Diffusion and creep: Application to deformation maps on NiO

Scripta METALLURGICA

Vol. 20, pp. 739-742, 1986 Printed in the U.S.A.

Pergamon Press Ltd. All rights reserved

DIFFUSION AND CREEP: APPLICATION TO DEFORMATION MAPS ON NiO M. Jim~nez-Melendo, A. Dominguez-Rodriguez, J. Castaing* and R. MArquez Departamento de Optica, Facultad de F~sica. ADtdo. 1065. 41080 SEVILLA (SPAIN) *Laboratoire de Physique des Mat~riaux, C.N.R.S. 92195 MEUDONCedex (FRANCE)

(Received January 28, 1986) (Revised February 27, 1986) Introduction The transition-metal oxides with NaCl structure have been the subject of high temperature deformation studies for many years and are now well documented (1-3). During high temperature creep experiments, the rate controlling mechanism of deformation can be dislocation climb (Dower law creep) or transDort of matter (diffusional flow). In both cases , the mechanism is related to the slowest diffusing species (1-3). Starting from the detailed work of Ashby in 1972 (4), the deformation mechanism maps received a considerable impetus and are now generally recognized as a powerful tool in the visual presentation of the mechanical data. The recent book of Frost and Ashby (5) gives an exhaustive l i s t of metal and ceramic deformation mechanism maps and includes a chapter on the rock-salt structure oxides. The work of Krishnamachari and Notis (6) on CoO is reviewed but nothing has been done about NiO, although the same a r t i c l e (6) displays results on both compounds. The reason is probably that the data used in the paoer (6) were not reliable for NiO, especially for diffusion. NiO is an oxide for which a considerable work on diffusion was made in the last years; we now know the cationic as well as the anionic d i f f u s i v i t y for various paths (bulk, qrain boundary, pioe) (7-10). I t is possible to establish the different deformation laws in this compound and compare them to experiments. A large amount of high temperature creep data is also known both for polycrystals (6,11,12) and for single Crystals (11,13). The present article was motivated by an interest in showing the maps according to the new data about the creep and diffusion of NiO. Experimental data I. Diffusion The data for nickel oxide and oxygen diffusion are displayed on Fig. 1 which summarizes the references (7-10,14). There is a good agreement for experimental results, except for oxygen where the old resuts of O'Keeffe and Moore (14) have to be discarded. They have been used previously in analyzing creep data, giving wrong interpretations for the creep mechanism (6). The data for grain-boundary oxygen diffusion are rather scattered; the authors have not yet concluded for the activation energy (10). We have plotted a line with an activation energy of 4.0 eV (Fig. 1) obtained for creep experiments (11); this is about 0.7 the bulk diffusion value, an usual result for short c i r c u i t d i f f u s i o n (15). The self-diffusion data must be combined to describe the molecular transport; in our case, a NiO molecule must be moved for a dislocation to climb or a grain to deform. A way to make this combination is by assuming that the composition is not changed; the relation between flux is then: JNi = Jo (I) By taking into account the diffusion in the l a t t i c e (1) and the grain boundaries (GB), we have: j~i + jGB = j ~ + j~B Ni

(2)

For the purpose of simplicity, an effective diffusion coefficient is introduced, which takes

739 0036-9748/86 $3.00 + .00 Copyright (c) 1986 Pergamon Press Ltd.

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into account the various diffusion paths (16): Deff = Dl + - ~ D GB

(3)

where 6 is the "thickness" of the grain b~undary and d is the grain size. Eq. (I) can be related to concentration gradients with DeTT. The coupling of eq. (1) allows us to write a molecular diffusion coefficient (16): 1 = 1 I mol Ni Eq. (4) is the origin of the formalism used by many authors, as reviewed in (16). Eq. (2) implies that a global composition of the solid is maintained, but allows deviations from composition in the lattice and in the grain boundary. To avoid that, i t is better to write the following relations: GB = j~B JNi (5)

and molecular diffusion coefficients can be deduced for both paths: 1 = 1 1

oT

mol

Ni

DB

(61

and the same equation with "l" instead of "GB". In this case, the effective molecular diffusion coefficient is: mol = ~-T- + DNi

+-j- ~+

(7)

Eq. (7) is different from eq. (4) and may alter the conclusions of many of the previous works reviewed in (1) and (16). GiB (Fig. I) Therefore, for any d, For NiO, we have seen that D << D~i and D~B << DN ~eff D~f f << UNi , and eq. (4) reduces to: Deff D~f f (8) mol = By using eq. (7), one finds once more eq. (8), Diffusion properties of NiO are insensitive to the mode of flux coupling. The data we have used to establish the deformation maps are summarized in Table I. 2. Creep data We have used results on the plastic deformation at high temperature of single crystals (11,13) and polycrystals (6,11,12). In the range of power law creep (single crystals and polycrystals at stresses o > 30 MPa), we have used the following creep law: ~ : A1 ~

(_~)n D~

The values of the parameters are given in Table I. There is a large number of models giving n values of about 3 (I). Experiments generally yield values far have used an average n = 7 deduced from NiO creep tests (11,13). For o < 20 MPa, viscous creep was found for polycrystals (11,12). I t was creep rate is controlled by diffusion in grain boundaries (11). The creep law oR E = AZ kT-~d 6D~B

(g) power law creep from 3 (1); we shown that the is: (10)

The parameters are given in Table 1. We chose the Ashby-Verral creep equation (17) because the grains where not deformed (11, 18). In such a case, the Nabarro-Herring or Coble creep is not relevant. Although the creep

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741

tests gave n = 1.4 (11,12), we used eq. (10) which is derived from a microscopic model based on diffusion (17). In the original equation, there is a term related to the grain boundary energy (17) whic~ for NiO has a value of about 2J/mc according to theoretical predictions reviewed in~9);~ this allowed us to approximate the original equation to eq. (10), which was shown to give creep rates too small by a factor of about 10 (11). 3. Deformation maps Deformation maps have been established on the basis of eqs. (9) and (10). For a grain size of 9 um, the map is plotted on Fig. 2; i t corresponds to a large amount of creep data (11,12). For T = 1300 °C, the map on Fig, 3 shows tha~,defgrmation of NiO cannot occur by l a t t i c e diffusion; i t would require d ~ 5 mmwith ~ ~ 10" ~ s-~. This fact stems from the large difference in diffusivities in the lattice and in the grain boundaries for NiO (Fig. 1). Contrary to the general situation,(5), diffusion coefficients in NiO are not deduced from plastic deformation experiments. This explains the residual discrepancy between experimental data and ~ on maps for the diffusion flow (Figs. 2 and 3). Because E is independant of d (eq. (9)) for single crystal deformation, we have reported the results on Fig. 2; in Fig. 3 we take the specimen size as d. The range of strain-rates is not as large as the one displayed (Figs. 2 and 3); this discrepancy is due to the scatter of the creep equation parameters for NiO single crystals (20). Krishnamachari and Notis (6) concluded that NiO creep is controlled by a recovery mechanism. Their results are shown in Fig. 2, in the field where ~ is independent of d; the map of Fig. 2 is in agreement with their conclusions. Conclusions and summary Nickel oxide is a compound where diffusion coefficients of both ions are known for all possible diffusion paths, taking advantage of this situation, we have established deformation maps, which for diffusional creep were based on theoretical models. They show a reasonable agreement with experimental data. Conditions for deformation by lattice diffusion (Nabarro-Herring creep) cannot be reached. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15, 16. 17, 18. 19, 20, 21.

References T. Bretheau, J. Castaing, J. Rabier and P. Veyssiere, Adv. Phys. 28, 835 (1979) T.E. Mitchell, L.W. Hobbs, A.H. Heuer, J. Castaing, J. Cadoz and J. Philibert, Acta Met. 27, 1677 (1979) J. Castaing, A. Dom~nguez-Rodr{guez and C. Monty, Deformation of Ceramic Materials 11, ed. by R.E. Tressler and R.C. Bradt, p. 141, Plenum Press, New York (1984) M.F.Ashby, Acta Met. 20, 887 (1972) H.J. Frost and M.F. Ashby, Deformation Mechanism Maps, Pergamon Press, Oxford (1982) V. Krishnamachari and M.R. Notis, Acta Met. 25, 1025 (1977) A. Atkinson and R.I. Taylor, Phil. Mag. A 39, 581 (1979) A. Atkinson and R.I. Taylor, Phil. Mag. A 43, 979 (1981) C. Dubois, C. Monty and J. Philibert, Phil. Mag. A 46, 419 (1982) A. Atkinson, F.CoW. Pommery and C. Monty, 3th Int. Conf. Transport in Nonstoichiometric Compounds, ed. by G. Simkovich and V.S. Stubican, p. 359, Plenum Press, New York (1985) M. Ji~nez-Melendo, A. Domlnguez-Rodr{guez, R. MArquez and J. Castaing, to be published M. Jim~nez-Melendo, J. Cabrera-CaBo, A. Dom(nguez-Rodriguez and J. Castaing, J. Phys. Lett. 44, 339 (1983) J. Cabrera-CaBo, A. Dom{nguez-Rodr{guez, R. M~rquez, J. Castaing and J. Philibert, Phil. Mag. A 46, 397 (1982) M, O'Keeffe and W,J. Moore, J, Phys, Chem. 65, 2277 (1961) A. Atkinson and A,D, LeClaire, Dislocations 1984, ed, by P, Veyssiere, L. Kubin and J. Castaing, p. 253, Editions du CNRS, Paris (1984) J. Philibert, Sol. St. Ionics 12, 321 (1984) M.F. Ashby and R.A. Verral, Acta Met. 21, 149 (1973) M. Jim~nez-Melendo, A, Dom~nguez-Rodr~guez, R, M~rquez and J, Castaing, Jo Phys, Coil, (1985) in press M, Ruhle and W. Mader, Basic Properties of Binary Oxides, ed, by A. Dom{nguez-Rodr~guez, J. Castaing and R. M~rquez, p. 297, Publicaciones Universidad de Sevilla, Sevilla (1984) A. Dom~nguez-Rodr~guez and J. Castaing, Rad, Effects 75, 309 (1983) A. DomTnguez-Rodr~guez, J, Castaing and J. Philibert, Mat. Sci. Eng. 27, 217 (1977)

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TABLE I. MATERIALDATAFOR NICKEL OXIDE Parameters

Values lxi019

A1

Comments

98 1.83x10-29 m3

A2

2.96x10-10 m

n

2230 K 7

D~'O

5x10"3 m2/s

4.0 eV TEMPERATL~E('C) ,:

4

~o

'

'

161

for

Fig.l: Tracer diffusion data NiO along dislocations (D~), grain boundaries~(D~,1 D~~ and

",,\ e

$

?

m~/t(O) 9

11

101~ULK I)IFF~IL-~ON ~

'

to6 L :.:~....~ . . . . .

,¢,mk

- J'~$"~:'~'-~

(9) (11)

(11) TEMPE nATURE(°C) 1400 1800

1000

NIO II04 ]

~

b~-3

oral, &:,u%o,~ \

e(,-').~'V \ •

.X

\ \.\

\

\

I

\

Xl I,¢2

(16 (17 (15 OS HOMOLOGOUS TEMPERATURE TITbl

I

STRESS O-(MPa)

(9)

POWER LAW CREEP

i

-1|

(11,13)

d=gpm

in the volume -,(D~i' D~lu. can be found in ref. (7-10) except for ~ the largest D~" (14)" for D~ B^ we have drawn a line corresponding .~mm to the creep activation energy of 4 eV (11) through the noints of ref. (i0) 16

N~Eu'I;

(21)

This value is very close to the creep data (ref. 11) This value was obtained f i t t i n g the data from ref. 10 with an activation energy of 4.0 eV Creep activation energy

O. 1 m2/s

~Ro .~..~ ~

(21) (21)

Melting point Average value deduced from NiO creep tests Pre-exDonential term of the anion lattice diffusion

5.6 eV DGB,o 0

(6) (B)

Burgers vector Shear modulus

1.1x1011Pa

TM

(17)

Ashby and Verra] constant Vacancy volume Grain boundary thickness

7x10"10 m b

Reference (11)

I t was obtained f i t t i n g the experimental data in eq. (9)

102

I'111

L~

' NiO

I~ -~

r.l~O'c/ ow~-t.Aw I

Fig.2: Stress-temperature map for NiO with grain-size d= 9 um. For power law creep, we show results for larger grain-size Since ~ is independant of d. a) ref.(6), b) ref.(11,13) and c) ref.(11)

/ : Fig.3: Grain size-stress deformation map for NiO at 1300°C. a) ref.(11,13) and b) ref.(11)

NORMAUSI[D STRESS O'/,U