed of the minerals sodalite, nosean, hauyne and lazurite; cubic aluminosilicate species with the formula [(Na,Ca).sub.4-8] [Al.sub.6][Si.sub.6][O.sub.24][([SO.sub.4],Cl,OH,S).sub.1-2] n[H.sub.2]O. The members of the group are most frequently found in association with nepheline or leucite in nepheline syenites or phonolites and related undersaturated rocks. Beautifully crystallized examples are found in volcanic ejecta at a number of localities.

The predominant crystal form for all four species is the dodecahedron, as illustrated by the nosean crystal on biotite in Figure 2 and the beautiful, blue hauyne crystal in Figure 3. Modifying forms are the cube as on the hauyne shown in Figure 4 and the octahedron. The sodalite from Mount Vesuvius in Figure 5 shows major dodecahedron faces plus a rectangular cube face. In addition traces of the {211} trapezohedron are present as the very narrow, highlighted lines at the intersection of the dodecahedron faces. On rare occasions, the cube and octahedron are the major or only forms present. As the sodalite family minerals are all isometric, untwinned crystals are almost always equally developed along all three crystal axes; i.e., they are equant.

The four species have an amazing propensity to form twins such as those of sodalite from Monte Somma, hauyne from Mendig in the Eifel District, and nosean from the Alban Hills shown in Figures 6-8, respectively. The frequency of twinning is far higher than that for most other minerals, and the authors estimate that perhaps half the crystals seen from all localities are twins. As an extreme, all the nosean crystals from Mendig seen by the authors have been twinned.

Twinning occurs about a three-fold, i.e., a [111] axis, to give forms approximating the idealized drawing shown in Figure 1. Twinned crystals are almost invariably elongated, with length to width ratios varying from about 2:1 (Fig. 6) to as much as 5:1 and rarely 10:1, with smaller ratios being most frequent. Typical examples are those in Figures 6-8, showing beautiful, elongated twins of sodalite, hauyne and nosean, respectively.

The progression from untwinned dodecahedron (a) to twinned crystal (b), and then rotation to a more convenient, pseudo-hexagonal orientation and elongation (c) is shown in Figure 9. The twin axis, [111], is shown in 9a and b. Note the reentrants at the terminations of the crystal and the co-planarity of the d and d' faces in the "prism" zone in Figures 9b and c, similar to those on natural crystals in Figures 6-8. In a geometric sense, most of any such "prism" face belongs to both halves of the twin simultaneously. In a real crystal, any spot must belong to one half or the other, but the actual pattern of intersection between the two halves may be very complex, much as it is on a Dauphine-twinned quartz crystal.

As stated before, dodecahedra of sodalite family minerals are frequently modified by minor cube and octahedron faces. Twins of such modified crystals may involve remarkable and somewhat confusing juxtapositions, shapes and numbers of cube and octahedron faces.

The faces in an untwinned cube can be envisioned as being arrayed in two groups of three about opposite ends of a threefold [III] axis. If twinning occurs about this axis as in Figure 9, two sets of six cube faces are generated, and these are arranged like two crowns around opposite ends of the elongated twin as in Figure 9d!

Octahedron faces, with their three-fold symmetry, are present in untwinned crystals such that the crystals' three-fold axes emerge at the centers of the faces. That is, in Figure 9a, an octahedron face would be an equilateral triangle at the intersection of the three dodecahedron faces where the twin axis emerges. On twinning, that octahedron face and the one at the opposite end of the crystal appear as the sums of pairs of equilateral triangles rotated 1800 with respect to each other; i.e., as symmetrical, six-pointed stars! The resultant twin of a dodecahedron modified by cube and octahedron is shown in Figure 9d, and, viewed down the pseudo-hexagonal axis, in Figure 9e. Discerning readers may wish to know what happened to the 12 remaining octahedron faces, since only 4 (2 from each half of the twin) have been accounted for. The answer is that they lie in the interior of the crystal relative to portions of the dodecahedron from the other half of the twin, and are thus not expressed on the twin's exterior.

Returning now to real crystals, fine examples of twinned nosean crystals with modifying cube faces from Mendig are shown in Figures 10 and 11. SEM photos showing modifying cube faces are shown in Figures 12 and 13. An incomplete (four-rayed, instead of six-rayed) twinned octahedron face appears on the crystal in Figure 13. The end-on view of the same crystal in Figure 14 shows more clearly the incomplete nature of the six-rayed star and the irregular growth of the crystal. It is regrettable that nature so seldom presents us with ideally grown, symmetrical crystals! Yet imperfect crystals are quite common, and not infrequently illustrated in crystal drawings from the older literature.

Numerous other examples of such twins could be illustrated by the authors, as shown by the citations in Table 1. No less than nine localities for twinned sodalite, two for hauyne, and four for nosean are known to them, and there are doubtless many more. It is interesting that the reported localities are so closely associated with volcanic regions, the Eifel District in Germany, and areas north of Rome and on Mount Vesuvius in Italy; all noted for their under-saturated, pyroclastic rocks. Surely there are examples of elongated twins of sodalite minerals from other areas, and the authors would appreciate word of them.

Elongated twins of sodalite family minerals have been reported repeatedly and since very early times. For example, vom Rath (1866) described elongated twins of sodalite from the Alban Hills in Italy, and Hubbard (1887) reported elongated nosean crystals from the Eifel district in Germany. Photographs of such crystals (including the nosean shown in Figure 15, taken from Hentschel (1987)) have also appeared in the literature. While some drawings depict equant twins of sodalite family minerals, we know of no instance of an author explicitly stating that the twins are not elongated.

In spite of the ubiquity of elongated twins, no source known to the authors comments on the cause of the elongation. A plausible mechanism for elongation follows.

CAUSE OF ELONGATION IN TWINNED SODALITE FAMILY MINERALS

Elongation of twinned sodalite family minerals is a kinetic phenomenon; i.e., it is caused by relatively fast growth of the terminal faces compared to the relatively slow rate of growth of the "prism" faces of the twin. This in turn is related to the ease with which new growth layers can be formed in a growing crystal. Thus, the final crystal form is kinetically (rate) controlled, and is not the normal, equant, equilibrium-controlled form.

Consider growth of the top face of the crystal shown schematically in Figure 16. Each small cube can be considered as either a single atom or a "unit cell" of the complete crystal. Initiation of a new growth layer involves deposition of a new cube at position 1. Such a cube, attached on one side only, adheres only very weakly to the crystal. In fact, at low degrees of supersaturation, such a building unit skitters about on the crystal surface, and will most likely fly off the crystal face before more cubes can adhere next to it. Once begun, though, a partially completed growth layer creates a ledge as shown in Figure 16. Along the ledge newly deposited cubes such as 2 and 3 are attached on two or three sides, respectively. Since bonding at these points is much stronger, cubes such as 2 and 3 are much less likely to detach themselves, and accretion to the growing face along the ledge is much faster than the initiation of a new growth layer as at one-contact positions such as 1. Hence, the limiting factor in c rystal growth is the creation of new growth layers or, put differently, the creation of ledges. It should be remembered, here, that the above argument applies only under conditions of low supersaturation of the solution from which the crystal is growing. At high supersaturations, the rate at which material is deposited at points such as 1 is so high that the rate at which such atoms or cubes fly off again is no longer limiting.

Under what conditions can growth ledges be maintained or created? A prime example is the presence of a screw dislocation in a crystal (Fig. 17). The self-propagating ledge ascending in a spiral about the screw dislocation promotes continuous and rapid growth in that direction while the absence of growth ledges on the side faces causes little or no growth laterally. Whisker crystals with length to width ratios of 10:1 or 1000:1 are thus created (Henderson and francis, 1989). Note that, except in the immediate neighborhood of the screw dislocation axis, the packing of unit cells is perfectly normal and strain free. In a real crystal, extending thousands of unit cells in all directions, strain at the screw axis is not important.

As shown in Figure 18, twinning can also afford a self-perpetuating growth ledge. This two dimensional representation shows that, at a twin reentrant, the first "cube" of a new growth layer is attached on two sides, not just one. This critical increment in stability makes the rate of growth within the reentrant faster than growth where no reentrant exists.

Returning to sodalite family twins, then, it could be said that the reentrants in the terminations of these twins promote relatively fast growth in the direction of the pseudo-hexagonal axis, while the absence of such reentrants in the prism zone causes growth to be slower laterally. This is not strictly correct, however, since growth in the twin reentrants has a vector component in the lateral direction as well as the longitudinal one. The correct way to put it is that the reentrant causes relatively rapid growth of the two faces comprising each reentrant, while the "prism" faces, each composed of two coplanar faces, one from each half of the twin, have no reentrants, and grow only slowly. The slow-growing prism faces act as boundary limits for, and limit the lateral growth of, the faces of the reentrant, and elongated twins result.

Note that the "fit" of a new cube within the reentrant of a twin is not as perfect as for a cube deposited at a partially completed growing ledge, or at a screw dislocation edge. The misfit can be either an angular one or a dimensional one, depending on the geometry of the reentrant. For this reason, the strength of attachment of such a cube is not as great as for one added to a ledge at a screw dislocation. Perhaps this in turn explains why the aspect ratio of whisker crystals formed by screw dislocations can be 10:1 to 1000:1, while that of elongated sodalite family twins is rarely even 10:1.

All the above is discussed in terms of a crude, diagrammatic model. In actual fact, accretion of material on a real crystal face or ledge is controlled by complex electromagnetic interactions. These can be and have been considered by various authors (e.g. Grigor'ev, 1965), and results of their calculations of attachment energies parallel those from the above much cruder model.

It might be pointed out that while rapid growth in twin reentrants only rarely produces elongated twins such as these, it commonly produces flattened twins. Good examples are spinel twins of isometric minerals such as diamond, magnetite, gold, and silver; and unusually flat twins of rhombohedral carbonate minerals such as calcite, siderite and rhodochrosite. Similarly, while the two halves of Japan twins of quartz may have undistorted, hexagonal cross sections, the area between the two limbs is often filled in by rapid growth within the twin reentrant, giving tabular crystals (Henderson and Francis, 1989).

Recognition that twinning can stimulate or accelerate the rate of growth of crystals and crystal faces is by no means new, and has been commented on by Tertsch (1926), Frank (1949) and Grigor'ev (1963) in fairly recent times. The importance of the reentrant angle of twins to their growth kinetics was already known to Becke (1889), and was stressed again by Frank (1949).

ISOMETRIC FORMS OTHER THAN THE DODECAHEDRON WHICH MIGHT FORM ELONGATED TWINS

The question arises as to whether forms in the hexoctahedral class of the isometric system other than the dodecahedron can yield similar, elongated twins. The prime requirement for such elongated twins is that the twinning operation yield a pseudo-hexagonal prism zone (hereafter called a belly band) of faces, each of which is made up of two coincident faces, one from each half of the twin. The twinning operation, of course, is a rotation of 180[degrees] about a three-fold, i.e., [111] axis. To meet the above conditions, it is sufficient to show that faces of the form lie in the zone [111], i.e., are parallel to the twin axis. To show that a face (hkl) lies in the zone [uvw], the zonal equation

hu + kv + lw = 0

must be satisfied (Dana and Pord, 1932, pg. 63). In the present case, [uvv] is equal to [111] and by substitution into the equation above, the condition becomes

h + k + l = 0, or h = -(k + 1).

That is, one index must be equal in value but opposite in sign to the sum of the other two. Because of the symmetry properties of the hexoctahedral class, this condition is equivalent to h = k + 1, where {hkl} are the indices of the form, listed in their conventional order with h[greater than]k[greater than]l[greater than or equal to]0.

Symmetry considerations then show that, if one face of the form satisfies the above equation there will exist a belly band of six (or twelve) faces which lie in the zone of the twin axis. Forms of the hexoctahedral class of the isometric system have the symmetry 4/m 3 2/m,. They are characterized by having three axes of four-fold symmetry, four axes of three-fold symmetry (one of which is our twin axis), six axes of two-fold symmetry, nine planes of symmetry, and a center of symmetry (Dana and Ford, 1932). Of these, the three-fold axes and center are of importance to our argument. First, a face shown by the zonal equation to be parallel to the [111] twin axis must, since this is a three-fold axis, have two more faces 120[degrees] apart from it in the zone. Second, by virtue of the center, each of these three faces must have one opposite it (180[degrees] apart from it), generating a group of six faces 60[degrees] apart from each other and lying in the twin-axis zone.

Alternatively, readers who are geometrically and mathematically inclined can reach the same conclusion as to the presence or absence of a belly band of faces at 60[degrees] from each other using Miller Indices alone. This can be done for the various isometric forms by the following sequence of operations: (a) choose a Ft [l11] twinning axis on a crystal model or drawing; (b) identify faces which may make up a belly band on twinning; (c) show that the Miller Indicesa of a chosen face apparently parallel to the twin axis do indeed satisfy the zonal equation as before; and (d) show that an adjacent face with a similar orientation is 60[degrees] from the first face. The last step can easily be done using the equation for calculating the angular distance between the poles of two faces, P (hkl) and Q (pqr) as given in Dana's Textbook (Dana and Ford, 1932, pg. 90):

cos PQ = hp + kq + lr/[square root of]([h.sup.2] + [k.sup.2] + [l.sup.2]) ([p.sup.2] + [q.sup.2] + [r.sup.2])

This can be simplified and, on substituting cos PQ = cos 60[degrees] = 1/2 reduces to:

1/2 = hp + kg + lr/[h.sup.2] + [k.sup.2] + [l.sup.2]

Actually, it can be shown algebraically that any form which satisfies the zonal equation will also satisfy the interfacial angle equals 60[degrees] requirement, thus making step (d) superfluous. That is to say, the same conclusion is arrived at using Miller Indices as is obtained by consideration of symmetry elements. It would be most disconcerting if this were not the case!

For those not wishing to do the calculations, the following conclusions are presented. The cube {100}, octahedron {111}, all trisoctahedra {hhl}, and all tetrahexahedra {hk0} do not yield belly bands since they cannot satisfy the zonal equation. As shown earlier, the dodecahedron {110} has a belly band of six faces. Of all the possible trapezohedra, {hll}, only the simplest, {211}, yields a belly band; again one of six faces. All those hexoctahedra, {hkl}, where h = k + l yield belly bands with twelve, not six, faces. An infinite number of hexoctahedra including {321}, {431}, {532}, {743}, {853}, and {20.13.7} satisfy this condition. However, the empirical observation that forms with low indices are far more common than those with high indices suggests that only the first two or three hexoctahedra listed above will occur as elongated twins with any frequency.

The shapes of the belly bands (shaded) for the dodecahedron, the {211} trapezohedron, and the {321} hexoctahedron are given in Figure 19, along with the shapes of the (extended) belly band faces in their twins on [111]. The shapes of the belly band faces change in the twins because (a) they are the sum of two such faces, and (b) they must be extended to follow the rapid growth of the terminal faces parallel to the pseudo-hexagonal c-axis. Their faces are delineated by their line of intersection with the fast-growing terminal faces, while the terminal faces are limited in their lateral extent by the line at which they intersect the slow-growing prism or belly band faces.

As can be seen from the shaded drawings below the first row in Figure 19, the faces which produce the prism have a large degree of overlap in the twin. This is fine in a geometric construction, but it is impossible in a real twinned crystal, because any small region of the twin must have a structure which corresponds to just one of the two orientations. The surface along which the two halves of a twin actually meet cannot be predicted by geometric construction, and may be quite complex. For this reason, these faces are labeled d/d' in Fig. 9, indicating that they are composed of contributions from each half of the twin.

In the pseudo-hexagonal frame of reference, the belly band faces of the untwinned dodecahedron can be assigned to the second order hexagonal prism {1120}. The belly band of the {211} trapezohedron then corresponds to a hexagonal prism, but one that is rotated 60[degrees] with respect to the prism of the dodecahedron; i.e., it is the first order hexagonal prism {1010}. Thus, an elongated twin of a crystal with both dodecahedron and {211} trapezohedron faces would exhibit a belly band of twelve faces derived from the two prisms. The interfacial angles in the prism zone would all be 30[degrees].

For the {321} hexoctahedron, using the pseudo-hexagonal frame of reference, a belly band of not six but twelve faces is observed. The calculated interfacial angles between adjacent pairs of prism faces alternate between 38[degrees]13' and 2l[degrees]47', so that the sum of the two is exactly 60[degrees]. This belly band constitutes a dihexagonal prism, {4150}, the angles of which are exactly those reported above. For the general case of hexoctahedra {hkl} satisfying the zonal equation h = k + 1, the Miller Indices of the corresponding dihexagonal prism are (2l + k k-l 2k + l0}.

The terminal faces of the isometric forms referred to a pseudo-hexagonal axis system are various positive and negative rhombohedra and scalenohedra. Thus, we find that the isometric forms which can produce twins with belly bands composed of pairs of coplanar faces, one from each half of the twin, are limited to the dodecahedron, the {211} trapezohedron, and those hexoctahedra for which h = k + l. (A more general treatment of forms and faces analyzed in the dual framework of the isometric and hexagonal systems is available on request from the second author.)

ELONGATED, TWINNED CRYSTALS OF OTHER SIOMETRIC MINERALS

Having observed that elongated twins of sodalite-family minerals are very common, we might ask whether other minerals also form elongated twins on [11l]. A brief commentary on the subject follows.

First, it should be noted that the authors have not yet seen elongated, twinned dodecahedra of the fourth mineral of the sodalite family, lazurite. Perhaps it is significant that neither Dana's System nor any of several other standard references mention twinning of lazurite, while twinning is always noted for the other three members of the group. Still, the existence of elongated lazurite twins is quite probable.

Are there other minerals occurring in dodecahedra and reported to form such twins? The answer is yes. Just such a twinned dodecahedron of sal ammoniac is pictured in Dana's System of Mineralogy (Palache et al., 1951). Very similar twins of sal ammoniac were reported from Arniston in Great Britain by Shand (1910), and from Mount Vesuvius in Italy by Scacchi (1874). The perspective used in the crystal drawings of Palache et al. and Shand (Figs. 20 and 21) makes it difficult to tell whether these twinned dodecahedra were elongated, and the text in all three cases fails to mention elongation. We determined elongation by drawing an unelongated twin using SHAPE, rotating and sizing it to match these drawings, and superimposing the two in the computer. As it turns out, Fig. 20 shows a somewhat elongated crystal (aspect ratio about 1.5:1), while Fig. 21 shows no elongation.

Sphalerite too has been reported to form twinned dodecahedra. Lacroix (1896) reported and figured such crystals from Pontpean in France (Fig. 22), while Niggli's Tabellen (1927) includes a crystal drawing of such a twin from the Harz Mountains in Germany. Again, in neither case is elongation mentioned. Our procedure shows these crystals to be drawn without elongation.

It should be noted that sphalerite has a lower (tetrahedral) symmetry than the hexoctahedral minerals discussed above. The dodecahedron and cube are permissible forms on sphalerite crystals and would appear in twins formed by rotation about a threefold axis just as they do in sodalite, for example. However, the octahedron is not a permissible form on sphalerite crystals, and is replaced by faces of the positive and negative tetrahedra. Often, only one tetrahedron is present. If a sphalerite crystal with faces of the dodecahedron and one tetrahedron were twinned, it would display a single six-pointed star at one end of the crystal but not at the other. The pseudohexagonal twin would appear to be hemihedral!

What other isometric minerals might form elongated, dodecahedral twins? Those most likely to do so must (a) occur frequently in dodecahedra and (b) form twins by rotation about a [111] axis. Members of the garnet family come immediately to mind as frequently forming crystals where the dodecahedron is the sole or dominant form. However, garnets are not reported to twin about [111]. Fluorite and boracite are excellent possibilities as each occasionally forms dodecahedra, and twinning about [111] is known. It is quite possible that elongated twins exist somewhere in collections. In the spinel family, magnetite offers a possibility. The other 16 common, isometric minerals listed in Dana's Textbook (Dana and Ford, 1932, Appendix B) do not occur often in dodecahedra and/or do not twin on [111].

Are there elongated twins of the {211} trapezohedron or the permitted hexoctahedra? Analcime and the garnet family minerals frequently form {211} trapezohedra, but neither is reported to twin. Leucite occurs predominantly in {211} trapezohedra and is frequently twinned, but does not twin by rotation about [111]. Perhaps diamond, which twins on [111] and is found occasionally in hexoctahedra, offers some possibilities.

As it happens, the authors' predictions as to what isometric forms can generate belly bands, and what isometric minerals are likely to form elongated twins, were in part anticipated by work done 120 years ago. After the above was written, the text of the original paper by Scacchi (1874) on twins of sal ammoniac was finally obtained. In it, he not only described simple twinned dodecahedra of sal ammoniac; he also showed and correctly interpreted sal ammoniac twins with far less common forms. His crystal drawings (reproduced here as Fig. 23) do not show just another example of a twinned dodecahedron; rather, they show a twinned {211} trapezoherdon! It is interesting that some of the trapezohedron faces which might have appeared in the crystal's termination are missing (but are shown in our Figure 24). Had they been present, the crystal would have had a much less pointed termination. Also reported by Scacchi (his crystal drawing, reproduced here in Figure 25) were twins with dodecahedron and {211} trapezohedron faces! Note that the drawing shows the pseudo-dihexagonal prism comprised of twelve faces predicted by the authors. And finally, he noted that, very rarely, he even observed the {321} hexoctahedron in combination with the above forms! He also measured and calculated interfacial angles for the forms he postulated, thus confirming his interpretation.

In addition, Hintze (1892) described sodalite crystals from the Alban Hills near Rome as shown in his crystal drawing reproduced in Figure 26. Along with

the fairly common dodecahedron and cube faces of such twins, he also shows the much rarer {211} trapezohedron. Interestingly, while Scacchi's sal ammoniac crys tals lacked the set of terminal {211} faces mentioned above and thus were quite pointed, Hintze's sodalite crystals retained both sets of terminal {211} faces and thus had a very blunt termination. On the other hand, Hintze's crystals with both {110} and {211} faces lacked the set of six {211} trapezohedron faces in the prism zone which were present in Scacchi's crystals. It is not clear what Mother Nature's rules are as to whether certain faces of a form are present or missing.

Hintze (1879) also illustrated sodalite twins from Mount Vesuvius which include the dodecahedron, trapezohedron, cube, and octahedron (Fig. 27). The illustration on the right is of a symmetric contact twin, rather than the penetration twins which are the focus of this paper. The one on the left is of a much more complex intergrowth, with missing or unevenly developed faces and complicated interfaces between the twinned individuals. This one reminds us of one of the hazards of crystal drawings: it is often hard to tell whether the drawing is of an actual crystal or an idealized one!

Scacchi, Hintze and the other crystallographers of long ago deserve great credit for the fine work they did with far poorer tools for measurement and computation than we have today.

CONCLUSION

The sodalite family minerals are by far the best exemplars of the elongated twins of isometric minerals. There are isolated examples of similar twins of sphalerite and sal ammoniac, but only a few other species are likely to form such twins.

ACKNOWLEDGMENTS

The authors are greatly indebted to E. van der Meersche for photographs, Maria Rosaria for research assistance with the literature, and Dr. Carl A. Francis (Harvard) for the loan of specimens for study.

REFERENCES

BECKE, F. (1889) Em Beitrag zur Kenntnis der Kristallformen des Dolomites, Tschermach's Mineral. Petrogr. Mitt., 10, 93-152.

DANA, E. S., and FORD, W. E. (1932) A Textbook of Mineralogy. Fourth Edition, John Wiley and Sons, New York.

FRANK, F. C. (1949) The influence of dislocations on crystal growth. Discussions of the Faraday Society, 5, 186-187.

GRIGOR'EV, D. P. (1965) Ontogeny of Minerals. English translation by the Israel Program for Scientific Translations, 39.

HENDERSON, W. A., JR., and FRANCIS, C. A. (1989) On right angle bends in filiform pyrite. Mineralogical Record, 20, 457- 464.

HENTSCHEL, G. (1987) Die Mineralien der Eifelvulcane. Lapis Monographie, Munchen, Germany, 88-89.

HINTZE, C. (1879) Handbuch der Mineralogie. Vol. 2, Verlag von Veit und Ca, Berlin, p. 888-904.

HINTZE, C. (1892) Handbuch der Mineralogie. Second Edition, Vol. 2, Verlag von Veit und Ca, Berlin, p. 903.

HUBBARD, L. L. (1887) Beitrage zur Kenntnis der Noseanfuhrenden Auswurflinge des Laacher Sees. Mineralogische und Petrographische Mittheilungen, 8, 356-399.

KLEIN, C. (1879) Neues Jahrbuch fur Mineralogie, Geologie und Paleontology. E. Schweizerbart'sche Verlagshandlung, Stuttgart, p. 534-535.

LACROIX, A. (1896) Mineralogie de la France et de Ses Colonies. vol. 2, p. 527.

LLOTI, L. (1994) I minerali del complesso vulcanico dei Colli Albani. Rivista Mineralogica Italiana, 17, 9-31.

NIGGLI, P. (1927) Tabellen zur Allgemeinen und Speziellen Mineralogie. Gebruder Borntraeger, Berlin, p. 35.

PALACHE, C., BERMAN, H., and FRONDEL, C. (1944) System of Mineralogy of J. D. Dana and E. S. Dana. Seventh Edition, Vol. 1. John Wiley and Sons, New York, p. 25.

PALACHE, C., BERMAN, H., and FRONDEL, C. (1951) System of Mineralogy of J. D. Dana and E. S. Dana. Seventh Edition, Vol. 2. John Wiley and Sons, New York, p. 15-16.

SCACCHI, A. (1874) Contribuzioni Mineralogiche per Servire alla Storia dell'Incendio Vesuviano. Memoria Estratta dal Vol. VI degli Atti della R. Accademia della Scienze Fisische e Matematiche di Napoli, p. 28-35.

SHAND, S. J. (1910) On a group of minerals formed by the combustion of pyritous shales in Midlothian. Mineralogical Magazine, 15, 404-405.

TERTSCH, H. (1926) Trachten der Kristalle. Forschungen zur Kristallkunde, Vol. 1, Berlin.

VOM RATH, G. (1866) Mineralogisch-Geognostiche Fragmente aus Italien. Zeitschrift der Deutschen Geologischen Gesellschaft, 18, 487-642.
           Localities for elongated twins of isometric minerals.
       Species/Locality                            Elongation [*]
Sodalite
  Wannenkopfe, Eifel district, Germany                 +
  Pollena quarry, Monte Somma, Napoli,
    Campania, Italy                                    +
  San Vito quarry, Mount Vesuvius,
    Napoli, Campania, Italy                            +
  Mount Vesuvius, Napoli, Campania, Italy              +
                                                       -
  Monte Cavalluccio, near Sacrofano,
    Roma, Lazio, Italy                                 +
  Castellaccio de Petrignano, near Vetralla,
    Viterbo, Lazio, Italy                              +
  Carcarelle, near Vetralla, Viterbo, Lazio, Italy     +
  Alban Hills, Roma, Lazio, Italy                      +
                                                       -
  Insel Laven, Langesundfiord, Norway                  +
  Synthetic                                            +
Hauyne
  Mendig, Eifel district, Germany                      +
                                                       +
  Alban Hills, Roma, Lazio, Italy                      -
Nosean
  Mendig, Eifel district, Germany                      +
  Laacher See, Eifel district, Germany                 +
 Alban Hills, Roma, Lazio, Italy                       +
  Tobia, near Vetralla, Viterbo, Lazio, Italy          +
Sal Ammoniac
  Amiston, Midlothian, Great Britain                   -
  Eruption of 1872, Mount Vesuvius,
    Napoli, Campania, Italy                            +
  Synthetic                                            +
Sphalerite
  Pontpean, France                                     -
  Harz Mountains, Germany                              -
       Species/Locality                        Source/Reference
Sodalite
  Wannenkopfe, Eifel district, Germany Coll. WAHJr.
  Pollena quarry, Monte Somma, Napoli,
    Campania, Italy                    Coll. WAHJr.
  San Vito quarry, Mount Vesuvius,
    Napoli, Campania, Italy            Coll. WAHJr.
  Mount Vesuvius, Napoli, Campania,    Goldschmidt, 1922; Scacchi, 1847
Italy
                                       Hintze, 1879
  Monte Cavalluccio, near Sacrofano,
    Roma, Lazio, Italy                 Coll. WAHJr.
  Castellaccio de Petrignano, near
Vetralla,
    Viterbo, Lazio, Italy              Coll. WAHJr.
  Carcarelle, near Vetralla, Viterbo,  Coll. WAHJr.
Lazio, Italy
  Alban Hills, Roma, Lazio, Italy      Goldschmidt, 1922; vom Rath, 1887
                                       Hintze, 1879, 1892
  Insel Laven, Langesundfiord, Norway  Klein, 1879; Goldschmidt, 1922
  Synthetic                            Dana, 1892
Hauyne
  Mendig, Eifel district, Germany      Coll. WAHJr.
                                       Coll. E. van der Meersche
  Alban Hills, Roma, Lazio, Italy      Liotti, 1994
Nosean
  Mendig, Eifel district, Germany      Hentschel, 1987
  Laacher See, Eifel district, Germany Goldschmidt, 1922; Hubbard, 1887
 Alban Hills, Roma, Lazio, Italy       Yale Univ., Cahn Coil. #2960
  Tobia, near Vetralla, Viterbo,       Coll. WAHJr.
Lazio, Italy
Sal Ammoniac
  Amiston, Midlothian, Great Britain   Goldschmidt, 1922; Shand, 1910
  Eruption of 1872, Mount Vesuvius,
    Napoli, Campania, Italy            Scacchi, 1874
  Synthetic                            Palache et al., 1951
Sphalerite
  Pontpean, France                     Goldschmidt, 1922; Lacroix, 1897
  Harz Mountains, Germany              Niggli, 1927


(*.)The symbol + indicates that (1) crystals observed by the authors were elongated, or (2) the text and/or figures of the referenced papers stated and/or showed elongation. The symbol -- indicates that neither the text nor the figures showed elongation to be present. It should be noted that some authors may not have considered elongation to be of significance, and may have deliberately drawn an equant twin.
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Author:Henderson, Jr., William A.; Richards, R. Peter; Howard, Donald G.
Publication:The Mineralogical Record
Geographic Code:1USA
Date:Mar 1, 2000
Words:5465
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