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Rotation of terraces around screw dislocation in polymer single crystals
Solid State Communications,Vol. 16, pp. 201—205, 1975.
Pergamon Press.
Printed in Great Britain
ROTATION OF TERRACES AROUND SCREW DISLOCATION IN POLYMER SINGLE CRYSTALS Jacques Rault Laboratoire de Physique des Solides, Université Paris-Sud, 91405 Orsay, France (Received 18 September 1974 by S. Amelinckx)
Polymer crystals generally present, around screw dislocations, a discrete rotation of terraces over each other, always in the same sense. In the proposed model, this rotation in flat or pyramidal single crystals is due to the distortion of the cell which appear in order to relax the surface stress created by the folds. The relation between the chirality of the translationrotation of the terraces and the chirality of the screw dislocation gives information about the nature (tensile or compressive) of the surface stress parallel to the folding plane.
LAMELLAR single crystals of polymers grown from dilute solution have been intensively studies. These crystals have a crystalline layer of about 100 A, with thin “amorphous” layers at the surface, and present several sectors.13 In each sector, the folding planes containing the polymer chains linked by the folds are parallel to the growth face. Figure 1 shows the different types of observed polyethylene monocrystals with (llO)~.and (100), sectors. Around a screw dislocation, the terraces parallel to the folding planes demarcate the sectors, but unlike the case of solid spiral growth, these terraces are twisted from each other by the same angle and in the same direction. Figure 2 shows this effect observed in polymer crystals; the purpose of this paper is to show that this effect can be explained by the distortion of the crystal lattice which occurs in the bulk of the lamella in order to relax partly the surface stress due to the distortion of the chain at the folds.
in an epitaxial layer due to the misfit between it and the substrate. The surface stress is separated in two distinct parts according to its origin, as shown in Fig. 3: (a) The inter-fold interaction, which is due to the steric hindrance of the folds belonging to two consecutive folding planes, yields a tensile surface stress a,,. This stress is relaxed by tilting the polymer chain with respect to the normal to the lamella. This repulsive interaction between folds accounts for the pyramidal shape of the polyethylene single crystals’ and the twist around the b axis of the lamella in the polyethylene spherulites.7 .8 This type of repulsive interaction exists also in paraffin monocrystals between the methyl groups at the ends of the chains. (b) The intra-fold interaction, which is due to the bending and twisting of the carbon chain at the folds, yields a surface stress Or parallel to the folding plane. This stress can be tensile or compressive, depending on the configuration of the carbon atoms in the folds and on the distance between chains. ~r, unlike the stress a,,, is not relaxed by the deformation of a planar single crystal into a pyramidal crystal, but by distortion of the crystalline cell of the polymer.
In Fig. 3, we have represented adjacent polymer chains of polyethylene (PE) parallel to the c axis, linked by the folds containing five carbon atoms, of which four are in gauche position, according to the model of Frank.3 The plane of Fig. 3 (a) is the folding plane (1 rO) of Fig. 3 (b).
It is obvious that the magnitude of the distortion depends on the thickness of the lamella, (i.e. the chains length 1) because of the elastic restoring stress. In cyclic
The stress in the layers of folds at the surface of the polymer lamella should be compared to the stress 201
202
ROTATION OF TERRACES AROUND SCREW DISLOCATION
Vol. 16, No.2
a)
I~oZ~~iI __~~~i /
b)
__
b)
-
-~
________
amorphous Crytaltine
b
-~--~-~l
/ /
,
p=
~
FIG. 2. (a)copolymer Rotated terraces a screw dislocationas in a block PE—PS.around The screw is right-hand
/ ________
as the translation lapping crystallinerotation layers are ofuncoupled the terracesby(b). theOver“amorphous” layers.
C
paraffmns (1 18 A) the lattice is triclinic, while in polyethylene the lattice is orthorhombic like in normal paraffins, but slightly distorted.
) b ‘a / ‘~/~-‘~4~ -
~
- —.
-
q= -4 e
FIG. 1. (a) Single crystal of polyethylene with 4 or 6 sectors. These crystals have generally a pyramidal shape, caused by the staggering of adjacent folds. (b) and (c) Opening of the crystal by an angle ~ positive (b) or negative (c) distorts the orthorhombic cell of PE in two different ways with respect to the direction of the growth faces. The Volterra process for creating a disclination is possible if a tilt boundary is created between the two lips S 1 and S2, or if a screw dislocation is added.
This very weak distortion in polymer crystals could be detected by X-ray and electron diffraction.2’° For example in PE the (010) and (100) reflections forbidden in paraffin by the symmetry of the orthorhombic cell are seen. Information about the distortion is given by the observation or moire patterns’0” in dark-field electron microscopy on bilayered crystalline polymers. The change in spacing and direction of the fringes on crossing sectors gives the magnitude of the change in spacing of the crystalline planes in the different sectors, but not the sign. For example, in PE the distortion of the orthorhombic cell [Fig. 3 (b)J by shearing along the (100) direction can occur in two ways: the diagonal containing the folds could be shorter or longer than the 0r along folding plane diagonal containing nothe folds. In the first(IlO)f,is case, the a surface stress
ROTATION OF TERRACES AROUND SCREW DISLOCATION
Vol. 16, No.2
)
a
.1-’>
in (b) or removed in (c), the disclination is negative or positive. The opening of the crystal as shown in this figure involving the breaking of the chains at the folds is not possible.
~Y’”
~‘v”~
203
The process drawn in Fig. 1(b), c is however
t-~ C~
>1
>~
)
b
__________ ~
-
possible when there is a screw dislocation in the middle of the single crystal. The relaxation of surface stress by distortion of the orthorhombic cell could be easily done by adding a disclination. The “amorphous layers” of folds, uncouple the overlapping crystalline layers [Fig. 2 (b)] this effect must be observed in all bi-layer systems involving a crystalline part and an “amorphous part”. The angle ~ of rotation of the sectors (or of the terraces) in two overlapping lamellae is negative (b) or positive (c), according to the nature of the stress; compressive or tensile along the growth
~.
-
FIG. 3. (a) the polyethylene chains in the folding plane 3 (1 JO), areand linked by folds carbon Bending twisting of theinvolving chains in5 the foldsatoms. leads to a high surface energy. (b) the distortion of the carbon chains in the folds leads to a surface stress 0r which has been drawn in the folding plane (1 rO),. Steric hindrance between two folds in consecutive fold plane leads to a stress a,,. This stress decreases if the chains are tilted from the normal to the plane of figure (folding surface). In pyramidal single crystals, this surface stress a,,, is released, whereas the surface stress 0r is not.
faces parallelrotation to the folding the single crystal. The discrete fo the planes terracesofmust be always in the same sense. The chirality of this translationrotation is equal (b) or opposite (c) to the chirality of the screw dislocation, and depends on the nature of
compressive stress, while in the second case °r is tensile, The angle of shear found in PE in single crystals is 7’; the change of the angle 0 at the center of the single crystal, between boundaries of the sectors, is equal to ~ 7’. Similar distortions appear in Polyoxymethylene (POM) polyoxyethylene (POE) and Poly’4 methyl— pentene 1 (P4MP). The distortion could not be reduced to a single. shear; however, the relative difference of spacing between folding plane and non-folding plane gives a change 0 in the angle of a sector at the center of the crystal of 12.6’ for POMand 4’ for (P4MP). The distortion of the cell appears in the sectors of a single crystal, eityer if there is a certain amount of edge dislocations for relaxing the structure, or if the crystal is cut along a surface S perpendicular to the surface of the lamella allowing the opening of the two lips s
terraces is the same as the screw dislocation. By the proposed model the cell in PE is sheared as drawn in the Fig. 1 (c). The distance between adjacent chains in a folding plane (110) is greater than the distance in (110) plane in the (110), sectors. The surface stress Or defined parallel to the growth faces is a tensile stress. In polypropylene crystallized from the melt ~ and in polyoxy—ethylene—polysterene5 (POE—PS) crystallized from diluted solution the relation between the chirality of the rotation of the terraces and of the screw dislocation are equal like in PE. The surface stress Or for these polymers are laso tensile stress. In POM the two chiralities are opposite. At the screw dislocation is added a negative disclination [process of Fig. 1 (b)] The surface stress is a compressive stress; the spacing of
1
and S2 of the crystal. Figures 1 (b) and (c) show the two ways of opening the crystal leading to the two opposite distortions of the cell. This process of deformation of the crystal is the Volterra process for creating a disclination or a rotation dislocation. If matter is added
the polymer the magnitude of the discrete rotation depends on the conditions of the crystallisation. 1. DISCUSSION In the PE the observed chirality of the rotated
.
(2 0.0) planes-is smaller than the spacing of(0 2. 0) planes in the (0 2. 0)~sectors. In P4MP no screw dislocation with more than two layers has been observed. Rotation of terraces has not yet been observed, so we cannot conclude on the nature of the surface stress.
204
ROTATION OF TERRACES AROUND SCREW DISLOCATION
The order of the rotation between two consecutive terraces in nO; the number n of distorted sectors being 4 for PE and P4MP and 6 for POM, and 0 the angle of shear of the crystal cell. This gives for POM a rotation (1 0 20) three times higher than for PE. .
.
,
The observed rotation of overlapping terraces are of this order of magnitude (— 3°),and seems to be higher for POM than for PE. Quantitative comparisons are however difficult because the rotation of terrace are not always observed, and seems to depend drastically on the experimental conditions; temperature of crystallization, solvent, annealing. It is obvious that the smaller the thickness 1 of the lamellae, the greater is the rotation, the bulk restoring force decreases with 1 while surface stress is generally constant. Then, at the lowest possible temperature of crystallization, (for high supercooling) this effect would be maximum. However, it is to be noticed that if the supercooling is too high, folds at the surface of the lamellae could be non regular and loose. In this case, the distortion could not appear as the surface stress a,. decreases and the orientation is random. But if the crystal is annealed, folds become tight and oriented in the same direction in each ~ This would cause the rotation of terraces to appear around the screw dislocation, if friction between amorphous layers is not too high. In polyethylene annealing near 85°C, edge dislocation concentration increases from l0~up to 2 ~14 We think that this fact must lines per cm appearance, or the enhancement be 10i0 connected to the of the surface stress a,.. Planar or pyramidal crystals of type b, c could exist if material is added or removed between the two lips Si and S 2, involving a tilt boundary, or a random distribution of edge dislocations in all the
Vol. 16, No.2
sectors. The distance between the edge dislocations in a tilt boundary is d = b/tg4O b being the Burgers vector of the dislocation, this gives d 10_i p. In a single crystal of mean length 10 p the dislocation concentration is then 10 9-lines/cm2 an order of magnitude which corresponds to the observations. It should be interesting to check if in polymer single crystals, the cell distortion occurs during annealing and involves the appearance of dislocations. ,
.
.
,
Our model does not take into account the surface stress a,, due to the interactions between adjacent folds because this stress decreases with annealing (folds becoming shorter) while the described effect seems to be enhanced by annealing and also because the distortion which would result in the case of a,, > a,. would give for PE a chirality of the rotated terraces opposite to that observed. The a,, stress is smaller in the pyramidal single crystal than in flat single crystal whereas the a,. stress, due to the intra-fold interaction does not change in first approximation. The surface stress 0r relaxed by the described distortion of the crystalline cell in flat or pyramidal single crystals account for the rotation of the terraces around screw dislocations. This model is different from the interpretation of Keller which involves the concept of a planar crystal transforming into pyramidal crystal.6 The observation of the rotated terraces around screw dislocations enables us to know whether the surface stress a,. along the folding plane growth face of the single crystal, is a tensile or a compressive stress; the angle of rotation gives the order of magnitude of the distortion of the crystalline cell.
REFERENCES 1.
NIEGISH W.D. and SWAN P.R.,J. App!. Phys. 31, 1906 (1960).
2.
RENEKER D.H. and GEIL P.H.,J. App!. Phys. 31, 1916 (1960).
3.
BASSETT D.C., FRANK F.C. and KELLER A.,Phil. Mag. 8, 1739 (1963).
4. 5. 6.
GEILB.G., SYMONS N.K’J. and SCOTT R.G.,J. App!. Phys. 30, 1516 (1959). BOTZ B., KOVACS A.J., BASSETT G.A. and KELLER A.K.,Ko!loidZ.U.Z. Polymer, 209, 115 (1966). KELLER A.,Kolloid Z.UZ. Polymer, 219, 118 (1967).
Vol. 16, No.2
ROTATION OF TERRACES AROUND SCREW DISLOCATION
7.
HOFFMAN J.D. and LAURITZEN J.I.,J.R. Nat. Bur. Standard 65A, 297 (1961).
8.
CALUERT P.D. and UHLMANN D.R.,J. Polym. Sci. 11,457(1973).
9.
NEWMANNB.A.andKAYH.F.,J.Appl.Phys. 38,4105(1967).
10. 11.
205
12.
AGAR A.W., FRANK F.C. and KELLER A.,PhiL Mag. 4,32(1959). BASSETT D.C., FRANK F.C. and KELLER A.,Nature London 184,810(1959); BASSETT D.C.,Phil. Mag. 10, 595 (1964). KHOURI F. and BARNES J.D.,J.R. Nat. Bur. Standard, A76, 225 (1972).
13.
WITENHAFFER D.E. and KEONIG J.L.,J. App!. Phys. 39,4982(1968).
14.
HOLLAND V.F.,J. App!. Phys. 35,3235(1964).
15.
FRIEDEL J.,Dislocations, Pergamon Press (1964).
16.
GEIL P.H.,J. App!. Phys. 33,642(1962).
Pergamon Press.
Printed in Great Britain
ROTATION OF TERRACES AROUND SCREW DISLOCATION IN POLYMER SINGLE CRYSTALS Jacques Rault Laboratoire de Physique des Solides, Université Paris-Sud, 91405 Orsay, France (Received 18 September 1974 by S. Amelinckx)
Polymer crystals generally present, around screw dislocations, a discrete rotation of terraces over each other, always in the same sense. In the proposed model, this rotation in flat or pyramidal single crystals is due to the distortion of the cell which appear in order to relax the surface stress created by the folds. The relation between the chirality of the translationrotation of the terraces and the chirality of the screw dislocation gives information about the nature (tensile or compressive) of the surface stress parallel to the folding plane.
LAMELLAR single crystals of polymers grown from dilute solution have been intensively studies. These crystals have a crystalline layer of about 100 A, with thin “amorphous” layers at the surface, and present several sectors.13 In each sector, the folding planes containing the polymer chains linked by the folds are parallel to the growth face. Figure 1 shows the different types of observed polyethylene monocrystals with (llO)~.and (100), sectors. Around a screw dislocation, the terraces parallel to the folding planes demarcate the sectors, but unlike the case of solid spiral growth, these terraces are twisted from each other by the same angle and in the same direction. Figure 2 shows this effect observed in polymer crystals; the purpose of this paper is to show that this effect can be explained by the distortion of the crystal lattice which occurs in the bulk of the lamella in order to relax partly the surface stress due to the distortion of the chain at the folds.
in an epitaxial layer due to the misfit between it and the substrate. The surface stress is separated in two distinct parts according to its origin, as shown in Fig. 3: (a) The inter-fold interaction, which is due to the steric hindrance of the folds belonging to two consecutive folding planes, yields a tensile surface stress a,,. This stress is relaxed by tilting the polymer chain with respect to the normal to the lamella. This repulsive interaction between folds accounts for the pyramidal shape of the polyethylene single crystals’ and the twist around the b axis of the lamella in the polyethylene spherulites.7 .8 This type of repulsive interaction exists also in paraffin monocrystals between the methyl groups at the ends of the chains. (b) The intra-fold interaction, which is due to the bending and twisting of the carbon chain at the folds, yields a surface stress Or parallel to the folding plane. This stress can be tensile or compressive, depending on the configuration of the carbon atoms in the folds and on the distance between chains. ~r, unlike the stress a,,, is not relaxed by the deformation of a planar single crystal into a pyramidal crystal, but by distortion of the crystalline cell of the polymer.
In Fig. 3, we have represented adjacent polymer chains of polyethylene (PE) parallel to the c axis, linked by the folds containing five carbon atoms, of which four are in gauche position, according to the model of Frank.3 The plane of Fig. 3 (a) is the folding plane (1 rO) of Fig. 3 (b).
It is obvious that the magnitude of the distortion depends on the thickness of the lamella, (i.e. the chains length 1) because of the elastic restoring stress. In cyclic
The stress in the layers of folds at the surface of the polymer lamella should be compared to the stress 201
202
ROTATION OF TERRACES AROUND SCREW DISLOCATION
Vol. 16, No.2
a)
I~oZ~~iI __~~~i /
b)
__
b)
-
-~
________
amorphous Crytaltine
b
-~--~-~l
/ /
,
p=
~
FIG. 2. (a)copolymer Rotated terraces a screw dislocationas in a block PE—PS.around The screw is right-hand
/ ________
as the translation lapping crystallinerotation layers are ofuncoupled the terracesby(b). theOver“amorphous” layers.
C
paraffmns (1 18 A) the lattice is triclinic, while in polyethylene the lattice is orthorhombic like in normal paraffins, but slightly distorted.
) b ‘a / ‘~/~-‘~4~ -
~
- —.
-
q= -4 e
FIG. 1. (a) Single crystal of polyethylene with 4 or 6 sectors. These crystals have generally a pyramidal shape, caused by the staggering of adjacent folds. (b) and (c) Opening of the crystal by an angle ~ positive (b) or negative (c) distorts the orthorhombic cell of PE in two different ways with respect to the direction of the growth faces. The Volterra process for creating a disclination is possible if a tilt boundary is created between the two lips S 1 and S2, or if a screw dislocation is added.
This very weak distortion in polymer crystals could be detected by X-ray and electron diffraction.2’° For example in PE the (010) and (100) reflections forbidden in paraffin by the symmetry of the orthorhombic cell are seen. Information about the distortion is given by the observation or moire patterns’0” in dark-field electron microscopy on bilayered crystalline polymers. The change in spacing and direction of the fringes on crossing sectors gives the magnitude of the change in spacing of the crystalline planes in the different sectors, but not the sign. For example, in PE the distortion of the orthorhombic cell [Fig. 3 (b)J by shearing along the (100) direction can occur in two ways: the diagonal containing the folds could be shorter or longer than the 0r along folding plane diagonal containing nothe folds. In the first(IlO)f,is case, the a surface stress
ROTATION OF TERRACES AROUND SCREW DISLOCATION
Vol. 16, No.2
)
a
.1-’>
in (b) or removed in (c), the disclination is negative or positive. The opening of the crystal as shown in this figure involving the breaking of the chains at the folds is not possible.
~Y’”
~‘v”~
203
The process drawn in Fig. 1(b), c is however
t-~ C~
>1
>~
)
b
__________ ~
-
possible when there is a screw dislocation in the middle of the single crystal. The relaxation of surface stress by distortion of the orthorhombic cell could be easily done by adding a disclination. The “amorphous layers” of folds, uncouple the overlapping crystalline layers [Fig. 2 (b)] this effect must be observed in all bi-layer systems involving a crystalline part and an “amorphous part”. The angle ~ of rotation of the sectors (or of the terraces) in two overlapping lamellae is negative (b) or positive (c), according to the nature of the stress; compressive or tensile along the growth
~.
-
FIG. 3. (a) the polyethylene chains in the folding plane 3 (1 JO), areand linked by folds carbon Bending twisting of theinvolving chains in5 the foldsatoms. leads to a high surface energy. (b) the distortion of the carbon chains in the folds leads to a surface stress 0r which has been drawn in the folding plane (1 rO),. Steric hindrance between two folds in consecutive fold plane leads to a stress a,,. This stress decreases if the chains are tilted from the normal to the plane of figure (folding surface). In pyramidal single crystals, this surface stress a,,, is released, whereas the surface stress 0r is not.
faces parallelrotation to the folding the single crystal. The discrete fo the planes terracesofmust be always in the same sense. The chirality of this translationrotation is equal (b) or opposite (c) to the chirality of the screw dislocation, and depends on the nature of
compressive stress, while in the second case °r is tensile, The angle of shear found in PE in single crystals is 7’; the change of the angle 0 at the center of the single crystal, between boundaries of the sectors, is equal to ~ 7’. Similar distortions appear in Polyoxymethylene (POM) polyoxyethylene (POE) and Poly’4 methyl— pentene 1 (P4MP). The distortion could not be reduced to a single. shear; however, the relative difference of spacing between folding plane and non-folding plane gives a change 0 in the angle of a sector at the center of the crystal of 12.6’ for POMand 4’ for (P4MP). The distortion of the cell appears in the sectors of a single crystal, eityer if there is a certain amount of edge dislocations for relaxing the structure, or if the crystal is cut along a surface S perpendicular to the surface of the lamella allowing the opening of the two lips s
terraces is the same as the screw dislocation. By the proposed model the cell in PE is sheared as drawn in the Fig. 1 (c). The distance between adjacent chains in a folding plane (110) is greater than the distance in (110) plane in the (110), sectors. The surface stress Or defined parallel to the growth faces is a tensile stress. In polypropylene crystallized from the melt ~ and in polyoxy—ethylene—polysterene5 (POE—PS) crystallized from diluted solution the relation between the chirality of the rotation of the terraces and of the screw dislocation are equal like in PE. The surface stress Or for these polymers are laso tensile stress. In POM the two chiralities are opposite. At the screw dislocation is added a negative disclination [process of Fig. 1 (b)] The surface stress is a compressive stress; the spacing of
1
and S2 of the crystal. Figures 1 (b) and (c) show the two ways of opening the crystal leading to the two opposite distortions of the cell. This process of deformation of the crystal is the Volterra process for creating a disclination or a rotation dislocation. If matter is added
the polymer the magnitude of the discrete rotation depends on the conditions of the crystallisation. 1. DISCUSSION In the PE the observed chirality of the rotated
.
(2 0.0) planes-is smaller than the spacing of(0 2. 0) planes in the (0 2. 0)~sectors. In P4MP no screw dislocation with more than two layers has been observed. Rotation of terraces has not yet been observed, so we cannot conclude on the nature of the surface stress.
204
ROTATION OF TERRACES AROUND SCREW DISLOCATION
The order of the rotation between two consecutive terraces in nO; the number n of distorted sectors being 4 for PE and P4MP and 6 for POM, and 0 the angle of shear of the crystal cell. This gives for POM a rotation (1 0 20) three times higher than for PE. .
.
,
The observed rotation of overlapping terraces are of this order of magnitude (— 3°),and seems to be higher for POM than for PE. Quantitative comparisons are however difficult because the rotation of terrace are not always observed, and seems to depend drastically on the experimental conditions; temperature of crystallization, solvent, annealing. It is obvious that the smaller the thickness 1 of the lamellae, the greater is the rotation, the bulk restoring force decreases with 1 while surface stress is generally constant. Then, at the lowest possible temperature of crystallization, (for high supercooling) this effect would be maximum. However, it is to be noticed that if the supercooling is too high, folds at the surface of the lamellae could be non regular and loose. In this case, the distortion could not appear as the surface stress a,. decreases and the orientation is random. But if the crystal is annealed, folds become tight and oriented in the same direction in each ~ This would cause the rotation of terraces to appear around the screw dislocation, if friction between amorphous layers is not too high. In polyethylene annealing near 85°C, edge dislocation concentration increases from l0~up to 2 ~14 We think that this fact must lines per cm appearance, or the enhancement be 10i0 connected to the of the surface stress a,.. Planar or pyramidal crystals of type b, c could exist if material is added or removed between the two lips Si and S 2, involving a tilt boundary, or a random distribution of edge dislocations in all the
Vol. 16, No.2
sectors. The distance between the edge dislocations in a tilt boundary is d = b/tg4O b being the Burgers vector of the dislocation, this gives d 10_i p. In a single crystal of mean length 10 p the dislocation concentration is then 10 9-lines/cm2 an order of magnitude which corresponds to the observations. It should be interesting to check if in polymer single crystals, the cell distortion occurs during annealing and involves the appearance of dislocations. ,
.
.
,
Our model does not take into account the surface stress a,, due to the interactions between adjacent folds because this stress decreases with annealing (folds becoming shorter) while the described effect seems to be enhanced by annealing and also because the distortion which would result in the case of a,, > a,. would give for PE a chirality of the rotated terraces opposite to that observed. The a,, stress is smaller in the pyramidal single crystal than in flat single crystal whereas the a,. stress, due to the intra-fold interaction does not change in first approximation. The surface stress 0r relaxed by the described distortion of the crystalline cell in flat or pyramidal single crystals account for the rotation of the terraces around screw dislocations. This model is different from the interpretation of Keller which involves the concept of a planar crystal transforming into pyramidal crystal.6 The observation of the rotated terraces around screw dislocations enables us to know whether the surface stress a,. along the folding plane growth face of the single crystal, is a tensile or a compressive stress; the angle of rotation gives the order of magnitude of the distortion of the crystalline cell.
REFERENCES 1.
NIEGISH W.D. and SWAN P.R.,J. App!. Phys. 31, 1906 (1960).
2.
RENEKER D.H. and GEIL P.H.,J. App!. Phys. 31, 1916 (1960).
3.
BASSETT D.C., FRANK F.C. and KELLER A.,Phil. Mag. 8, 1739 (1963).
4. 5. 6.
GEILB.G., SYMONS N.K’J. and SCOTT R.G.,J. App!. Phys. 30, 1516 (1959). BOTZ B., KOVACS A.J., BASSETT G.A. and KELLER A.K.,Ko!loidZ.U.Z. Polymer, 209, 115 (1966). KELLER A.,Kolloid Z.UZ. Polymer, 219, 118 (1967).
Vol. 16, No.2
ROTATION OF TERRACES AROUND SCREW DISLOCATION
7.
HOFFMAN J.D. and LAURITZEN J.I.,J.R. Nat. Bur. Standard 65A, 297 (1961).
8.
CALUERT P.D. and UHLMANN D.R.,J. Polym. Sci. 11,457(1973).
9.
NEWMANNB.A.andKAYH.F.,J.Appl.Phys. 38,4105(1967).
10. 11.
205
12.
AGAR A.W., FRANK F.C. and KELLER A.,PhiL Mag. 4,32(1959). BASSETT D.C., FRANK F.C. and KELLER A.,Nature London 184,810(1959); BASSETT D.C.,Phil. Mag. 10, 595 (1964). KHOURI F. and BARNES J.D.,J.R. Nat. Bur. Standard, A76, 225 (1972).
13.
WITENHAFFER D.E. and KEONIG J.L.,J. App!. Phys. 39,4982(1968).
14.
HOLLAND V.F.,J. App!. Phys. 35,3235(1964).
15.
FRIEDEL J.,Dislocations, Pergamon Press (1964).
16.
GEIL P.H.,J. App!. Phys. 33,642(1962).