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PROPRIÉTÉS DES DISLOCATIONS CHARGÉESTHE STUDY OF DISLOCATION - POINT DEFECT
INTERACTIONS BY THE MEASUREMENT OF CHARGES ON DISLOCATIONS
R. Whitworth
To cite this version:
R. Whitworth. PROPRIÉTÉS DES DISLOCATIONS CHARGÉESTHE STUDY OF DISLO- CATION - POINT DEFECT INTERACTIONS BY THE MEASUREMENT OF CHARGES ON DISLOCATIONS. Journal de Physique Colloques, 1973, 34 (C9), pp.C9-243-C9-246.
�10.1051/jphyscol:1973942�. �jpa-00215417�
PROPRIE TES DES DISL OCA TIONS CHA RGEES
THE STUDY OF DISLOCATION - POINT DEFECT
INTERACTIONS BY THE MEASUREMENT OF CHARGES ON DISLOCATIONS
R. W. WHITWORTH
D e p a r t m e n t o f Physics, University o f B i r m i n g h a m , E n g l a n d
R6sumk. - Les defauts sur les dislocations-coin sont principalement des crans et des lacunes lies, les deux pouvant Etre charges. Pour des dislocations fraichement introduites dans NaCl a la temperature ambiante, les defauts predominants sont des lacunes cationiques likes. L a charge sur ces dislocations a ete determinee et apporte une mesure de la concentration des lacunes dans le cceur. Cette concentration depend du mouvement antkrieur des dislocations, et en utilisant des cristaux avec des concentrations en defauts ponctuels bien connues, il a Cte niontre que les dis- locations accumulent non seulement les lacunes libres niais aussi les lacunes liees aux irnpuretks.
Une saturation de charge est atteinte pour environ une lacune pour deux sites sur le caeur.
Ces charges sont determinees par des considtrations cinetiques. L'etablissement de l'kquilibre thermodynamique ntcessite une diffusion qui conduit a un changement dans la charge, la forma- tion d'une atmosphere chargee conipensatrice et peut-6tre l'ancrage du ccrur par les impuretb.
Les theories de l'equilibre des charges doivent tenir conipte de la maniere dont est distribute la charge sur le cceur. Les observations de la teniperature isoClectrique fournissent une source d'informations sur les conditions d'equilibre au cceur de la dislocation.
Abstract. - Defects on edge dislocations are principally jogs and bound vacancies, both of which may be charged. F o r freshly introduced dislocations in NaCl a t room temperature the only significant defects are bound cation vacancies. The charge on such dislocations has been deter- mined and provides a measure of the concentration of vacancies on the core. This concentration depends o n the previous Inovenlent of the dislocations, and by using crystals with known point defect concentrations it has been shown that dislocations sweep up not only free vacancies but also vacancies bound to impurities. A saturation charge is reached a t about one vacancy per two sites o n the core.
These charges are determined by kinetic considerations. The establishment of thermal equili- brium requires diffusion which leads to a change in the charge, the formation of a compensating charge cloud, and possibly the pinning of the core by impurities. Theories of the equilibrium charge have t o take account of the way the charge is accomnlodated o n the core. Observations of the isoelectric temperature provide a source of information about the equilibrium conditions a t the dislocation core.
1. Introduction. - H o w m u c h d o we k n o w a b o u t t h e n a t u r e o f t h e c o r e o f a n edge dislocation ? I s t h e end of the e x t r a half plane straight o r jogged, a n d if jogged w h a t kind of jogs a r e present a n d in what n u m b e r s ? H o w m a n y point defects a r e there o n t h e dislocation core, a n d c a n they glide with t h e disloca- tion or d o t h e y a c t as pinning points ? T h e s e questions a r e very h a r d t o a n s w e r espel-imentally. Microscopes c a n n o t resolve such details, a n d i n f o r m a t i o l ~ f r o m t e c l ~ n i q u e s like internal friction relies t o n considerable extent o n t h e models used in its interpretation.
In i o n i c crystals s o m e steps can b e taken t o w a r d s solving s u c h problems by mc:isuring the electric charge t r a n s p o r t e d by :I movinf d i s l o c a ~ i o n . A perfectly straight < 110 > j 110 j e d f e ciislocntion in the N a C l s t r u c t ~ l r e 112s c q ~ ~ a l ni11iiber5 of' ions o f each sign a l o n g its core. But a scal dislocation will u s ~ ~ a l l y have a n excess 01' iona 01' o n c sign o n its core, giving it a net c h a r g e . T h i s is illustrntecl in figure 1 , which shows s o m e of t h e d e f t c i s that c a n be prescnt o n the dislocation core. T h c half-jog H has a charge - J c
o o ~ ~ ~ ~ 3 ~ ~ o o o o ~ o , . . . . . . .
:- .,?', '-: .. ..+'. . ;:, .,+, -; .+ ,:-, :2, <:., . -.
~ ... .. .., - - - - ... :.+: tj-:
m o o 3 9 4 r,, 3 @ I ~ ' B .: 'i. - + -. - - - -
' I F
* fi ,3 V-@-'Z>5L + [ooi]
FIG. 1. - Diagram in (110) plane of end of extra half-plane of edge dislocation of Burgers vector + a [110]. Solid circles represent ions in the plane of the paper and broken circles represent ions a distance ) h above and below the paper. The half-plane ends at the dislocation line AB, and contains a full-jog F, a half-jog H, and a bound cation vacancy V 1121.
a n d t h e vacancy at a cation site o n the c o r e V h a s a charge - c : t h e full-jog F is uncharged. A s t h e structure consists o f r o w s of ions o f t h e s a m e sign perpendicular t o t h e plane of' t h e d i a g r a m , these defects maintain their charge \+hell t h e dislocation glides, a n d their charge is tliercl'ore t r a n s p o r t e d with the dislocation. J o g s o n a screw dislocation c a n be
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1973942
charged, but this charge cannot be transported in the direction of glide of the dislocation, and it is therefore difficult to detect experimentally.
When a crystal is deformed primarily on one slip system at a relatively low temperature dislocation loops will expand on their slip planes, and the resulting dislocations will become jogged only by a small number of intersections with other dislocations and by occasional cross glide. There is negligible anion diffu- sion so that the anion sub-lattice can be taken as defining the position of the end of the extra half-plane.
There are, however, cation vacancies present, and cation sites on the core may be occupied or vacant, leading to a net dislocation charge.
This paper first reviews some measurements of vacancy concentrations on edge dislocations in NaCI, and then proceeds t o consider the nature and applica- bility of theories of thermal equilibrium charges.
2. Measurements of charge on edge dislocations in NaCl at room temperature. - Of the many kinds of experiment performed to observe the effects of charges on dislocations the most fruitful have been those based on a technique developed by Remaut and Vennik [I] and illustrated in figure 2. A crystal is
FIG. 2. - Movement of excess dislocations in a bent crystal under tensile and compressive stresses along its length.
bent to introduce an excess of dislocations of one mechanical sign, and a small cyclic stress is then applied along its length. This moves the dislocations as indicated and gives rise to an electric polarization perpendicular to the stress, which can be detected as a pd between electrodes on tlie surfaces. It has been shown [2] that near the neutral filament of a bent crystal a large majority of tlie dislocations are of tlie types shown in figure 2, and by ~rsing a specimen cut from the centre of a bent crystal it has been possible t o convert Remaut and Vennik's idea into a quantita- tive measurement of charge [ 3 ] . Figures 30 and 12
FIG. 3. - 0)-b) Typical loops of strain E and pd between the electrodes as functions of stress in cyclic tests on a nominally pure crystal of NaCl (N 92 with - 0.24 ppm excess divalent cations) and on a crystal doped with 14 mole ppm M n b + (NM 94) [5]. The elastic contribution to the strain is shown as the tangent to the lower pol.tion of the loops 0). c ) V as defined in loops b ) as function of the plastic strain c,, for these
pairs of loops.
show examples of loops indicating how tlie strain and the pd between the electrodes vary witli stress during cycling, and figure 3c shows that the pd varies linearly witli the plastic contribution to tlie strain. From the slope of this graph it is possible to determine the charge q per unit length of dislocation line tliougli the result is liable to error by a constant factor 11 2: 1 to 1.5 due to the presence of dislocations of the unwant- ed type.
The converse, and more difficult, experiment has been performed [4] in which a large pd was applied across the electrodes and a small change in length of the specimen was detected. This experiment gave values of the charge consistent with those obtained in the same specimen Sroni the polarization under a n applied stress.
Tn all these experiments the stress was less than the macroscopic flow stress, but it was large enough to move tlie dislocations over appreciable distnnccs, a n d i n this process (1 was observed to change. Figure 4 shows as a n exaniple a series of results on a specimen doped witli 14 ppm oS M n + + . much of which was
present as impurity-vacancy pain [ 5 ] . The charge was negative, and its ~nagnitude increased witli the plastic strain amplitude c, until it saturated at a value of about one vacancy per two cation sites along the core.
On standing tlie charge decreased, but i t could be increased again by further cycling at high amplitudes,
The observed charges are most readily explained by tlie sweeping up of vacancies lying on tlie slip plane.
T H E STUDY OF DISLOCATION - POINT DEFECT INTERACTIONS C9-245
FIG. 4. - Results of experiment to measure dislocation charge in Mni+-doped crystal ( N M 94) a t room temperature [5].
The graphs show the charge q (in units of el(/) divided by a n unknown constant 11 z I to 1.5. Observatioiis were made in the order 1, 2, 3, ... Measurements i n graphs b) to e ) were made
at times I after the group (1).
In tlie specimen of figure 4. tlie concentration of free vacancies was deduced from ionic conductivity measu- rements to be of tlie order of 1.7 x l o u 8 , and for
E , ~ = 2 x tlie dislocations move distances of about 2.5 x lo4 Burgers vectors. On average each site on tlie dislocation will therefore encounter 4 x free vacancies, and sweeping these up could not give tlie observed cliarge. However: each site will encounter of tlie order of 0.2 vac:incies bound to impurity ions, and tlie dislocation must sweep up many of these vacancies to acquire its charge.
The high charges swept u p involve a large electro- static cnergy, so that they cannot possibly be in thermal equilibrium. TIic fact that such cliarges are observed shows that thc process of sweep up depends on short range forccs and is comparatively unin- fluenced by the amount of cliargc else\vllere 011 the dislocation. Hoivevel-. the clinrgc \\~liicli a dislocation can transport seems to reach a niasimum at about one vacancy per two sitcs. and this suggests t l i ; ~ t ;I dislo- cation cnnnot transport vacancies on two adjacent sites. A possible cxplanatiori of this is given in [ 5 ] .
When a highly charged dislocation is left at rest in the crystal i t loses some of its charge by thc ciifTusion of vacancies OH' its core to lo\vcr the electrost:itic energy. The tott~l cncrgy \vill also be lo\vered by ionic conduction in rhe clcctr-ic field aro~incl thc dislocation to set up a cornpensating sp:icc charge tirour!cl i t .
3. Thermal equilibrium theories. - In the absence of anion diffusion dislocations such as we have been considering can come into equilibrium with the rest of the crystal only by the migration of cation vacancies.
N o jogs are formed in such a process, and the equili- brium concentration f of cation vacancies o n the core will be given approximately by
f
.- = z e x p , , ; f ( g + , , I 1
- E ) ) d M
1 - 1
where rw is the concentration of free cation vacancies in distant parts of the crystal, g,, is the freeenergy of binding of a cation vacancy to a core site and aE/dM is the increase in the electrostatic energy of the whole system resulting from the addition of one vacancy to the core [6], [7]. The charge cloud satisfies the Debye- Hiickel equation, and in NaCl at room temperature has a radius of a few hundred lattice spacings.
When impurity cations are mobile they may diffuse t o the dislocation core, but they cannot move with the dislocation as it glides. They will modify the net charge, but their charge will not be detected in an experiment which involves moving the dislocation.
They act as pinning points and their accumulation on the core can be studied in internal friction expe- riments [8].
At higher temperatures anions can also migrate ; the dislocation will become jogged and may also Iiave anion vacancies on its core. All these defects must come into equilibrium with the point defects in the crystal. Tlie theory becomes somewhat compli- cated [9]. and two limiting approximations have been developed. The well known theory of Eshelby, Newey, Pratt and Lidiard [lo] makes an (( infinite source/sink approximation )). in wliich i t is in effect assumed that a vacancy is f'ornied by reversing the sign of a jog (adding a cation to H in Fig. I ) and that tlie supply of jogs is unlimited. Tlie latter assumption is clearly not correct except at very lo\v cliarge densities ; the equilibrium nuniber ofjogs on the core and tlie entropy of distributing tlie charge amongst them has to be taken into account in ciilculating the equilibrium charge [7]. [9]. At tlie other eutreme a theory based on the work of Lifsliitz and Geguzin [I I] would ignore tlie jogs and consider only bound vacancies on tlie core with d i f i r e n t binding cnergies for anion and cation vacancies.
In both of these theories the dislocation will be negatively charged at temperatures well into the extrinsic region, because some of the excess cation vacancies will condense onto thc core. But at higher temperatures the sign of the cliarge may be reversed, for. il' tlie energy to crei~te 21 cation vacancy at a jog is Ie\s th:in that to creatc a n anion vacancy, o r if the binding energy of cation v:ic;incies io tlie core is less than t l i z i t of' anion v;icnncies, the dislocation will becomc positively charged. The temperature at which
C9-246 R. W. WHITWORTH the charge reverses sign is known as an isoelectric
temperature.
In figure 5 are collected the results of all experiments on NaCl purporting to have observed this isoelectric temperature. They are very scattered, but even if they presented a consistent set of facts we would still have the problem of whether to interpret them in terms of jogs or bound vacancies or both. This is a subject well worthy of careful experimental attention, for it is one of the only measurements in physics which leads fairly directly to information about the equilibrium structure of the dislocation core.
But there is a difficulty in attempting to measure dislocation charges at these temperatures, and it also limits the range of materials on which such experiments can be performed. It is that ionic or other types of electrical conductivity of the material will tend to cancel any electrical signals generated by the motion of dislocations. In NaCl with 3 ppm of impurity at 480OC the time constant for the decay of such a signal is about 4 11s. T o obtain reasonable signals the dislocations must be moved in times comparable with o r shorter than this. It is not a trivial matter to extend techniques developed at room temperature into this interesting region.
FIG. 5. - Observations of isoelectric temperatures Ti in NaCl crystals with free cationvacancyconcentrations a. o Davidge [13], V Spencer and Plint [14], A Kliewer and Koehler [I51 (from elastic modulus anomaly), SB Strumane and de Batist [16].
An observation by Schwensfeir and Elbaum [I71 lies in the intrinsic range and cannot be included in this graph.
References [ l ] REMAUT, G. and VENNIK, J., Phil. Mag. 6 (1961) 1.
[2] WHITWORTH, R. W., Phil. Mag. 10 (1964) 801.
[3] WHITWORTH, R. W., Phil. Mag. 15 (1967) 305.
[4] TURNER, R. M. and WHITWORTH, R. W., Phil. Mag.
IS (1968) 531.
[5] HUDDART, A. and WHITWORTH, R. W., Phil. Mag. 27 (1973) 107.
[6] BASSANI, F. and THOMSON, R., PItys. Rev. 102 (1956) 1264.
171 WHITWORTH, R. W., Pltys. Stat. Sol. ( 6 ) 54 (1972) 537.
[8] PHILLIPS, D. C. and PRATT, P. L., Phil. Mag. 21 (1970) 217.
[9] WHITWORTH, R. W., Phil. Mag. 17 (1968) 1207.
[lo] ESHELBY, J. D., NEWEY, C. W. A., PRATT, P. L. and LIDIARD, A. B., Phil. Mag. 3 (1958) 75.
[ I I ] LIFSHITZ, I. M. and GECUZIN, Ya. E., Fir. Tverd. Tela 7 (1965) 62.
[I?] WHITWORTH, R. W., Phil. Mag. 11 (1965) 83.
[I31 DAVIDCE, R. W., Phys. Stat. Sol. 3 (1963) 1851.
1141 SPENCER, 0. S. and PLINT, C. A., J. Appl. Phys. 40 (1969) 168.
[IS] KLIEWER, K. L. and KOEHLER, J. S., Phys. Rev. 157 (1967) 685.
[I61 STRUMANE, R. and DE BATIST, R., Phys. Stal. Sol. 6 (1964) 817.
[I71 SCHWENSFEIR, R. J. and ELBAUM, C., J. Phys. & C h e ~ ~ t . Solids 28 (1967) 597.
DISCUSSION P. HAASEN. - It appears to be useful to compare
the charged and screened dislocation in an ionic crys- tal with that in a se~niconductor (see Labusch and Schroter, Plij*s. Stat. Sol. (1971)).
R. W. WHITWORTH. - The theory in reference [7]
is developed in a sufficiently general way to apply t o semiconductors if the electronic charges on the core are in localised states. However the evidence is that the electron states in a semiconductor form a degenerate band, and the detailed the or^ of this pro- blem has not yet been worked out.
H. L. FOTEIMK. - YOU mentioned that at lo~v temperatures dislocations sweep vacancies from irnpu- rity-vacancy dipoles or impurity-vacancy aggregates.
What sort of interaction takes place during the sweep- ing process ? Is it something like dislocation -impu- rity-vacancy-dipole (aggregate) cutting mechanism ?
R . W. WHITWORTH. - I think this is probably so.
F. GRANZER. - Due to atomistic calculations of core configurations around straight dislocations and dislocation jogs the exact potential distribution in these regions \+rill be available in the near future, allo\+zing the calculations of binding energies bet~vecn vacancies and dislocations to a light degree of appro- ximation. I n such calculations the relasation of thc ionic configuration after the incorpor~ition of the
\.acancy or the i~i~purity-\.~lcanc\l-:issociatc will he taken into account.
