Jouma/ oIG/aci%g)', Vol. 20, No. 84, 1978

A DIRECT DETERMINATION OF THE ELECTRICAL CHARGE ON

AN UPPER LIMIT DISLOCATIONS IN

By D . M. JONC ICH

FOR ICE*

(D epartment of Physics and Materials Research Laboratory, University of Illino is at UI-bana- Champaign, Urbana, Illino is 6180 1, U.S.A. )

J. H OLDER ,

(D epartment of G eology and Materials Research Laboratory, Un iversity of Illin ois at Urbana- Champaign , Urbana, Illinois 6 1801, U.S.A. )

and A. V. GRANATO

(D epartment of Physics and Materials Research Laboratory, University of Illin o is a t U I-bana- Champaign , U rbana, Illinois 61801 , U .S .A. )

ABSTRACT. A d irect determination of the upper li m it fo r the electri c cha rge d ensity a long dislocations in ice has been ca rri ed out by measuring the simulta neous e fTects of an electric fi eld and a mecha nica l stress on the movement of a low-a ngle tilt boundary in an ice single crys ta l. The dete rminat ion is ind epend ent of the geomet ry of the dislocat ions o r the distribution of the ch a rge a long them. No measurable e fTeels of the electri c field on boundary motion were found, requiring that the charge d ensity be less tha n o nc uni t of ch a rge for every 300 atomic lengths of dislocat ion. This es tima te is less than la rge previous es tim a tes, but is consistent with smaller proposed values.

RESUME. Une determination directe de la limite slI/Jerieure de la charge ilectriqlle des dislocatioll s dalls la .I:lace . Pour dew'miner directement la li mite superieurc de la cha rge e lectrique le long d es dislocations d e la g lace, o n a mesure les e fTe ts simul tanes d' u n champ electrique e t d ' une contra inte m eca niquc sur le Illouvelllcnt d 'une face de fa ible inclina ison da ns un m onocrista l de g lace. La mesurc ne d e pend pas de la geomet ri c des dislocations ni de la distribution des ch a rges elect riqucs le lo ng d'ell cs. On n'a p as troll\'e d 'e fTet m esurable du champ electrique sur le mouvemcnt d e la face lant que la cha rge eta it inferi eure a unc unite pour 300 longueurs de d islocation . Cettc cstin1ation est infericurc a ux {'o n es ,·a lcurs avancccs antericurc rncn t, n1ais corrobore des eva luations proposees plus faibl es .

ZUSAMM EN FASSUNO. Eille direkte Beslimrl1lll1g de,. oberell Gre/l ze J;ir die eleklrische Ladling all Verset':lIllgell in Eis. D ie obere Grenze filr die c1ektrisch e L ad ungsd ichte ent lang von Versetzunge n in Eis wurde durch die g leichze itige M essung der Wirkungen eines e1ektrischen F eldes und einer m echa ni schen Spannung auf die Bewegung e iner schwach geneigten GrenzAiichc in e inem Eis-Einkrista ll dirckt bestilllmL. Die Bestimmung ist una bha ngig von der Geometri c dcr Vcrsetzungen oder vo n der Lad ungs"e rt e ilung lii ngs dieser Versetzungen. Es ergaben sich ke ine mcssbarcn EfTe kte des e1ektrischen Fcldes auf die Bewegung der GrenzAa che, sofern die Lad ungsdi chte ger ingcr a ls eine Lad ungseinheit fil r j e 300 a toma re \ ·c rsc t7.ungs­einheiten war. Dicse Schatzung liegt un te r den hbheren VVe rLe n, d ie frLih er vo ra usgcsetz t wurd en, stimmt j cdoch mit den Anna hmen kleincrer VVertc ilbc rein .

:\ NUMBER of prev io us studies have suggested tha t dis locations in ice are electri ca ll y c ha rged (Brill a nd Ca mp, 1957; l tagaki, 1970, 1978; M ae a nd Higas hi , 1973; No li , (973). Unfortuna tel y, there has been no d efinite ex perimenta l determination of this cha rge. T he previous studi es we re indirec t mea surements of the d islocation cha rge, and the res ulting va lues estima ted fo r the charge d ensity range over seve ra l orders o f magnitude. Brill a nd Camp (1957), Noli ( 1973), and Mae a nd Higashi (1973) reported small but obse rva ble cha nges in the low-frequency (space-c ha rge) region of the dielectric constant for p last ica ll y­d eformed sample. T hey associa ted this phenomeno n with a dislocatio n charge on the order of one uni t or less o f c ha rge per 106 atomic lengths of d islocation . On the other ha nd , I tagaki (unpub lished) reported la rge changes in the di elec tric constants of sam ples with deform a tion. H e interprets his X-ray topographic observa tions (Itagaki , 1970) of dislocations in samples ac ted upon by a n applied a.c. elec tr ic fi eld (60 H z) in te rms ofa cha rge density of one uni t of cha rge per 10- 102 atomic dislocation lengths.

* T his research was supported in part by the Na tiona l Sc ie nce Foundat ion und er contract DMR- 76-0 1058 a nd DMR-77-'0556 .

54~

544 JOURNAL OF GLACIOLOGY

The purpose of the present note is to report a direct determination of an upper limit for the charge density of edge dislocations in ice. The determination is based on the observation of the motion of a low-angle tilt boundary, made up of an array of parallel, edge dislocations, under the influence of both an applied mechanical stress cr and an electric field E. For every dislocation segment in the boundary the mechanical force per unit length is bcr, where b is the Burgers' vector, and the electrical force per unit length is AE, where A is the charge per unit length. For the particular values of cr and E for which the observed displacements (or velocity) of the boundary are equal, the magnitude of the charge per unit length is given entirely in terms of those val ues

.\ = bcr/E.

This determination is independent of the nature of the dislocation geometry and of any assumptions about the distribution of the charge along the dislocation.

The single-crystal specimens used in the study were grown by a zone-refining process. The apparatus is similar to that described by Ramseier (unpublished), and is described elsewhere (Joncich, unpublished, p. 52- 53). Individual samples measuring 2 X I X I cm3

were cut from the 7 cm diameter ingot with a hot-wire saw, and were oriented (to within about 2°) using crossed polarizers. The c-axis lay parallel to one of the 1 cm directions.

A low-angle tilt boundary of approximately 3° was introduced into the specimen by applying a 2 kg mass near to the center of the specimen, in a three-point bending jig, for about 24 h. The specimen temperature during all the tests was approximately -15°C.

The sample was then mounted as shown in Figure 1. The two metal plates were frozen to the two 1 X 1 cm2 faces of the sample. A mechanical stress was applied by applying a mass M on the right-hand metal plate, and a electrical field was applied between the two electrodes. The left-hand brass plate was rigidly fixed, while the right-hand copper plate was free to move. The displacement of the wall could be monitored optically for rough measurements (> 0.01 mm), or alternatively the vertical displacement of the right-hand electrode could be measured. For a given displacement d of the wall, the vertical displacement of the right-hand plate is xd tan (J, where (J is the tilt-angle boundary. The vertical displacements were measured with a Statham displacement gauge (model UC3) used with a PAR model ]B-S lock-in amplifier. The output of the amplifier was displayed on a strip-chart recorder, and the system was calibrated over a range of 0.2 mm using a micrometer screw gauge. The sample

C-AXIS ~ M

DISPLACEMENT GAUGE

Fig. I. Sample configuration for measurements of the effects of electric and mechanical forces on a low-angle tilt boundary. The left-hand plate is brass and the right-hand plate is copper.

DETERMINATION OF DISLOCATION CHARGE 545

a nd jig were placed within a chamber inside which the temperature was maintained a t - 15 QC to within I deg during the m easurements.

For the measurements the tilt boundary was first moved with a m echanical stress . Then, with the mechanical stress still applied, an electric potential difference of 3 250 V was applied between the two metal plates .

This electric field could not be maintained indefinitely, but decayed with a time constant of about five minutes . This decay results from the build-up of space c ha rge at the non-ohmic contacts with the electrodes; this value of the time constant is in agreement with previous m easurements (Engelhardt and o thers, 1969). H ence, for the present measurements , the electric potential was switched be tween 0 and ± 3 250 V with a period of about 30 s. The resulting electric field in the sample was then either 0 or at least 1 500 V /cm.

The results for one of the severa l measurements a re shown in Figure 2. The stress of 0.2 bar was applied at time t = o. After an initia l transient period of a bout 30 s the wall velocity is consta nt, at 0.24 mm/h , in agreement with the observations of Higashi a nd Sakai ( 1961 ).

0.5

z 0.4 o Cl: u ~ • 0.3 >-

~ 02 ~ ~O'~

o

FIELD OFF

0.5 1.0 1.5 2.0

TI ME --+- MINU TES

Fig. 2 . Measured vertical displacement DJ the elld DJ the sample as aJlIllctioll DJ time, with {J cOllstant mechallical stress oJ O. 2 bar alld the indicated periodic electric fields.

The electric potential was switc hed between 0 a nd ± 3 250 V at the times indicated. In no case was there any observable change in velocity, so only a n upper limi t for the cha rge d ensity can be es timated from the results. As noted , the field inside the sample should be at least 1 500 V /cm during the brief cycles (local field corrections would increase this qua ntity), a nd a conservative es timate for the resolu tion of the velocity is ± 2% . From Equation ( I), the cha rge density of the edge disloca tions must be less than

0.02 (bcr /E ) = 7 X 10- 4 e/A.

This corresponds to only about one unit of cha rge for every 300 atomic lengths of dislocation. The dislocations in the tilt boundary are of the same sign so that this charge density limit should apply directl y to the edge dislocations in the boundary.

The edge dislocation charge density is much less tha n the upper limit proposed by Itagaki ( 1970), but is consistent with the values es timated by Higashi a nd Sakai (196 1) fo r screw dislocations. In fact, the edge di slocations could be expected to have the grea test charge d ensity because they have the largest number of da ngling bonds per unit length (Osipiyan a nd Smirnova, 1968) .

JOURNAL OF GLACIOLOGY

In summary, the present results indicate that dislocations in ice are not heavily charged elec trically, so that any charge present is probably associated with a small number of ionic defects distribu ted a long the dislocation (Mae and Higashi, 1973) rather than a la rge intrinsic charge associated with each dangling bond at the di slocation core. Further, the results suggest that the large dielectric relaxation peak in ice (Schiller, 1958) is not the result of charged dislocation motion.

ACKNOWLEDGEMENT

The authors are indebted to Dr K. ltagaki of the U .S. Army Cold R egions R esearch and Engineering Laboratory for his advice concerning the apparatus for the growth and prepara­tion of the ice samples.

MS. received 9 November 1977 and in TevisedfoTm 15 FebTu01Y 1978

REFERENCES

Bri ll , R., and Camp, P. '957. Influence of pressure on the dielectric properties of ice. Nature, Vo!. 179, No. 4560, p. 623-24.

Engelha rdt, H ., and others. 1969. Protonie conduction of ice. Pa l·t II: low temperature region, [by] H. Engelhardt, B. Bullemer, N. Rieh!. (In Riehl , N., and others, ed. Physics of ice: proceedings of the international symposium 011

physics of ice, Munich, c ermGlry, September 9 - I4 , [968. Edited by N. Rieh!, B. Bullemer, H. Ellgel/lardt. New York, Plenum Press, p. 430- 42. )

Higashi, A. , and Sakai, N. 196 1. Movement of small a ngle boundary of ice. JouTllal of the Faculty of Science, Hokkaido University, Ser. 2, Vo!. 5, No. 5, p. 221-37.

Itaga ki , K . 1970. X-ray topograph ic study of vibrating dislocations in ice und er a n AC electric fi eld . Advances ill X -Ray Analysis, Vo!. 13, p. 526- 38.

Itagaki, K. '978. Dielectric proper ties of dislocation-free ice . .Journal of claciology, Vo!. 21 , No. 85, p. 207- 17. Joncich, D. M. Unpublished. The p lastic behavi or of predeforrned ice crystals. [Ph.D. thes is, University of

Illinois, 1976.] Mae, S., and Higashi, A. ' 973. Effects of p last ic deformat ion on the dielectric properties of ice. C(ystal Lattice

Difects, Vo!. 4, No. 4, p. 295- 308. NolI , G. 1973. Influence of plasti c deformation on the electrical properties of ice Ih single crystals. (In Whalley,

E., and others, ed. Physics and chemistry of ice: papers presellted at the Symposium on the Plrysics and Chemist~v of Ice, held in Ottawa, Canada, [4- 18 August [972. Edited by E. Whalley, S. J . J ones, L. W. Cold. Ottawa, Royal Society of Canada, p. 350- 55. )

Osip iya n, Yu. A., and Smirnova, 1. S. 1968. Perfect dis locations in the wurtzite lattice. Plrysica Status Solidi, Vo!. 30, No. I , p. 19- 29.

R amseier, R. O. Unpublished. Growth and mechanical properties of river and lake ice. [Ph.D. thes is, Universite Laval, Quebec, '971.]

Schi ller, P. 1958. Die mechanische R elaxation in rei nen Eiseinkristallen. Zeitsclzrift fi,r Physik, Bd. ' 53, Ht. I,

p. 1- 15·