NORSK GEOLOGISK TIDSSKRIFT 45

THE ATTITUDE OF THE RHOMBIC SECTION IN TRICLINIC FELDSPARS

with a note on •diclinic' crystals BY

ToM. F. W. BARTH and KARI THORESEN

(Mineralogisk Geologisk Museum, Sarsgt. l, Oslo 5) Abstract. The position of the rhombic section has been calculated for triclinic feldspars of various chemical compositions, of various degrees of disorder, and of various degrees of mechanical lattice deformation.

The relative high frequency of crystals of 'diclinic' symmetry is due to the ease with which polysynthetic twinning on a unit cell scale takes place in triclinic crystals having the a or the y interaxial angle close to 90°.

Introduction In the triclinic system a crystal edge Ob is not normal to a crystal face, f, see Fig. l. The plane that passes through Ob and through the line RR' that is normal to the projection OP of Ob is called a rhombic section with regard to Ob and f. Obviously the position of this section depends on the interaxial angles a, {J, y. In triclinic feld­spars the conventional crystallographic setting makes Ob the b-axis, while f is (010). The angle (] is the angle between the a-axis and the trace of the rhombic section on (010). The angle s between the basal (001)-cleavage and the rhombic section differs only slightly from the angle (].

As pointed out by TuNELL (1952) incorrect formulas for the calcu­lation of these angles are found in the literature. The correct relations are:

cot (] = cos a*

= cos(001/\010) = cot {J

cot y cot y cot a*

cots =

-­

cos y

cos a

cos Y sin {J

84 TOM. F. W. BARTH AND KARI THORESEN

l / / /

/ / /

/

Fig. l. Definition of a rhombic section.

The Plagioclases

G. VOM RATH (1876) found that periclines ( = albitic feldspars of the Alpine veins) exhibited polysynthetic twin lamellae having b as twin axis and a non-crystallonomic face which he called the rhombic section as composition plane.

The function of this composition plane is to make the disconti­nuity in the crystalline lattice across the twin plane as small as possible. Again, in this plane the rates of growth of the faces (110) and (ITO) are equal (GOLDSZTAUB and SAUCIER 1959).

As the interaxial angles change in the plagioclase series, so the

i/ 1,0

30

20

10

10

THE ATTITUDE OF THE RHOMBIC SECTION

* cot &, = c osa(

co ty

85

20+----.----.----.�---.----.----r----�--�----.---� o 10 20 30 50 Ab

60 70 80 90 100 An

Fig. 2. The relation of the position of the rhombic section (expressed by a) and the composition of the plagioclases. The full curve is calculated from meas­urements of the interaxial angles of natural plagioclases compiled by Wiilfing (see TuNELL 1952). The stippled curve refers to measurements on heated plagio-

clases and on synthetic material.

rhombic section changes. This was first systematically investigated by ScHMIDT (1915). It is graphically illustrated in Fig. 2.

In the plagioclases exhibiting pericline twinning the position of the composition plane ( = the rhombic section) is revealed by a series of fine striations on (010). By measuring the angle between the basal cleavage and the striations, the chemical composition of the crystal is indicated.

However, it was soon noticed that the composition plane of peri­cline twins, particularly in sodic plagioclases, did not generally coin­cide with the rhombic section calculated from the usually accepted crystallographic data. Many authors have claimed that from measure­ments of the position of this plane no accurate conclusions can be drawn as to the chemical composition of the feldspar.

The explanation of the discrepancies became evident with the knowledge of the permanent disorder of the Al-Si distribution induced

86 TOM. F. W. BARTH AND KARI THORESEN

Ta ble l. Variation in a of heated albites

Authigenic albite heated at 1065°-11200 C. (a* and y after Baskin 1956.)

Unheated* ............ .......... . l day . . . . . . . . . . . . . . . . . . . . . . . . . . 2 days . . . . . . . . . . . . . . . . . . . . . . . . . . 3 days* . . . . . . . . . . . . . . . . . . . . . . . . . 4 days . . . . . . . . . . . . . . . . . . . . . . . . . . 5 days . . . . . . . . . . . . . . . . . . . . . . . . . . 7 days . . . . . . . . . . . . . . . . . . . . . . . . . . 9 days . . . . . . . . . . . . . . . . . . . . . . . . . .

11 days . . . . . . . . . . . . . . . . . . . . . . . . . . 14 days . . . . . . . . . . . . . . . . . . . . . . . . . . 18 days . . . . . . . . . . . . . . . . . . . . . . . . . . 29 days . . . . . . . . . . . . . . . . . . . . . . . . . .

Albite from Schmirntal heated at 1000°-10500 C. (a* and y after Brown 1960.)

90 days of heating 96

106 151

* average of two values.

a*

86°17' 86°16' 86°141 86°08' 86°08' 86°08' 86°09' 86°20' 86°13' 86°14' 86°04' 86°09'

86°55' 87°33' 90°00' 90°00'

'Y

87°48' 88°21' 88o29' 88°53' 89°06' 89°24' 89°57' 90°17' 90°18' 90°17'

90°17'

90°19'

90°14' 90°12' 90°00' 90°00'

a

30°39'

23°52'

21 °53' 17°08' 13°07'

8°51' 0°41'

--4°23' --4°30'

--4°16'

--4°05'

--4041 l

into plagioclases exposed to heat. The angles of a high-temperature plagioclase are different from the angles of a low-temperature plagio­clase of the same chemical composition; intermediate stages are also known. Pericline feldspars give a around 10°, indicating that they grew in a disordered state at low temperatures (LAVES and ScHNEIDER 1956). Such differences in the axial angles obviously affect the position of the rhombic section, and, as seen from Fig. 2, the effect is particu­larly large for sodic plagioclases.

It is of interest, therefore, to see how a changes by heat treatment of plagioclases, particularly of albite, in which the change is most pronounced.

BASKIN (1956) measured authigenic albite that was heated for 29 days; his data, together with additional data of BROWN (1960) and LAVES and CHAISSON (1950), are exhibited in Tables l and 2, and in

THE ATTITUDE OF THE RHOMBIC SECTION

Table 2. Variation in 11 of high and low albite (a* and y taken from Laves and Chaisson 1950)

From literature (Dana 1909) ........ Unheated (Amelia) . . . . . . . . . . . . . . . . Heated at 1060° C for 3 weeks . . . . . . Amelia) Heated at 1060° C for 3 weeks . . . . . . (Amelia) Synthesized at 300° C Synthesized at 450° C

(1..1 and

..

30'

30'

30'

88

301

87'

• • • • o • • o o o o . o

• • • o o o • • • • • o .

a*

86°24' 86°20' 86°00'

86°00'

86°08' 86°10'

•

�· ........ ·-·-·-·-- .. o ·--·-·-1-·-·-·--·--

"

88°08' 87°39' 89°36'

90°09'

90°02' 90°04'

87

11

27°25' 32°41'

5°43'

-2°10'

�011' �057'

30'

20'

10'

o·

85' L-----+-----+------t------l------l-----�-10' 7 14 21 28 35 days or heating

Fig. 3a. Variations in a*, y and 11 of heated albites. See Tables l and 2. Å =

11 of 3 Amelia albites and 2 synthetic albites. (LAVES and CHAISSON 1950).

88 TOM. F. W. BARTH AND KARI THORESEN

Fig. 3: a* varies only slightly, y increases rapid.ly, passes 90° and keeps on changing for 10 days. After 10 days the curve flattens, and the change in y is apparently completed. a decreases from 30°, unheated, to -4°, heated. Baskin's experiments strongly indicate that after 10 days complete disorder was reached.

It is surprising, therefore, that BROWN (1960), by heating another albite for a longer time, eventually obtained a monoclinic crystal (see Fig. 3 b). In Brown's case both a* and y go towards 90°, and the question arises: How does a change when a* and y reach 90° at the same time? At this point, 90°, cos a*

= cot y = O. Thus the function is discontinuous but its limiting value is - 45°. This limiting value exists even if the function itself is discontinuous at this point:

Jf a* and y reach 90° at the same time, a goes toward ±45° (case 1) .

el.: ond f

91"

90"

30'

89"

30'

a a• 30'

87°

301

85" o•

as• '------+-----+------"1-------' -,o· 91 98 105 doys of heoting

Fig. 3b. Variations in a*, y, and a ( = full curve) by very long heating of albite (BROWN 1960).

THE ATTITUDE OF THE RHOMBIC SECTION 89

Microcline and Adularia The 'triclinicity' of microcline varies from a maximum value, desig­nated by l, to zero ( = monoclinic symmetry). This variation affects the position oP the rhombic section.

In Table 3 data of LAVES (1950) and of ITO and SADANAGA (1952) are listed together with the corresponding calculated values of the angle a. It is seen that in these microclines a varies in the range ,...., ( -70° to -83 °) ; for adularias the range is ,...., ( -67° to - 79°). This is graphically shown in Fig. 4.

By observations on natural microcline REINHARD and B.AcHLIN (1936) found variations of the composition plane of the pericline twins from -75° to -90°.

BASKIN (1956) investigated the changes of the crystallographic elements of authigenic microcline exposed to heat. From his data the corresponding changes in the position of the rhombic section were calculated. They are displayed in Table 4 and Fig. 5. It is of more than ordinary interest that the angle a*, as it reaches 90°, remains at 90° during continued heating although the crystal is triclinic; the

Table 3. Variation in a of microcline and adularia (a* and y taken from Laves 1950}

Microcline

Pikes Peak . . . . . . . . . . . . . . . . . . . . . . . lvigtut .. . . . . ... . ... . .. . . .. . . . . . . . Hundholmen . . . . . . . . . . . . . . . . . . . . . Madagascar . . . . . . . . . . . . . . . . . . . . . . . Skede . . . . . . . . . . . . . . . . . . . . . . . . . . . Paotze* . . . . . . . . . . . . . . . . . . . . . . . . .

Adularia

St. Gotthard Vesuvius ........................ . Vesuvius . . . . . .. . . . . ... . . . . ... . . . . Vesuvius (after heating to 1000° C) .. •Valencianite', Mexico .. ...... . . .. .

a*

89°46' 89°43' 89°35' 89°38' 89°40' 89°42'

89°50'

89°50'

89°51'

89°54'

89°50'

* (a* and y taken from Ito and Sadanaga 1952) . 6

"

91 °59' 92°10' 92°22' 92°03' 92°15' 90°50'

90°40'

90°33'

90°32'

90°30'

90°24'

(J

-83°24' -82°37' -80°07' -79°52' -81°36' -70°16'

-75°58'

-73°11'

-74°23'

-78°57'

--67°30'

90 TOM. F. W. BARTH AND KARI THORESEN

Variatlon in6 of microcline Adularia

��.· 6' and r 70'

13' 75'

3d 80' g� 85'

3d 90'

g1' 85'

30'

l I I I I o'

sxf.

l -75'

3d -70 sg' -55'

Fig. 4. Values of a*, y and a in some microclines and adularias. See Table 3. From left to right: Pikes Peak, lvigtut, Hundholmen, Madagascar, Skede, Paotze, St. Gotthard, Vesuvius I, Vesuvius Il, Vesuvius (heated), 'Valenci­anite'. Data from LAVES (1950) and from !To and SADANAGA (1952). x = a*,

0 =y, .. = (J.

Table 4. Variation in f1 of heated authigenic microcline (a* and y after Baskin 1956)

Heated at 1120° C

Unheated* ...................... . 7 days ......................... .

14 days ......................... . 21 days ...... . ....... . ....... . . . . 28 days ....................... .. . 35 days ......................... .

• average of two values.

a*

90°26' 90°17' 90°00' 90°00' 90°00' 90°00'

y

87°39' 88°50' 89°19' 89°27' 90°00' 90°00'

(J

-79°40' -76°26'

90°00' 90°00'

THE ATTITUDE OF THE RHOMBIC SECTION

"'-* ond r

d.*

15' ---

--------- ............ __

45'

15'

�� '�

............. -----...... ----------------

--

..

, ....•...

---······--· ..

, . •'

,,'' ,•

,.

-70"

-7s•

-80"

-es•

- 90•

f!(30'..__ ___ ----!:" ____ :i------+-----+::------L 7 14 21 28 days of heating

91

Fig. 5. Variation in a•, y, and a of heated microcline. See Table 4. Data from BASKIN (1956).

angle 'Y keeps on changing; eventually it comes to 90°, and the crystal becomes monoclinic.

It is worthy of note that a* and 'Y do not reach 90° at the same time; as a* becomes 90°, a becomes 90° and remains constant although 'Y is still changing.

Consequently, if the crystal approaches monoclinic symmetry, and if a* reaches 90° ahead of r. a becomes stationary at 90° until it disappears (case 2).

The Anorthoclases DONNA Y and DoNNA Y (1952) measured the crystallographic elements of synthetic mixed crystals of the series albite-orthoclase. Their data and the corresponding values of the angle a are shown in Table 5 and Fig. 6. *

• An inspection of Table 5 indicates that the angle y measured on the material of 80 Ab is slightly in error (about 8 minutes of are too high). This small deviation makes a large change in angle a.

In Fig. 6 the thick a-curve is supposed to be correct; the thin line indicates the peculiar, irregular change of a if the high y-measurement is correct.

92

cJ:*' ond

r

91'

301

301 89'

30'

88'

30' 87'

301

TOM. F. W. BARTH AND KARI THORESEN

·-·-·---·-·--===:::::::::::::=::=::=·==--·

-·

-·-;-i

/ //

\ \ \ \ \ \

6'

-2'

-3'

-4'

-s•

-6'

3d '----+---+---+-----+-----+---+---1---....,.---+----L -7' 100 95 Ab

92 88 84 80 75 Moi%Ab

72 58 54 Or

Fig. 6. Variation in a*, y, and u of the high-temperature alkali-feldspar series. See Table 5. a* and y = stippled curves. u = full curve. The thin curves indi­

cate a probably erroneous measurement of y and the corresponding value of u.

66 70 80 90

100

Data from DoNNAY and DoNNAY (1952).

Table 5. Variation in u of anorthoclases (a* and y after Donnay and Donnay 1952)

Weight % ab a* y

• • o . o . o o . o • • • • • • o o • • • • • • • • o . o 90°00' 90°00' • • o • • • o • • • o . o . o • • • o o • • • • • • o • • 88°29' 90°07' • • • • • • • o . o . o o . o o o o • • • • o o o • • o . 87°27' (90°17') • • o . o • • o o • • o o o • • o o • • • • • • • o o o . 86°29' 90°10' • • • • o • • • o o • • • • • • • o o • • o o • • • o o . 85°49' 90°11'

(1

--4°20' (-6°17') -2°42' -2°31'

In this series the angles a*, y, and a change regularly with the composition. a* and y reach 90° at the same time. a goes toward -45°. The variation in a is in principle the same as in the heat ed al bites.

THE ATTITUDE OF THE RHOMBIC SECTION

Table 6. Variation in a of anorthoclase and moonstone, Korea

(a* and y after I to and Sadanaga 1952)

A northoclase, Chilposan

Na-rich .. . . . .... .. .... .. . .. .. .. . .

Na-rich . .. . ... .... ...... .. . . .... .

Moonstone, Minchon.

Na-rich .... ............ . . .. . . .. . .

Na-rich ................ . .. .. .... .

Na-rich . ...... .... ...... .... . ... .

d.*'

a*

88°18'

87°22'

86°27'

and Anorthoclase f

Moonstone

Na-rich Na-rich Na-rich Na-rich

91'

30'

OC1

30'

89'

l 3d 88'

3d

87'

3d

Na-rich

90°00'

90°00'

90°00'

6' 90'

50'

30'

a o' L-------�---L--�--�L_--�--------�0'

93

(J

Fig. 7. Position of a in anorthoclase and moonstone. See Table 6. Symbols as

in Fig. 4. Data from !To and SADANAGA (1952).

Moonstones are exsolved anorthoclases. !To and SADANAGA (1952) demonstrated that in moonstone (from Korea) exsolved phases of various compositions coexist, some monoclinic, some triclinic. From the crystallographic data of Ito and Sadanaga the u-values for the triclinic phases were calculated. See Table 6.

94 TOM. F. W. BARTH AND KARI THORESEN

With reference to Fig. 7 it is seen that in the exsolved phases in moonstone y = 90° over a range of composition.

lf y reaches 90° ahead of a*, a becomes stationary at 0° until it disappears (case 3).

The Mystery of •Diclinic' Crystals

It is worthy of note that the orientation of the (100) plane is left un­changed by pericline twinning because y* = 90°. Indeed, the data of Ito and Sadanaga show that in the pericline twins the direct angle y, and in the albite twins the reciprocal angle y* persistently equal 90°, irrespective of the nature of the mother feldspar (monoclinic or tri­clinic) from which the twinned phases were produced by exsolution.

This peculiar geometry must be correlated with the fact that peri­cline twins have the direct b-axis, and albite twins the reciprocal b*-axis for twin axis; therefore a crystal with y = 90° will make pericline twinning easier than albite twinning, whereas the opposite is true for a crystal with y* = 90°. The ease with which polysymmetry synthesis takes place in a triclinic crystal when one of its direct inter­axial angles is 90° is known, for instance, from the wollastonite group (see below).

But this is not the full story. The tendency in triclinic crystals for the angles a or y to assume 90° is peculiarly interesting - compare the angles in the heated authigenic microcline.

Similar phenomena appear, for example, in the wollastonite group:

a {J

Wollastonite . . . . . CaSi08 90°00' 95°16' 103°25'

Pectolite . . . . . . . . Ca1 NaHSi308 90°00' 95°10' 103°00'

Schizolite . . . . . . . (Ca, MnhNaHSi309 90°00' 95°22' 101 °06'

In the morphotropic series pectolite-schizolite the interaxial angles {J and y change regularly with increasing amounts of manganese, whereas the angle a remains stationary at 90°.

In a remarkable study of polymorphism ITO (1950) has shown the way in which monoclinic protowollastonite is transformed in to triclinic wollastonite by a special kind of gliding (twinning) on a unit cell scale

THE ATTITUDE OF THE RHOMBIC SECTION 95

('twinned space groups'). By this transformation ane angle (a) remains 90o.

A similar mechanism explains the fact that either angle y or angle a* in same of the triclinic feldspar crystals examined in this paper remains 90° over a considerable temperature interval (or compositional interval).

Another interesting fact is the large fraction of triclinic minerals exhibiting ane interaxial angle very dose to 90°, for example, kyanite a = 90°05', crossite a = 90°05', hjortdahlite y = 90°06', fairfieldite y = 90°05', etc.

These peculiarities were noticed by same of the old crystallogra­phers befare the space group theory was developed, and by them re­ferred to as diclinic crystals.

Summary

The results of the present calculations are:

l. Heating of albite gives conflicting results. One series. of experi­ments indicates that albite heated at 1120° C after 10 days becomes completely disordered, as a changes from +30°39' to about -4°30'. Prolonged heating has no further effect on the interaxial angles, or on a. Other materials heated at slightly lower temperature (1050° C) seem to approach true monoclinic symmetry. a* and y regularly approach 90° in such a way that a stays rather constant at about -4 °30'. But as monoclinic symmetry is reached, and a*

and y simultaneously reach 90°, a very rapidly goes toward -45°. 2. In natural microclines and adularias the reported values of a are

in the range -70° to -83° and -67° to -79° respectively. By heating, microcline approaches monoclinic symmetry. The angle a* reaches 90° ahead of y. The angle a varies first unsystematically, but as a* reaches 90°, a reaches -90° and from then on stays con­stant at 90°, until the crystal becomes monoclinic and a dis­appears.

3. In synthetic alkali feldspars of composition from Ab to Or, the

first 1/3 of the series is triclinic. With increasing Or-content, a slowly changes from -2°30' to -4°20' at 30 mole per cent Or. From 30 to 33 mole per cent Or - the interval in which the crystal becomes monoclinic - a rapidly changes from -4°20' to -45°.

96 TOM. F. W. BARTH AND KARI THORESEN

4. Cryptoperthite lamellae in moonstone exhibit a constant a-value of exactly 0°, for the lamellae are pericline twins in which the

angle y = 90°. 5. 'Diclinic' crystals are isomorphous to one of the 'twinned space

groups' of Ito, and are explained by the special properties of such space groups.

REFERENCES

BASKIN, Y. 1956. Observations on heat-treated authigenic microcline and

albite crystals. Jour. Geol. 64, pp. 219-224.

BROWN, W. L. 1960. Lattice changes in heat-treated plagioclases. Z. Kristallogr.

113, pp. 297-329.

DoNNAY, G. and DONNAY, J. D. H. 1952. The symmetry change in the high­

temperature alkali-feldspar series. Amer. Jour. Sei. Bowen vol. pp. 115-

132.

GoLDSZTAUB, S. and SAUCIER, H. 1959. Sur la section rhombique dans la

made du pericline. Bull. Soc. fran-;:. Min. Crist. 82, pp. 99-100. !To, T. 1950. X-ray Studies on Polymorphism. Maruzen Co., Ltd. Tokyo 1950.

!To, T. and SADANAGA, R. 1952. The lamellar structure of certain microcline

and anorthoclase. Acta Cryst. 5, pp. 441--449.

LAVES, F. 1950. The lattice and twinning of microcline and other potash feld­

spars. Jour. Geol. 58, pp. 548-571.

and CHAISSON, U. 1950. An X-ray investigation of the 'high-low' albite relations. Jour. Geol. 58, pp. 584-592. and ScHNEIDER, T. 1956. "Ober den rhombischen Schnitt in sauren

Plagioklasen. Schweiz. Min. Petr. Mitt. 36, p. 622. VOM RATH, G. 1876. Die Zwillingsverwachsung der triklinen Feldspater nach dem

sog. Periklingesetze und iiber eine darauf gegriindete Unterscheidung derselben. Sitz.-Ber. Kgl. Preuss. Akad. Wiss., Berlin 1876, pp. 147-174;

Neues Jahrb. 1876, pp. 689-715. REINHARD, M. and BA.cHLIN, R. 1936. "Ober die gitterartige Verzwillingung

beim Mikroklin. Schw. Min. Petr. Mitt. 16, pp. 215-225.

ScHMIDT, E. 1915. Die Winkel der kristallographischen Achsen der Plagioklase.

Chemie d. Erde, 1919, l, pp. 351-406.

TUNELL, G. 1952. The angle between the a-axis and the trace of the rhombic

section on the (010)-pinacoid in the plagioclases. Amer. Jour. Sei.

Bowen vol., pp. 547-551.

Accepted for publication June 1964

Printed March 1965