N. N. Gornostaev.

On New Laws of Feldspar–Quartz Intergrowths of the Granophyric Type.

From the Geological Laboratory of the Tomsk Technological Institute.

(With 5 drawings).

In the petrographic treatment of material from young eruptions of igneous rocks in the Kirghiz steppe, I had occasion to come upon several laws governing the formation of micropegmatitic intergrowths of quartz in feldspar; moreover, they reveal a very clear connection with the crystallographic properties of both minerals. Of these laws, three proved to be new, not yet described in the literature on the subject known to me.

The rock of hand specimen (and thin section) No. 16—237 is a medium-grained, somewhat porphyritic quartz augite diorite, consisting of a hypidiomorphic-granular aggregate of apatite, magnetite, pinkish-violet-gray titaniferous augite, finely flaky biotite (very little), and extremely sharply—and finely—zoned porphyritically protruding plagioclase with fine twin striation; the plagioclase is sometimes bordered by a rim of anorthoclase or by micropegmatitic intergrowths of the latter with quartz; the last to crystallize were anorthoclase, quartz, and their micropegmatitic intergrowths, which take a fairly substantial part in the composition of the rock.

This diorite composes a low hill in the southern part of the Semei-tau mountains (60 versts southwest of Semipalatinsk), situated 5 versts south of the settlement of Petrograd and 8 versts east of the village of Znamenskoe, representing a hypabyssal facies or, perhaps, even the root portion of the augite liparites and augite andesites developed in the Semei-tau. In any case, the final solidification of the diorite described took place at a depth not exceeding 300 m, reckoned from the present eroded land surface, and most probably at a depth of even less than 200 m.

The abundance of granophyric intergrowths and the size of the quartz ingrowths, which permitted a rather precise determination of their orientation by means of E. S. Fedorov’s universal method, prompted me to undertake a closer study of these intergrowths. Indeed, it seemed that, under conditions of rapid crystallization of granophyric eutectics in a viscous medium poor in mineralizers, the laws of intergrowth of the two minerals might prove to be different in comparison with those established earlier, chiefly by Academician A. E. Fersman, for the written structures of pegmatites¹; namely, they might differ from the latter by a lesser correctness of the geometrical mutual relations of the crystalline lattices of both minerals. Probably in this same sense one should also understand F. Yu. Levinson-Lessing’s suggestion² concerning the different nature of the written structures of pegmatites and feldspar–quartz eutectics. In reality, however, it turned out that although, alongside the already known laws, new laws were found, the geometricity and regularity of the latter are in no way less than those of the old laws, and that, from a purely crystallographic point of view, there is apparently no difference between the two types of written structures, if only one abstracts

…on the scale of the phenomena. From this, in turn, it follows that, since the difference in the physicochemical conditions of crystallization has almost no effect on the regularity of intergrowths, the latter must be due to causes lying deeper in the structure of the crystalline lattices themselves.

My attention was first attracted by a grain of anorthoclase of rounded-rectangular form, almost isometric, only slightly elongated along \([001]\), so that along its middle, coinciding at first sight with the plane of the second pinacoid \((010)\), there was situated a thin platy quartz inclusion, hook-like bent at one end. This inclusion divided the feldspar crystal along its length into two almost equal halves, and therefore the homogeneous anorthoclase grain in itself at first gives the impression of a Carlsbad twin, until the observer realizes what the matter is. Besides this platy inclusion, in the grain described there are also several small micropegmatitic quartz inclusions, which are divided into differently oriented groups in such a way that within each group the inclusions extinguish simultaneously. All of them are confined to the outer parts of the feldspar grain, whereas its center is entirely homogeneous, if one does not count the above-mentioned thin inclusion and one thin, barely noticeable twin lamella of anorthoclase, situated almost perpendicular to the first. The simultaneous presence of cleavage cracks along both pinacoids, clearly visible thanks to the exceptional freshness of the feldspars, made it possible to carry out a detailed and fairly accurate investigation on the universal stage. The results of the measurements are summarized in the following table (Table 1) and are illustrated by the appended gram-stereographic projection of the elements of the optical ellipsoid of the anorthoclase, its cleavage planes, and the optical axes of two quartz inclusions, whose position could be determined (Drawing 1).

Table 1. Anorthoclase.

Optical axes:
\(A\)—toward oneself \(13\frac12^\circ\)
\(14^\circ\)
\(13\frac12^\circ\)
\(\overline{13\frac12^\circ}\)

\(B\)—away from oneself \(38\frac12^\circ\)
\(39^\circ\)
\(39^\circ\)
\(\overline{39^\circ}\)

\[ 2V = -52^\circ \]
\[ -53^\circ \]
\[ -52\frac12^\circ \]
\[ \overline{2V = -52\frac12^\circ} \]

\[ (010):(001)=90\frac12^\circ \]
\[ (010):(001)=89\frac12^\circ \]
\[ \text{(the angle is taken between the poles of the pinacoids).} \]

Thanks to the preservation of darkness upon inclinations in different directions about the \(H\) axis of the universal stage in the case of sections close to perpendicularity to \([100]\) (the first crystallographic axis), the planes of the ellipsoid suc-

they are smoothed out with some fluctuation; however, the agreement of the mean values leaves nothing better to be desired. The cleavage along \((010)\) is expressed in the form of cracks, not running quite straight, but composed of stepwise-joining segments, which explains the fluctuations in the measurements of the cleavage; the cleavage along \((001)\), despite the large angle of inclination, is expressed very distinctly. From the drawing it is easy to derive also the extinction angle on the cleavage planes, namely—

Extinction angles:

\[ \angle Np : (001)\ \text{on}\ (010) = -2^\circ . \]

\[ \angle Np : (010)\ \text{on}\ (001) = \sim 0^\circ . \]

By the angle of the optic axes this feldspar belongs to anorthoclase, which is a representative of the alkaline feldspars in the liparites of the Semeytau; true, this grain deviates somewhat from the usual type of anorthoclase, being similar in this respect to the feldspar from Lille Frogner¹, with an increased content of \(\mathrm{Al_2O_3}\), \(\mathrm{CaO}\), and with a small amount of \(\mathrm{Na_2O}\).

As for the quartz intergrowths, the first of them—the lamellar one—proves in fact to be elongated along the plane of the second pinacoid, the normal to the thin section of the principal section having the coordinate \(N = 241^\circ\), and the optic axis is inclined in it toward the observer at an angle of about \(44^\circ\) (after reduction to the refractive index of the segments \(n = 1.52\), we obtain the value \(43^\circ\)).² If we now turn to drawing 4, where the faces and zones of the feldspar studied are plotted in gnomostereographic projection (for simplicity of construction the geometrical constants of orthoclase are adopted), and in grammastereographic projection the axes of the quartz intergrowths observed by me are plotted (marked by triple circles and by the sign \(Qu_i\), where \(i\) corresponds to the serial number of the intergrowth), then it is seen that the axis of the intergrowth \(Qu_1\), within the limits of accuracy of graphical constructions and observations, may be regarded as coinciding with the grammastereographic projection of the zone \([\overline{2}10]\), passing through the faces \((\overline{1}20)\) and \((001)\) of the feldspar, with which, therefore, the prismatic zone of quartz coincides. In this case one of the faces of the rhombohedron of quartz may coincide with the plane \((010)\) almost exactly (and perhaps quite exactly).

The second intergrowth has, for the section perpendicular to the thin section of the principal section, the coordinate \(N = 330^\circ\), and the optic axis in it is inclined toward the observer at an angle of about \(65^\circ\), or, after correction for the difference of the refractive indices of quartz and of the glass of the segments, \(63^\circ\). When transferred to the diagram of drawing 4, we obtain a very remarkable regularity with respect to the feldspar. Namely, if a small circle is drawn, 52° distant from the point \(Qu_2\) and representing the geometrical locus of possible gnomostereographic projections of the faces of the principal rhombohedra of quartz, then this circle passes through the poles of the faces \((\overline{1}10)\), \((011)\), \((\overline{2}03)\), \((111)\), \((\overline{1}21)\), and \((\overline{1}20)\), and very close to the pole of the face \((211)\) of the feldspar. Assuming that one of the faces of the rhombohedron of quartz coincides with \((\overline{1}10)\), and drawing through \(Qu_2\), as through a pole, meridians spaced from one another by \(60^\circ\), we immediately see that the remaining faces of both rhombohedra will coincide respectively with the faces \((211)\) (almost complete coincidence), \((011)\), \((\overline{2}03)\), \((\overline{1}21)\) (complete coincidence), as is shown in the drawing, where the poles of the supposed faces of the rhombohedron are encircled by dotted circles. Thus the faces of the rhombohedra of quartz coincide with a whole series of important faces of the feldspar.

In addition, two more grains of anorthoclase with the same miropigmatitic intergrowths of quartz were studied. One of them, of rounded-oval form, is almost entirely filled with the latter, which here form only two indivi—

individual. The first individual (designated, in the general sequence, as No. 3) strongly predominates, and the intergrowths composing it are at first arranged in bands parallel to one another, which toward the end widen and diverge, curling in a curly fashion, so that the general pattern recalls a Greek palmette; this impression is further strengthened by the fact that, in place of the curls of the palmette, there are whimsically curved intergrowths of the second individual (No. 4). The results of the feldspar measurements are presented in Table 2. With this orientation the measurements are made rather easily, although, in establishing the plane of the ellipsoid perpendicular to Nm, a stauroscopic eyepiece was also used. Since only one cleavage according to (001) is visible, it is

Thin section No. 16—237.
Table 2.
Anorthoclase.

Optical axes: A—toward oneself 55°  2V = −50°

\[ \frac{55^\circ}{55^\circ} \]

impossible to calculate the extinction angles. However, from drawing 2 it is evident that this angle on the plane of the second pinacoid (010) is about 10°. Using the data from the study of the following grain, it is possible here as well to orient the quartz intergrowths, the measurements of which gave the following results.

Intergrowth No. 3. Principal section \(N = 308^\circ\); the angle of inclination of the optical axis toward oneself is very large. In order nevertheless to determine the position of this axis, two more principal sections were found, no longer perpendicular to the thin section: I. \(N = 299^\circ,\ H =\) pr. \(20^\circ\), and II. \(N = 317\frac{1}{2}^\circ,\ H =\) l. \(21^\circ\) (corrections for the refractive index are not needed at such \(H\)). The position of the optical axis is determined very well, as is evident from the drawing.

Intergrowth No. 4. Principal section perpendicular to the thin section: \(N = 268\frac{1}{2}^\circ\). The optical axis is inclined away from oneself at an angle of \(41^\circ\)¹), or, with correction for the refractive index, \(-40^\circ\). For checking, an oblique principal section to the thin section was taken: \(N = 248\frac{1}{2},\ H =\) l. \(16^\circ\). As is evident from the drawing, the agreement of the results is excellent.

The angle between the axes of the intergrowths \(Qu_3\) and \(Qu_4\), measured by means of the graduated circle, is equal to \(97^\circ\), or, in other words, \(83^\circ\), which is very close to the angle \(84^\circ 33'\) formed by the axes of the well-known quartz twin according to the face (2221)²). After transferring to drawing 4, we see that both intergrowths conform to A. E. Fersman’s Adun-Chilon law, and in fact intergrowth No. 3 is already transitional to the orientation according to the Mursinsk law³).

¹) Mean of three readings: \(42\frac{1}{2}^\circ,\ 39^\circ\), and \(42\frac{1}{2}^\circ\).
²) Here and below, for hexagonal crystals the symbols of E. S. Fedorov are used.
³) A. E. Fersman, op. cit., 1214 and 1215.

Finally, perhaps the most interesting grain of anorthoclase has only one system of quartz intergrowths, oriented in parallel. The feldspar grain itself has the form of a small, short rectangle, the larger dimension of which is elongated along (001). Almost in the middle of the long side there adjoins, by a narrow and short neck, a rounded spot of the same anorthoclase, the diameter of which is about twice the linear dimensions of the rectangular grain. In this second area there are abundant, characteristically angular—triangular, hook-shaped, etc.—parallel intergrowths of quartz, bounded by straight faces running in three directions, with small angles between the latter. On careful examination it proves that both areas, of such different form, constitute one and the same homogeneous crystal of anorthoclase, containing, apart from the intergrowths mentioned, no other inclusions disturbing its homogeneity, such as twin lamellae, other minerals, etc. The rectangular area, as has already been noted, is entirely devoid of quartz intergrowths. During measurement one had to be very attentive, for, with an orientation similar to that of the first grain, the difficulties were the same. The results are given by Table 3 and Drawing 3. The quartz intergrowths gave:

Thin section No. 16—237.  Table 3.  Anorthoclase.

Optical axes: A—away from oneself 35°  B—toward oneself 16°  \(2V = -50^\circ\)

\[ \begin{aligned} &35^\circ\\ &34\tfrac{1}{2}^\circ\\ &35^\circ\\ \hline &35^\circ \end{aligned} \qquad \begin{aligned} &16^\circ\\ &16^\circ\\ \hline &16^\circ \end{aligned} \]

Extinction angles:

\[ < Np_1 : (001)\ \text{on}\ (010) = +8\tfrac{3}{4}^\circ. \]

\[ < Np_2 : (010)\ \text{on}\ (001) = -3^\circ. \]

\[ (010):(001)=89\tfrac{1}{2}^\circ \]

\[ \text{(angle between the cleavage planes).} \]

A principal section, perpendicular to the thin section—\(N = 9^\circ\), inclination of the optical axis away from oneself \(52^\circ\), or, with correction for the refractive index—\(51^\circ\). The latter position was checked by observing a principal section oblique with respect to the thin section, whose coordinates are: \(N = 354^\circ\), \(H =\) left \(19^\circ\). In addition, it proved possible to determine the positions of those three planes by whose mutual combination all the quartz intergrowths under consideration were bounded. Plane \(\alpha\), the most highly developed, coincided with the plane (010) of the feldspar; plane \(\beta\) has the coordinates: \(N = 6^\circ\), \(H =\) left \(8^\circ\); and \(\gamma\)—\(N = 44^\circ\), \(H =\) left \(2^\circ\).

In its optical properties the feldspar proves to be anorthoclase, making it possible to carry out the proper setting also for the preceding grain.

After reducing the measurement data to the diagram of Drawing 4, where for simplicity of construction the monoclinic crystal complex of orthoclase has been adopted,

with respect to which the corresponding ellipsoid of the given anorthoclase is oriented. According to the data for the latter grain, as the most typical, it turns out that the axis of the quartz intergrowth coincides quite strictly with the zone passing through the faces \((120)\) and \((0\overline{1}2)\), or:

\[ \begin{array}{c|c|c} \overline{1} & 20\overline{1}2 & 0\\ \times\times\times & & \\ 0 & \overline{1}201 & 2 \end{array} = [421]. \]

The planes \(\beta\) and \(\gamma\), bounding the intergrowths, prove to be possible faces of feldspar, namely: \(\beta\) coincides (almost) with the face \((122)\), and \(\gamma\)—exactly—with \((123)\).

Especially remarkable is the circumstance that almost all faces of quartz of primary importance, under the given orientation, coincide with possible faces of feldspar, as is indicated on the diagram, where the quartz faces are designated by dotted circles. Thus, the faces of the quartz prism \((0\overline{1}01)\), \((01\overline{1}0)\), \((0011)\), and \((0101)\) coincide respectively with the faces \((1\overline{2}0)\), \((0\overline{1}2)\), \((\overline{3}44)\), and \((120)\) of feldspar, although for the two middle faces deviations from coincidence of \(1^\circ\)—\(2^\circ\) are in fact observed. The coincidence of the rhombohedron faces is still better: \((\overline{1}01)\) coincides exactly with \((0\overline{1}0)\), \((\overline{1}110)\)—with \((\overline{2}43)\), \((1011)\)—with \((40\overline{3})\), and \((\overline{1}101)\)—approximately with \((\overline{3}10)\). The face \((11\overline{1}0)\) coincides exactly with \((524)\), and only for the quartz face \((1011)\) is there no feldspar face with a sufficiently simple symbol. Even the faces \(\alpha\), \(\beta\), \(\gamma\) receive rational symbols of quartz faces*: \(\alpha\), as coinciding with \((0\overline{1}0)\)—\((1\overline{1}01)\), \(\beta\)—\((17\overline{5}2)\), and \(\gamma\)—\((43\overline{5}2)\). Comparing the results presented above with the laws of graphic intergrowths in pegmatites established by A. E. Fersman (cf. drawing 5, representing a reproduction of the regularities established by A. E. Fersman according to his own diagram, supplemented by the laws marked with crosses and recorded here), we see that laws Nos. 1, 2, and 5 are new, whereas Nos. 3 and 4 are found on A. E. Fersman’s diagram; but, on the other hand, between the new and the old laws there is decidedly no fundamental difference in the regularity of the geometrical relations of the spatial lattices of both minerals, and the new laws are no less, and perhaps even more, geometrically consistent than the old ones. The latter result is somewhat unexpected, for, as was indicated above, in eutectic structures poor in mineralizers one would rather expect to encounter random groupings. It may therefore be thought that the crystalline atomic lattices of quartz and feldspar stand in such a relation that, in general, they are capable of adapting themselves very easily to one another in different orientations, and this closeness of theirs gives both minerals the possibility of forming regular combinations under the most varied conditions. It is by this last circumstance that one should also explain the frequent occurrence precisely of quartz–orthoclase granophyric structures.

The anorthoclase of the third grain, investigated optically, differs from ordinary anorthoclase in that, on the plane of the third pinacoid, it has an extinction angle with the opposite, usual direction. This does not depend on observational errors: for a more exact position of the cleavage crack I used objective No. 3 (the work was done on a large E. Leitz microscope with a universal stage by R. Fuess), and, in order to see the grain, placed a drop of water between the upper segment and the objective, thereby arranging a kind of immersion system. For determining the plane of the ellipsoid a stauroscopic eyepiece was used; moreover, by inserting also gypsum and mica plates¹, I attempted to produce various interference colors. And nevertheless, in no way was it possible, for the cleavage crack, to obtain inclinations of the stage greater than \(9^\circ\), while for the plane of the ellipsoid—less—

¹ In the position of extinction.

To the article by N. N. Gornostaev: “On New Laws of Feldspar–Quartz Intergrowths of the Granophyric Type”

SLIDE No. 16 237,
Anorthoclase and quartz.

Drawing 1.

Optical ellipsoid and cleavage planes of anorthoclase, and axes of quartz intergrowths.
(Gram-stereographic projection)

Optical ellipsoid and the (001) cleavage plane of anorthoclase, and axes of quartz intergrowths.
(Gram-stereographic projection)

Anorthoclase and quartz.

Drawing 2.

To the article by N. N. Gornostaeva: “On New Laws of Feldspar–Quartz Intergrowths of the Granophyric Type.”

THIN SECTION No. 16–237.

Drawing 3.

Optical ellipsoid and planes of cleavage of anorthoclase; axis and boundaries of the quartz intergrowth.
(Gram-masters stereographic projection)

Drawing 5.

Position of the quartz axes in various written intergrowths with feldspar.

Between \(+B\) and \(-B\) — Adun–Chilong law.
\(+C\) — Murzinka law.
Rose — Rose law.

Points circled indicate intergrowths with acidic plagioclases (after A. E. Fersman).
Crosses at the numbers 1, 2, and 5 — axes of new laws.
Arrows at the numbers 3 and 4 indicate axes of observed old laws.

To the article by N. N. Gornostaev, “On New Laws of Feldspar–Quartz Intergrowths of the Granophyric Type”

Faces and edges of feldspar (anorthoclase)

Optical ellipsoid of anorthoclase and axes of quartz inclusions in gnomostereographic projection.

Fig. 4.

or the mean, with repeated readings, coincided with the numbers given in the table. It is therefore necessary to acknowledge that this anorthoclase has a small, but negative, extinction angle on the plane (001). If the optical data for anorthoclases are compared with the chemical data, it may be noted that the small magnitude of the (positive) extinction angle is connected with an increased content of CaO (or K₂O) ³, and the possibility is not excluded that in the present case there is a variety especially rich in the anorthite component (or, conversely, in the orthoclase component), which will of course become clear only after an appropriate chemical investigation.

Tomsk, April 1924.

1. J. D. Dana. The System of Mineralogy. 6th Ed.—New-York, 1901, 324–325. ↩↩

2. Because of the thinness of the intergrowth it is impossible to determine the angle exactly. ↩↩

3. Cf., for example, Hintze, Handbuch der Mineralogie, II, 1419–1425. ↩