Phys Chem Minerals (1988) 16: 298-303 PHYSlC$ [ CHEMISTIIY [ MINERALS �9 Springer-Verlag 1988

Twinning in Tetragonal Leucite David C. Palmer, Andrew Putnis and Ekhard K.H. Salje Department of Earth Sciences, University of Cambridge, Downing Street, Cambridge, CB 2 3 EQ, England

Abstract. The change from cubic to tetragonal symmetry in natural leucite, KA1SizO6, involves two types of twin- ning, which appear sequentially with decreasing tempera- ture: (1) lamellar, associated with the point group symmetry reduction m3m to 4/mmm; (2) merohedric, associated with the change 4/mmm to 4/rn. Twin orientations have been deduced from X-ray precession photos and TEM diffrac- tion patterns and images. These are confirmed by theory, using the concept of spontaneous strain and the symmetry relations between adjacent domains. Lamellar twins have boundaries parallel to {101} of the cubic phase, and are cross-cut by the merohedric twins, which have irregular boundaries with x and y in adjacent domains interchanged. On an electron microscopic scale, the distortion arising from twin intersections is revealed by a curvature of one twin wall adjacent to another, and by needle-shaped do- mains. The macroscopic orientation of the lamellar twins is related to the lattice parameters and hence the magnitude of the spontaneous strain. This in turn leads to the charac- terisation of the order parameter for the m3m to 4/mmm transformation.

1. Introduction

Leucite, KAISi206, is a characteristic mineral of K-rich, SiO2-poor volcanic rocks, and is often found as porphyrob- lasts with euhaedral, pseudo-cubic symmetry. Optically these crystals are seen to consist of repeated lamellar twins (sometimes quite coarse) often in several orientations.

Wyart (1940) using X-ray diffraction showed that leucite at room temperature is tetragonal, space group I41/a, and this has been confirmed in a more recent structure refine- ment by Mazzi et al. (1976). Peacor (1968) showed that at high temperatures leucite becomes cubic, with space group Ia3d, which is the topological symmetry of the low-T form. The precise determination of twin-orientations has been previously investigated using X-ray precession photo- graphs; Korekawa (1960, 1969) found that adjacent twin domains were related by a refection of the lattice across a pseudo mirror-plane (the composition plane of the twin) parallel to {101} of the tetragonal form. On < 0 1 0 > pho- tos, this was represented by a tripling of {101} reflexions and a quadrupling of all the others. Heating the crystal during X-ray exposure caused twin-related spots to co- alesce, becoming a single reflexion at temperatures greater

than about 650 ~ C. Sadanaga and Ozawa (1968) disputed Korekawa's results, observing an apparent asymmetry in the disposition of {101} reflexions, which implied an inco- herency between domains. Their twin law had adjacent do- mains related by a rotation about a pseudo diad, parallel to < 101 > . Such twins later became incoherent, they ar- gued, due to boundary adjustment to minimise strain at lower temperatures.

Recent work has begun to shed new light on the cubic to tetragonal inversion in leucite, in particular suggesting that two transformations may be involved, with an interme- diate phase stable over a narrow temperature interval be- tween the 141/a (tetragonal) and Ia3d (cubic) fields. Neutron structure refinements on natural leucites, carried out at dif- ferent temperatures (Grrgel et al. 1984) point to such a structure, with tetragonal symmetry and space group 141/ acd. Lange et al. (1986) detected two peaks, separated by about 17 ~ C, on a DSC trace of natural leucite, which they correlated with the two transformations I41/a to I41/acd and I4~/acd to Ia3d. A similar effect was detected on DTA traces by Faust (1963).

Using X-ray precession photography on a leucite crystal with just one twin set, combined with TEM images and diffraction patterns, we have been able to unambigu- ously determine the twin law for the lamellar twins (called "pseudomerohedric" by Mazzi et al. 1976). The existence of a second type of twinning, "merohedric" (Mazzi et al. 1976), which cannot be deduced from diffraction patterns, is confirmed by TEM micrographs. The orientations of these twin types are consistent with theory - using the idea of two separate symmetry reductions during the cooling of originally cubic leucite - and we show how the mutual orientations of the lamellar twins are related to the magni- tude of the spontaneous strain.

2. Experimental Methods

Two samples of natural leucite were used during this work (details given in Table 1). Compositions were determined by electron microprobe analysis: analysing for K, Na, Ca, A1, Si, Fe, Mn, Mg, Ti and Cr, with oxygen measured by difference. Standard correction procedures were applied. During analysis a defocussed incident electron beam was used, to reduce the risk of K, Na loss induced by radiation damage to the specimen.

A single crystal of L999 (diameter about 5 ram) was prepared for analysis. Ten spot analyses were made over

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Table 1. Details of Natural Leucites Used in This Work

Number L 999 L 28054 (N.L. 1)

Composition Ko.97Alo.99Feo.olSi2.olO 6 + trace Ti

Cell a 13.057• ~."

Constants c 13.753___0.003

Description Single crystals, with pseudo-cubic symmetry;

Locality Unknown; Harker Collection, Cambridge

References Bismayer (pers. comm.) Ruscher et al. (1988)

Ko.9sCao.ozAlo.gsFeo.o 1 Si2.olO6

13.055 • 0.002 A_

t 3.749 __ 0.002/~

Crystals in Nosean-Leucitophyre

Rieden, Essen, W. Germany

Taylor and Henderson (1968) Mackenzie and Guilford (1980)

�9 Errors are 2 a errors from least-squares refinement

the surface of the crystal, to test for zoning, but the resulting compositions were identical within experimental error, so an average was taken. For the L28054 sample, a thin-sec- tion of the rock containing large leucite crystals up to 5 mm in diameter, was used. A total of 15 spot analyses, over 4 different grains were made. The results were consistent, and the only differences between grains were the concentra- tions of minor amounts of Ca and Fe. The average of all the analyses is given in Table 1.

Lattice parameters were determined by least-squares re- finement of about 30 indexed lines on X-ray powder photo- graphs. A ' H u b e r ' Guinier Camera, using monochromatic CuK~I radiation and operating under vacuum was used. Samples were ground under acetone and mixed with stan- dard powdered silicon. The resulting paste was spread evenly over 'my la r ' film, and mounted in the camera when dry. Exposures lasted 3 days, and the films were indexed with reference to the Si standard - which also allowed a correction for film-shrinkage to be made.

A number of X-ray precession photographs were taken with different single crystals of L 999, before a suitable crys- tal was found. The final crystal was a cleavage fragment from a larger grain; prior to selection this had been cleaned with acetone and checked optically for impurities. The cleavage fragment showed no twins on an optical scale. The crystal was mounted on a glass fibre on a set of arcs and aligned so that an < 0 1 0 > axis was parallel to the incident X-ray beam. The crystal and its arcs were then transferred to a ' S T O E ' precession camera and exposed for a week with the < 0 1 0 > axis as the precession axis, using monochromatic MoK~I radiation. The resulting photo is shown in Figure 1 (individual single crystals of L28054 were not available for X-ray work).

Samples of leucite were prepared for transmission elec- tron microscopy by ion-beam bombardment of thin crystal- slices mounted on copper supporting rings. Specimens were examined in a JEOL JEM 100 CX electron microscope oper- ating at around 100 KV.

3. Results

Figure 1 shows a precession photo obtained from a single crystal of leucite (L999) with < 0 1 0 > as the precession axis. Only two twin orientations are present, which cause the doubling o f spots parallel to (101)*. The (101)* row remains unsplit, hence the twin law is a reflection o f the lattice across the pseudo mirror plane (101). On an electron

Fig. 1. < 010 > Precession photo of leucite, L999, exposed for one week with MoK~I radiation. Twinning of two domains, (1) and (2) across common (101) planes gives rise to doubling of spots parallel to the unsplit row

microscopic scale, similar patterns are obtained across the boundaries of the lamellar features illustrated in Figure 2, these are therefore lamellar twins. Such twins are cross-cut by a network of curved, irregular boundaries, enclosing do- mains with differing contrast. Diffraction patterns taken across such boundaries show no splitting of spots as ob- served for the lamellar twins. The domains, although they resemble antiphase domains, cannot be such because under bright field and dark field imaging conditions the contrast in adjacent domains can be varied by tilting the specimen. This suggests that they are twins, and we correlate them with the 'merohedr ic ' twinning referred to by Mazzi et al. (1976); here the x and y axes in adjacent domains are inter- changed whilst the z axis remains common to both.

A complex twinning microstructure has been observed in all natural leucites studied. It is common to find fine scale lamellar twinning within much coarser lamellar twins, with both stages overlain by the merohedric twin network (Fig. 3 a). Also common are 'needle twins ' : fine lamellae terminating at sharp points. Various stages in the apparent

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Fig. 2. TEM micrograph of twins in an ion-beam thinned sample of leucite, L28054. Lamellar twins with opposite contrast in adja- cent lamellae are overlain by a complex network of merohedric twins showing curved domain boundaries. The scale bar represents 3000 A

formation of such twins have been observed in the same section (Fig. 3b) - including fight-angled domain walls, similar to those discovered in Gd2(MoOg)a (Yamamoto et al. 1977a, b). Splitting at the tips of the needles has also been found (Fig. 3 c). Lamellar twins are seen to interact with each other at twin intersections, usually resulting in the curvature of a domin wall close to the intersection with another wall (Fig. 3 d).

Detailed observation of twin morphologies has been hampered by specimen beam damage, which causes a grad- ual mottling effect, with damaged regions appearing as bright blebs in the illuminated area (Fig. 3b). After only a few minutes under a 100KV beam all the microstructural detail disappears.

4. Discussion

During the cooling of a substance which undergoes a displa- cive phase transformation at some lower temperature, fluc- tuations in the order parameter occur on a local scale (al- though on a macroscopic scale the symmetry is still that of the supergroup) and reach a critical level close to the transition temperature (To). Below Tc a spontaneous distor- tion builds up, resulting in a structural strain, which may cause twinning throughout the crystal so as to minimise macroscopic strain. The "spontaneous strain" is defined as that part of the strain due entirely to a phase transforma- tion (Salje et al. 1985), and increases with decreasing tem- perature. The m3m to 4/mmm transformation in leucite in- volves no change in the contents of the unit cell, and is due to an instability at the centre of the Brillouin Zone, giving a linear coupling between the order parameter and the strain. The spontaneous strain therefore has the symme- try of the active representation of the order parameter. This is an irreducible representation of the supergroup (m3m)

apart from the identity, which becomes the identity repre- sentation for the subgroup (4/mmm). For this symmetry change in leucite it would therefore be: E~, which is repre- sented by the eigenvectors: 2z 2 - x 2 - y 2 (tetragonal) and: x 2 - y 2 (orthorhombic). The tetragonal eigenvector corre- sponds to an extension parallel to z, with contractions par- allel to x and y. The different twin orientations in leucite reflect the fact that the initial extension could have occured parallel to any one of the three symmetry-related < 001 > directions in the cubic phase. Assuming that only the tetra- gonal representation (2Z2--xZ--y 2) is active (and ignoring all potential coupling with other representations), then in terms of the components, eli of the spontaneous strain ten- sor, this is equivalent to: 2ea3 - el 1 - e22 (with principal axes x~, x2, xa parallel to the crystallographic axes x, y, z respectively). The spontaneous strain tensor for a single twin domain (1) is therefore:

0 - 2 e l l

The form of the tensor for domains in other twin-orien- tations can be found by operating with those symmetry elements which disappear in the low-T phase (Sapriel 1975). In this case the symmetry change can be represented by the loss of the < 111 > triads, which formerly related x, y and z axes; (ie. x ~ z , y---,x, z ~ y etc.). So the strain tensors for the other two orientations (2) and (3) are:

/ell 0 ; S ( 3 ) = I 00 ell

0 e~l 0 ell

At the boundary between two twin domains (k, /), all strain components must be equal, ie

[Sij (k) - S~j (/)]x~ x j = 0

hence:

3el a x 2 - 3ea ~ z 2 = 0

giving the condition that x = _+ z at the domain boundary. So the domain wall must be parallel to a {101} plane. Under 4/mmm point group symmetry, a single domain wall may exist in any one of eight possible orientations: (101), (10i), (011), (012) and their negatives. Adjacent domains are re- lated by a reflection of the lattice across {101}. This is in agreement with our experimental findings.

When a crystal contains domain walls in more than one orientation, each domain wall remains parallel to the appropriate (101) plane of the cubic phase - since the mutu- al orientation of boundaries is defined by the (cubic) super- group symmetry. An < 0 1 0 > precession photo would therefore be the superposition of two identical patterns, each from a single twin-pair, with one pattern rotated through 90 ~ relative to the other. Operating in this way on Figure 1, a pattern identical to that of Korekawa (1969) is obtained. It must be noted, however, that these orienta- tions are maintained only at a macroscopic scale. On a microscopic level, the angular deviation between the tetra- gonal (101) planes and their cubic counterparts means that twin-intersections are highly strained, and consequently ap- pear distorted. This is illustrated in Figure 4a: the angular misfit, 'o) ' between unstrained lattices, induced by a right- angled twin boundary causes a lattice distortion which

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Fig. 3a-d. TEM micrographs of twin interactions in L28054. (a) Boundary between two coarse twin lamellae which show fine-scale internal lamellar twinning. The boundary has become highly distorted and the whole region is overlain by merohedric twins, Co) Various stages in the growth of 'needle' twins. At ' A ' two right-angled domain walls are too far apart to interact, however at 'B ' a pair of domain walls are close enough for their strain fields to interact, causing a mutual attraction of the opposite walls. At 'C ' the domain walls have coalesced close to the junction with the dark coloured domain, resulting in a 'needle' twin. The needle at ' D ' has migrated into the light-coloured domain from its former position, as the matrix closes about its tip. (c) Splitting at the tip of a needle twin. (d) Triple twin intersections; pairs of lamellar twins in different orientations interact within the matrix, causing the domain walls to curve close to the intersection. The scale bar represents 3000

grows in magni tude closer to the junct ion (Fig. 4b). This si tuation has been previously described by Y a m a m o t o et al. (1977a, b), Torr6s et al. (1982a, b) and Salje et al. (1985); in these papers the domain boundaries are described in terms of an array of dislocations, and it is assumed that the mater ial behaves isotropical ly and is an elastic contin- uum, which is a valid approximat ion for leucite because the twinning is relatively coarse ( > 700 ~) . This approach

shows that the resulting stress can be represented by a force, ' fc ' , acting on the misfit wedge (Fig. 4a), causing the do- main wall near the junct ion to become rounded, with a radius of curvature p ropor t iona l to fc/a where cr is the ho- mogeneous stress associated with the domain wall itself (Salje et al. 1985). The resulting geometry is shown schemat- ically in Figure 4b. I t has been shown (Torr+s et al. 1982a, b; Y a m a m o t o et al. 1977a, b; Salje et al. 1985) that it is

302

Fig. 4a, b. Right-angled domain walls. (a) The angular misfit, 'o9' between two parts of unstressed lattice adjacent to the corner of a twin domain causes an effective force, f~, which acts on the misfit wedge. (b) An elastic lattice distortion causes the domain wall to curve so that the two twin walls remain mutually perpendicular away from the corner

Fig. 5a-d. Formation of needle twins. (a) Two right-angled domain walls separating two domains (one stipled, the other white) are too far apart to interact. (b) Another pair of domains are sufficiently close for mutual attraction to occur; with a fast enough cooling rate this activated state can be overcome (e), and the resulting needle twin migrates further into the surrounding domain under the influence of the strain field between its tip and the new planar boundary (d)

energetically favourable for two r ight-angled domain walls to combine as a 'needle twin ' , and so reduce the surface area o f dis tor ted domain wall. Such a step requires an acti- vat ion energy, dependent on the separat ion of the two do- main walls. But the driving force for format ion of needle twins will be control led by the cooling rate; slow cooling would lead to the product ion of small numbers o f ' needles ' , each formed from a coalescing pa i r of r ight-angled twin domains. Once formed, the embryo needle twin will re t reat from its initial posit ion, into the matr ix - as the surrounding domain closes like a zip a round it - under the influence of the high strain field at its tip (i l lustrated in Fig. 5). Fas t cooling leads to many more needle twins, but there is insuf- ficient t ime for needles to migrate far into the matrix. Our T E M observat ions show that needle twinning is a common feature in leucite, a l though the embryo stage shown in Figure 3b is extremely rare. However this microtextural phenomenon does provide an indicator of the cooling histo- ry o f the mineral. A spontaneous split t ing of the needle tip occurs once the radius of curvature reaches a critical value (Torrrs et al. 1982 a, b) - i l lustrated in Figure 3 c.

The other type of junct ion observed in leucite is the triple junct ion, where three non-equivalent domains meet - Figure 3d. The disort ion caused by angular mismatch between domains is shown in Figure 6.

Lamel lar twins may become internally twinned if cool- ing is rapid. In this case, the initial twinning is too coarse to counteract the macroscopic strain as the crystal is cooled, so a second generat ion of twins is p roduced inside the first. Figure 3 a shows that the former twin boundar ies are now extremely complex and distorted.

Since the lamellar twinning is induced by a spontaneous

Fig. 6. A triple twin-junction. Elastic lattice distortions are required to overcome the angular misfit between adjacent domains (A, B, C), resulting in the curvature of domain walls close to the junction. Arrows indicate the directions of the effective force on the domain walls

strain, the observed morphologies can be used to determine the magni tude o f the strain, and ul t imately the order pa- rameter itself. The relat ion between the twin angle '~0' (de- fined in Fig. 1) and the spontaneous strain is deduced using the relat ions between strain tensor components and lattice parameters evaluated by Schlenker et al. (1978):

ell=ezz=(a+ao)/ao and e33=(c--ao)/ao where ao is the cell-edge for the cubic phase extrapola ted to the temperature in the te t ragonal phase. This allows the

magnitude of the spontaneous strain, es, to be expressed in terms of ~0:

05 = 4 t a n - 1 c/a- 180 ~

= 4 t a n _ 11+e33 180o l + e t l

~s = ~ (Redfern and Salje 1987, 1988) n

2 2 = ~ e l 1 if- e22 -~ e23 = V 6 e l 1

=1 /~ i - t a n ( 1 8 0 + 05)/4 [ -

2 + tan (1 80 + r

Because of the l inear coupling between order parameter and spontaneous strain therefore, measurement of ~p allows the order parameter for the m3m ~ 4/mmm t ransformat ion to be determined.

F o r the symmetry reduction 4/mmm to 4/m, the {110} mir ror planes are lost, and become the composi t ion planes (pseudo mir ror planes) for merohedr ic twins. Adjacent do- mains therefore have common " z " axes, but their x and y axes are interchanged. Because the periodicities paral lel to x and y axes are identical, the presence of merohedric twinning cannot be inferred from diffraction patterns. However, because the structure factors for (hkl) and (khl) reflexions are generally different, the two twin orientat ions show different diffract ion contras t when viewed in a trans- mission electron microscope under bright- and dark-field conditions. Figure 2 shows typical images of such twins. The irregular boundar ies presumably represent the isotropic strain associated with such twinning. Merohedr ic twins ap- pear to be a ubiqui tous feature of all na tura l and synthetic leucites.

5. Conclusion

The displacive phase t ransformat ion in leucite from cubic to te t ragonal symmetry involves two separate symmetry re- ductions, m3m to 4/mmm and 4/mmm to 4/m which give rise to lamellar and merohedric twinning respectively. The macroscopic orientat ions of the twin boundar ies are sym- metry control led and temperature- invariant . However the twin angle, ~0, is related to the spontaneous strain (and hence to the order parameter for the displacive phase transit ion) and increases with decreasing temperature. On a microscop- ic level, the ferroelastic behaviour is revealed by a complex twin texture with significant interactions between neigh- bouring lamellar twins, which can be interpreted by elastic cont inuum theory. In part icular , the presence of needle twins, and their morpho logy provides an indicator of the cooling rate of the mineral. This microtexture remains inde- pendent of the overlying merohedric twin network.

Acknowledgments. We would like to thank Tony Abraham and Ian Marshall for their invaluable technical assistance. DCP ac- knowledges receipt of a NERC research studentship. ES thanks

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NERC and EEC for financial support. This is Cambridge Earth Sciences contribution no. 1244.

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Received March 30, 1988