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Dislocation charges in KBr crystals
.I. Phys. Chem. Solids Vol. 53, No. 5, pp. 651455, Printed in Great Britain.
1992
DISLOCATION
0022-3697/92 $5.00 + 0.00 Pergamon Press plc
CHARGES
IN KBr CRYSTALS
HUANG SONGW and R. LABUSCH~ Department
of Physics, East China University of Chemical Technology, Shanghai 200 237, China (Received
10 June 1991; accepted in revised form
16 October
130 Meilong
Road,
1991)
Abstract-The dislocation charge in KBr is investigated at room temperature. Artificial sources are introduced at one specimen surface to make sure that dislocations move only in one direction during the first stages of plastic deformation. This technique leads to remarkably consistent and reproducible results. Our specimens contained a majority of divalent anion impurities and the dislocation charge turned out to be positive, in agreement with the sweep-up model of Whitworth, with a value is 0.27 elementary charges per unit cell. Keywords:
Dislocation,
charge, defect, strain, potassium
bromide.
vectors give rise to the same strain rate but to opposite electrical current densities. If we assume for the sake of simplicity that only edge dislocations in a single glide system are mobile, the strain rate is da/dt =(pA +~o)bo and the current density in the glide direction is j = (~6 - pi)q~, where v is the average absolute value of the velocity, b the length of the burgers vector, q the charge per unit length and pD+, p; the densities of dislocations with positive and negative burgers vectors, respectively. From these relations we obtain q =j(p& + pi)/ (p,’ - ~6 )/(da/dt). Screw dislocations are not supposed to carry charges and therefore contribute only to da/dr but not to j. If they are also involved
INTRODUCTION possibility that dislocations in ionic crystals may contain charged jogs in their cores was first recognized by Seitz [l]. Meanwhile there is, in fact, plenty of experimental evidence for charge transport by moving edge dislocations and it is believed that the charges are due to single vacancies in the dislocation cores (equivalent to pairs of jogs). Whitworth [2] described this process by a sweep-up model. Charges are picked up and left behind by a moving dislocation. The charge per unit length increases initially and reaches, through the competition of these two processes, a steady state value proportional to the concentration of charged point defects. Consequently the observed charge and its sign is a measure of the type of concentration of impurities in the crystal. For reasons to be discussed below, it is difficult to determine the sign and magnitude of the dislocation charge experimentally so that it is not surprising that sometimes different experiments gave different results. Whitworth [3] suggested, from a collection of the results for alkali halides, that divalent impurity cations give rise to a negative and divalent impurity anions to a positive charge. Most of the work done so far has been concentrated on NaCl crystals. In the present work we have investigated the dislocation charge in KBr. A major difficulty in the measurement of disThe
we obtain 4 =i(~$ + P; + (PJP&P,)/(P: - P; )/ (da/d?), where p: and p, are the densities of edge and screw dislocations, respectively, and p(eand pr their mobilities. In some investigations in the past the simple relation q = j/(du/dr) was assumed. As a rule, the contribution of screw dislocations introduces only a correction of the order of unity to this simplified formula but the mixing of dislocations with positive and negative sigma causes considerable uncertainty not only about the magnitude but even about the sign of q. Removal of this uncertainty by experimental means is not straightforward. For instance, in his investigation of NaCl, Whitworth [4] assumed the dislocation sources to be in the volume so that dislocations move preferentially from the interior of the specimen to the surface, and he placed the electrical contacts accordingly. This assumption may be valid, but was not further proved. Kataoka et al. [5] used a superposition of compression and bending to introduce a surplus dislocation density with one
location charges in alkali halides arises from the fact that charged edge dislocations with opposite burgers t Iqstitut fiir Angewandte Physik der TU Clausthal Sommerfeld Str. 6, D-3392 Clausthal-Zellerfeld, Germany. 651
652
HUANGSONGYUamd
sign of the burgers vector. This principle had also been used by Whitworth [3] and by van Dingenen [6] in earlier papers. ( p: - p; ) was determined from the degree of bending. However, this surplus concerns the total dislocation density while the charge transport depends only on the mobile density. If (p: - p;)/(p: + p;) is small for the total densities (0.1 in [5]), an accidental surplus of the same order of magnitude with one sign of b or the other in the mobile dislocation density due to inhomogeneities seems possible. In the present work we have tried to overcome this difficulty through the introduction of artificial dislocation sources by scratching one of the side faces of the specimen. Figure la shows a section of a specimen that was scratched only and Fig. lb another one where the scratching was followed by a small degree of deformation. Obviously, there are glide bands
Fig.
R. LAWSCH
emanating from the scratches into the undeformed volume. No slip traces were observed at this stage of deformation on the opposite side of the specimen. Therefore we are reasonably sure that in the early stages of plastic deformation the majority of the dislocations is moving away from the scratched surface. EXPERIMENTAL
PROCEDURES
The KBr single crystals used in the present experiments were purchased from E. Merck Chem. Co. (suprapur). According to the supplier’s analysis and to the experimental analysis using ICP-Atomic Emission Spectrum ps-6 (Baird Co.) they contained 6 ppm divalent cation impurities and 10 ppm divalent anion impurities. The size of the specimens was approximately 2 x 4 x 6 mm. They were prepared by cleavage along
1 Scratched surface of a KBr crystal. (a) Scratched
only, (b) scratched
and deformed.
Dislocation charges in KBr crystals
{lOO}-faces. The specimens were annealed for 2 h at 650°C and cooled to room temperature over a period of 12 h. This treatment removed most of the damage introduced by cleaving and served to decrease the dislocation density and to lock the remaining dislocations by Cottrell clouds. These effect will be reflected in the result of experiments as shown in Fig. 3. After this the specimens were chemically polished in a solution of 13% methanol, 22% glycerin, 3% ethanol and 2% ammonia, washed in dry ethanol and finally rinsed in butanol. Scratches were introduced on one of the large side faces by pulling a diamond needle across the surface in the direction of the compression axis. The needle had a radius of curvature of 15 p at the tip and a load of 0.1 N was applied. The distances between scratches are about OSmm. Circular indium electrodes, 3.5 mm in diameter, were evaporated on the scratched surface and on the opposite surface. The specimen was then mounted between quartz stamps in a compression apparatus. The two quartz stamps compressed the specimens absolutely parallel, otherwise the deformation might have been inhomogeneous and excess dislocations of one sign could have been introduced. At the same time the specimen must be kept perpendicular to the quartz stamps and not bend; otherwise negative charge appears on the concave side and positive charge appears on the convex side. Small brass platelets with thin wires attached were clamped to the indium spots by a soft spring which applied a load of only about 0.01 Nmm-’ on the contact areas. Plastic deformation was done at room temperature by stepwise increases of the load on the upper mobile stamp. An edge dislocation moving in crystals sweeps up many of the anion vacancies
Strain (xl 03) Fig. 2. Transported charge vs plastic strain for three different KBr specimens. The specimens were deformed in compression at room temperature, a few minutes after
PCS 53,x
6
I
0
1.5
I
I
3
4.5
Strain (xl 03)
Fig. 3. Charge transport in specimens that were scratched and then kept at room temperature for 24 h before plastic deformation.
it encounters, and therefore the dislocation core is charged. After each increase we waited until further change in specimen length became unobservable at the resolution of our apparatus. At that time we took a reading of the change in length and of the charge that had been transported through the specimen. The latter was monitored with a Keithley 610B-instrument that was used as a coulomb meter. In this mode the bias current through the electrometer is less than lo-“A. The total duration of the experiment was less than lo’s, so that drift errors are smaller than 10-12 c. RESULTS
In Figs 2, 3 and 4 we have plotted the transported charge Q, vs the unreduced strain E = al/l. Figure 2 shows the results for three specimens that were deformed immediately after scratching one
0
1.5
3
4.5
Strain (xl@)
Fig. 4. Charge transport in unscratched specimens. Q would be zero if the mobile dislocation density were completely symmetric with respect to the sign of the burgers vector.
654
HUANC SONGYU
side. According to our remarks in the Introduction, dislocations in these specimens move only in one direction near d6 = 0. The saturation of Q at large 61 which is also seen in Figs 3 and 4 is most likely due to an increasing number of dislocations moving in the opposite direction. At high degrees of deformation the dislocation sources will be distributed over the volume at random so that equal numbers are moving in opposite directions and the net charge transport becomes zero. In all cases the scratched surface of the specimen became negative under plastic deformation, indicating that the dislocations carry a positive charge in our material. Figure 3 shows the results for three specimens that were “annealed” for 24 h at room temperature between scratching and deformation. The results are qualitatively similar to those in Fig. 2 but the initial slope of Q(e) is significantly lower. The reason could be that fresh dislocations have a somewhat higher charge per unit length than the annealed ones, or that our artificial dislocation sources are pinned by the annealing so that grown-in sources in the bulk play a greater role. Figure 4 shows results of nominally symmetric specimens that had not been scratched before deformation. The charge transport is definitely, but not by orders of magnitude, lower than in the scratched specimens and the scatter between different specimens is much larger. This demonstrates that accidental asymmetries in the mobile dislocation density can lead to erroneous results if only a small surplus of dislocations with one sign of b is introduced. Two glide systems, both under 45” to the specimen axis are equivalent in our geometry. Slip line observations of the corresponding side faces show that usually, in the early stages of deformation, only one of these is operative while later on, double glide is the rule. For both slip systems we have da/dt = &.d{ldt and j = $. I/A, where I is the current perpendicular to the specimen axis and A the cross-section of the contacts. Therefore the slope of dQ/de at t = 0 is equal to jA/(da/dt) and, assuming that the contribution of screws to dc/dt is insignificant, we obtain q = (dQ/dr)b/A, where A is the contact area. From a least square fit of our data to the function Q(E) = Q,( 1 - exp( - L/E,,)) which is empirical and as shown in the figures, we obtained the values of dQ /de at e = 0 and from these the charges per unit length. In the three specimens of Fig. 2 their values are 6.93 x lo-“, 6.74 x lo-“, and 6.27 x lo-‘i Cm-i, respectively, with an average value of q = 6.62 x lo-“Cm-‘. This is equivalent to 0.27 elementary charges per unit cell in the dislocation core. Only one third of this value is obtained if Fig. 3 is formally
and R.
LABUSCH
evaluated in the same way, but this has no different physical significance. Figure 4 shows that for the majority of unscratched specimens dQ/de is rather small because in these the mobile dislocation density as completely symmetric with respect to the sign of the burgers vector. Accidentally, some of the dQ/dE values are rather large, but these have no physical significance. DISCUSSION The present work should be considered as a promising first step and has to be continued and expanded for more information on the mechanism of charge transport by dislocations. So far, we can only draw a few conclusions. The sign of the dislocation charge q. together with the fact that divalent anion impurities are predominant in our material, is in agreement with results of Tyapnina and Kolomitsev who studied systematically the dependence of q on impurity content in NaCl, and also with Whitworth’s sweep-up model. It will be interesting to investigate in the future KBr with a majority of divalent cation impurities where the opposite sign is expected. The CRSS of our material was 0.5 to 1 MPa. At this value the dislocation charge of KC1 found by Kataoka et al. was of similar magnitude but, as expected, of the opposite sign because their specimens were doped with Ca. The sweep-up model, cannot be checked in detail from our results. An increase of q along the dislocation path which is predicted by this model would lead to a positive curvature of the Q(E)-curves which is not observed in our results. Consequently q must have been at, or close to, its saturation value already at the beginning of the experiment. On the other hand, steady state experiments in the past yield an average of q over the life of a mobile dislocation. Its value depends on the ratio between the path necessary to acquire the equilibrium charge per unit length and the total path between creation at a source and immobilisation in tangles or pile-ups. The corresponding correction may not always be negligible because the path to saturation can be rather long: the maximum number of elementary charges per unit length that can be picked up along a path of length p is PC,, where c,, is the area density of charged vacancies in the glide plane. Therefore, we can estimate a minimum value of p after which the dislocation charge becomes stationary from the condition ec,p 2 q. In our case, for instance, we obtain p > 6pm. Scratching produces dislocation half loops at the surface which must have been expanded at least to this depth by the scratching alone.
Dislocation charges in KBr crystals
In conclusion, the experimental results indicate that the q dislocation charge of per unit length is equal to the equilibrium
charge
which is associated
only with the edge component of dislocation loops and the positive charge q indicates that there must be enough anion vacancies present paired with impurities for the dislocation to sweep them up in larger numbers than the cation vacancies.
655 REFERENCES
1. Seitz F., Rev. mod. Phys., 23, 328 (1951). 2. Whitworth R. W., Phil. Mug. 51, 857 (1985). 3. Whitworth R. W., Adv. Phys. 24, 203 (1975). 4. Whitworth R. W., Phil. Mug. 10, 801 (1964). 5. Toshikiko Kataoka, Colombo L. and Li J. C. M., Phil. Mug. A49, 409 (1984). 6. Van Dingenen E., Phil. Mug. 31, 1263 (1975). 7. Tvauunina N. A. and Kolomiitsev A. I.. Sov. Phzs. c;,dtarrogr., 18, 549 (1974).
1992
DISLOCATION
0022-3697/92 $5.00 + 0.00 Pergamon Press plc
CHARGES
IN KBr CRYSTALS
HUANG SONGW and R. LABUSCH~ Department
of Physics, East China University of Chemical Technology, Shanghai 200 237, China (Received
10 June 1991; accepted in revised form
16 October
130 Meilong
Road,
1991)
Abstract-The dislocation charge in KBr is investigated at room temperature. Artificial sources are introduced at one specimen surface to make sure that dislocations move only in one direction during the first stages of plastic deformation. This technique leads to remarkably consistent and reproducible results. Our specimens contained a majority of divalent anion impurities and the dislocation charge turned out to be positive, in agreement with the sweep-up model of Whitworth, with a value is 0.27 elementary charges per unit cell. Keywords:
Dislocation,
charge, defect, strain, potassium
bromide.
vectors give rise to the same strain rate but to opposite electrical current densities. If we assume for the sake of simplicity that only edge dislocations in a single glide system are mobile, the strain rate is da/dt =(pA +~o)bo and the current density in the glide direction is j = (~6 - pi)q~, where v is the average absolute value of the velocity, b the length of the burgers vector, q the charge per unit length and pD+, p; the densities of dislocations with positive and negative burgers vectors, respectively. From these relations we obtain q =j(p& + pi)/ (p,’ - ~6 )/(da/dt). Screw dislocations are not supposed to carry charges and therefore contribute only to da/dr but not to j. If they are also involved
INTRODUCTION possibility that dislocations in ionic crystals may contain charged jogs in their cores was first recognized by Seitz [l]. Meanwhile there is, in fact, plenty of experimental evidence for charge transport by moving edge dislocations and it is believed that the charges are due to single vacancies in the dislocation cores (equivalent to pairs of jogs). Whitworth [2] described this process by a sweep-up model. Charges are picked up and left behind by a moving dislocation. The charge per unit length increases initially and reaches, through the competition of these two processes, a steady state value proportional to the concentration of charged point defects. Consequently the observed charge and its sign is a measure of the type of concentration of impurities in the crystal. For reasons to be discussed below, it is difficult to determine the sign and magnitude of the dislocation charge experimentally so that it is not surprising that sometimes different experiments gave different results. Whitworth [3] suggested, from a collection of the results for alkali halides, that divalent impurity cations give rise to a negative and divalent impurity anions to a positive charge. Most of the work done so far has been concentrated on NaCl crystals. In the present work we have investigated the dislocation charge in KBr. A major difficulty in the measurement of disThe
we obtain 4 =i(~$ + P; + (PJP&P,)/(P: - P; )/ (da/d?), where p: and p, are the densities of edge and screw dislocations, respectively, and p(eand pr their mobilities. In some investigations in the past the simple relation q = j/(du/dr) was assumed. As a rule, the contribution of screw dislocations introduces only a correction of the order of unity to this simplified formula but the mixing of dislocations with positive and negative sigma causes considerable uncertainty not only about the magnitude but even about the sign of q. Removal of this uncertainty by experimental means is not straightforward. For instance, in his investigation of NaCl, Whitworth [4] assumed the dislocation sources to be in the volume so that dislocations move preferentially from the interior of the specimen to the surface, and he placed the electrical contacts accordingly. This assumption may be valid, but was not further proved. Kataoka et al. [5] used a superposition of compression and bending to introduce a surplus dislocation density with one
location charges in alkali halides arises from the fact that charged edge dislocations with opposite burgers t Iqstitut fiir Angewandte Physik der TU Clausthal Sommerfeld Str. 6, D-3392 Clausthal-Zellerfeld, Germany. 651
652
HUANGSONGYUamd
sign of the burgers vector. This principle had also been used by Whitworth [3] and by van Dingenen [6] in earlier papers. ( p: - p; ) was determined from the degree of bending. However, this surplus concerns the total dislocation density while the charge transport depends only on the mobile density. If (p: - p;)/(p: + p;) is small for the total densities (0.1 in [5]), an accidental surplus of the same order of magnitude with one sign of b or the other in the mobile dislocation density due to inhomogeneities seems possible. In the present work we have tried to overcome this difficulty through the introduction of artificial dislocation sources by scratching one of the side faces of the specimen. Figure la shows a section of a specimen that was scratched only and Fig. lb another one where the scratching was followed by a small degree of deformation. Obviously, there are glide bands
Fig.
R. LAWSCH
emanating from the scratches into the undeformed volume. No slip traces were observed at this stage of deformation on the opposite side of the specimen. Therefore we are reasonably sure that in the early stages of plastic deformation the majority of the dislocations is moving away from the scratched surface. EXPERIMENTAL
PROCEDURES
The KBr single crystals used in the present experiments were purchased from E. Merck Chem. Co. (suprapur). According to the supplier’s analysis and to the experimental analysis using ICP-Atomic Emission Spectrum ps-6 (Baird Co.) they contained 6 ppm divalent cation impurities and 10 ppm divalent anion impurities. The size of the specimens was approximately 2 x 4 x 6 mm. They were prepared by cleavage along
1 Scratched surface of a KBr crystal. (a) Scratched
only, (b) scratched
and deformed.
Dislocation charges in KBr crystals
{lOO}-faces. The specimens were annealed for 2 h at 650°C and cooled to room temperature over a period of 12 h. This treatment removed most of the damage introduced by cleaving and served to decrease the dislocation density and to lock the remaining dislocations by Cottrell clouds. These effect will be reflected in the result of experiments as shown in Fig. 3. After this the specimens were chemically polished in a solution of 13% methanol, 22% glycerin, 3% ethanol and 2% ammonia, washed in dry ethanol and finally rinsed in butanol. Scratches were introduced on one of the large side faces by pulling a diamond needle across the surface in the direction of the compression axis. The needle had a radius of curvature of 15 p at the tip and a load of 0.1 N was applied. The distances between scratches are about OSmm. Circular indium electrodes, 3.5 mm in diameter, were evaporated on the scratched surface and on the opposite surface. The specimen was then mounted between quartz stamps in a compression apparatus. The two quartz stamps compressed the specimens absolutely parallel, otherwise the deformation might have been inhomogeneous and excess dislocations of one sign could have been introduced. At the same time the specimen must be kept perpendicular to the quartz stamps and not bend; otherwise negative charge appears on the concave side and positive charge appears on the convex side. Small brass platelets with thin wires attached were clamped to the indium spots by a soft spring which applied a load of only about 0.01 Nmm-’ on the contact areas. Plastic deformation was done at room temperature by stepwise increases of the load on the upper mobile stamp. An edge dislocation moving in crystals sweeps up many of the anion vacancies
Strain (xl 03) Fig. 2. Transported charge vs plastic strain for three different KBr specimens. The specimens were deformed in compression at room temperature, a few minutes after
PCS 53,x
6
I
0
1.5
I
I
3
4.5
Strain (xl 03)
Fig. 3. Charge transport in specimens that were scratched and then kept at room temperature for 24 h before plastic deformation.
it encounters, and therefore the dislocation core is charged. After each increase we waited until further change in specimen length became unobservable at the resolution of our apparatus. At that time we took a reading of the change in length and of the charge that had been transported through the specimen. The latter was monitored with a Keithley 610B-instrument that was used as a coulomb meter. In this mode the bias current through the electrometer is less than lo-“A. The total duration of the experiment was less than lo’s, so that drift errors are smaller than 10-12 c. RESULTS
In Figs 2, 3 and 4 we have plotted the transported charge Q, vs the unreduced strain E = al/l. Figure 2 shows the results for three specimens that were deformed immediately after scratching one
0
1.5
3
4.5
Strain (xl@)
Fig. 4. Charge transport in unscratched specimens. Q would be zero if the mobile dislocation density were completely symmetric with respect to the sign of the burgers vector.
654
HUANC SONGYU
side. According to our remarks in the Introduction, dislocations in these specimens move only in one direction near d6 = 0. The saturation of Q at large 61 which is also seen in Figs 3 and 4 is most likely due to an increasing number of dislocations moving in the opposite direction. At high degrees of deformation the dislocation sources will be distributed over the volume at random so that equal numbers are moving in opposite directions and the net charge transport becomes zero. In all cases the scratched surface of the specimen became negative under plastic deformation, indicating that the dislocations carry a positive charge in our material. Figure 3 shows the results for three specimens that were “annealed” for 24 h at room temperature between scratching and deformation. The results are qualitatively similar to those in Fig. 2 but the initial slope of Q(e) is significantly lower. The reason could be that fresh dislocations have a somewhat higher charge per unit length than the annealed ones, or that our artificial dislocation sources are pinned by the annealing so that grown-in sources in the bulk play a greater role. Figure 4 shows results of nominally symmetric specimens that had not been scratched before deformation. The charge transport is definitely, but not by orders of magnitude, lower than in the scratched specimens and the scatter between different specimens is much larger. This demonstrates that accidental asymmetries in the mobile dislocation density can lead to erroneous results if only a small surplus of dislocations with one sign of b is introduced. Two glide systems, both under 45” to the specimen axis are equivalent in our geometry. Slip line observations of the corresponding side faces show that usually, in the early stages of deformation, only one of these is operative while later on, double glide is the rule. For both slip systems we have da/dt = &.d{ldt and j = $. I/A, where I is the current perpendicular to the specimen axis and A the cross-section of the contacts. Therefore the slope of dQ/de at t = 0 is equal to jA/(da/dt) and, assuming that the contribution of screws to dc/dt is insignificant, we obtain q = (dQ/dr)b/A, where A is the contact area. From a least square fit of our data to the function Q(E) = Q,( 1 - exp( - L/E,,)) which is empirical and as shown in the figures, we obtained the values of dQ /de at e = 0 and from these the charges per unit length. In the three specimens of Fig. 2 their values are 6.93 x lo-“, 6.74 x lo-“, and 6.27 x lo-‘i Cm-i, respectively, with an average value of q = 6.62 x lo-“Cm-‘. This is equivalent to 0.27 elementary charges per unit cell in the dislocation core. Only one third of this value is obtained if Fig. 3 is formally
and R.
LABUSCH
evaluated in the same way, but this has no different physical significance. Figure 4 shows that for the majority of unscratched specimens dQ/de is rather small because in these the mobile dislocation density as completely symmetric with respect to the sign of the burgers vector. Accidentally, some of the dQ/dE values are rather large, but these have no physical significance. DISCUSSION The present work should be considered as a promising first step and has to be continued and expanded for more information on the mechanism of charge transport by dislocations. So far, we can only draw a few conclusions. The sign of the dislocation charge q. together with the fact that divalent anion impurities are predominant in our material, is in agreement with results of Tyapnina and Kolomitsev who studied systematically the dependence of q on impurity content in NaCl, and also with Whitworth’s sweep-up model. It will be interesting to investigate in the future KBr with a majority of divalent cation impurities where the opposite sign is expected. The CRSS of our material was 0.5 to 1 MPa. At this value the dislocation charge of KC1 found by Kataoka et al. was of similar magnitude but, as expected, of the opposite sign because their specimens were doped with Ca. The sweep-up model, cannot be checked in detail from our results. An increase of q along the dislocation path which is predicted by this model would lead to a positive curvature of the Q(E)-curves which is not observed in our results. Consequently q must have been at, or close to, its saturation value already at the beginning of the experiment. On the other hand, steady state experiments in the past yield an average of q over the life of a mobile dislocation. Its value depends on the ratio between the path necessary to acquire the equilibrium charge per unit length and the total path between creation at a source and immobilisation in tangles or pile-ups. The corresponding correction may not always be negligible because the path to saturation can be rather long: the maximum number of elementary charges per unit length that can be picked up along a path of length p is PC,, where c,, is the area density of charged vacancies in the glide plane. Therefore, we can estimate a minimum value of p after which the dislocation charge becomes stationary from the condition ec,p 2 q. In our case, for instance, we obtain p > 6pm. Scratching produces dislocation half loops at the surface which must have been expanded at least to this depth by the scratching alone.
Dislocation charges in KBr crystals
In conclusion, the experimental results indicate that the q dislocation charge of per unit length is equal to the equilibrium
charge
which is associated
only with the edge component of dislocation loops and the positive charge q indicates that there must be enough anion vacancies present paired with impurities for the dislocation to sweep them up in larger numbers than the cation vacancies.
655 REFERENCES
1. Seitz F., Rev. mod. Phys., 23, 328 (1951). 2. Whitworth R. W., Phil. Mug. 51, 857 (1985). 3. Whitworth R. W., Adv. Phys. 24, 203 (1975). 4. Whitworth R. W., Phil. Mug. 10, 801 (1964). 5. Toshikiko Kataoka, Colombo L. and Li J. C. M., Phil. Mug. A49, 409 (1984). 6. Van Dingenen E., Phil. Mug. 31, 1263 (1975). 7. Tvauunina N. A. and Kolomiitsev A. I.. Sov. Phzs. c;,dtarrogr., 18, 549 (1974).