Intragranular gliding in domal salt

Tectonophysics - Elsevier Publishing Company, Amsterdam Printed in The Netherlands

INTRAGRANULAR

GLIDING IN DOMAL

SALT

W.M SCHWERDTNER Department of Geology, University of Toronto, Toronto, Ont. (Canada) (Received December 19, 1966)

SUMMARY Model fabric

patterns

for translation

gliding

in rock salt are con-

structed on the. basis of two metallurgical theories for intragranular slip. For statistically homogeneous types of pure mesoscopic distortion, Calnan and Clews’ theory predicts the intragranular rotations leading to patterns of preferred orientation of < 100 > . Dillamore and Roberts’ theory, on the other hand, permits rotational fluctuations of the principal axes, which makes the models more realistic. Eleven different model patterns, referred to principal axes of deviatoric mesoscopic stress, are obtained for different types of distortion, but five models are considered to be most applicable to domal salt. The various model patterns are subsequently compared with natural halite fabrics for 13 domains of fairly homogeneous strain in two Gulf Coast Domes. These domains (specimens) were taken from macroscopic folds, whose axes and axial “planes” serve as common reference elements for natural fabrics and models. It is assumed that the directions of greatest finite extension and compression are subparallel to fold axes and axial plane normals, respectively. In some fabric diagrams for domal salt, < 100 > -poles outline maxima, and distinct but generally incomplete girdles. Other diagrams show a trend toward random orientation of < 100 > . Most of the former diagrams exhibit fabric patterns that resemble those of the five realistic models after Dillamore and Roberts. This suggests translation gliding to be the dominant mechanism of tectonic flow, which may be succeeded by annealing recrystallisation, whereby the deformational patterns are increasingly blurred and finally destroyed. INTRODUCTION

Translation gliding has long been supposed to be the dominant mechanism of tectonic flow in domal salt. However, direct evidence for translation, such as intragranular slipbands, has apparently not been found. This is not surprising in view of the “rapid” rates of recovery and annealing of halite. Even in experimentally tested polycrystalline halite, grains did not exhibit conspicuous signs of slip, although the bulk behaviour of the test specimens suggested this creep mechanism (Le Compte, 1965). Tectonophysics,

5 (5) 353-380

353

Annealing recrystallisation in polycrystalline solids need not lead to random grain orientation, but the original deformation pattern can be more or less retained (Barrett, 1952, p.486). Thus the grain fabric of domal salt may well reflect extensive intragranular slip, although the grains have undergone annealing recrystallisation. Fabric diagrams for halite from two Gulf Coast domes have recently been published (Clabaugh, 1962a,b; Schwerdtner, 1966; Muehlberger and Clabaugh, 1968). These natural fabric patterns may now be compared with model fabrics for translation gliding. Two metallurgical theories of slip-rotation will be used to construct qualitative model patterns for halite. This appears justified, as the plastic behaviour of salt crystals has been shown to be similar to that of cubic metals (Pratt, 1953). Lattice rotations and fabric patterns, in the above metallurgical theories, are referred to directions of external stress, acting on specimens of polycrystalline metal. Application of these theories to halite thus requires a reconstruction of the over-all stress directions for mesoscopic domains of domal salt (large hand specimens). This will be attempted before constructing the model fabrics.

C

Fig.lA. Central flow lamina with converging flow lines in two-dimensional flow. The rectangular domain undergoes a plane distortion. R. Central flow lamina with converging flow lines in three-dimensional flow. A divergence of imaginary flow laminae above and below the central lamina leads to a homogeneous thickening of the rectangular domain. F’ .2. Homogeneous distortion of large domain (initial domain, A) due converging flow to two- % mensional (pure shear, B) and three-dimenelonal (triaxial strain, C). The initial domain already contatns slightly folded markers due to local irregularities in the early pattern of horizontal lamfnar flow toward the dome. Similar folds have been produced experimentally (Ramberg, 1964). 354

Tectonophyatce, 5 (5) 353-380’

MEGASCOPIC

DEFORMATION

The analysed specimens of rock salt were generally taken from the limbs of tight flow folds (Donath and Parker, 1964), the governing structural feature in Gulf Coast domes (Muehlberger, 1958). Balk (1949) considered these steeply plunging folds to be due to buckling, but the compositional homogeneity of the Gulf Coast salt suggests folding of markers (bedding) during convergent laminar flow (Fig. 1). The distortional part of the deformation may be idealised as in Fig.2. Note that only those gentle folds become tight whose axial planes are originally subparallel to directions of flow. Convergent radial flow is characteristic for early stages of doming (Balk, 1949; Kupfer, 1963, fig.9), and continues as long as the salt flows upward, under lateral compression. The presence of tight folds in upper domal levels indicates that the normals to their axial “planes” are in fact directions of large finite shortening, whereas fold axes are directions of finite extension. It will be assumed that the direction of maximum deviatoric compression al ’ is subnormal to the axial surface, and that the principal plane 02 ‘, 03 ' is subparallel to the axial “plane”, anywhere within the limbs of macroscopic folds. One of the seven salt specimens, taken from macroscopic folds in Winnfield salt dome, contains internal buckling folds (parallel to the corresponding large fold) and boudins (Fig.S), which can be used to reconstruct principal directions of over-all finite strain (Ramberg, 1959). Note that

Fig.3. Hand specimen of rock salt (x l/2) from Winnfield Dome with deformed interbeds of anhydrite (dotted) and dark stringers (dashed). u3 ' and a2 ’ are approximately parallel to axis and axial plane of folding, respectively.

Tectonophysics, 5 (5)353480

355

large components of simple shear along the axial plane of the tight folds can be excluded, because the less elongate fragments of the competent anhydrite are parallel to the faint bedding in the incompetent salt (Ramsay, 196’7, fig.3-50). Closely aligned grains of anhydrite (Fig.ZO), which are known to indicate the direction of greatest extension, along the bedding (Schwerdtner, 1964, p.64), thus yield the principal direction of maximum finite extension. It appears that the strain was nearly irrotational, and that the principal directions of deviatoric over-all stress are approximately parallel to the principal directions of finite strain. It should be emphasised that drawing, rolling and compression of polycrystalline metals involves heterogeneous stresses and strains, within the entire strip or sheet (Wever and Schmid, 1930; Hill, 1950). In particular the “external” stresses in rolling are more complex than the simple model of uniform compression normal to the plane of rolling, and uniform tension in the direction of rolling. The latter model has, however, been successfully used in deriving the intragranular slip-rotations during rolling. It may thus be permissible to assume a homogeneous state of mesoscopic stress throughout specimens of folded salt, when constructing qualitative model patterns for translation gliding. Little is known about the relative magnitudes of deviatoric stress, during the tectonic flow of salt. Three possible deviators will be considered in constructing the model fabric: uniaxial compression, pure shear, and a state of stress defined by the principal equation 3-l-2=0.

MODEL

FABRICS

Plastic

Properties

FOR INTRAGRANULAR

SLIP

of halite

The elastic limit of salt crystals is very low (Mendelson, 1962a). However, the permanent deformation under low stresses does not proceed at an appreciable rate, before a certain amount of shearing stress along the potential slip plane is reached. This stress is called the critical resolved shear stress rc. It is practically independent of the stress component normal to the slip plane (Dommerich, 1934), and hence rc is not a function of hydrostatic pressure. Consider a salt crystal with a given orientation relative to an applied stress Ta. Slow gliding on several lattice planes will generally start at very low resolved shear stresses (Ta cos @ cos A). C#Jis the angle between T, and the slip plane normal, whereas A is the angle between Ta and the slip direction. As Ta increases, rapid slip will commence on that plane where 7c is first reached. After sufficiently large strains, intracrystalline rotations can be observed. They have been studied in large crystals of aluminum (Taylor and Elam, 1925; Taylor, 1927). Based thereon, general rules as to the behaviour of single cubic crystals under uniaxial tension and compression were formulated (Barrett, 1952, p.3’71). In tension tests with single crystals, translation gliding along one slip system (single slip) moves the glide direction towards the axis of tension until rc is reached on another slip plane and gliding along a second slip system starts. During this conjugate duplex slip, the lattice rotates in such a way that the shear stresses at the two active slip systems remain equal.

356

Tectonophysics,

5 (5) 353-380

The stable end position is reached when the two glide directions and the axis of tension as bisectrix lie in one plane. In compression tests, the normal to the active gliding plane moves towards the compression axis until conjugate slip starts. The stable position is reached when the two poles of the active slip planes and the compression axis as bisectrix lie in one plane. Maddin et al. (1948, 1949) performed uniaxial tension tests with single crystals of alpha brass, which undergo cross-slip (two active slip planes with common slip direction). The orientation of the slip planes is asymmetrical with respect to T,. Note that the gliding on both planes commences although TC is only reached for one slip system. The plane with T c is generally called primary slip plane, whereas the other one is termed cross-slip plane. The lattice rotation due to cross-slip corresponds with that of single slip. Conjugate slip generally occurs in an advanced stage of deformation, together with cross-slip. The ease of cross-slip is controlled by the stacking fault energy of a particular cubic mineral (Seeger, 1957, p.243). At room temperature, halite glides on ( 110) and (1001 . It is uncertain whether slip along (1111 occurs at room temperature, but it has been observed at 100°C (Tammann and Salge, 1928). At 400°C, the slip planes are (1101 , (1111 and Cl001 (Wolff, 1935, p.147). The direction of gliding is always < 110 >. The critical resolved shear stresses for halite at room temperature were determined by Dommerich (1934): ~11~ = 76.4 + 3.5 g/mm2 rlll = 187 t 8 g/mm2 7100 = 238 + 10.6 g/mm2 Wolff (1935, pp.158-162) estimated the critical resolved shear stresses at 4OO”C, without measuring strain. His values correspond with the appearance of microscopic slip lines. Wolff encountered difficulties in obtaining consistant values of TC. Some of his values were above those for room temperature, others were markedly lower. Since the critical resolved shear stress for cubic crystals decreases with increasing temperature, Wolff’s highest values cannot represent true rc. His lowest values should be closest to the actual critical resolved shear stresses, and were thusnsed in this paper. 7110 N 38 g/mm2 (approx. rc at 400°C) 7111 - 107 g/mm2 7100 N 120 g/mm2 It is certain that the temperatures during the deformation of the folded salt rocks were higher that 2O’C. However, the ratio of the critical resolved shear stresses 7110: ~~1~: T 1oo at 400°C is reasonably close to that at 20°C, and this may also be assumed for the intermediate temperatures. Only the ratio of the above critical shear stresses appears in the mathematical expressions below. So far, initial translation gliding under stresses below 7c (Mendelson, 1962a, p.2167, fig.lB,3) has been disregarded. This initial slip may occur during the tectonic flow of rock salt, and hence may be rather important. It is assumed that halite always slips most readily along {llO] and least easily along (1001, such that the above ratio is approximately valid for initial gliding. Dommerich’s (1934) values of 7c will be used for the construction of the model fabrics, as the mean temperature in a rising salt dome is probably closer to room temperature than to 400°C. Tectonophysics, 5 (5) 353-380

357

No systematic studies of the slip rotations in halite seem to have been made, although they have been occasionally reported (Wolff, 1935, fig.4). Hence the general rules for intragranular rotation of cubic metals will be applied to halite. No experimental study of cross-slip in halite is known to the author. Mendelson (1962a, p.2180, fig.10; 1962b, p.2185) suggests that cross-slip on { 1001 occurs together with single slip on 1110). Some of the observations of Wolff (1935, p.152-153, 157) seem to indicate cross-slip on { 1101. He noted “secondary” gliding on (110) after “primary” slip on (111). Both slip systems had apparently the same slip direction, and, occasionally, the shear stress resolved on the secondary glide plane was very low. It is thus assumed that cross-slip takes place during the plastic deformation of halite.

Theories

of translation

gliding in polycrystalline

metals

The intragranular rotations of individual grains in polycrystalline metals have never been studied experimentally. Instead, a number of theories has been developed to predict the behaviour of the grains in polycrystalline domains during uniaxial compression, tension, and pure shear (Dillamore and Roberts, 1965, pp.31’7-328). Occasional comments on triaxial states of stress have also been made’(for example by Tucker, 1954, p. 655.) In a polycrystalline aggregate, the directions of principal stress may vary from grain to grain, and each grain may be heterogeneously strained. This has been considered in the advanced theories by Calnan and Clews (1950, 1951) and Dillamore and Roberts (1964). They assume that cohesion at the grain boundaries is retained during deformation. At least five slip systems must operate in every brain of an aggregate that undergoes a homogeneous strain (Mises, 1928). Calnan and Clews (1950, 1951) consider the deformation as heterogeneous and let some grains undergo single and duplex slip, while most grains undergo multiple slip (three or more slip systems have equal shear stresses). Rules of intragranular rotation due to multiple slip have been derived by Rickus and Mathewson (1939, p.246). The resultant rotation is obtained by adding the components of rotation due to single slip on all the slip systems involved. Consequently, there is no resultant rotation when the slip systems are symmetrically disposed about the direction of applied stress Ta. The corresponding crystal orientations are “stable end positions” and define a given deformation fabric (Calnan and Clews, 1950). Dillamore and Roberts (1964, p.282 assume that the multiple slip is generally confined to the boundary regions of the grains, and that it can be ignored when predicting the final grain orientation. They refer to experiments with very coarse aluminum aggregates, where this marginal multiple slip has been observed. Dillamore and Roberts (1964) thus consider the deformation of individual grains as closely similar to the deformation of single crystals. Only those “end positions” of conjugate slip are stable, which see a continuous reorientation of the lattice during directional fluctuations of stress (Tucker, 1954, p.655; Dillamore and Roberts, 1964, p.284). Lattice rotations due to cross-slip are subsequently considered by rotating the “stable end positions” according to single slip on the cross-slip plane. This procedure does not 358

Tectonophyslcs, 5 (5)353480

exclude cross-slip during the early stages of conjugate slip (Dillamore and Roberts, 1964, p.265). As pointed out above, the directions of principal stress acting on the individual grains will vary throughout a polycrystalline aggregate. Calnan and Clews (1950) suppose that the applied uniaxial stress Ta, in the initial phase of elastic deformation, is homogeneously propagated, through the total aggregate. After slight elastic strains, intergranular stresses are created, and the resultant principal stresses acting on the single grains tend to become oblique Ta. Translation gliding may start on any number of slip planes with equal resolved shear stresses. If a grain deforms by conjugate slip, the effective stress may be represented by a resultant stress T,. This direction of effective stress, at the start of conjugate slip, can be approximately located (Calnan and Clews, 1950), and hence the slip rotation of the grain can be predicted. Dillamore and Roberts (1964, p.282) assume that any stresses due to intergranular constraints are relieved by slip representing only a minor part of the total grain deformation. Its contribution to the final fabric pattern is neglected. This means that the principal stresses acting on every grain parallel the principal directions of applied stress. Lattice rotations of cubic minerals are conlreniently represented by the rotation of T, in the “fixed” unit triangle (Fig.4). For biaxial stress, one of the principal axes lies in the unit triangle, whereas the other axis is located on the great circle normal to the first axis (Dillamore and Roberts, 1964, p.282). Once two principal axes are fixed, the orieritation of the third one is automatically determined. It should be emphasized that the intracrystalline rotations under biaxial or triaxial deviatoric stress have not been studied experimentally, but represent a combination of the uniaxial rotations. Thus the lattice rotates in such a way, during single slip, that the direction of maximum tensile stress approaches the slip direction, while the axis of compression moves towards the slip-plane normal (Tucker, 1954, p.655, fig.C; Dillamore and Roberts, 1964, p.262). A similar rule can be formulated for conjugate slip. Tucker (1954, p.655) considers a triaxial state of stress whose deviatoric part is biaxial. The present deviatoric stress, however, is triaxial. It will be assumed that a given slip direction rotates toward tHat principal (tensile) stress which contributes most to the total resolved shearing stress.

Model fabrics

of halite

General statement The quasi-homogeneous domains analysed by Clabaugh (1962b) can have been subjected to essentially biaxial or triaxial homogeneous deviatoric stress. Hence model patterns for both types of stress will be considered. The predeformational fabrics of the present halite rocks are assumed to be random. This appears justified in view of the relativeJy poor grouping in “sedimentary” halite fabrics (Wardlaw, 1964; Wardlaw and Schwerdtner, 1966). It is unknown whether at very low strain rates halite deforms predominantly by multiple slip, or else bg conjugate slip. Consequently, the Tectonophysics,

5 (5)

353-380

359

crystallographic Fig.4. Unit triangle . and main crystals in Stereographic projection.

directions

of cubic

Fig.5. Model fabric for pure shear (maximum compression vertical) according to Calnan and Clews (1951). Curves indicate areas of concentration of (100). Maximum density in overlapping areas. M = minima; + = weak concentration due to 1110) (111).

Fig.6. Model for uniaxial compression (vertical) after Calnan and Clews (1951). A = maximum; dotted areas = sub-maxima; blank = minima. Fig.7. Superposition

of main curves in Fig.5 and 6 for triaxial stress

(see text). 360

Tectonophysics. 5 (5)35%380

theories by Calnan and Clews (1950, 1951), and Dillamore and Roberts (1964) must be separately applied. The latter theory predicts different patterns for moderate, large and extreme distortion. This renders several model patterns, which shall be compared with the natural patterns. Calnan and Clews’ (1950, 1951) theory cannot readily be applied to cases of triaxial stress. Furthermore, when applied to pure shear, the theory predicts many incorrect slip rotations (Dillamore and Roberts, 1965, p.323; Tucker, 1954, p.655). Dillamore and Roberts’ (1964) theory on the other hand, appears to be particularly suited for the application to biaxial and triaxial tectonic stresses in rock salt. It does not assume an initial elastic phase of deformation, but supposes minor gliding due to intergranular constraints under very low shear components of stress. Fluctuations of the principal axes are considered, which undoubtedly occur during the tectonic flow of rock salt. Both theories require that the most favourable slip system(s), for a sufficient number of stress directions, be determined. Single slip in facecentred cubic metals can occur on four {ill} planes. There are three < 101> directions on every plane, which results in twelve possibilities of single slip (Boas and Schmid, 1931, p.72). Consequently, such a crystal has twelve potent&l slip systems. Halite has twenty-four slip systems. There is at least one favourable slip system in a given grain of any orientation relative to the applied uniaxial stress T,. For this slip system, I cos @ cos XI is a maximum. If a mineral possesses several planes of slip (for example, {ill) and {loo) ), there will be several critical resolved shear stresses. Commonly these rc have different magnitudes. Hence, the relative resolved shear stress (cos $I cos A) will no longer determine the most favourable slip planes. The values of 1 cos $ cos A 1 are now relative to the various TC. Consequently, the most favourable slip system corresponds now to the maximum value of I cos $ cos A/ TC I (Calnan and Clews. 1951. p.624). > ICOS 4~2 cos A2/7111) , (100) [Oil] is the If ICOS @1 COS h1/T1(~0) more favourable slip system. The above inequality can also be written as I cos $1 cos x1 1 > ) *

cos $2 cos A2 1

For pure shear, the most favourable slip system corresponds to a value Tmax = 1 (a, b, - at b t)/TC I. The direction cosines of the compression axis with respect to a slip-plane normal and slip direction are a, and b,, and those of the tensile axis with respect to the same slip-plane normal and slip direction are at and bt. For the triaxial state of stress defined by the sum of the principal stresses 3-2-l = 0, 7mruc = The latter direction cosines relate the l(3Qbc - 2Utbt - am bm)/Tc). slip-plane normal and slip direction to the direction of intermediate principal stress. Model patterns after Calnan and Clews The application of Calnan and Clews’ (1950, 1951) theory to halite has been discussed elsewhere (Schwerdtner, 1966). Fig:5 shows the model pattern for pure shear (ignoring the density gradients of the “maxima” and “minima”). Partial diagrams considering the scatter about each of the five stable orientations (Table I) were superimposed. During the necessary Tectonophysics, 5 (5)353480

361

TABLE I Stable lattice orientations for pure shear predicted by Calnan and Clews’ (1950,1951) theory Direction of maximum Direction of maximum compression 0 ‘1 (normal to axial planes) tension (a ‘3)

< 100 >

< 100 > , < 110 >

< 110 >

< 100 > ) < 110 >

< Ill>

< 110 >

Resulting preferred orientation (lattice planes parallel to CJ;, ah and lattice directlons parallel to u ‘3) < lOO> on { 100) c 1101 < llO> on {loo} Cl101 < ill> on (110)

and and

rotations on the Schmidt net, the two crystallographic directions involved in each operation have to remain within the corresponding maxima for tension and compression (Schwerdtner, 1966, fig.8 and 9), whose scatter was arbitrarily chosen. The resulting diagram is more rigorous than the one previously published (Schwerdtner, 1966, fig.11). The previous pattern was obtained by setting the lattice into the five ideal orientations (Table I) and rotating < lOO> and < 011 > individually (Mellis, 1954). The present model for pure shear (Fig.51 must new be modified to apply to a triaxial stress, where the maximum compression is greater than the maximum extension. This will lead to a stronger influence of the compression pattern (Fig+61 on the model fabric. Such an effect can be achieved by superimposing the compression pattern on the fabric for pure shear (Z’ig.5). The major changes in the pattern for pure shear are indicated in Fig.7, where only the main contours of Fig.5 are considered. The only major change is the appearance of a complete girdle normal to the unique axis of compression. The new girdles decrease the density of all previous maxima. It is clear that a model fabric for triaxial stress would be even more qualitative than the model for pure shear. Hence no such model was constructed but the pure-shear pattern can be modified as outlined above. Model patterns for pure shear after Dilhmore and Roberts The most favourable slip systems in halite for 13 points in the unit triangle were determined and listed in Table II. The first letter always refers to the slip normal, and the second to the slip direction. The number of points considered aplxars to be sufficient for constructing the model. Every point in the triangle may coincide with either the compression axis, or else the tension axis. Hence the two possibilities must always be taken into account (Table II). Several orientations of the second principal stress (Fig.81, for every point in the unit triangle (Table II) are considered. The resulting slip-rotations are listed in Table II, where the first letter always denotes the compression axis, and the second one the tension axis. For example, when the orientation of the stress axes is LI, they will rotate toward 7N by gliding on Mi and KI. At 7N, AI is the most favourable slip system, and the stress axe8 rotate towards AI. Near Q 23 ,& , however, multiple slip on EF, FC,, DG, GD takes over, which moves the stress axes to AI. 362

Tectonophysics,

5 (5) 353380

With the exception of (loo} < 001> , all end positions of conjugate duplex slip are unstable (Table II), because asymmetric multiple slip occurs at these points. However, there are these stable positions of multiple slip ( (IlO} < 110 > , I0011 < 001> , and ClOOl < 001> ). Before applying Tuckers (1954) criterion of stability, it must be specified in which way the principal axes may fluctuate. It may be reasonable to assume that these fluctuations take the form of rotations within the three principal planes (Dillamore and Roberts, 1964, p.265). If this concept is applied to halite, it can be seen from Fig.8 and Table II that all three end positions of symmetric multiple slip are unstable. ( lOO\ < OOl> is stable regardless of the direction of rotational fluctuation. However, all end positions of symmetric multiple slip are stable, if the small rotations are confined to two principal planes (Table II and Table III). In any natural case, the rotational fluctuations may or may not be limited in this sense. Consequently, different model fabrics will be constructed to cover both possibilities. Rotation about the compression axis, or else the tension axis may be disallowed (Table III). The final orientations ClOO} < 001> , { 1101 < 110 > , [OOl) < 110 > , { 110 1 < 001 > for conjugate and multiple slip are not stable during cross-slip. The stress orientation AC, for example, sees EF and FE as operative conjugate slip planes. B is the normal to the common crossslip plane. The normals of the other potential cross-slip planes are K, L, M, N. Cross-slip will move the compression axis from A toward D. Since the slip directions are not altered, there is no tendency for the tensile axis to move away from C. The compression axis will tend to take up a position, where the cross-slip rotations and the normal slip rotations cancel each other. This position is close to [540]. The total slip may be pictured as occurring simultaneously on pairs of planes forming steplike folds (Maddin et al., 1949, p.533). Hence the amounts of gliding on an octahedral cross-slip plane will equal the amount of gliding on the corresponding normal slip plane. The amount of cubic

Fig.8. Orientation of principal Tectonophysics,

5 (5)

353-360

stress axes with respect to unit triangle. 363

TABLE

II

Normal

slip rotations

Orientation compression axis A C A B A H A -I D C D G D M D L D 12 D 8 N H N G N E N 7 1 L 1 H Pl C BP C

tension C A B A H A -I A C D G D M D L D 12 D 8 D H N G N E N 7 N L 1 H 1 C Pl C :; :;

a’; ;I

BP:

G

z3 :: p3 Q5

:: p3

2

364

letters

Most favourable slip systems

Rotation of stress axes towards:

EF,FE EF,FE DG,GD DG,GD EF,FE,DG,GD EF,FE,DG,GD EF,FE,DG,GD EF,FE,DG,GD EF,FE,HI,IH EF,FE,HI,IH AH,AI,BE,BF AH.AI,BE,BF KF,NH KF,NH KI,NE KI,NE HI,IH,EF,FE HI,IH,EF,FE HI,IH,EF,FE HI,IH,EF,FE KF,MD

no rotation no rotation no rotation no rotation no rotation no rotation no rotation no rotation no rotation no rotation no rotation no rotation D12 12D D8 8D DC CD DC CD AH Hl 2G G2 3E E3 AI AI AI AI AH HA AC CA AC CA AB BA AC CA AC CA DG G2 AC CA BF BF KI

SXiS

:;

kapital

for pure shear’

of:

KF,MD hlI,LF MI,LF KI,LD KI,LD AI AI KI.MI K&MI DG,GD,EF,FE DG.GD,EF,FE EF,FE EF.FE EF,FE EF,FE DG,GD DG,GD EF,FE EF,FE EF,FE EF,FE AI,BF AI,BF EF,FE EF,FE BF BF KI

and numbers

.~

refer

--

-~

to Fig.4 and 8. Tectonophyelcs,

5 (5) 353-330

TABLE II (continued) Orientation of: compression axis

Most favourable slip systems tension axis KI EF,FE EF,FE BF BF AI AI DG,GD DG,GD AH,AI,BE,BF AH,AI,BE,BF MI MI AI AI EF,FE EF,FE DG,GD DG,GD DG,GD DG,GD EF,FE EF,FE EF,FE EF,FE DG,GD DG,GD MI MI DG,GD DG,GD DG,GD DG,GD DG,GD DG,GD EF,FE EF,FE DG,GD,EF,FE DG,GD,EF,FE AI,BE AI,BE EF,FE EF,FE EF,FE,HI,IH EF,FE,HI,IH EF,FE,IH,HI EF,FE,IH,HI

Tectonophysics,

5 (5) 353-380

Rotation of stress axes towards: KI AC CA BF BF AI AI AB BA DG GD MI MI AI AI AC CA AB BA AB BA AC CA AC CA AB BA MI MI AB BA AB BA AB BA AC CA IA IA D8 GD AC CA DC CD DC CD

365

TABLE I11 Permitted rotations in principal End positions

compression (110 {lo0 i < 110 > {llO} < 100 >

planes for pure shear’

Rotations about:

disallowed disallowed permitted

axis

intermediate principal axis

tension axis

permitted permitted permitted

permitted permitted disallowed

’ {llO} < llO> and {loo] < llO> are stable if no rotations occur about the compression axis. {llO} < 100> is stable when no rotations occur about the tension axis.

cross-slip, however, will be equal to the sum of normal slip. The components of rotation are proportional to the various amounts of slip. The final stress orientation DG sees AI, AH, BE, BH as operative gliding planes. The normals of the corresponding cross-slip planes are K, L, M, N. During cross-slip, the compression axis moves towards A and the tension axis towards B. Near P2Q2 in Fig.8, the rotations due to multiple slip and cross-slip are almost balanced. Before reaching complete balance, however, the normal slip systems DG, GD take over. The normals of the new cross-slip planes are C, A, L, M, N. Subsequent slip rotations move the stress axes toward [504]B. The final stress orientation DG balances slip on EF, FE, HI, IH (Table II). The normals of the corresponding cross-slip planes are A, B, K, L, M, N. During cross-slip, the compression axis moves from D toward PI, while EF, FE become the operative normal slip systems. The balance of the normal slip rotations is now upset, and there is resultant rotation of the compression axis towards A. B, K, L, M, N are the normals of the new cross-slip planes, resulting in a component of rotation towards B. Rotational balance is reached at [540]. In real crystals, it is always possible that some potential cross-slip planes cannot operate. If the cross-slip planes M and L should not operate there is no resultant slip rotation and the end position DC is stable under cross-slip. However, if A, B, M, N are the poles of the active cross-slip planes, the compression axis will move from D toward PT rather than toward PI. Although the balance of the normal slip-rotations is now upset, the active slip systems are the same at PI, and the rotation

direction

of the compression

axis due to normal

slip is un-

changed. There is, however, a rotation component due to cross-slip on B, M, N, which keeps the compression axis away from the cubic plane. The scatter resulting from such unpredictable rotations will be qualitatively considered in the model diagrams. The final stress orientation AH sees EF, FE, DC, GD as operative slip systems. The normals of the corresponding cross-slip planes are B, C, K, L, M, N. In the initial phase of cross-slip, the rotations toward K, L, M, N cancel, and the compression axis begins to move from A towards Ps (Fig.8). However, as soon as the compression axis has left A, it will be directed toward pS rather than Pa. Similarly, the compression axis is moved from H toward Q13. Near P6613, EF and FE are the normal-slip systems, which move the tension axis toward C and the compression axis back toward A. The latter component of rotation, howeyer, is more than 366

Tectonophystcs,

5 (5) 353-680

Fig.9. Model for large pure shear with rotational fluctuation of all three principal axes (after Dillamore and Roberts, 1964). Orientation of principal axes as above. Fig.10. Model for large pure shear with rotation about maximum and intermediate principal axes (after Dillamore and Roberts, 1964). Scatter assumed. wu

r.-

--

Fig. 11. Model for large pure shear with rotation about minimum and intermediate principal axes (after Dillamore and Roberts, 1964). Areas of maximum density are hatched. Ffg.12. Modification Tectonophysics.

5 (5) 333-380

of Fig.10 after very large strain. 367

TABLE

IV

Normal slip rotations for the three-dimensional distortion’ ..__ ._-._ ._.-.~ ..__~ .-. . Most favourable Slip rotation Orientation of principal stress axes slip system minimum maximum intermediate maximum stress stress stress stress EF,FE stable A B C’ 1~ DG,GD stable A C A C HI,IH stable B r\ DG,GD stable C B 1~ HI,IH stable A C A EF,FE stable B C -1 DG,GD,EF,FE stable H A H DG,GD,EF,FE stable A -I -1 DG,GD,EF,FE stable A H -1 A DG,GD,EF,FE stable H A II DG,GD,EF,FE stable -I A DG,GD,EF,FE stable -I H EF,FE,HI,IH G stable D C EF,FE,HI,IH stable D G C G EF,FE,HI,IH stable D C D EF,FE,HI,IH stable G C D C EF,FE,HI,IH stable G D EF,FE,HI,IH stable C G BF,CD H 7 I N H BF,CD I N 7 DG,GD,EF,FE stable N 7 H N DG,GD,EF,FE stable H I A H DG,GD,EF,FE N 7 A N DG,GD,EF,FE H I A H DG,GD,EF,FE 1 L A L DG,GD,EF,FE 1 H I 11 BE ,CG I L 1 BE ,CG I H L I 1. DG,GD,EF,FE stable H 1. 1 DG,GD,EF,FE H stable DG,GD A stable 620 Q29 EI:,FE stable A 629 A DG,GD B :;: EF,FE C :;; Q20 EF,FE C ($9 EF,FE,HI,IH stable :;: G27 EF,FE,HI,IH D stable 627 EF,FE,HI,IH D G :;; ME,MI G :;: ;27 EF ,FE ,HI,IH C :24 627 D EF,FE,HI,IH C EF,FE A Zf7 Zf’: EF,FE A C &I C HI,IH B i:; Pl C HIJH B Pl Cl HI,IH stable ($1 EF,FE C stable %I EF,FE A p2 Q2 C A DG.GD p2 ‘Capital

368

letters

and numbers

refer

of principal

axes towar

intermediate stress

minimum stress

stable stable stable stable stable stable stable stable stable stable stable stable stable stable stable stable stable stable stable A I A I stable I stable A stable A 1 C B stable stable B G C stable C stable G B stable A stable A B B stable

stable stable stable stable stable stable stable stable stable stable stable stable stable stable stable stable stable stable A stable A I stable I stable I stable A I A B C C B stable C G C stable G stable stable B stable A B A stable B

to Fig.4 and ti.

Tectonophysics,

5 (5) 353480

TABLE

IV (continued)

Orientation of principal maximum stress

intermediate stress

Q2

p2 C p2 82

z2 C p3 p3 G

pH9

Q23 p5 B5

Qlo 2: t$"

I? Q19 Q19 Q31 Q31

%6 p3 G ;; Q23 p9

:23

:f8

axes

minimum stress

:26

BG26 Q26 B9

z3 Q13 628

stress

:10 Q30 ZO p5 Q1o Q13 Q28 B6 Q28 z3 :z z1 Q’:,

Moat favourable slip system

Slip rotation maximum stress

intermediate stress

of principal

axes toward: minimum stress

HIJH DG,GD HI,IH EF,FE EF,FE,HI,IH AI,BF EF,FE,HI,IH EF,FE,HI,IH EF,FE,HI,IH EF,FE,HI,IH EF,FE,DG,GD LD,LF EF,FE,DG,GD, EF,FE,DG,GD EF,FE,DG,GD EF,FE,DG,GD AI KF DG,GD DG,GD HIJH HIJH EF,FE EF,FE KG EF,FE CG EF,FE DG,GD DG,GD MI MI EF,FE EF,FE

B B stable stable D D stable stable C C I I stable stable A A A K B B C C A A K C C C A A M M C C

A stable A B stable C D C D stable stable A I A I stable hkl hkl C C A B B B hkl B D B H I I hkl A B

stable A B A C stable C D stable D A stable A I stable I I F A A B A C C G A G A I H hkl I B A

balanced by rotation toward D due to gliding on the new cross-slip planes B, K, L, M, N. The componental rotations of the compression axis cancel each other at [540]. According to Dillamore and Roberts (1964, p.2921, the model patterns of halite should vary according to this scheme: “large” strain -+ “very large” strain --+ extreme strain. Considering three possible cases of stress fluctuation, we obtain (100) < 001 > --+ (100) < 001 > plus girdle * tensile axis +(540, 450) < 001 > . or else, IlOOl < 001 > , IllO) < OOl> --+(llOOJ < OOl> , 1110) plus girdle -L tensile axis --+ (540, 450 1 < 001 >, and finally, (100) < 001 > , fool} < 110 > ) {IlO! < 110 > & {loo} , Tectonophysics,

5 (5) 353-380

369

I

Fig. 13. Modification

of Fig.11 after very large strain.

Fig.14. Modification

of Fig.12 after very large strain.

(0011 < 110 > i 110) < 110 > plus three girdles in the principal planes __) (540, 450 1 < 001 >. Seven model patterns can be drawn (Fig.%15) representing the different stages in the above schemes. Extremely large strains may not occur in salt domes, and hence Fig.15 can probably be neglected in the subsequent comparison. Model Pattenzs for triaxial distortion after Dilkzmore and Roberts The assumed deviator is defined by the equation 3-2-l = 0. Let one of the three principal axes lie in the unit triangle. The other two must then be located on the corresponding great circle. For any fixed orientation, there are six possibilities of labeling the principal axes (Table IV). The stable end positions due to conjugate and multiple slip are the same as for pure shear. I 100 1 < 001 > is stable under all rotational fluctuations of the stress axes, whereas (110 1 < 110 > , j 001 1 < 110 > and ! 110 1 < 001 > are stable for small rotations confined to two principal planes (Table V). The subsequent rotations due to cross-slip are essentially the same as those for pure shear. The development schemes of the patterns are as follows: ilOO) < OOl> + (100) plus girdle 1 tensile axis --+ t540,4501 , or else, 11001 , (1101 b IlOO~ , (1101 plus a girdle -l tension axis + 1540, 450 1 < 001> , or else, (loot < 001 >, (0011 < 110 > __, (1001 < OOl>, (001) < llO> plus girdle L to compression and tension axes + 1540, 4501 < 001 > 3 and finally, 370

Tectonophysics, 5 (5) 353-300

TABLE V Permitted rotations about principal axes for the three-dimensional

distortion

Rotation about:

End positions

compression {llO} {loo} < llO> {llO}

permitted disallowed permitted

axis

intermediate principal axis

tension axis

disallowed permitted permitted

permitted permitted disallowed

ilOO1 < 001 >, (1101 < 110 > ----A (1001 ) fllOl plus girdles -L intermediate and minimum principal stress d (540, 4501 < OOl>. This renders nine model patterns, five of which are identical with the corresponding models for pure shear. The remaining patterns are shown schematically in Fig.l6-19. Range

of application

of models

In Dillamore and Roberts’ theory (1964), given Tc-ratios determine a definite model pattern for each stress deviator. The present model fabrics may thus merely apply to the plastic deformation of rock salt at room temperature, as the rc-ratios for higher temperatures are poorly known. For example at 200°C, additional stable orientations of the lattice could occur, or else the presently stable orientations could become unstable. It

Fig.15. Model fabric for extreme pure shear (after Dillamore Roberts, 1964).

and

Fig. 16. Model for large triaxial distortion with rotational fluctuations about the intermediate and minimum principal axes (after Dillamore and Roberts, 1964).

Tectonophysics,

5 (5) 353380

371

Fig.17. Model for large triaxial distortion with rotational fluctuations about maximum and minimum principal axes (after Dillamore and Roberts, 1964). Fig.18. Modification

of Fig.16 after very large strain.

Fig.19. Modification

of Fig.17 after very large strain.

Fig.26 300 poles to < 100 > of the hand specimen (Fig.3) from Winnfield Salt Dome (Schwerdtner, 1966, fig.3). 2 3-2-l-O; N = axes of small folds; I~~ID = lineation of anhydrite grains. 372

Tectonophysics,

5 (5) 353480

may be demonstrated, however, that large changes in the Tc-ratios have little effect on the present model patterns (Fig.%19), which seem to reflect mainly the crystallographic relationships of slip in halite. For any given orientation of the stress axes in pure shear, it is easy to find that T,-ratio which equally favours the present slip systems (Table II) and some additional slip system(s). For the stress orientations HI and IH, the present most favourable slip systems are DG, GD, EF, FE. In order that KF and MD should become equally favourable, ~~~~~~~~~ (0.41 at room temperature) has to become 0.60. Sirnilarly~11~,/~1,,~ has to change from 0.31 to 0.68 for BF, CD to become equally favourable. Greater values for the two ratios render the dodecahedral planes unfavourable. It is clear that these changes of the Tc-ratios are very large. By comparison, the changes according to the maximum errors of the ‘c at room temperature (Dommerich, 1934) are from 0.41 to 0.45 and from 0.31 to 0.35. For the stress orientation HI, the lattice rotations due to slip on KF, MD, or else on BF, CD cancel, and hence HI may be a stable orientation. The stability criterion of Tucker (1954) cannot be applied, however, as it requires “exact” values of the three Tc-ratios. The stable orientation HI would lead to additional submaxima in the plane normal to the compression axis, and may change the present models only slightly. The stress orientation IH is not stable, even if KF, MD or BF, CD are the most favourable slip systems. Similarly, the remaining stress orientations (N7, 7N, NE, EN, Ll, 1L) that may be expected to become stable for changed*r,-ratios can be checked. None of these orientations are stable for slip on (1101, 111.11 or {lOOI. The presently stable orientations (Table III) will be considered next. For {lo01 < OOl>, the cubic or octahedral systems could be active only if ~100 , ~111 < T 110. This appears highly unlikely on the basis of the experimental data. There is no resultant rotation of the stress axes at (110) < OOl> and IlOO} < llO>for cubic, dodecahedral or octahedral slip. Finally, the stress orientations 1110) < 110 > are stable for dodecahedral and cubic slip, whereas octahedral slip renders them unstable. This changes the corresponding model patterns for pure shear (Fig.11 and 14) into patterns for three-dimensional distortion (Fig.16 and 18), which is.not serious for the present comparison with natural fabrics. In distinguishing between model patterns for “large” strain and “very large” strain, it was assumed that cross-slip does not become a significant factor in the lattice rotation, until the distortion is “very large”. However, halite may well undergo large amounts of cross-slip, after relatively small amounts of finite strain. This may be expected at higher temperatures (Dillamore and Roberts, 1964, p.292), and would make the model patterns for “large” strain obsolete. It follows that the model fabrics for “very large” strain (Fig.12, 13, 14, 18, and 19) should be most relevant to the present domal salt.. Note that neither the breadth of model girdles nor the density of their submaxima can be predicted. FABRIC PATTERNS FOR DOMAL SALT General

description

Thirteen petrofabric Tectonophysics, 5 (5) 35-80

diagrams for halite from the Gulf Coast domes 373

have been published so far. Clabaugh (1962b, Muehlberger and Clabaugh, 1968) analysed twelve specimens of .rock salt from macroscopic folds in the Winnfield and Grand Saline Salt Domes. The present author determined the fabric pattern in a sample with numerous small folds from Winnfield Salt Dome. The latter fabric diagram (Fig.20) is accurately oriented with respect to three mesoscopic structural elements. Clabaugh’s fabric diagrams, on the other hand, are referred to geographic coordinates (Fig.21, 22). It would be advantageous to present Clabaugh’s fabric patterns as rotated diagrams (axial planes horizontal), such that all fabric diagrams would have common reference axes. In Fig. 22A,B,C,E and F, however, the orientation of the axial “planes” was not measured underground, but constructed by the present author from the attitudes of bedding on the map (Hay, Foose and O’Neill, 1962, fig.5). These orientations may be very inaccurate. Furthermore, Clabaugh’s diagrams do not contain poles of fold axes or lineations, and hence the orientation of these new axes of reference is unknown. It may be assumed, that the plunge of the fold axes is fairly close to the dip of the corresponding axial planes. Even if the orientation of an axial “plane” is very accurate, it may be rather oblique to the direction of maximum compressive stress. Unfortunately, the actual deviation of the compression axis from the axial plane normal cannot be estimated, as was outlined above. In view of these difficulties, no rotations were performed, and Clabaugh’s (Muehlberger and Clabaugh, 1968) original diagrams are shown (Fig.21, 22). The only diagram oriented with respect to the fold axes (Fig.20) shows three major maxima for < 100 > (perpendicular to the axial planes, and subparallel as well as subnormal to the lineation). Three poorly defined girdles exist perpendicular to these maxima. Oblique maxima occur within the girdle parallel to the axial planes as well as in the girdle parallel to the lineation. Clabaugh’s fabric diagrams show various patterns. If there are three main maxima, two of them lie approximately in the axial plane, whereas the third one is perpendicular to it (Fig. 21B,C, 22D). This third maxima can be connected, by means of a girdle, with one of the maxima in the axial plane (Fig.21D,E, 22D). The girdle usually includes oblique maxima or submaxima. Fig.2lB and 22B have all these features, as well as a girdle parallel to the axial “plane” including oblique maxima. Many diagrams from Winnfield Salt Dome exhibit a considerable scatter of < 100 > . Two halite diagrams from Grand Saline Salt Dome (Fig. 21A,F) have distinct fabric patterns apparently unrelated to the axial planes.

Fig.21. Clabaugh’s (Muehlberger and Clabaugh, 1968) diagrams from Grand Saline Dome. > 3-2-l-O. Great circles (solid) indicate axial “planes”, dashed lines probable orientation of principal planes normal to maximum compression. Tectonophysics,

5 (5) 353-380

375

376

Statistical significance

of maxima

Maxima and submaxima within girdles of conventional fabric diagrams should not be considered as statistically significant, if only 200 poles, each representing an individual grain, have been plotted (Stauffer, 1966). Where three mutually perpendicular poles represent a cubic mineral, such maxima must be interrelated, thus increasing the probability of their statistical significance. Furthermore, submaxima are probably significant if they are .parallel or normal to megascopic structural elements. Clabaugh (1962a, p.13) concluded that the maxima, minima and girdles in her diagrams for the Grand Saline salt dome were indeed statistically significant, but she did not discuss any submaxima. Some of the diagrams from Winnfield salt dome (Fig.22A,C) contain maxima and submaxima of doubtful significance.

COMPARISON

BETWEEN

NATURAL

PATTERNS

AND MODEL

FABRICS

The two model fabrics after Calnan and Clews (1950) are basically similar to those after Dillamore and Roberts (1964). However, the former do not predict the girdles normal to the tensile and intermediate strain axes, which appear in most of the natural patterns. Hence the scatter in none of the natural fabric diagrams can be explained on the basis of Calnan and Clew’s theory, although it predicts the maxima and submaxima. Consequently, the subsequent comparison will be confined to the ten models (excluding extreme strain) after Dillamore and Roberts (1964). Fig.20 represents a natural pattern for very large triaxial strain. The relative amounts of principal stress, however, are unknown, and the actual shear stress may be closer to either of the two model deviators. Hence five models for very large strain (Fig.12, 13, 14, 18 and 19) must be compared with Fig.20. One of the models (Fig.14) agrees rather well with the natural pattern, whereas the other models deviate significantly. Due to meager information about the magnitude and fluctuation of mesoscopic strain, ten model patterns must be compared with Clabaugh’s (Muehlberger and Clabaugh, i968) diagrams. Only one natural pattern (Fig.ZlC) is similar to a model for large strain (Fig.9), and even this pattern represents a transition stage to a model for very large strain (Fig.19). Most of the natural patterns resemble Fig. 14, 19, or Fig.13. No clear fabric pattern is developed in Fig.22E, and no similarity with any model is apparent. Fig.LlA,F and 22A may represent domains where the axial “plane” is clearly oblique to the compression axis. If the principal plane is oriented as assumed, the natural patterns become similar to Fig.14 and 19. Some of the diagrams show rather incomplete girdles as compared with the model patterns (Fig.13, 14, and 19). This would be in accordance Fig.22. Clabaugh’s (Muehlberger and Clabaugh, 1968) diagrams from Winnfield Salt Dome. > 3-3-l-O. Great circles (solid) indicate axial “planes”, dashed lines probable orientation of principal planes normal to maximum compression. Tectonophysics, 5 (5) 353-380

377

with Dillamore and Roberts’ (1964) theory, which predicts incomplete girdles for most magnitudes of strain. Also, it should be kept in mind that the two special deviators assumed for the models will approximate the present examples of natural distortion to a greater or lesser degree. CONCLUSIONS

The comparison between natural fabrics and models has been made by subjective inspection rather than by statistical methods. Such would be desir?ble in order to determine objectively the degree of similarity. The close resemblance of some natural patterns and models suggests, however, that rock salt flows by intragranular slip. Unfortunately, the weight of this argument is greatly reduced by the number of model fabrics used in a single comparison. Better information about the individu~ finite strains of the quasi-homogeneous. domains would help to decrease the number of possible models. There should be definite differences in the natural fabrics, because the ratio of the three principal strains may vary considerably, as well as the rotation of the principal axes. The comparison becomes more subjective, as the scatter in the natural fabrics increases. This scatter need not be ‘due to recrystallization, but may reflect heterogeneities of mesoscopic strain within the specimens. ACKNOWLEDGEMENTS

Sincere thanks are due to Drs. W.T. Holser (La Habra, Calif.), Hans Ramberg (Uppsala), and Q.M. Anderson (Toronto, CM.) for critically reading the manuscript. Mrs. P.S. Clabaugh (Austin, Texas) kindly provided copies of her unpublished fabric diagrams.

REFERENCES Balk, R., 1949. Structure of Grand Saline I3ome, Van Zandt County, Texas. Bull. Am. Assoc. Petrol. Geologists, 33, 1’791-1829. Bnrrett, C.S., 1952. Structure of Metals. McGraw-Will, New York, N.Y., 661 pp. Boas, W. und Schmid, E., 1931. Zur Deutung der Deformationstexturen von Metallen. 2. Tech. Physik, 12: 71-75. Calnan, E.A. and Clews, C.J.B., 1950. Deformation textures in face-centred cubic metals. Phil. Mag., 41: 1085-1100. Cnlnan, E.A. and Clews, C.J.B., 1961. Development of deformation textures in metais, 2. Phil. Mag., 42: 616-635. Clabaugh, P.S., 1962a. Petrofabric analysis of salt crystals from Grand Saline salt dome. M.A. Thesis, Univ. Texas, Austin, Texas, 29 pp. Clabaugh, P.S., 196213.Petrofabric study of deformed salt. Science, 136: 389-391. Dillamore, I.L. and Roberts, W.T., 1964. Rolling textures in face-centred cubic and body-centred cubic metals. Acta Met., 12: 281-293. Dillamore, I.L. and Roberts, W.T., 1963. Preferred orientation in wrought and annealed metals. Met. Rev., 10 (39): 271-380. Dommerich, S., 1934. Festigkeitseigenschaften bewlsserter Salzkristalle, 4. Richtungsabhlngigkeit der Streckgrenze gleichmfssig abgelaster Steinsalzstzbchen. Z. Physik, 90, 189-196. 378

Tectonophysics,

5 (5) 353-380

Donath, F.A. and Parker, R.B., 1964. Folds and folding. Bull. Geol. Sot. Am., 55: 45-62. Hill, R., 1950. The Mathematical Theory of Plasticity. Clarendon Press, Oxford, 355 pp. Hoy, R.B., Foose, R.M. and O’Neill, B.J., 1962. Structure of Winnfield Salt Dome, Winn Parish, Louisiana. Bull. Am. Assoc. Petrol. Geologists, 46: 1444-1459. Kupfer, D.H., 1963. Structure of salt in Gulf Coast Domes. Proc. Symp. Salt, lst, Cleveland, Ohio, pp.104-123. Le Compte, P., 1965. Creep in rock salt. J. Geol., 73, 469-484. Maddin, R., Mathewson, C.H. and Hibbard, W.R., 1948. Unpredicted cross-slip in single crystals of alpha brass. Trans. AIME, 175: 86-105. Madin, R., Mathewson, C.H. and Hibbard, W.R., 1949. The active slip systems in the single axial extension of single crystalline alpha brass. Trans. AIME, 183: 527-534. Mellis, O., 1954. Einiges zur Geometrie der Lagekugelbesetzung. Tschermaks Mineral. Petrogr. Mitt., 4: 13%144. Mendelson,,S., 1962a. Dislocations and plastic flow in NcCl single crystals, 1. J. Appl. Phys., 33: 2175-2181. Mendelson, S., 196213.Role of surfaces in plastic flow of NcCl single crystals, 2. J. Appl. Phys., 33: 2182-2186. Mises, R.V., 1928. Mechanik der plastischen Form’rinderung von Kristallen. 2. Angew. Math. Mech., 8: 161-184. Muehlberger, W.R., 1958. Internal structure of the Grand Saline Salt Dome, Van Zandt County, Texas. Univ. Texas, Bur. Econ. Geol.,Rept. Invest., 38, 18 pp. Muehlberger, W.R. and Clabaugh, P.S., 1968. Internal structure and petrofabrics of salt domes. Symp. Diapirs, New Orleans, 1965 - Am. ASSOC.Petrol. Geologists, in press. Pickus, M.R. and Mathewson, C.H., 1939. Theory of the origin of rolling textures in face-centred cubic metalc. J. Inst. Metals, 64: 237-260. Pratt, P.L., 1953. Similar glide processes in ionic and metallic crystals. Acta Met., 1: 103-104. Ramberg, H., 1959. Evolution of ptygmatic folding. Norsk Geol. Tidsskr., 39: 99-152. Ramberg, H., 1964. Note on model studies of folding of moraines in Piedmont glaciers. J. Glacial., 5(38): 207-218. Ramsay, J.G., 1967. Folding and Fracturing of Rocks. McGraw-Hill, New York, N.Y., 568 pp. Schwerdtner, W.M., 1964. Gefiigestudien an Anhydritbanken im Benther Salzstock (Werk Ronnenberg). Kali Steins, 4: 64-70. Schwerdtner, W.M., 1966. Preferred orientation of halite in a “saltseismogram”. Proc. Symp. Salt, Znd, Cleveland, Ohio, pp.7+84. Schwerdtner, WM., 1968. Preferred orientation of anhydrite in salt stock of Benthe, northwestern Germany. Can. J. Earth Sci., in press. Seeger, A., 1957. The mechanics of glide and work hardening in face-centred cubic and hexagonal close-packed metals. In: G.C. Fisher, W.G. Johnston, R. Thomson and T. Vreeland Jr. (Editors). Dislocations and Mechanical Properties of Crystals. Wiley, New York, N.Y., pp.247-329. Stauffer, M.R., 1966. An empirical-statistical study of three-dimensional fabric diagrams as used in structural analysis. Can. J. Earth Sci., 3: 473-489. Tammann, G. und Salge, W., 1928. Einfluss des Druckes auf die Reibung beim Gleiten llngs der Gleitebenen von Kristallen. Neues Jahrb. Mineral. Palaeontol., Abt.A, 57: 117-130. Taylor, G.I., 1927. Distortion of crystals of aluminium under compression, 2. Proc. Roy. Sot. London, Ser.A, 116: 1638. Taylor, G.I. and Elam, C.F., 1925. Plastic extension and fracture of aluminum crystals. Proc. Roy. Sot. London, Ser. A, 108: 28-51. Tucker, G.E.G., 1954. Discussion on preferred orientation. J. Inst. Metals, 82: 655-656. Wardlaw, N.C., 1964. Bromide in some Middle Devonian salt rocks of Alberta and Saskatchewan. Proc. Intern. Symp. Williston Basin, 3rd, Regina, Saskatchewan Billings Geol. Sot., Montana, pp.270-273. Tectonophysics,

5 (5) 353-380

379

Wardlaw, N.C. and Schwerdtner, W.M., 1966. Halite-anhydrite seasonal layers in the Middle Devonian Prairie Evaporite Formation, Saskatchewan, Canada. Bull. Geol. Sot. Am., 77: 331-342. Wever, F. und Schmid, W.E., 1930. Texturen kaltverformter Metalle. 2. Metallk., 22: 133-140. Wolff, H., 1935. Richtungsabhangigkeit des Translationsmechanismus von Steinsalzkristallen in hijheren Temperaturen. Z. Physik, 93: 147-165.

380

Tectonophysics,

5 (5) 353-380