J. Phys. Chem. 1983, 87, 4022-4024
4022
Electric Currents Associated with Dislocatlon Motion in Ice V. F. Petrenko Institute of Solid State Physics of the Academy of Sciences, Chernogolovka, Moscow District, USSR
and R.
W. Whltworth'
Department of Physics, University of Birmingham, Birmingham B 15 2TT. England (Received: August 23, 1982; In Final Form: December 8, 1982)
Single crystals of ice were bent so as to introduce an excess of edge dislocations of one mechanical sign, and then deformed in tension with liquid Hg/In electrodes on their surfaces. An electric current was observed during plastic deformation which corresponds to the motion of dislocations carrying a small positive charge.
Introduction The structure of the core of a dislocation in ice is not yet k n o ~ ~ - but, ~ , l -whatever ~ the structure may be, it is in principle possible for a dislocation with an edge component to carry an electric charge. In its simplest form4 a dislocation charge can arise from an imbalance between the number of dangling bonds that have protons on them and the number that do not. Even if the dangling bonds are not clearly identifiable (as in the case of a noncrystalline core) this charge is built into the structure by the orientations of the molecules surrounding the core, and the charge must move with the dislocation as it glides. Such a charge may be thought of as arising from the trapping of Bjerrum defects at the core. A charge may also arise from the trapping of ions,5 but it is an open question whether ions would glide with the core or tend to act as pinning points. In equilibrium the core charge will be screened by a compensating charge of point defects in the surrounding lattice. Experiments to observe the dislocation charge are relevant to the understanding of the nature of the dislocation core and to theories of its m ~ b i l i t y . ' , ~Itagaki'~~ *~ applied electric fields to ice crystals in which dislocations were being observed by X-ray topography and reported evidence of the movement of dislocations which he attributed to their having a positive charge of a t least O.Ole/a, where e is the charge of a proton and a is the lattice parameter. However, when Joncich, Holder, and Granatog attempted to influence the movement of a tilt boundary by the application of an electric field, they observed no effect and deduced an upper limit to the possible charge of 0.003ela. The interpretation of these experiments will be considered later. In this paper we describe the converse experiment in which a small current is observed due to the movement of dislocations during plastic deformation. Such currents have been the subject of much study in the alkali halides5 and groups 2-6 compounds.lOJ1 Our method, which is (1) R. W. Whitworth, J . Glaciol., 21, 341 (1978). (2) R. W. Whitworth, Phil.Mag.A , 41, 521 (1980). (3) R. W. Whitworth, J. Phys. Chem., this issue. (4) J. W. Glen, Phys.Kondens. Muter., 7,43 (1968). (5) R. W. Whitworth, Adu. Phys.,24, 203 (1975). (6) R. W. Whitworth, J. G. Paren, and J. W. Glen, Phil.Mug., 33,409 (1976). (7) K. Itagaki, Adu. X-ray Anal., 13, 526 (1970). (8) K. Itagaki, CRREL Report 79-25, ADA 078775, 1979. (9) D. M.Joncich, J. Holder, and A. V. Granato, J . Gluciol., 20, 543 (1978).
0022-3654/83/2087-4022$0 1.50/0
based on that originated by Remaut and Vennik,l* uses a monocrystalline specimen that has been bent to introduce an excess of dislocations of one mechanical sign. When this specimen is deformed in tension along its length as shown in Figure la, dislocations of the majority type move toward the upper surface, and if they are charged they produce a current between the electrodes E, and E,. Experimental Technique The experiments were performed on monocrystalline specimens of the purest available ice. These were grown by the method of Glen13from triple-distilled water which had been passed six to eight times through an Elga deionizing ion-exchange column and then filtered through an 0.2-pm micropore filter. The water was boiled under reduced pressure for 8-10 h at 35-40 "C in a cleaned glass desiccator, and then frozen in the same desiccator with continuous pumping to avoid the absorption of COz during growth. Single grains grew from the water surface into square glass tubes (6 X 6 X 100 mm3) placed in the water a t 45" to the vertical. Freezing took place in a cold room at -4.5 "C with thermal insulation around the bottom and sides of the desiccator; the average rate of growth was 1 cm per day. Since the ice crystals growing from the surface normally have the c axis perpendicular to that surface the crystals that form in the tubes usually have the c axis at 45" to their length. They were extracted from the tubes by gentle melting and the melted layer was removed by polishing on a filter paper. Only those crystals were used which had the c axis close to 45" to the length and parallel to one pair of long faces. The crystals were bent to a final radius of about 5 cm in a four-point bending jig at -4.5 "C. A constant load of about 50 g was used and the deformation took about 2 h. The deformation occurred by slip on the (0001) plane but the orientation of the a axes in this plane was not determined. After bending the curvature was too great to perform the simple tension experiment indicated in Figure la, and a thinner straight specimen was therefore cut from the bent crystal as shown in Figure lb. The thinning was performed by gentle scraping similar to the action of a microtome. The ends were frozen into holders with a small amount of triple-distilled water and the specimen mounted (IO) Yu. A. Osip'yan and V. F. Petrenko, Zh. Eksp. Teor. Fiz., 69, 1362 (1975) (Sou. Phys. JETP,42, 695 (1975)). (11) V. F. Petrenko and R. W. Whitworth, Phil. Mug. A , 41, 681 (1980). (12) G . Remaut and J. Vennik, Phil.Mag.,6, 1 (1961). (13) J. W. Glen and M.F. Perutz, J . Glaciol., 2, 395 (1954). 0 1983 American Chemical Society
The Journal of Physical Chemistry, Vol. 87, No. 21, 1983 4023
Dislocation Motion in Ice
Flgure 1. (a) Bent crystal containing an excess of dislocations of one sign. When deformed in tension the majority dislocations move toward the upper electrode E,. (b) Illustrating how tensile specimen is cut from bent crystal.
r---, I
mhr
4
'
1/11
I
0
'0
I
1
100
200
time (si Flgure 3. Recordings of change of length AI and current I during tensile deformation. Load is applied and removed at times indicated by the arrows.
I? I
I
0
100 time
200
(SI
Flgure 4. As in Figure 3 for different specimen. Flgure 2. Specimen mounted for tensile deformation experiment.
for tensile deformation as shown in Figure 2. The electrodes were formed from Hg-In amalgam, which adheres well to the surface but remains liquid down to -30 "C so that it does not interfere with the deformation. The tensile deformation was performed under creep conditions at stresses between 1 and 10 MN m-2 in an electrically screened enclosure inside a temperature controlled chamber. The currents were measured with a Keithley Model 610C electrometer. For a correct measurement of current the input impedance of the electrometer has to be much less than the impedance of the specimen;14this limits the experiments to temperatures below -15 "C, because above this temperature the surface conductivity of the sample bypasses the electrometer. Most measurements were made at -20 "C at which temperature the dc resistance of the sample corresponded to a confl-l m-l. During deforductivity of 5 X to 5 X mation the current between the electrodes and the change in the length of the specimen were recorded continuously on a two-pen recorder.
Results A typical recording is shown in Figure 3. It will be seen that even with no load applied there is a current Io of the order of a few picoamperes. I t corresponds to an emf of about 10 mV, the origin of which is unclear but is likely to be some electrochemical process in the ice-electrode system. This current differed in magnitude and sign from one specimen to another and was observed to decrease gradually with a time constant of the order of 1h at -20 "C. The stress is applied and deformation commences at (14)Yu. A. Osip'yan and V. F. Petrenko, Dokl. Acad. N a u k SSSR, 226,803 (1976) (Sou. Phys. Dokl., 21,87 (1976)).
TABLE I specimen d, expt no. mm no. 71
66
809 810
3
3
3 2
stress, I,, temp, MN bm "C m-z min-'
AI,
lo3.
pA
(sale)
11 12 12
1.1 1.05 0.95
1.8 1.6 1.4
1 2 3
-20 -20 -20
4 5 6 7-8 2 6 7
After 1 2 h -20 6.2 62 -20 6.2 90 -20 6.2 112 -40 6.2 15 -20 3.3 14 -20 5.0 65 -20 5.0 75
0.5 0.5 1.0 0.065 1.0 1.2 2.1
0.1 5 0.10 0.14 0.08 1.3 0.3 5 0.50
After 12 h -20 3.3 -20 3.3 -20 2.8 6.8 -20
2.3 1.7 5.0 3.0
0.94 0.58 2.6 1.8
11 12 1 1
2.8 2.8 2.8
44 52 35 45
the point marked 1, and it can be seen that this leads to a change A I in the current I. The sign of A I is always correlated with the sense of the bending of the specimen in such a way that the dislocations appear to carry a positive charge. Figure 4 shows the results for a different specimen in which the sign of Io is opposite to A I and the deformation produces a reversal of the total current. Before interpreting AZ as a dislocation current it is necessary to check that it does not result from a change in the resistance of the specimen caused by the deformation.15 This was done by applying an external constant voltage source of 1-100 V and observing that the current so produced was not significantly influenced by starting (15) G. Noll,
J. Glaciol., 21, 277 (1978).
4024
The Journal of Physical Chemistty, Vol. 87,No. 21, 1983
or stopping the plastic deformation. In Figure 3 it will be noticed that there is some creep after the removal of the load and also that the current does not change abruptly on loading or unloading. These effects result from friction in the testing system; when the friction was reduced as in the case of Figure 4 the behavior was more like that expected. All values of Al were taken after such transients were over. The results for the most reliable experiments are given in Table I which shows values for Al and the corresponding rates of change of length I From these results the charge per unit length q of straiggt dislocations emerging parallel to the electrodes can be calculated from the equation16
where b, is the component of the Burgers vector along the length of the specimen and d is the width of the electrodes measured perpendicular to the plane of Figures 1 and 2. Because the directions of the a axes are not known the value of b, is uncertain by a factor of between 1 and cos 30°; for simplicity b, is always taken to be a l d 2 . The dislocation charge may be expressed in the dimensionless form q a l e , and for each measurement it is expressed in this way in the last column of Table I. In all cases the sign of the dislocation charge was positive.
Discussion For the four specimens shown the values of q calculated from the first few periods of tensile deformation (expt no. 1, 2, and 3 ) are similar in magnitude. At higher deformations the values for q appear to decrease, which is expected because the tensile deformation introduces dislocations of both mechanical signs and eq 1 ceases to be valid. These experiments therefore indicate that the charge transported by the dislocation is of the order of +2 X 10-3e/a. This value will be a lower limit because we have used blocking electrodes so that the charge flow within the (16) A. V. ZaretakE, Yu. A. Osip'yan, V. F. Petrenko, and G. K. Strukova, Fit. Tverd. Tela, 19, 418 (1977) (Sou. Phys. Solid State, 19, 240 (1977)).
Petrenko and Whitworth
ice will produce a polarization at the surface and the full current may not be recorded by the electrometer. The charge transported may not represent the actual charge at the core of the dislocation because of the possible effects of screening by mobile point defects. The dislocations will be surrounded by a Debye-Huckel charge cloud involving both Bjerrum defects and ions, and any motion of this cloud that contributes to the current requires the movement of both kinds of defect. The screening radius appropriate to this problem is therefore that determined by the minority carriers which are the ions. When estimates based on other experiments on similar specimens1' are used, this radius is of the order of 50 pm, which may be compared with the average spacing of the dislocations introduced by bending which is about 5 pm. The dislocations are not therefore expected to have individually identifiable screening clouds and the effect of screening on the results should be small. The dislocation charge estimated here is less than the lower limit of Itagaki'b and comparable with the upper limit set by Joncich et ale9A possible difficulty with the latter experiment is that when static fields are applied to the ice the current that flows will produce polarization at the blocking electrodes so that the electric field acting on the dislocations is less than that envisaged in the paper; it is true that the authors note a decay of current with time and therefore only apply the field for periods of 30 s, but they will be observing surface conduction and polarization in the interior may build up faster than this. Similar difficulties may be expected to apply in the experiment by Itagaki where the frequency of the electric field was sometimes as low as 0.03 Hz. Acknowledgment. These experiments were performed while V. F. Petrenko was working at the University of Birmingham with support from the Nuffield Fellowship funds. We are grateful to Dr. J. W. Glen for valuable discussions. Registry No. Water, 7732-18-5. (17) V. F. Petrenko, R. W. Whitworth, and J. W. Glen, Phil. Mag., in press.
