Overview No. 6

OVERVIEW

NO. 6 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQP

INTERACTION BETWEEN AND DISLOCATIONS T. E. MITCHELL, Department

of Metallurgy

POINT DEFECTS IN OXIDES

L. W. HOBBS and A. H. HEUER

and Materials Science. Case Western Cleveland, OH 44106, U.S.A.

Reserve

University,

and

J. CASTAING, Laboratoire

de Physique

(Rewired

J. CADOZ

and J. PHILIBERT

des Materiaux, Centre National de la Recherche Bellevue, 92190 Meudon, France

Scientifique,

zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA 1979: in rerisedforni 13 April 1979)

23 Junuory

Abstract-The results and conclusions are presented of a Workshop entitled “The Interaction between Point Defects and Dislocations in Oxide Single Crystals”. held at Bellevue in June 1978. The central questions concerning point defects deal with experimental measurements and theoretical calculations of concentrations and mobilities of various species, the role of charge-compensating defects in the presence of aleovalent solutes, and the importance of extended defect arrays either as defect clusters or crystallographic shear planes. As far as dislocation behavior is concerned, there is an impressive amount of information available on the relationship between crystal plasticity and crystal structure of oxides: yielding, work hardening and recovery have been investigated, as have slip systems, dislocation core structures, dislocation dissociations and dislocation interactions. Questions remain as to the relationship of crystal structure and ionicity to the Peierls stress, and the role of climb and climb dissociation in a particular oxide to plasticity at high temperatures, Finally, the interaction of point defects and dislocations in oxides is discussed with respect to climb. solution hardening and the influence of non-stoichiometry.

Rkwmk-Nous presentons les resultats et les conclusions d’un atelier intitule ‘Les interactions entre defauts ponctuels et dislocations dans les oxydes’, qui s’est tenu en juin 1978 a Bellevue. Les questions principales concernent les mesures experimentales et les calculs theoriques des concentrations et des mobilites des divers defauts ponctuels, le role des difauts compensant la charge en presence de solutes aleovalents et I’importance de groupes de dtfauts etendus comme les amas et les plans de cisaillement cristallographiques. En cc qui concerne les dislocations, une quantite impressionnante de travaux concerne la relation entre la plasticite et la structure cristalline des oxydes. Ont ainsi ete ttudies: la limite elastique, I’ecrouissage et le revenu, les systtmes de glissement, les structures de coeur des dislocations, les dissociations des dislocations et leurs interactions. Des questions restent posees sur les relations entre la structure et le caractere ionique des cristaux et la contrainte de Peierls, ainsi que sur le role de la montie et de la dissociation par montee dans la plasticite dun oxyde particulier a haute temperature. Enfin. on discute I’interaction entre defauts ponctuels et dislocations dans les oxydes. en cequi concerne la montte, le durcissement en solution et l’influence de la non-stoechiometrie.

Zusammenfassung-Ergebnisse und SchluBfolgerungen einer Arbeitstagung mit dem Titel ‘Die Wechselwirkung zwischen atomaren Defekten und Versetzungen in Oxideinkristallen’. abgehalten in Bellevue im Juni 1978, werden vorgelegt. Die zentralen, die atomaren Defekte betrefienden Fragen behandeln experimentelle Messungen und theoretische Berechnungen von Konzentration und Beweglichkeit der verschiedenen Defekttypen, die Rolle von ladungskompensierenden Defekten bei aliovalenten Verunreinigungen und die Wichtigkeit von ausgedehnten Defektanordnungen wie Anhaufungen (‘clusters’) oder kristallografische Scherebenen. Im Hinblick auf das Versetzungsverhalten liegt eine beeindruckende Informationsvielfalt fiber den Zusammenhang von Kristallplastizitat und -struktur von Oxiden vor: FlieBverhalten, Verfestigung und Erholung wurden untersucht, wie such Gleitgeometrie, Kernstruktur der Versetzung, Versetzungsaufspaltung und Versetzungswechselwirkungen. Fragen bleiben offen, was die Beziehung zwischen Kristallstruktur, Ionizitlt und Peierlsspannung und zwischen der Rolle des Kletterns, der Kletterdissoziation in einem bestimmten Oxid und dem plastischen Verhalten bei hohen Temperaturen anbetrifft. Zuletzt wird die Wechselwirkung atomarer Defekte mit Versetzungen in den Oxiden im Zusammenhang mit Klettern, Mischkristallverfestigung und dem EinRuB der Nichtstochiometrie diskutiert.

1. INTRODUCTION Ceramic oxides are important not only to the traditional ceramics and refactories industries but are in-

creasingly emerging as potentially strong, monolithic solids for structural applications at high temperature. While a great deal of effort has been expended investi-

1677 *.M 2711 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA ,-A

MITCHELL zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDC et al.: OVERVIEW NO. 6

1678

gating the fracture mechanics of these materials, relatively little attention has been focused on their plastic

flow, which can become appreciable at temperatures above half the melting point. In this regime, interaction of point defects with dislocations is especially significant. At present, however, there exists only limited understanding of the plastic deformation processes, the identity of point defects, their mobility and aggregation, or the point defect-dislocation interactions operating in this important temperature regime. In order to clarify the present state of knowledge in this area, a Workshop entitled “Interaction Between Point Defects and Dislocations in Oxides” was held in the CNRS Laboratoire de Physique des Materiaux (LPM), Bellevue, France, 6-9 June 1978. This workshop, organized by the authors, brought together scientists from approximately 10 laboratories in France, England, Germany and the United States to discuss oxide plasticity in general and particular problems including (among others) climb, nonstoichiometry and solute effects on mechanical behavior. (A list of participants and observers is included in Appendix I.) In the report to follow, no attempt is made to provide an in-depth survey of the whole field of point defects and crystal plasticity in oxides. Rather, we have selected a number of areas relating to interaction between point defects and dislocations for emphasis.

Table 1. Kroger-Vink (atomic) notation for defects in oxides Electron Hole Vacancy Vacancy on M sublattice for compound MO Vacancy on 0 sublattice for compound MOCharged vacancies Neutral vacancy Interstitial _ Charged interstitial Foreign atom L on cation substitutional site Foreign atom S on interstitial site Defect complex, e.g. bound Schottky pair Normal lattice sites

f;, V VM

v,

V’

V’ V”M, V” 0

v;: . . v; ” Mi, Oi

M:13O!13M” 01’ zyxwvutsrqponmlk iY I LM Si (V’V,) M;, 06

complete freedom to create or destroy sites upon changes in external oxygen pressure, for example. (3) Mass balance. As in any chemical reaction, mass balance is essential. (4) Electrical balance. This is also necessary and separate from site balance and mass balance. The examples given below show typical reactions using Krbger-Vink notation and the corresponding relations between equilibrium defect concentrations through the law of mass action: (a) Schottky reaction for MgO

2. POINT DEFECTS 2.1 Description For present purposes, the important point defects are vacant lattice sites, interstitial atoms or ions, and foreign atoms or ions in either interstitial or substitutional positions. There is now increasing agreement that Kroger-Vink notation [l] is most convenient, since it uses an atomic basis with no assumption about ionicity. Table 1 contains the appropriate definitions and symbols. In this notation, only the effective charge on a point defect is noted; a substitutional A13+ ion in MgO, here considered for convenience to be ionic, is written as Al,,. In such strongly ionic crystals, one must separately add electrons and holes for any reaction as most species, e.g. vacancies, are charged. The defect chemistry approach consists of treating all entities as chemical species obeying laws of massaction equilibria, subject to the following rules. (1) Site relation. In a compound M,O,, M and 0 sites must always be in the ratio a:fi, but the total number of sites may change. (2) Site creation. Subject to Rule No. 1, there is [&.I 2 (1/4)‘13exp(m t Since [Al& 3 2[Vb], ppt/3kT). Note that the concentration of magnesium vacancies is approximately determined by the heat of precipitation.

K, = [V&l [I’,].

(b) Oxygen Frenkel reaction for Y,O, o. %

0; + v,

KAF = [Ol’ ][V;]. (c) Dissolution

of small amount of CaO in ZrO,

CaO ZrO, (d) Precipitation

Ca,“, + 06 + V,.

of MgAl,O,

from A1,03-doped

MgO M&,

+ 2Al,,

+ 6,

+ 40;

=

MgAl,O‘, (ppt)

C%,I zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPO CAl~,12 =w It goes without saying that the point defect chemistry of any particular compound can be decided only by recourse to experiment; both physical and computer experiments may be necessary. In recent years, much information on point defects in oxides has been accumulated using various spectroscopic techniques, as shown in Table 2. Many of the defects listed in Table 2 have been produced by irradiation; however,

1679 MITCHELL ei zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFE al.: OVERVIEW NO. 6 Table 2. Point defects identified in oxidest Examples

Symbol

Point defect 1. Oxygen vacancies

V;; [F center]

MgO, CaO, SrO, BaO, BeO, Al,O,. tetragonal GeO, MgO, CaO. SrO, BaO, BeO. ZnO.

.

Vi [F’, E; centers]

Al,Oj, MgAi,O,, Y,AI,O,,. ThO,, TiOZ, BaTiO,. GeOzT SiOz ( VOvO...) etc. [Fz, F,, F4 centers]

MgO. CaO

(V$ Vi)’ [Schottky pair] ( Vi N,$)’[F,: ten ter]

C’aO : Mg

MgO. CaO. SrO

MgO, CaO. SrO, BeO. ZnO.

2. Cation vacancies

AI,O,, MgAI,O,. tetragonal GeO,

b%Ob)“Ck,~.,.K centers1

MgO:(Li, Na), CaO:(Li. Na, K). SrO :(Li, Na, K)

.

(N, zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA V&O,)‘, (NM V&y [V,, VJ centers] MgO :(Cr, Fe. Mn, Al)

[Oh ~~(OH-~~(OH 3. Oxygen interstitials

4. Cation interstitials

-,b]’ [ Vo,, V’a centers]

MgO. CaO, SrO. Al,O,

Oi, 0: [I’, I- centers] -. (OhO,)’ or (O;),,, [H; centers]

A&O,, ZnO

‘?(Oi)a [H center]

SrO. BaO

M, (various charge states)

AI,O,, ZnO, TiOz_,

M,; or (MO),,

A&O,

MgO, CaO

t Details of many of these defects can be found in review articles by B. Henderson and J. E. Wertz, Ado. Phys. 17, 749 (1968) and A. E. Hughes and B. Henderson, in Point Defects in Solids (edited by J. M. Crawford, Jr. and L. M. Slifkin), Vol. 1, p. 381. Plenum Press, New York (1972). A comprehensive list of defects and references will be published separately by L. W. Hobbs as “A survey of point defects and their aggregates in oxide ceramics”. J. Am. ceram. Sot. deformation has also been shown to result in generation of spectroscopically-identifiable point defects [2-lo] and it seems clear that further progress will

occur in future on both point defect and dislocation fronts as spectroscopy is increasingly combined with deformation studies. 2.2. Difision

data

The other ‘traditional’ source of information on point defects in oxides comes from diffusion measurements [ll]. In alkali halide crystals, the combination of diffusion and ionic conductivity measurements has been effective in providing detailed information on point defects and their interactions [12,13]. Unfortunately, reliable ionic conductivity measurements in oxides are restricted to a few ‘fast ion’ conductors [14], whose plastic behavior has generally not received much attention. In oxides such as Al,O, and MgA120, whose plastic behavior has been and is widely studied, the low ionic conductivities have made experimentation difficult. Diffusion measurements of the oxides of interest are difficult because of the generally low values of the self-diffusion coefficients and the fact that in a number of cases of interest (Mg, Al, Si and 0) convenient radio-tracers do not exist. Techniques have developed (ion microprobe, nuclear micro-analysis) for using stable isotopes. The most recent data on the slower moving species (oxygen in most cases) for oxides of interest are shown in Fig. 1.

2.3 Defect energies Computational calculations of defect formation and migration enthalpies have been unusually successful in studies of ionic halides (151. This success has encouraged application to oxides (see Table 3). The record to date is probably best described as mixed: there is reasonabie agreement between theory and experimentally obtained formation and activation energies for UOz and transition metal oxides with the rock-salt structure, but there is still considerable uncertainty in both experimental and theoretical defect parameters for MgO. Al,O, and TiO,. Results to date, and comparison with experiment (where possible) are collected in Table 3. The most significant aspect of these data is that for oxides such as MgO and Al,O,, crystal purities required for native defects to have their equilibrium concentration are in the 10e9 or lower range, far beyond present state-of-theart techniques of crystal growing. Simple transition from ‘extrinsic’ to ‘intrinsic’ behavior with increasing temperature cannot be expected; complex temperature-dependent point defect concentrations can and probably do arise from precipitation and defect association reactions.

Non-stoichiometry in oxides can arise in two ways [16]. The most common type occurs in variable valence metal oxides such as Fel-,O, UOz+X, etc., where x can be controlled by Pal via the following

MITCHELL et al.: OVERVIEW NO. 6

1680

-

T”C

zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA examples being Co,_,O, Cu,_,O, Nil-,0

and Fe, -,O [ll]. TiOz_* for small x had been thought to be an anion vacancy case, but recent data suggest that the defect is the Ti interstitial [ 171. Non-stoichiometry in oxides also arises due to the dissolution of aleovalent solutes where charge compensating defects are necessary. Such aleovalent solutes can give rise to fractional concentrations >O.Ol or even >O.l. The best known examples are Ca,Zr1_.02_x (or corresponding Mg-doped or Y-doped ZrO& which is an anion vacancy case, and alumina-rich non-stoichiometric spine1 (Mg0.n A1203, n > l), which is a cation vacancy example [16]. This latter type of non-stoichiometric oxide is essentially a solid solution between stoichiometric MgA1204 and A18,3VA,1,,04(y-A1,03), a defect sljinel containing l/9 or 11.1% cation vacancies; an n = 3.5 crystal contains MgA1,04 and y-A1,03 in the ratio 1:2.5 and contains 7.9% cation vacancies. Such compounds are perhaps best written as

SLOWER SFECIES SELF - LIFFUSION

(MgAl204)l -xb416,3Vr,,JJ4)x. Similar considerations pertain to stoichiometric oxides containing unknown but aleovalent solutes, or 7 4 intentionally doped with small amounts of such 104/ T°K 4 solutes. Much work has been done with Fe-doped Fig. 1. Arrhenius plots of log (diffusion rate) vs reciprocal MgO, where the charge-compensating defect is temperature for the slower species (oxygen in most cases) known to be V& when the iron exists as Fe,, and in various oxides. References: TiO*: R. Haul and G. Diimbgen, J. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA phys. Chem. Solids 26, 1 (1965). NiO: M. Mg-doped A1203, where Vi defects are formed to O’Keefe and W. J. Moore, J. phys. Chem. Solids 65, 1438, compensate for Mgk, [ 181. I 5

I 6

\

,

2277 (1961): C. Dubois and C. Monty. To be published. A120J: K. P. R. Reddy and A. R. Cooper. To be published. Mg,Si04: S. M. Oh, K. P. R. Reddy, L. D. Major and A. R. Cooper, J. geophys. Res. To be published. MgA1204: K. P. R. Reddy and A. R. Cooper. To be published. UOz: A. B. Auskern and J. Belle, J. nucl. Mater. 3, 311 (1961). MgO: L. H. Rovner, Ph.D. Thesis, Cornell University (1966).: Y. Oishi and W. D. Kingery, J. them. Phys. 33, 905 (1960). Si02: R. Haul and G. Diimbgen, Z. Elektrochem. 66, 636 (1962).

(simplified) reaction@ to, - Fe1-=o 0; + v;l, + 2h’ and to* -=L

0; + 2h’.

Plots of log [defect concentration] vs log Pol, known as Brouwer or Krijger-Vink diagrams, for the various defect species are most useful for compact representation of large amounts of data. Point defects to accommodate non-stoichiometry can be cation or anion interstitials or cation or anion vacancies. Zn, +,O and TiOz-x are the best known cation interstitial non-stoichiometric oxides, while UO,.. is the best known anion interstitial example [ll]. Cation vacancies are somewhat more common, t The holes shown in these reactions are almost certainly localized, i.e. they exist as Fe;, (i.e. Fe3’) and U; but in the form of defect clusters.

2.5 Defect clusters and extended defects Throughout this discussion, there has been the implicit point of view that isolated point defects exist in oxides. In those cases that have been studied in detail (Fe, -,O, UOz+x, Fe-doped MgO), defect clusters or complexes are observed and are likely to be the rule rather than the exception, even in stoichiometric oxides like Al,O, of normal purity. The situation thus differs from alkali halides, where at elevated temperatures many isolated vacancies are present;. this difference occurs because the defects in oxides have a strong coulombic binding, due to their generally large charge. Table 4 collects available information on defect aggregation in oxides [19]. Computer calculations of the minimum energy configurations of these clusters in Fe1 _,O, UOz+x, etc. are now beginning to rationalize the structural data obtained from X-ray and neutron scattering [20]. There is also a sizeable group of oxides that form extended defects such as crystallographic shear (CS) planes [21]. Of the refractory oxides of interest for this paper (see Table 5), only reduced rutile (TiOz-,, x > 0.01) forms CS planes. Conceptually, corner sharing octahedra ‘shear’ so as to share edges, thereby eliminating oxygen sites. This occurs in an orderly manner on specific crystallographic planes; the various lower oxides of rutile, Ti,Ol,_t all contain CS planes at different spacings and on two families of crystallographic planes. Oxides forming CS planes are listed in Table 4.

Table 3. Computed defect energies in eV for formation (AH,) and motion (AH,,,) of various defects in oxides. Values in parentheses are AH, per defect, the lowest values giving the majority defect Oxide

Schottky

Cation Frenkel

Anion Frenkel

Ref.

AH,

MgO

I.? (3.9)

12.4 (6.2)

12.1 (6.1)

(a)

Mg vat. = 1.9.-2.2 Self-diff. = 2.8

UOZ

10.3 (3.4)

18.5 (9.3)

5.0 (2.5)

(c)

UVac. = 5.6 0 Vat. = 0.25 0 Int. = 0.6

TiOz

5.2 (1.7)

12.0 (6.0)

8.8 (4.4)

(e)

Al,03

28.8 (5.8) 26.0 (5.2)

14.0 (7.0) 14.2 (7.1)

19.9(10.0) 16.6 (8.3)

(g) (h)

Ref.

Comments Suggests that the interpretation extrinsic is correct(h!

(ct

of Mg self-diffusion data as being

Suggests Oi as the defect species in UOz+_r. Oxygen diffusion in UO2 has AH,,, of 1.3 eV““: differences from predicted value of 0.6eV probably due to defect aggregation. Good agreement between experimental and theoretical AHoxid~l,un(cl. Suggests that slightly reduced TiOl should contain V, and not Ti, as predominant defect. Some experiments suggest Tii, however”‘. CS planes form below - lOOOK; AH, clr 1.15 eV’“‘.

Al self-d&T.= 4.9 0 self-diff. = 6.1.. 8.1

(i) (j)

Increase of creep rate in polycrystals undergoing Nabarro~ Herring diffusional creep due to Fe*+ or Ti4+ doping suggests cation Frenkel as the majority defectck’. However, studies of dislocation substructures in Mg-doped and Ti4+-doped sapphire suggest that I$ and 0, are the dominant defects, evidence that the anion Frenkel is the majority defect’“.

References: (a) C. R. A. Catlow, I. D. Faux and M. J. Norgett, J. Phrs. C 9, 419 (1976); see also W. H. Gourdin, Ph.D. Thesis, Massachusetts (b) B. J. Wuensch, in Muss zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA Trunsport Phenomenu in Ceramics, p. 221. Plenum Press, New York (1975). (c) C. R. A. Catlow, Proc. R. Sm. A 353, 533 (1977); also J. them. Sot. Furuduy Truns. I1 74 1901 (1978). (d) See Fig. 1. (e) C. R. A. Catlow and R. James, to be published. (f) E. Yagi, A. Koyama, H. Sakaira and R. R. Hasiguti, J. phys. Sot. Jap. 42, 939 (1977). (g) G. J. Dienes, D. 0. Welch, C. R. Fischer, R. D. Hatcher, 0. Lazareth and M. Samberg, Phys. Rev. B 11, 3060 (1975). (h) C. R. A. Catlow, W. C. Mackrodt, R. James and R. Stewart, Phys. Reo,, to be published. (i) A. E. Paladin0 and W. D. Kingery, J. them. Phys. 37, 957 (1962). (j) See Fig. 1. (k) P. A. Lessing and R. S. Gordon, J. mater. Sci. 12, 2291 (1977). (I) B. J. Pletka, T. E. Mitchell and A. H. Heuer, to be published; D. S. Phillips, A. H. Heuer and T. E. Mitchell, to be published.

Institute of Technology (1977).

1682

MITCHELL et al.: OVERVIEW NO. 6 Table 4. Point defect aggregation in oxides? (aggregating defects underlined) Reaction

Aggregation 1. Conventional point defect condensation

mv, t nvoM,O.

dislocation loops, zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQP voids MgO, BeO, Al,O,, SiO?, ZrO, :(Ca, Y)O, UO,, MgA1204, loops YaAlsO,a

--

M mO. dislocation t?lM i + tlOi -----+

--

2. Vacancy and interstitial

2MX,+ Ox, -10,(g) Mo

+ -Fe” + 2Mb

ordering 2M& + fO,(g) %3Y;;, 3. Vacancy and cation ordering

NOaN”

+ 2M:” + 0; 2

2

5. Crystallographic shear

Y,OJ, Fe,-,O,, (Co,Zr1,Fe,Mg),_,Si0,_~

Nd, Sm, Gd)O, HfOz :CaO, Al,O,:SiO,

2NL + v, + 30°C --

Fe, -Ak VO,, uo2 MgO:Fe20j, MgO:A1203

$0, + 2M; - Moz 0; + 2M, 6Kf

TiO,, VO,, CeO, --x1

+ zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFED V-+0; ZrO, :(Ca, Y, Yb, SC,Er, Dy, La,

-M

N,OB % 4. Defect complexing

Examples

+x1

5M, + 4V; + M; + 30;

+ 302(g) - Mo

3N2Oa ZSN;

+ 4V h + N;’ + 90;

2M& +0x, -:0,(g) Moz

TiOz_,,WO,_., NblOS_x, + -V; + 2Mh zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONM TiOa :(V, Cr, Ga, Fe),O,, Nb,OS:(Ti,Zr,Ge,Ta)Oz, +0,(g) + M ;“’ + 4Mt WO, :(Nb,V),Os. ABSi,O, (pyroxenes) -I- -Y, + 30;

?M & t 0;

5

Nz03 MO’2N&

yN o MO, a a4NI, +

M ;“’ + 606

t Descriptions of these aggregate and extended defects can be found in reviews by J. S. Anderson, in Dejects and Transport in Oxides (edited by M. Seltzer and R. Jaffee), p. 25. Plenum Press, New York (1974); L. W. Hobbs, J. Physique 37 (C7), 3 (1976); and S. Mrowec, Ceramurgia 4, 47 (1978). A detailed survey with more extensive references will be published separately by L. W. Hobbs as “A Survey of Point Defects and Their Aggregates in Oxide Ceramics” in J. Am. ceram. Sot.

3.

DISLOCATIONS

IN

OXIDES

The development of dislocation theory, which emerged mostly from ex~rimental work on metals, has been extended over the years to covalent crystals such as Si and Ge [22] and to ionic crystals such as the alkali halides [23]. In oxides (as discussed above), although covalent bonding is significant in many cases, ionic charge effects probably have a dominant influence on the behavior of both point de fects and dislocations. The complexity of the crystal structures and the relationship between the anion and cation sublattices also have to be considered in order

to understand the structure of dislocations, as will be clear from the following brief treatment, which follows and extends some previous reviews [24-261. 3.1 Crystallography

and glide systems

Crystal structures of some of the basic ceramic oxides are summarized in Table 5; many can be described in terms of close-packing of anions (f.c.c. or h.c.p.), with the cations occupying octahedral or tetrahedral interstices. Glide systems which are observed by deformation of single crystals are summarized in Table 6. The easiest slip direction is in most cases

Table 5. Crystal structures of some oxides Oxide

Anion packing

Cation occupancy

WO

f.c.c. f.c.c.

All octahedral l/2 octahedral l/8 tetrahedral 2/3 octahedral l/2 octahedral l/2 octahedral l/8 tetrahedral l/2 tetrahedral l/2 cubic sites Tetrahedral

M&%0, AhO3

TiOa (rutile) MgaSiO, Be0 uo2

SiO, (quartz)

h.c.p. - h.c.p. - h.c.p. h.c.p. Simple cubic Not close-packed

sites sites sites sites sites sites sites sites

Other oxides FeO, COO, NiO, CaO Fe,O,, C&O.,, many Ferrttes Fez03

The*, PuO*

MITCHELL er al.:

1683

OVERVIEW NO. 6

Table 6. Slip systems of ceramic oxides zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHG (d, = distance between oxygen anions) Oxide

Slip system

Burgers vector

Other slip systems

MgO

(110) (ITO) (111) (li0) (f)@Jl) (1120) loll) (011) (loo), 1110:Wll

+(liO) = do : (Ii@ = 2d,, +(1120) = ..‘ 3do (oil)= 2d, [Ool] = 2do f(1120) = do $(iio)= .:2d, f (1120)

1001) (IiO), (111; (ITO) (110; (iTo> ;iZio: (lolo), (7102:(1120) ;110: [OOI] (100) [OlO]. [Okl) [lOO] :lioo; x1120), [oooij:toio; IllOl. 1111; (ITO) ;1120/, : 1OiOl [oool]

MgAJzO, A&O, TiO, Mg,SiO,

Be0 UO2 SiO, (quartz)

(Onof) (1010)+f(2110) TiO, Mg,SiOl DOZ SiO, cu,o

No i(1120)+? No

+ i(llO) + f(Oli0) + f(lOT0) +: (lOTO) + +(llzo)

References: (a) J. Hornstra, Mater. Sci Res. 1, 88 (1962). (b) M. H. Lewis, Phil. Mag. 17, 481 (1968). (c) G. Welsch, L. Hwang, A. H. Heuer and T. E. Mitchell, Phil. Mug 29, 1371 (1974). (d) M. Doukhan and B. Escaig, .I. Physique Left. 35, L181 (1974). (e) R. Duclos, N. Doukhan and B. Escaig, J. mater. Sci. 13, 1740 (1978). (f) P. Veyssiere, J. Rabier, H. Garem and J. Grilhe, Phil. Msg. A, 38, 61 (1968). (g) W. T. Donlon, T. E. Mitchell and A. H. Heuer, Phil. Msg. to be published. (h) T. E. Mitchell, B. J. Pletka, D. S. Phillips and A. H. Heuer, Phil. Mag. 34, 441 (1976). (i) J. B. Bilde-Sorensen, A. R. Tholen, D. J. Gooch and G. W. Groves, Phil. Mag. 33, 877 (1976). (j) T. E. Mitchell, B. J. Pletka, D. S. Phillips, W. T. Donlon and A. H.‘Heuer, in Ceramic Microstructures Westview Press, Boulder, Colorado (1977). (k) J. Cadoz, D. Hokim, M. Meyer and J. P. Riviere, Rev. Phys. Appl. 12, 473 (1977). (I) M. G. Blanchin and G. Fontaine, Phys. Stat. Sol. (a) 29, 491 (1975). (m) J. B. Vander Sande and D. L. Kohlstedt, Phil. Mag. 34, 653 (1976). (n) L. Trepied and J. C. Doukhan, J. mater. Sci. 13, 492 (1978).

iii’,

1976, p. 689.

1684

MITCHELL et al.:

OVERVIEW NO. 6 +

giving a cation fault, i.e. the partial Burgers vectors are inter-anion vectors. (b) For the oxides which have been analyzed in most detail (Al,O, and MgA120L), dissociation occurs by the separation of partial dislocations by climb rather than glide, under conditions where climb is occurring during deformation. In other oxides, it is not known whether the reported dissociations are by glide or climb. (c) Dissociation may be occurring at separations below the resolution limit of weak-beam dark-field microscopy (- 20 A). However, it does not appear that extensive glide dissociation occurs in any oxide, except perhaps at the dislocation core. This is surprising in view of the large Burgers vectors in many oxides, e.g. [OlO] = 10.2 A in Mg,SiO,, where dislocations are not observed to be extended.

T=‘C

SiO

(baral

zyxwvutsrqponmlkjihgfedcbaZYXWVUTS

2

I

104/

T”K

--c

Fig. 2. Plot of log (resolved yield stress) vs reciprocal temperature for various oxides deformed at strain rates 5 lo-4 s-1, References: MgA1204: T. E. Mitchell, L. 3.3 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA Peierls stress Hwang and A. H. Heuer, J. muter. Sci. 11, 264 (1976). The observation that dislocations tend to glide on A&O, (prismatic slip): T. E. Mitchell, B. J. Pletka, D. S. close-packed planes (large d spacing) in close-packed Phillips, W. T. Donlon and A. H. Heuer, in Ceramic Microstructures 1976, p. 689. Westview Press, Boulder, Colorado directions (small b) is in accordance with the traditional Peierls model of dislocation motion. The only (1977); J. Cadoz, These, Paris XI (1978). Mg,SiO,: J. M. Christie and A. J. Ardell, in Electron Microscopy in Minertheoretical investigation is an atomic calculation in alogy, p. 374. Springer, Berlin (1976). A&O, (basal slip): MgO by Woo and Puls [28] ; they calculate a Peierls M. L. Kronberg, J. Am. ceram. Sot. 45, 274 (1962). UOz: stress of -70 MPa for f(ll0) edge dislocations on J. F. Byron, J. nucl. Mater. 28, 110 (1968). SiO*: R. D. (710) planes, in accordance with the dislocation vel- Balta and K. H. G. Ashbee, Phil. Msg. 15, 931 (1967); Am. Mineral. 54, 1551 (1969). Ti02: K. H. G. Ashbee and ocity measurements of Singh and Coble [29] and with R. E. Smallman, Proc. R. Sot. A274, 195 (1963). NiO: A. the observed low temperature yield stresses of MgO. Dominguez-Rodriguez, J. Castaing and J. Philibert, Mater. It would be valuable to extend such calculations to Sci. Engng 27, 217 (1977). CaCO,: P. Braillon, L. Kubin and J. Serughetti, Phys. Stat. Sol. (a)45, 453 (1978). Cu,O: glide on { 100) and { 111) planes, in order to explain A. Audouard, These 3” Cycle, Paris 6 (1978). MgO: M. the slip anisotropy in MgO, and also to other crystal Srinavasan and T. G. Stoebe, J. mater. Sci. 9, 121 (1974).

structures. A number of interesting questions must be addressed.

(a) What is the importance of the charged row of ions at the end of the extra half planes of edge dislocations in most oxides (e.g. MgA1204, A&O,, TiOl, etc.)? (b) Is the core of the dislocation dissociated so as to aid dislocation motion by mechanisms such as Kronberg’s synchro-shear process? (c) Does the dislocation cope with its line charge by jogging onto alternately charged lines, or by climb dissociation into a pair of oppositely charged partial dislocations? (d) Is the dislocation core ‘cracked’ for large Burgers vectors, as suggested by Haasen [30] for covalent crystals? (e) Which, if any, of these processes can explain the slip anisotropy indicated in Table 6, for example, the preference for slip over the shorter [OOl] Burgers vector in TiO,, or {1210} (lOi0) in preference to {lOiO} i(l210) prismatic slip in A&O,?

3.4

Yield

stresses

The only oxides which exhibit plasticity at low temperatures are those with the rock salt structure (MgO, NiO, COO). Other oxide crystals deform plastically only at high temperatures, some only at large fractions of their melting temperature, e.g. MgAlzO*, T/T, > 0.8. Representative yield stress data are collected in Fig. 2; data are plotted only in the region where the stress is varying strongly with temperature for strain rates < - 10m4/s. The following general points can be made from Fig. 2. (a) Most of the oxides have a linear region of log (yield stress) vs reciprocal temperature, so that i - Jr,)” exp( -

AH/kT),

where n is a stress exponent and AH is an activation energy. Measurements of the strain rate dependence generally give values of n - 3-5 and activation energies approximately equal to that for self-diffusion

Dislocations models have been proposed in order to of oxygen (UOz is an exception). rationalize the observed behavior in MgA1204, (b) There is a general trend in Fig. 2 that the larger ALO,, zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA TiOz, Mg,SiO, and SiOZ, but atomistic calcuthe Burgers vector, the higher is the temperature lations of the dislocation core structure and Peierls required for plastic deformation. stress are necessary in order to provide a firmer basis (c) The impurity levels and stoichiometries in Fig. 2 of understanding. are uncertain. For example, the stoichiometries of

MITCHELL et cd.: OVERVIEW NO. 6

1685

Table 8. Dislocation node reactions observed by election microscopy Oxide

MgO Mg.40, A1203

Node reactions :coii]

+ :f loi]

+

uo2

At intersection of (011) and (101) = [l lT] zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA giio] = 0 >(b)

:[oli] + fflOl] + f[lTO] = 0 :G2110] + f[lTlO] + f[llZO] = 0 [oiiol + f[11210] + f[ll20] = 0

$[oiii] + $ioiil TiOl, Mg,SiO, cu,o

[Oil] + [lOi] + [loo] + [ool] + [loo] + [OIO] +

Ref.

Comments

+_f[iizo] [llO] = 0 _[loll = 0 [ITO] = 0

=

0

(4 Basal plane reaction Decomposition of prismatic dislocation in basal plane Pyramidal glide Intersection of (001) and (101) = [Ill] Small change of energy Small change of energy

(h)

f[oiil + gioi] + +[iTol= 0 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA

References: (a) B. Reppich and W. H&her, Phil. Msg. 30, 1009 (1974). (b) A. H. Clauer and B. A. Wilcox, J. Am. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA ceram. Sot. 59. 89 (1976). (c) M. H. Lewis, Phil. Mug. 17, 481 (1968). (d) G. Welsch, L. Hwang, A. H. Heuer and T. E. Mitchell, Phil. Mug. 29, 1371 (1974). (e) B. 1. Pletka, T. E. Mitchell and A. H. Heuer, d. Am. ceram. Sot. 57, 388 (1974). (f) J. Cadoz, D. Hokim, M. Meyer and J. P. Riviirre, Rer. Phys. Appl. 12, 473 (1977). (g) D. J. Gooch and G. W. Groves, Phil. Msg. 28, 623 (1973). (h) J. Cadoz and B. Pellissier, Scripta metal/. 10, 597 (1976). (i) M. G. Blanchin and G. Fontaine, Phys. Stat. Sol. (a) 29, 491 (1975). (j) J. M. Christie and A. J. Ardell, in Electron Microscop))in Mineralogy. p. 374. Springer, Berlin (1976). (k) G. Vagnard and J. Washburn, J. Am. cernm. Sot. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFE 51, 88 (1968). (1) C. S. Yust and C. J. McHargue, J. Am. w-am. Sot. 54, 628 (1971).

UOz, TiOz and Cu,O were not controlled and may vary with the testing temperature. The data for MgO are for ‘pure’ crystals whereas ‘impure’ crystals have much higher stresses; other oxides are of unknown purity, and aleovalent impurities are especially potent in increasing the yield stress. Quartz on the other hand is well known to be weakened by the presence of water as an impurity. All of these factors make the interpretations of the yield stress data uncertain. The correlation between the magnitude of the Burgers vector and the difficulty of dislocation motion indicates that a Peierls stress may be rate-controlling, much as has been suggested for double kink nucleation in semi-conductor crystals [22]. However, the correlation of the activation energies for dislocation motion and for diffusion suggest that the factors mentioned in the previous section may be important: e.g. diffusionally controlled motion of jogged dislocations, climb-dissociated dislocations, or dislocations with cracked cores. 3.5 Dislocation reactions A variety of dislocation reactions in oxides has been observed by transmission electron microscopy. Dislocation dipoles are a common feature of the dislocation substructure in all the oxides listed in Table 6. These probably form by the trapping of edge dislocations of opposite sign on parallel glide planes, but may also form by dragging of jogs formed by double cross-slip of screw dislocations. (It is important to realize that cross-slip requires the movement of dislocations onto relatively difficult slip planes such as \loO} in MgO, (lOi0) in Al,O,, etc.) Such dipoles are found to be unstable with respect to climb at high temperatures, forming either strings of loops by

self-climb [31], or faulted dipoles by climb dissociation [32]. Other dislocation reactions involve dislocations with different Burgers vectors meeting on the same plane or on intersecting planes. A reaction dislocation zyxwvutsrqpo b, will form from the reacting dislocations b, and b2 if, according to the Frank criterion, h: < b: + bi, where b3 = bl + b,. Dislocation nodes are formed such that b, + b2 + b3 = 0. A list of such node reactions is given in Table 8. Product dislocations form at the intersection of glide planes and may be sessile. For example, the reactions given in Table 8 for MgO and Ti02 produce dislocations parallel to [ 1li] with [ liO] Burgers vectors which could only move by climb or by glide on the unlikely (112) plane. 3.6

W ork

hardening

Like other crystalline materials, oxides work harden after yielding; this is followed by recovery which becomes increasingly important at high strains and high temperatures. During work hardening, the dislocation density increases rapidly with the formation of dislocation dipoles and dislocation networks by the reactions described in the previous section. The standard of comparison for 0, the work hardening rate (= dT/&), is in stage II for f.c.c. metals, where 0 _ p/300 (II = shear modulus). Stage II work hardening in f.c.c. metals is explained in terms of the decrease in slip distance as the dislocation density increases, with the formation of dislocation networks and cell structures; the precise details are controversial [33]. MgO behaves in much the same way, including the presence of an easy glide region, and work hardening in Stage II is due to dislocation interac-

1686

MITCHELL et al.: OVERVIEW NO. 6

transformation of the original glide dislocation structure to an almost uniform three-dimensional network of dislocations, such as would be expected for pure climb. It is also noteworthy that the widely separated dislocations are always dissociated by climb with faults lying on almost random planes. Climb dissociation becomes increasingly extensive with increasing deviations from stoichiometry (MgO-n A&O,), and at the same time, non-stoichiometric spine1 flows more easily at lower stresses and lower temperatures [see references in Tables (6811. (a) AlzO, in zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA basal glide. Even though only one glide Recovery will be discussed further in Section 4 with system operates, the work hardening rate is quite high respect to the relationship between steady state creep (5 ~/u/300).The reason is that the dipoles break up and constant strain-rate tests, the applicability of the into loops by self-climb and that the loops interact various climb models, and the importance of strucwith other gliding dislocations. A quantitative theory tural details such as climb dissociation. has been developed [35]. (b) A&O2 in prismatic glide. 0 is very high, -p/35. 4. INTERACTION OF DISLOCATIONS It appears that the [lOiO] screw dislocations decomAND POINT DEFECTS pose in the basal plane into two f (ll?O) dislocations

tions and the formation of networks [34]. It is likely that similar mechanisms apply to the deformation of UO1, Si02, TiOz and C&O in the temperature ranges of plasticity where dislocation climb is slow. However, there has been little systematic investigation of dislocations substructures as a function of strain. In the oxides that require very high temperatures for deformation (e.g. AlaO and MgAl,O,), the situation is different in that climb is significant as well as glide. Three cases are instructive.

(Table 4) so that a dislocation network builds up rapidly, hindering further prismatic glide [36]. (c) MgA120,. 0 is also high, -p/70, but the interpretation furnished by electron microscopy is quite different. The high stresses in spine1 enable multiple slip to occur during yielding so that a dislocation network is built up rapidly by the combined action of multiple slip and climb [37]. In view of these different processes, it is dangerous to extend the ideas to any other particular oxides; rather, systematic analysis of the dislocation substructures is necessary to isolate the important mechanisms. 3.7 Recovery Recovery can occur either by dislocation cross-slip (as in stage III of f.c.c. metals) or by dislocation climb. Cross-slip in oxides requires motion on difficult slip planes and it has not been studied very extensively, although it is assumed to be important in dislocation multiplication by double cross-slip. A stage III recovery region is not observed in MgO crystals up to 400°C so that long-range cross-slip may be too difficult in this material [34]. In oxides deformed at high temperatures, climb becomes increasingly important. There are three types of mechanisms: (a) pure climb (Nabarro climb), (b) climb-controlled glide and (c) work hardening-climb recovery [25]. The latter mechanism operates in Al,O, deformed at high temperatures in basal and prismatic glide [35,36]. The work hardening process was described in the previous section; the climb recovery process is the annihilation of loops by diffusion, such that a constant flow stress is reached when the rate of formation of new loops from dipoles is balanced by the rate of annihilation of old loops by climb. In MgA120,, a constant flow stress region is also reached after a maximum in the stress-strain curve. The constant flow stress region corresponds to the

The most important phenomena affected by interaction of point defects and dislocations are climb and glide, as observed through macroscopic properties such as solution hardening and effects of nonstoichiometry on plastic deformation. These are discussed in this section. 4.1 Climb It will be clear from the previous section that deformation at elevated temperatures is a prominent theme in oxide plasticity, and climb and climb-controlled creep were major topics of discussion at the Workshop. Large quantities of creep data, i.e. high temperature dead load deformation studies, exist in the literature [25]. Virtually all these data can be described by a constitutive creep law relating the steady state creep rate &, stress 0, and temperature T of the form & = Au” exp( - AHfk T). Experimental results are usually described in terms of the stress exponents n and activation energies AiY. n values for oxides (as for metals) are typically between 3 and 5 and AH can usually be correlated with the self-diffusion coefficients of one of the species (in principle the slowest). The transient creep portion of the load-time curves is rarely analyzed; on the other hand, variation of i,, at constant o and T with Po, for non-stoichiometric variable-valence oxides can give important information on the rate-controlling species during creep. Constant strain rate tests at high temperatures can in principle give the same information as constant stress creep tests. In fact, opinion at the Workshop was voiced that constant strain rate tests might be preferable, in that they emphasize that transient creep is simply related to the work-hardening region of the u+ curve, and that steady state creep occurs when there is a balance between work hardening and recovery, i.e. when the work-hardening rate goes to zero.

MITCHELL

et al.:

OVERVIEW

NO. 6

1687

Much of the data have been interpreted in terms of argument is based on the recognition that dislocations can act as perfect sources or sinks for point one of several climb-controlled glide models (Weertman-creep), which give n’s of 3-5 and AH defects and that changes in the defect concentrations (creep) = AH (self-diffusion). Such models are but a affect both majority and minority defects alike through the ambipolar coupling field [43]. variant of general work hardening-recovery models, which unfortunately do not yet appear to have been 4.2 Solution hardening derived with theoretical rigor. One exception is the Systematic data on solution hardening in oxides work h~dening-r~overy model mentioned above for are limited to MgO and A120s [44] but there is genbasal slip in sapphire, which is microscopic in origin [3S]. In this model, work hardening occurs due to eral agreement that aleovalent impurities in all oxides may make a significant contribution to the yield interaction of glide dislocations with small prismatic stress. The hardening due to isovalent impurities (e.g. loops; these loops form by breakup of dipoles, themselves formed by edge trapping. Recovery involves the Fe’+ in MgO; Cr3+; Fe3+, Ti3+ in A&O,) is quite low and is interpreted in the same way as for substitudiffusive annihilation (climb) of these loops. tional solution hardening in alloys. In other words, The pure climb model of Nabarro is rigorous but solution hardening is due to a local elastic interaction its universality is still to be established. It has been suggested for creep of 0” sapphire [38] and for stoi- between the dislocation and the solute atom, caused chiometric spine1 [39], both of which have high glide by a combination of the size and moduli differences. Pletka et al. [453 find that the size difference is more resistance, and this mechanism may always be imporimportant in Al,O, but more data are required in tant at high temperatures when glide is difficult. One other systems. possible way to establish whether or not pure climb Solution hardening by aleovalent cations is very is occurring is careful measurement of specimen shape rapid (e.g. Fe 3i, A13”, Cr3* in MgO; Ti4+ in Al,O,). as a function of creep strain; inverse barrelling during This is interpreted in terms of the local interaction a compression test cannot possibly occur in glide but between dislocations and the aleovalent cation with is expected in pure climb [40]. Two major climb-related questions discussed at its charge-compensating defects (see Section 2). There length at the Workshop concerned the magnitude of are two general types of interactions. stacking fault energies (SFE) in oxides and the effect (a) Elastic interactions with the asymmetric (tetraof changes in stoichiometry on climb force. With gonal) distortion produced by the defect complex. regard to the first question, good data now exist indiThis has been applied successfully to the cases of cating that the SFE in Mg0.n Al,O, spine1 decreases MgO and Al,Os [44]. markedly with increasing zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA n but that the dissociation (b) Electrostatic interactions with the electrostatic invariably involves climb rather than glide (see refer- dipole (or more generally, multipole) produced by the ences in TabIe 7). Theoretical calculations of SFE in defect complex. There are again two possibilities: one spinets [41 J, whife showing that some climb faults is that the dislocation shears the dipole and thereby have relatively low energy, do not show any marked increases its energy; this interaction is, however, too reduction with increasing n, as is observed; furthersmall to explain the results in MgO and Al,O, [44]. more, the calculations show the SFE to be quite The other possibility is that there is an electrostatic anisotropic, while the faults of the widely climbinteraction between the charged dislocation line and dissociated dislocations in spine1 lie on a number of the charged defect cluster. The development of this planes [42]. Finally the calculated SFEs are more model has been successful in explaining the plastic than two orders of magnitude greater than indicated anisotropy of alkali halides containing divalent by the width of the extended dislocations. cations [46], i.e. the difference in the yield stress for The experiments suggest that the wide stacking {IlO: and { 100; slip, but the theory has not been faults may be stabilized by condensation of vacancies; applied to oxides. further work, both ex~rimental and theoretical, is Clearly solution hardening in oxides is in its needed to confirm this notion. infancy, both experimentally and theoretically. A point of considerable debate at the Workshop (a) More experimental data are needed. was whether changes in point defect concentration, (b) A better understanding is required of the as can be achieved by changing the P,,, of a variable charge-compensating defect and the elastic and valence oxide or a stoichiometric oxide containing variable valence solutes, affect the climb force on a electrostatic fields generated by the cluster. (c) Solution hardening theories all suffer from the dislocation; a related question is whether, because of vacancy-interstitial concentration problem of using linear elasticity theory for local the different around a dislocation, climb itself (or climb dissoci- interactions, where linear elasticity must break down. ation) can cause spatiai variation in non-stoichioAtomistic cakculations are necessary. (d) The theories are generally 0 K calculations withmetry. The view of many was that the climb force was independent of Po2, for example, but that the out thermal activation. There is generally an athermal region at higher temperatures, which has been climb rate was not, provided that the rate-controlling species was not changed by the change in PO>.This explained in MgO in terms of the induced relaxation

1688

MITCHELL et al.: Table 9. Variable valence non-stoichiometric

TO

+x

Fe, -,O co, _,o Ni, -,O TiOzmX uo2+,

cu*_xo

OVERVIEW NO. 6

oxides whose plastic deformation has been studied

Range of x

Temperature range (“C)

Corresponding Po, (atm)

Ref.

-0.35 to 0.25 0.05 to 0.15