Deformation twinning in calcite, dolomite, and other ...eps.berkeley.edu/~wenk/TexturePage/Publications/1979_Twinning-C… · Mechanical twinning or deformation twinning has been

Phys. Chem. Minerals 5, 141-165 (1979) PHYSICS CHEMISTRY MIHERALS © by Springer-Verlag 1979

Deformation Twinning in Calcite, Dolomite, and Other Rhombohedral Carbonates

D.J. Barber 1 and H.-R. Wenk z

1 Physics Department, University of Essex, Colchester, Essex, England 2 Department of Geology and Geophysics, University of California, Berkeley, California 94720, U.S.A.

Abstract. Transmission electron microscope (tern) observations of single and multiple twins in calcite and dolomite are presented, and the results are analysed by means of selected area diffraction and trace analysis. Simple twinning in rhodochrosite and kutnahorite is also analysed. It is shown that the ordered carbonates, such as dolomite, have a common twinning plane {01 i2} and this appears to be their only mode of deformation twinning. The carbonates with higher symmetry, such as calcite, have {01i8} as the primary twinning plane but calcite itself has other twinning mechanisms, of which the most important is illustrated. Crossing and stopping twins are also discussed. It is shown that twinning in calcite, which occurs predominantly at low temperatures, is characterized by the generation of large numbers of glide dislocations.

1. Introduction

Mechanical or deformation twinning occurs widely in minerals and constitutes an important mechanism in deformation regimes of high strain rates. Although deformation twinning has been studied extensively, especially in metallic systems, remarkably little is known even now about the mechanism by which twins are nucleated and propagate. In general, the lower the stacking fault energy of a crystal, the lower is the stress to nucleate twins (Venables, 1964a and b) but the higher is the stress to propagate twins.

Interest in the atomic movements produced during twinning has grown, following the recognition that there is often a link between phase transformations of the displacive type and the shears associated with twinning. This correlation is now known to exist in minerals (cf. Coe and Kirby, 1975) as well as in simple structures. Moreover, in the case of the c~-fi (non-displacive) transformations in quartz and aluminum phosphate, it has been beautifully demonstrated that the phase boundary is manifest as microdomains of Dauphin6 twinning (a configuration of low strain) in dynamic equilibrium (Van Tendeloo et al., 1975; Van Goethem et al., 1977).

0342-1791/79/0005/0141/$05.00

142 D.J. Barber and H.-R. Welak

Laves (1952a and b) was the first to point out that there is likely to be a correlation between ordering in an alloy, or compound, and the ability of the substance to twin. Later, Laves (1960) proposed that there is a very intimate relationship between twinning and ordering phenomena in certain felspars.

In this paper, we report and interpret electron microscope observations of the structure of deformation twins and the surrounding host crystal (or matrix) in several rhombohedral carbonates, some of which are ordered.

2. Previous Work

Mechanical twinning or deformation twinning has been recognized as an important mechanism in carbonate minerals and twinning in calcite in particular has been the subject of numerous papers. The early work of Pfaff (1859), Dove (1860), Reusch (1867), Baumhauer (1879), Miigge (1883) and Johnsen (1902) showed that twins are easily introduced into a calcite crystal by the firm application of a blade across the edge of the cleavage rhomb; these are the so-called 'pressure twins.' A study of naturally deformed calcite by Rose (1868) showed that multiple twinning could create crystallographic channels in the interior of crystals. Much later, Griggs, Turner and their colleagues (cf. Griggs et al., 1953; Turner et al., 1954) investigated experimentally-deformed Yule marble and calcite single crystals and established the crystallography of the deformation elements in calcite. They interpreted their macroscopic observations in terms of glide and twinning and they were able to predict tension and compression axes from the orientations of twins. Work on calcite has also been performed by a number of Russian workers; in particular Garber (1938, 1947) and Startsev et al. (1960) studied elastic twinning. Elastic twins can be introduced by applying pressure on a cleavage face of calcite with a sharp point and the twins are completely or partially expelled by the crystal when the pressure is removed. Elastic twins are normally wedge-shaped and taper to a point within the crystal; they are easily observed with a polarizing microscope. The early literature of twinning in calcite is well presented in the book by Klassen-Neklyudova (1964).

Compared with the wealth of data about calcite, the literature about twinning in dolomite is sparse. There is even less information about the structural analogues of calcite, magnesite (MgCO3), rhodochrosite (MnCO3) and siderite (FeCO3), or analogues of dolomite, such as kutnahorite ({Ca,Mn}CO3). It was early recognised by crystallographers studying the morphology of crystals that the twin laws in calcite-like carbonates (with spacegroup R3c) are different from those of dolomite-like carbonates (R3) (cf. Palache et al., 1951). Deforma- tion twinning is no exception. Rogers (1929) was first to report how the different crystallography of twins in calcite and dolomite could be used to distinguish between the two minerals. Much later Turner et al. (1954) reported both the twinning and glide elements in dolomite rocks. Work by Higgs and Handin (1959) on experimentally-deformed single crystals of dolomite agrees essentially with Turner et al.'s conclusions. Dolomite and calcite differ markedly in that

Deformation Twinning in Rhombohedral Carbonates

Table 1. Indices and letter symbols for crystallographic hedral carbonates

planes in rhombo-

Rhombohedral Hexagonal Letter morphological morphological symbol cell indices cell indices

Hexagonal structural cell indices (used in this paper)

170 21i0 a 1 2i10 01i i2i0 a z i2i0 10l ii20 a 3 ii20 100 1011 rl 10i4 010 i101 r2 1104 001 0111 r 3 0114 011 1012 el i018 101 1102 e 2 1108 110 0112 e 3 0118 i l l 2021 fl i012 l i l 2201 f2 I102 i l i 0221 f3 0112

143

twinning in calcite dominates at low temperatures, while in dolomite it is more common at high temperatures. In geological situations twinning in carbonates is never predominant as a deformation mechanism, in the sense that even extensive twinning cannot, by itself, account for large strains. Turner (1963) has noted that twinning in naturally deformed dolomite rocks is less common and less profuse than e-twinning in calcitic marbles because dolomite does not twin at low temperatures.

3. The Crystallography of Twins

3.1. General

All the carbonates under consideration are rhombohedral and possess good cleavage on the rhombohedral planes which, when referred to the rhombohedral axes, index as {100}. The majority of papers, however, have discussed the crystallography of the rhombohedral carbonates in terms of hexagonal axes. In morphological work a small hexagonal cell is commonly used which is one quarter the height, along the e-axis, of the true X-ray structural cell. With this morphological cell the faces of the cleavage rhombohedron index as { 10i 1 }. In the literature the observed morphological faces have been assigned letter symbols so that, for example, the cleavage planes are referred to as rl =(1011), r2 ~ (1101) and r 3 = (0] 11). Goetze and K ohlstedt (1977) have used a morphological cell when discussing possible Burgers vectors for calcite. X-ray and electron diffraction patterns cannot, however, be properly indexed using the morphological cell, so in this paper we shall discuss all observations in terms of the true structural cell, in which the cleavage rhomb indexes as {1014}. Table 1 shows the equivalences between the indices for important lattice planes. We

144 D.J. Barber and H.-R. Wenk

Calc i te

s e n positive ~", ' /~, '

a

/ i . i f

Dolomite

c axis host • ~ I L • c axis host

/ /

i

~, sense el! ~ ~ , . ; ,~ 1 ¢ ~ . . f : - , e = (OI i8) negativ (0112)

_ _ _ _ \

\ \ c axis twin "- ~ C axis twin

b Fig. la. Twinning on e~-{0118} in calcite, sense positive, viewed along a (2110) direction. The carbonate groups, denoted as black triangles, actually lie in the {0001} planes parallel to the viewing direction but the triangles are drawn to indicate their alternate orientations in adjacent planes. The exact arrangement of carbonate groups on the twin plane is not known, b Twinning on f=- {0112} in dolomite, sense negative, viewed along a ~21i0) direction• The calcium and magne- sium atoms form an ordered array and are denoted by open and closed circles

shall use four-digit Miller-Bravais hexagonal indices and zone-symbols (cf. Ni- cholas, 1966) as in our earlier papers (Barber and Wenk, 1976, 1979; Barber, 1977). Paterson and Turner (1970) show the disposition of these planes on a basal stereographic projection.

3.2. Calcite

For calcite, CaCO3 (symmetry R3e), the dimensions of the hexagonal structural unit cell are a---4.990 A and c = 17.061 A. Several twin forms are known (cf. Deer et al., 1962; Palache et al., 195l), including twinning on the basal plane, but most of these twin laws only apply to growth twins.

The most common deformation twinning law is on e~{01T8}, for which the shear displacement is in the positive sense, in the direction < 0221 > , The positive sense is illustrated in Fig. 1 a, in which the twinning (lower) layers of a crystal which has positive e-axis upwards, are displaced in a sense opposed to the positive e-axis of the untwinned layers. During deformation twinning the e-axis moves through an angle of 52.5 ° while the plane of the carbonate groups, which is perpendicular to the e-axis, must be rotated through the same angle. In e-twinning the composit ion plane is normally the twin plane,

Paterson and Turner (1970) have reported more minor deformation twinning in calcite on the r -{1014} and f={01i2} planes, with composition planes r and f respectively. Weiss and Turner (1972) have stated that the sense of r-twinning is positive. It should be noted that the r-plane is the usual slip plane.

3.3. Dolomite

Dolomite, Cao.sMgo.sCO3 has symmetry R3, lower than that of calcite; this is because there are alternating layers of Ca and Mg atoms parallel to the

Deformation Twinning in Rhombohedral Carbonates 145

basal plane. Only small deviations from the stoichiometric Ca/Mg ratio of unity can be tolerated (Goldsmith, 1959). Partial substitution of the Mg ions in dolomite by Fe ions gives the isostructural mineral, ankerite. Substitution of Mg atoms by Mn gives the rather rare mineral, kutnahorite. For pure dolomite the lattice parameters of the hexagonal structural unit cell are a--4.81 A and c= 16.01 A.

Dolomite, in accord with its lower symmetry, possesses fewer twin forms than calcite and only one type of deformation twinning is known. This mechanism is f-{01i2} twinning which occurs with an f composition plane. The shear displacement is in the < 0111 > direction and according to Turner et al. (1954) is in the negative sense (Fig. 1 b), as first postulated by Fairbairn and Hawkes (1941). The f-plane is a slip plane for dolomite, as shown by Barber (1977), but slip is thought to occur in the positive sense.

The absence of e-twinning in dolomite is scarcely surprising since in dolomite the {0118} planes contain both Ca and Mg atoms, while the f planes do not. A shear on the e-planes would bring like species of cations into closer-than- normal proximity, as pointed out and illustrated by Bradley et al. (1953).

4. Experimental

The examples studied include both naturally-deformed rocks and experimentally- deformed rocks and single crystals. Most of the experimental deformation util- ised either a Griggs-type (Griggs, 1967) solid-medium compression apparatus or a gas apparatus (Griggs et al., 1960). Also some compression tests on single crystals were performed on an Instron machine without confining pressure. A micro-indentation hardness tester, fitted with a Knoop diamond indenter was also used on single crystal cleavage plates of the carbonates investigated. Microindentation is a simple way of introducing deformation twins and it was performed with loads of 50 or 100 p. Samples were examined optically in thin section and then ion-thinned for further examination by high voltage transmission electron microscopy (hvem). The indented crystals, which carried arrays of indentations, were thinned predominantly from one side, in order to preserve the indented regions. The majority of the electron microscopy was carried out on an EM7 high voltage microscope operated at 1 MV. Some observations were also made using a JEM 200 kV electron microscope. Except where stated in the figure captions, the electron micrographs which appear in this paper were taken at 1 MV.

5. Results - R3e Carbonates

5.1. Primas7 Twinning on e=-{Ol18} in Calcite

Single crystals, oriented to favour e-twinning, compressed without confining pressure, usually fail by fracture before many twins are introduced. With the application of confining pressure high twin densities can be achieved and some parts of the sample often contain twinning on e~ only (primary twinning).


=2

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x . × O × ' x . 4 H

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ooo,~ ,o,~,.~

Fig. 3a-d . e twins in experimentally deformed calcite, a VW 132 (see caption to Fig. 2). Electron beam parallel to [1210], twin and matrix both diffracting strongly, b Stereographic projection and schematic of zone axis diffraction pattern corresponding to (a), showing disposition of planes and crystal axes. x :Host reflection; - : twin reflection e VW 132. Secondary e twinning in host and primary e twin, forming ' chevron ' type of configuration. The secondary twins do not cross the primary e twin boundaries but terminate at them. Slip is initiated at the terminations in the narrow primary e lamella present in this example. 200 kV micrograph, d VW 141 (compressed normal to {10i4} at 600 ° C, 15 kb). Crossing twins in calcite deformed at high temperature show the creation of high densities of dislocations at the intersections. The crossing twin Iamella is out of contrast but it is almost horizontal in this micrograph


If crystals are compressed to strains > 10%, there is usually profuse secondary e-twinning and the primary e-twins show pronounced curvature. Such specimens are not easily analysed by (tern) or (hvem) methods. For low strains (~2%), primary twin lamellae predominate and these are normally planar and parallel, having thicknesses comparable with the untwinned matrix lamellae. Lamellar thicknesses are then typically ~ 1 lain, as shown by Fig. 2 a. The twin boundaries commonly contain closely spaced arrays of twinning dislocations, although this is not an essential characteristic, as also noted by Braillon and Serughetti (1976). A twinned lamella can normally be distinguished from untwinned crystal because the former usually contains numerous glide dislocations generated by the twinning while the untwinned volume may not. Figure 2b shows an example, with a low density of pre-existing dislocations in the matrix lamellae. However, deformation twinning can generate glide dislocations in both twin and matrix (this gives a V-type configuration) and on other occasions there is a narrow fringe of dislocations just spilling into the lamellae from the twin boundaries.

Selected area diffraction and trace analysis of these primary twins confirms that e---{0118} is both the twinning and composition plane. With the electron beam parallel to an appropriate < 1120 > direction, the primary twin boundaries are perpendicular to the plane of image projection and a simple diffraction pattern from both matrix and twin simultaneously is obtained. Figure 3 a shows an e-twin thus oriented, together with selected area diffraction (sad) pattern and corresponding stereographic projection. This projection is directly comparable with the S-projection of calcite twins discussed by Pabst (1955) and with Figure 1 a. The indexing of the diffraction pattern shows indisputably that the {0118} twin and composition planes are common and that e-twinning rotates the c-axis through 52.5 °. In their recent paper, Braillon and Serughetti (1976) have reported similar observations.

During twinning lattice planes are rotated and transformed, sometimes into planes of the same type, sometimes into planes of other types. This was first noticed by Mfigge (1883) and then recognised by Borg and Turner (1953) as the explanation of secondary twin lamellae rotated by primary twinning in calcite (cf. Sect. 5.2.). Understanding the rotations and transformations produced by twinning becomes simple with the aid of transformation matrices, which have been derived for e-twinning in calcite by Pabst (1955). We shall now adopt this approach in considering the nature of the slip dislocations seen in the microtwin lamellae formed by intensive primary e-twinning (cf., Fig. 2 b).

The systematic i014 row in the (sad) pattern uniquely determines the direction of the c-axis for the twin because the twin is diffracting strongly and the twin reflections are readily identified. The long dislocations and dipoles of Fig. 2b suggest that the slip direction for the dislocations created during twinning lies in or close to the foil plane [approximately (1210)] and that the trace of the slip plane is the line QQ' in the stereographic projection presented in Fig. 3b. If this reasoning is correct, the dislocations are associated with slip on the basal plane, possibly in the ( i010) or (1120) directions. But basal slip is certainly not a common mechanism in calcite (although it does occur in dolomite and recently Turner and Orozco, 1976, have presented evidence


for it in calcite). One is therefore hesitant to invoke basal slip as the slip mechanism associated with e-microtwinning. A more reasonable explanation emerges if one seeks to find which crystallographic plane is transformed to (0001) by the action of e-twinning. This can be found from the appropriate twin-transformation matrix. For an e l - (5018) twin, the matrix for the Miller- Bravais indices of planes is found to be:

= 1/3 - 2/3 1/3 /0

0 l/3 - 1/3 1/6] L ~ - 8 / 3 0 8/3 1 / 3 / 1 /~

where the suffixes T and H represent twin and host matrix respectively. This is equivalent to Pabst's (1955) matrix for a (1012) twin in the morphological cell in the three-index notation which Pabst presents in the form 11/3 1/3 . 2/310 1 . 0]. [4/3 2/3 . 1/31. The four-by-four matrix correctly transforms (1018)~(T018)r, (1210)u~(i2i0)r, (1508)H~(2110)r etc. Investigation also shows that one of the f planes, (5012)/~(0006)r, i.e., its trace in a (1210) section after twinning will appear to be basal. The existence of a slip on f in calcite at room temperature was established by Griggs et al. (1953) and later the slip direction was shown to occur for, let us say, (i012) slip in one of the equivalent [0221] or [2201] directions (cf. Paterson and Turner, 1970).

The direction [2201] when plotted on a stereographic projection is coincident with the pole (1504) which lies on the great circle terminating at P and P' which is the zone [4041] (clearly the slip direction must lie in the slip plane). The (1012) transforms to (0006) as twinning on (1058) occurs, the slip direction [s.d.~] apparently rotates until it becomes co-incident with the (l120)r pole at [s.d.r] in the zone (0001) as indicated with trace QQ'. In this manner a deformation which was almost certainly initiated as f slip appears to look like basal slip when twinning is completed. The reason why slip occurs on f and not r is also apparent: the resolved shear stress on f1-(5012) is 0.82 where r is the shear stress on the twin plane el; the resolved shear stress on r~-(10i4) is 1.28 z but it is in the wrong sense to cause slip.

The need for slip to accompany microtwinning is fairly obvious when one considers the need to relax the intense stresses produced by the shape change on twinning at the surfaces of the lamella. The generation of dislocations by twinning was noted in the etching experiments on calcite by Keith and Gilman (1960) and Startsev et al. (1960). Undoubtedly these dislocations are intimately involved in the question of twinning and detwinning. It has been observed by several workers (cf. Klassen-Neklyudova, 1964) that a twin can be removed from calcite by reversal of the stress system which produced the twin (detwinning). But an attempt to reintroduce the twin invariably causes the crystal to fail, usually by parting on the twin plane. This probably has only a weak correlation with the density of dislocations in the twin boundary (twinning dislocations) because this is variable and can be kept low if the twin is propagated slowly. Parting on detwinning and attempting to retwin is more probably caused by the creation of a high density of slip dislocations in the crystal and matrix


immediately adjacent to the twin boundary. Repeated twinning and detwinning will cause these regions to work-harden very rapidly.

5.2. Multiple Twinning on e=_{Ol18} in Calcite

Single crystals and grains deformed to strains of a few percent at low temperatures and in orientations favourable to twinning commonly show multiple twinning, i.e., twinning one1 and either e2 or e3. In homogeneously strained regions a 'chevron' or 'herringbone' type of structure is created, as illustrated by Barber and Wenk (1976) with the secondary e2 twins in primary matrix and primary twin making equal angles with the primary el twin plane to form the chevrons. The widths of the secondary twin lamellae are invariably much less than those of the primary lamellae and they are usually well below the limit of optical resolution. Figure 3c shows a multiply-twinned region in a crystal of Iceland Spar compressed at room temperature. Here the secondary lamellae are only ~ 0.1/~m in thickness and typically there are many dislocations associated with them, so that the total dislocation density is quite high (~ 10 7 cm- 2). Two particular points should be noted: (1) these are not crossing or intersecting twins (as defined by Cahn, 1953; 1955), because the secondary twins terminate at the primary twin boundary; they are called stopping twins; and (2) all of the twins on e2 were formed after the primary twinning on el; i.e., they are true secondaries. Point (2) is established because the work of Borg and Turner (1953) and Pabst (1955), as discussed earlier, shows that any pre-existing e2 twin is rotated by el twinning in calcite through 22 ° to appear as a trace of {1120}.

The termination of a blunt twin lamella (i.e., one which does not taper down via the incorporation of twinning dislocations) within a region of the crystal and not at an internal boundary must generate intense stresses. In calcite these are normally relieved by cleavage. In heavily twinned calcite such fractures need not extend to an external surface but often link nearby terminating twin lamellae and are therefore internal crystallographic voids. These voids should be distinguished from the voids or channels produced by multiple twinning where the twins actually cross each other, which are known as Rose channels, following their excellent description and explanation by Rose (1868).

Crossing twins occur infrequently in single crystals oriented for e-twinning and deformed to low strains so we have observed Rose channels only rarely. As stated earlier, most secondary twins terminate on the primary twins in intensively twinned crystals, where twinning occurred first on el, then later on e 2 or e 3. Crossing or interpenetrating twins are more likely to occur in calcite which is not so extensively twinned, for example, in mediumgrade marbles. In such cases we have observed Rose channels, which in the thinned sections have a rhombohedral form. In Iceland Spar oriented to favour e-twinning but compressed at high temperatures, the crossing of twins is readily accomplished, but usually without the creation of Rose channels. This results from the greater ease with which plastic deformation occurs at the crossings. Figure 3d shows small tangles of dislocations evidently created to relax the


high stresses at the crossing twins in a sample, VW 141, deformed at 600 ° C. In samples deformed at lower temperatures, the passage of one twin through another is less common. When it occurs, microcracks are often produced on the cleavage plane, as later demonstrated for r twins (Sect. 5.4). Cahn (1955) has similarly reported the generation of cracks at twin intersections in molybdenum. Alternatively, when crossing occurs in more heavily strained samples there is always deformation of the surrounding material and, frequently, secondary twinning in the crossed twin. The density of dislocations and the heterogeneity of the deformation make detailed analysis difficult. But the general features are in accord with the observations of Mahajan and Chin (1974) on cobalt-iron alloys.

5.3. Twinning in Biaxial Calcite

Some naturally-deformed calcites have excited interest because they exhibit a high degree of biaxiality. One such sample which we have investigated had a value for 2 V~ of approximately 45 °. This sample has evidently undergone extensive deformation at low temperature. It contains a high density of twins and microtwins, with many internal voids, some of which have clearly been generated at twin intersections. In general the dislocation density is high (~ l0 s cm -2) but regions can be found where the density is lower and partial recovery with subgrain formation is the most recent process. The biaxiality appears to arise from repeated twinning and recovery of the crystal and is in general agreement with the ideas proposed by Hauser and Wenk (1976), who predicted optical properties and particularly 2 V~ of microtwinned calcite. Figure 4a shows a multiply-twinned region where there are microcracks and partially-formed sub-grain boundaries, while Fig. 4b shows a recovered region, with well-formed sub-grains. Elsewhere, even where twins are absent, dislocation densities are high, as shown in Fig. 4c, indicating that deformation and recovery are competitive.

5.4. Twinning on r = { l104} in Calcite

Minor twinning on r was noted by Griggs and his colleagues in several of their studies and the nature of the twin-shear which produces a rotation of the e-axis through almost 90 ° is commented on by Palache et al. (1951,Vol. 2, p. 145),

Twinning on r occurs in both matrix and e-twin lamellae in calcite crystals which were oriented and compressed to produce extensive twinning on e at room temperature. On inspecting an {2110} thinned section the r-twin lamellae are readily identified because they form chevron-like configurations with half- angle (between r and primary el) equal to ~70 °. Therefore they are easily distinguished from e2 and e 3 lamellae. Some aspects of the electron microscopy of r-twinning have already been illustrated by us (Barber and Wenk, 1976). We shall now show that (tem) proves that r is both the composition and twin plane and that the e-axis is rotated through 91 °.


o

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o

=

o

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O


TrO4H,'~

co,i, ~ "------~2~ oo~i~t,,in

.. "~,TOST + × x +

t ~ " ÷ - . ~ _ ~ _ _ t r o c e of

I . . . .

\ :. .. 7'/090g H

o_oo~...~ i.// ~300T 3300~

C 1 [ 0 4 H , T

F i g . 5 a-c. r ~ {i 104} twins in experimentally deformed calcite. a VW 132 with a high density of twinning dislocations in the twin boundaries (200 kV). b VW 134 (compressed normal to (1010} at 500 ° C, with 10% strain), r twin with electron beam parallel to [2110]; twin and matrix diffracting for g = 1 i025 (200 kV). c Stereographic projection corresponding to a showing schematic zone axis diffraction pattern and disposition of planes and crystal axes. • : Host reflections; x : twin reflections ; + :double diffraction

F igure 5a shows an r - twin in a {2110} foil, together wi th a na r rower second- a ry e twin. There are numerous twinning d is loca t ions in the twin bounda r i e s and slip has occur red locally, r - twin lamel lae can be imaged in da rk field using ref lect ions which, confusingly, at first appea r to be long to the ma t r ix rec iproca l lattice. In fact, for var ious foil or ien ta t ions , it first seemed tha t no twin ref lect ions could be obta ined . Closer analysis , however , showed slight spl i t t ing o f cer ta in spots and an a p p a r e n t doub l ing o f the size of the ma t r ix unit cell. The explana- t ion is tha t the twin and mat r ix ref lect ions exact ly or closely superpose in m a n y cases and this is i l lus t ra ted by Fig. 5b and c. The la t ter shows zone


Calcite

~ ~ ; , axis in twin

i / ~ I •

r=(lO~4) positi>ve

c axis in host

Fig. 6. Drawing of r twin, looking down (2110) direction showing the pseudomerohedry of matrix (angle of obliquity = 47 min of arc) and the movement of c axis through 90 ° by twinning. The drawing shows that an r twin is similar to an antiphase boundary, because only the stacking of the carbonate groups is seriously disturbed by twinning

axis diffraction pattern corresponding to the (sad) of Fig. 5 a diagrammatically set within the corresponding stereographic projection. It can be seen, for example, that 3300u and 000.12 r are almost coincident. The electron diffraction and trace analysis results are consistent only with r as both twin and composition plane. The near-superposition of the matrix and twin reciprocal lattices is an indication that pseudomerohedry is exhibited by the atoms of the real lattices. Cahn (1954) has discussed merohedry in crystals and the r-twinning law in calcite now emerges as another example of pseudomerohedry in which the (i108) matrix planes of the cation sublattice are misaligned, but by only 11/2 ° with respect to the (1102) cation planes in the twinned lattice. This is clearly shown by the drawing of a (2110) section presented in Fig. 6. Furthermore, d(1Tos)=l.912 A, d(1To2)=3.855 A so that ,'~*(llOS)- ~'~*~-- (11o2),- and 4110o)- 4.335 A, d(oo04)=4.265 A so that d*(35oo)~2d*(oo06):

The twinning transformation matrix for r twinning, derived by inspection of electron diffraction,patterns for (1104) twins is as follows."

j6 lj3 lj4,( / = ~ - 1/6 1/6 1/3 1/4~

K t -1 /23 1 / 3 - 2 / 3 00) " L r 2 0 \ I / ~

The interaction of an r-twin with an e-twins is illustrated in Fig. 7a and b. At the crossing a block of material is formed which is shown by its diffraction pattern to have been doubly-twinned. Analysis of these blocks in several in- stances of crossing r-twins shows that the e-twins usually predate the r-twins. A few observations of r-twins terminating at the e-twin interfaces bear this out. The strain imposed in maintaining coherency in the region of the junction is relieved by slip or by additional micro-twinning and this can be seen in Fig. 7b, in which two very narrow secondary e-twins terminate on the primary e-twin boundaries where they produce minute voids. Occasionally the crossing


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of e-twins by r-twins is accommodated by parting on one r-surface of the central block to give a channel with a rhombohedral cross-section. But in general the situation at crossing twins in calcite is even more complicated than illustrated here, with the activation of several deformation systems and the creation of many dislocations. Nonetheless, the crossing of e-twins by r-twins shows marked similarities with observations of crossing twins in some metal alloys (cf., Mahajan and Chin, 1974).

5.5. Other R3c Carbonates - Rhodochrosite

A search for deformation twins in geological specimens of other R3e carbonates was unrewarded, apart from a quartz-rhodonite-rhodochrosite-bearing rock, Sci. 1707, from the Bergell Alps in which the rhodochrosite exhibited numerous twin lamellae when viewed in thin section (Wenk and Maurizio, 1978). The quartz grains contained deformation lamellae indicating that the twins in the carbonate were likely to have formed during deformation.

Several twins in the rhodochrosite were investigated by (hvem) and their (sad)'s were used to make trace analyses of the twins. In every case the twin was found to conform to the e-twinning law of calcite. Figure 8a shows one of the twins, all of which took the form of lamellae with parallel boundaries. Within the twinned material there are numerous planar defects, in rather poor contrast, which appear tb" be small stacking faults, presumably generated during twinning.

6. Resu l t s - R3 C a r b o n a t e s

6.1. Twinning in Dolomite

The crystallography of the twins in deformed dolomite rocks and in numerous experimentally-deformed single crystals and polycrystals has been examined by (hvem) and trace analysis. In every case the twins have been found to correspond with the reported twin law, with f - {0112} as both twin and composition plane.

In dolomite, as in calcite, although twinning dislocations are not necessarily present in the twin boundaries, it is rare to find twins which are not associated with a local increase in dislocation density. Dislocation-free twins are seen only in the highest-grade (most recovered, usually recrystallized) dolomite marbles; these are' annealing twins.' In general, twins are either fringed with dislocations or may be associated with dislocation arrays and other defects (e.g., voids) which are stable against annealing. Figure 8b shows an f-twin, together with rows of equilibrated voids and linking dislocations in Fauske dolomite. We are uncertain as to the reasons for the frequent association of voids and twins. The chains of voids probably arise from the healing of cracks; neither twins nor voids are completely eliminated during recrystallization but they may be swept into close proximity.


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= ~

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Deformation twins in dolomite have been available for study through our current work (Barber etal., 1977; Heard etal., 1978) on experimentally- deformed single crystals, using CO2 gas as confining medium. In general agreement with the results of Higgs and Handin (1959), crystals compressed parallel to the c-axis at temperatures in the range 3000-600 ° C deform by f-twinning. Minor f-micro-twinning also occurs in orientations favouring slip on the basal plane; in such cases the microtwins are parallel lamellae which propagate without significant additional generation of dislocations.

Analysis of the complete (sad) patterns enables one to derive the transformation matrix for an f-twin in dolomite, but it is highly irrational, as follows: (!) 4 33

= [ 1/3 -2 /3 1/3 /03

~ - 15/33 1/3 -4/33 7 /33]

L 7" \ - 5 2 / 3 3 0 52/33 - 1 9 / 3 3 / ,

The explanation for this unlikely-looking matrix is that for an f=(1012) twin, for example, there is no close-packed plane with continuity across the twin boundary apart from (1210), which has been taken as the plane of the S projection in this instance (Fig. l b). The plane (1018) approximates to the plane of coincidence but from the (sad) pattern, the proper indices emerge as (707.52).

In dolomite crystals yielding principally by twinning, the twins are variable in width and they are not always plane parallel lamellae (i.e., coherent) so that high densities of dislocations sometimes occur in the twin boundaries. Figure 9 a shows a twin containing incoherent boundary dislocations and cleavage cracks within the lamella. It should be noted, however, that the twinning has not injected dislocations into the surrounding matrix, as commonly occurs when calcite twins. However, where the shape change cannot be achieved solely by twinning, there may also be extensive fracture, which may itself create many dislocations. But the crossing of twins in dolomite is often achieved during deformation at strain rates ~ 10- s s without significant fracture occurring, local stresses being relieved by slip or, at sufficiently high temperatures, by climb. An example of crossing twin is presented in Fig. 9b and the contrast between this micrograph and those for calcite is very marked. The dislocation densities generated at twin intersections in dolomite are seldom as high as those in calcite at similar strains. In Fig. 9 b the foil has been tilted to produce maximum visibility of the dislocations, which has also rendered the twin boundaries in low contrast.

6.2. Twinning in Kutnahorite

The same rock suite from which we described deformed rhodochrosite in the previous section also contains the mineral kutnahorite which, like dolomite, has an ordered arrangement of cations. Optical microscopy showed that the kutnahorite contained twins, which were examined by (hvem) after ion-thinning.


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Fig. 10. f twin in kutnahorite (specimen Sci 1707-2 from Piz Cam, Bergell Alps)

X-ray microprobe analysis showed the composition of the carbonate grains to be approximately (Mgo.21Mno.20Feo.07Cao.sa)CO3 (Wenk and Maurizio, 1978).

Several twins in this mineral were studied by (hvem) coupled with (sad) trace analysis methods. An example of a kutnahorite twin is shown in Fig. 10. Its trace analysis, in common with the other examples, shows that kutnahorite twins according to the dolomite f-twinning law, as might well be expected. The mineral ankerite, Cao.5(Fe, Mg, Mn)o.sCO3 is also reported to twin in the f-planes, in accord with its structural similarity to dolomite.

7. The Deformation of Carbonates by Microindentation

Knoop indentations produced on cleavages of Iceland Spar with a 50p load (long diagonal of indenter parallel to (047~1)) found to be accommodated by microtwinning, some cleavage and the generation of many dislocations. The


measured hardness had a value of 315.5 K.H.N. (long diagonal of indenter parallel to (1120)). The indentations in calcite are very long and narrow, as compared with those produced on the cleavage surfaces of other rhombohedral carbonates.

Figure 11 a shows the microstructure a few microns below and slightly to one side of an indentation in calcite. In every case examined, the microtwins conformed to the e-twinning law and the dislocations mostly appeared to be resultant from the twinning process. Note that where such narrow microtwins intersect, the crossing is apparently effected with ease, by the creation of localized slip, in the absence of cleavage or further secondary twinning. The successful use of indentation for the production of twins led to attempts to produce twinning in other carbonates by the same mechanism. However, in the cases of magnesite, rhodochrosite and dolomite, microtwins were completely absent in the material adjoining the indentations. In all three cases, large numbers of glide dislocations were in evidence and cracking was absent. The appearance of the heavily deformed material under one such indentation in rhodochrosite is shown in Fig. 11 b. The scale of the structure is perhaps too fine for this micrograph to reveal the nature of the short dark features to be seen in it. They are not microtwins but closely spaced dislocation dipoles which lie directly under the central ridge of the Knoop diamond. Measured values of hardness for magnesite, rhodochrosite and dolomite were 608, 145 and 628 K.H.N. respectively (long axis of indenter parallel to ~1120) in cleavage face).

8. Discussion and Conclusions

The results presented in this paper are in general accord with results obtained by other workers using light optical methods, but extend the earlier observations by illustrating the distributions of sub-optical twins, cracks and dislocations. It has been shown that there are marked differences in the behavior of calcite and dolomite, not just because of the differences in their twin laws and the temperature range for twinning, but because of the high dislocation densities produced external to the twin boundaries by twinning in calcite. These dislocations, whose creation is not reversible, easily account for the limited number of twinning/detwinning operations possible in calcite. The lower dislocation densities noted in twinned dolomite and at twin intersections in that mineral are perhaps partly explained by the greater ease with which local stress relaxation can be achieved at higher temperatures. But the results of the indentation experiments do seem to indicate that calcite is somewhat unique, in having a lower yield stress for twinning than for glide at room temperature. Neither magnesite nor rhodochrosite could be made to twin by microindentation.

It has been found by Bowden and Cooper (1962) that the velocity of twin propagation in calcite is considerably less than that found in zinc, for example, and less than the velocities normally found for dislocation propagation. The stress distribution at the tip of a twin is similar to that at a crack tip and it is well known that dislocations are produced when a propagating crack is slowed down or temporarily arrested. The dislocations generated by twinning


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in calcite may have their origins in the low velocity of twin propagation, which in turn may be a consequence of the atomic rearrangements necessary when calcite twins (the reorientation of the carbonate groups). Presumably this rear- rangement is more easily achieved in twinning at higher temperatures, as in dolomite. No information is available about twin velocities in dolomite.

The ordered R3 carbonates have a single deformation twinning law with f as composition and twin plane, while the R3e carbonates CaCO3, MnCo3 and FeCO3 have e-twinning as the primary twinning mechanism. These findings give strong support to existing ideas about the differences between ordered and disordered carbonates. The only anomaly is, possibly, MgCO3 which twins on {i104} according to Klassen-Neklyudova (1964). We have been unable to verify this point.

There does not seem to be a clear correlation between microhardness values and the mechanisms of stress relief. The two softest carbonates examined, calcite and rhodochrosite, deform by very different mechanisms: calcite twins with ease, rhodochrosite glides with ease. The two hard carbonates do not twin, but exhibit limited amounts of glide.

The behavior of crossing twins in calcite shows considerable similarities to multiple twinning in some of the harder or more brittle metals deformed at room temperature. With dolomite, which only twins at elevated temperatures, correlation is less evident. The accommodation of strain at twin intersections in calcite can be achieved either by localized cleavage or slip. Except at low strains, both mechanisms are normally operative. The crossing of twins in heavily strained calcite is usually accomplished by secondary twinning within the crossed twin. An exception is the crossing of narrow microtwin lamellae of comparable width, which can apparently be accommodated by dislocation glide. In dolomite the crossing of twins commonly occurs with only the operation of localized slip as a stress relief mechanism.

Acknowledgements. We wish to thank the National Science Foundation (NSF grant No. EAR 78 23848), the Science Research Council (SRC grant GR/A/14599) and NATO (grant i611) for grants in partial support of this work. We thank Imperial College, England, for access to the 1 MV electron microscope; also Dr. A.C. McLaren for hospitality to D.J. Barber and access to the 200 kV electron microscope at Monash University, Australia. Dr. O.K. Joshi made the microhardness measurements, Dr. M.S. Paterson kindly supplied specimen 4080 XD (Fig. 14) and Dr. R. Bradshaw supplied the specimen of Fauske marble.

References

Barber, D.J.: Dislocation structures in deformed and recovered dolomites. Tectonophysics 39, 193-)i3 (1977)

Barber, D.J., Heard, H.C., Paterson, M.S., Wenk, H.R.: Stacking faults in dolomite. Nature 269, 789-790 (1977)

Barber, D.J., Wenk, H.R. : Defects in deformed calcite and carbonate rocks. In: Electron microscopy in mineralogy, Wenk, H.R. (ed.). Berlin, Heidelberg, New York: Springer 1976, pp. 428-442

Barber, D.J., Wenk, H.R.: On geological aspects of calcite microstructure. Tectonophysics 54, 45-60 (1979)

Baumhauer, H.: l~ber k/instliche Kalkspath-Zwillinge nach 1/2 R. Z. Kristallogr. 3, 588-59l (1879)


Borg, 1., Turner, F.J.: Deformation of Yule Marble Part VI. Bull. Geol. Soc. Am. 64, 1343 1352 (1953)

Bowden, F.P., Cooper, R.E.: Velocity of twin propagation in crystals. Nature 195, 1091-1092 (1962)

Bradley, W.F., Burst, J.F., Graf, D.L. : Crystal chemistry and differential thermal effects of dolomite, I l l . Geol. Surv. Rept. 167, 207-217 (1953)

Braillon, P., Serughetti, J.: Mechanical twinning in calcite. Phys. Status Solidi A: 33, 405-413 (1976)

Cahn, R.W.: Plastic deformation of alpha-uranium; twinning and slip. Acta Metall. 1, 49-70 (1953)

Cahn, R.W. : Twinned crystals. Philos. Mag. [Suppl.] 3, 363 445 (1954) Cahn, R.W. : Mechanical twinning in molybdenum. J. Inst. Met. 83, 493-496 (1955) Coe, R.W., Kirby, S.H. : The orthoenstatite to clinoenstatite transformation by shearing and rever-

sion by annealing: Mechanism and potential applications. Contrib. Mineral. Petrol. 52, 29-55 (1975)

Deer, W.A., Howie, R.A., Zussman, J.: Rock forming minerals, vol. 5. London: Longmans 1962, pp. 242~43

Dove, H.W. : Optische Notizen. Ann. Phys. 110, 286-290 (1860) Fairbairn, H.W., Hawkes, H.E. : Dolomite orientation in deformed rocks. Am. J. Sci. 239, 617 632

(1941) Garber, R.I.: Residual stresses in plastically deformed crystals of rock-salt. Zh. Eksp. Theor.

Fiz. 8, 746-752 (1938) Garber, R.I.: Mechanism of twinning of calcite and sodium nitrate during plastic deformation.

Zh. Eksp. Theor. Fiz. 17, 48~52 (1947) Geothem, L. Van, Landuyt, J. Van, Amelinckx, S.: The alpha-beta transition in amethyst quartz

as studied by electron microscopy and diffusion. Phys. Status Solidi A: 41, 129 137 (1977) Goetze, C., Kohlstedt, D.L, : The dislocation structure of experimentally deformed marble. Contrib.

Mineral. Petrol. 59, 293-306 (1977) Goldsmith, J.R. : Some aspects of the geochemistry of carbonates, in : Researches in geochemistry,

vol. I, Abelson, A. (ed.). New York: John Wiley & Sons 1959, pp. 336-358 Griggs, D.T.: Hydrolytic weakening of quartz and other silicates. Geophys. J.R. Astron. Soc.

14, 19 31 (1967) Griggs, D.T., Turner, F.J., Borg, I., Sosoka, J.: Deformation of Yule marble: Part V, Effects

at 300 ° C. Bull. Geol. Soc. Am. 64, 1327-1342 (1953) Griggs, D.T., Turner, F.J., Heard, H.C.: Deformation of rocks at 500°C to 800 ° C. In: Rock

deformation, Griggs, D.T. and Handin, J. (eds.). Geol. Soc. Am. Mere. 79, 39-104 (1960) Hauser, J., Wenk, H.R.: Optical properties of composite material (microtwins, exsolution

lamellae, solid solution). Z. Kristallogr. 143, 188-219 (1976) Heard, H.C., Wenk, H.R., Barber, D.J.: Experimental deformation of dolomite single crystals to

800 ° C. Eos Trans. Am, Geophys. Union 59, 249 249 (1978) Higgs, D.V., Handin, J.: Experimental deformation of dolomite single crystals. Bull. Geol. Soc.

Am. 70, 245-278 (1961) Johnsen, A.: Biegungen und Translationen. Neues. Jahrb. Mineral. 2, 133-153 (1902) Keith, R.E., Gilman, J.J.: Dislocation etch pits and plastic deformation in calcite. Acta Metafl

S, 1-10 (1960) Klassen-Neklyudova, M.V.: Mechanical twinning of crystals. New York: (trans. J.E.S. Bradley)

Consultants Bureau 1964 Laves, F.: 13ber den Einflug yon Ordnung und Unordnung auf mechanische Zwillingsbildung.

Naturwissenschaften 30, 546 (1952a) Laves, F.: Mechanische Zwillingsbildung in Feldspaten in Abhfingigkeit yon Ordnung-Unordnung

der Si/A1-Verteilung innerhalb des (Si, A1),Os Geriistes. Naturwissenschaften 30, 546 547 (1952b) Laves, F.: 1 feldspati e le loro relazioni di fase. Rend. Soc. Mineral. Ital. 16, 69-100 (1960) Mahajan, S., Chin, G.Y. :The interaction of twins with existing substructure and twins in cobalt-iron

alloys. Acta Metall. 22, 1113-1119 (1974) Mtigge, O.: Beitr~ge zur Kenntnis der Strukturflgtchen des Kalkspathes. Neues Jahrb. Mineral.

1, pp. 32 54; 81-85 (1883) Nicholas, J.F.: The simplicity of Miller-Bravais indexing. Acta Crystallogr. 21, 880 881 (1966)


Pabst, A.: Transformation of indices in twin gliding. Bull. Geol. Soc. Am. 66, 897-912 (1955) Palache, C., Berman, H., Frondel, C.: The system of mineralogy of Dana, vol. 2. New York:

Wiley 1951, pp. 141-217 Paterson, M.S., Turner, F.J.: Experimental deformation of strained calcite crystals in extension.

In: Experimental and natural rock deformation, Paulitsch, P. (ed.). Berlin, Heidelberg, New York: Springer 1970, pp. 109-I41

Pfaff, F. : Versuche fiber den Einflul3 des Drucks auf die optischen Eigenschaften doppeltbrechender Krystalle. Ann. Phys. 107, 333-338 (i859)

Reusch, E.: l~ber eine besondere Gattung yon Durchgfingen in Steinsalz und Kalkspath. Ann. Phys. 132, 441 451 (1867)

Rogers, A.F. : Polysynthetic twinning in dolomite. Am. Mineral. 14, 245 Rose, G. : l~ber die im Kalkspath vorkommendeu hohlen Canfile. Abh. Konig. Akad. Wiss. Berlin.

23, 57-79 (1868) Startsev, V.I., Bengus, V.Z., Lavrent'ev, F.F., Soifer, L.M. : Formation of dislocations in the twinning

of calcite. Kristallogr. 5, 737-743 (1960) Tenderloo, G. Van, Eanduyt, J. Van, Amelinckx, S. : Electron microscopic observations of domain

structure and the diffuse electron scattering in quartz and in aluminum phosphate in the vicinity of the ~-/~ transition. Phys. Status Solidi A. : 30, K. 11 (1975)

Turner, F.J. : Some geometrical aspects of experimentally induced twinning in minerals. In : Deforma- tion twinning, vol. 25: Reed-Hill, R.E., Hirth, J.P., Rogers, H.C. (eds.). Met. Soc. (AIME) Conf. Proc. London: Gordon & Breach Scientific Publishers 1963, pp. 156-176

Turner, F.J., Griggs, D.T., Heard, H.: Experimental deformation of calcite crystals. Bull. Geol. Soc. Am. 65, 883-934 (1954)

Turner, F.J., Griggs, D.T., Weiss, L.E., Heard, H. : Plastic deformation of dolomite rock at 380 deg C. Am. J. Sci. 252, 477 488 (1954)

Turner, F.J., Orozco, M.: Crystal bending in metamorphic calcite and its relation to associated twinning. Contrib. Mineral. Petrol. 57, 83-97 (1976)

Venables, J.A. : The electron microscopy of deformation twinning. Phys. Chem. Solids 25, 685 692 (1964a)

Venables, J.A.: Nucleation and propagation of deformation twins. Phys. Chem. Solids 25, 693 700 (1964b)

Weiss, L.E., Turner, F.J. : Some observations on translation gliding and kinking in experimentally deformed calcite and dolomite. In: Fracture and flow of rocks, Monograph 16: Heard, H.C. et al. (eds.). Am. Geophys. Union Monograph. 1972, pp. 95-107

Wenk, H.R., Maurizio, R. : Kutnahorite, a rare Mn mineral from Piz Cam (Bergell Alps). Schweiz. Mineral. Petrogr. Mitt. 58, 97-100 (1978)

Received June 27, i979

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