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EXPERIMENTAL APPROACH OF TYPE C GRAIN BOUNDARY SELF-DIFFUSION IN SILVER
P. Gas, S. Poize, J. Bernardini
To cite this version:
P. Gas, S. Poize, J. Bernardini. EXPERIMENTAL APPROACH OF TYPE C GRAIN BOUNDARY SELF-DIFFUSION IN SILVER. Journal de Physique Colloques, 1990, 51 (C1), pp.C1-477-C1-482.
�10.1051/jphyscol:1990174�. �jpa-00230342�
COLLOQUE DE PHYSIQUE
Colloque Cl, supplement au nol, Tome 51, janvier 1990
EXPERIMENTAL APPROACH OF TYPE C GRAIN BOUNDARY SELF-DIFFUSION IN SILVER
P. GAS, S. POIZE and J. BERNARDINI
Laboratoire de MBtallurgie, U A 443, Facult6 des Sciences et Techniques St JBrdme, Case 511, Avenue Escadrille Nomandie-Niemen, F-13397 Marseille Cedex 13, France
Resume: L'auto diffusion intergranulaire de I'argent a et6 etudiee dans un grand domaine de temperatures (150<T(OC)<630) et de profondeurs de penetration volumiques (0.01<JDt(nm)<2500). Ces conditions permettent de swivre le passage d e cinetiques de type B vers des cinetiques de type C.
Des critPres expkrimentaux definissant la validit6 de chaque type de cin6tique sont ainsi propos6s. Dans une certaine mesure ces resultats justifient l'utilisation du mod6le de Fisher pour l'autodiffusion.
Abstract: Grain boundary self-diffusion of silver has been studied in a wide range of temperatures (150<T(OC)<630) and of lattice penetration depths (0.01<JDt(nm)<2500). These conditions allow us to follow continuously the passage from type B to type C kinetics. Experimental criteria for the observation of both types of kinetics are proposed.
There is no real contradiction betwe:?n these results and the use of the classical Fisher's mode: for grain boundary self diffusion.
I. INTRODUCTION
The rapid diffusion along dislocations and grain boundaries (gb), with jump frequencies orders of magnitude higher than in the lattice is of great importance for fundarental as well as technical. reasons (see for ex. /l/ and /2/). It is however difficult to study boundary properties without any influence of the lattice. In a polycri.stalline sample, lattice diffusion and short circuit diffusion along dislocations, surfaces and grain boundaries generally take placc simultaneously. Following Harrisson classification / 3 / , the two processes may theoretically be separated when the condition:
is fu!fiJl ed. Tn expression (l), (D. t)0. 5 is the lattice penetration depth fixed by the lattice diffusion coefficient (D(T)) and the annealing time (t);
6 represents the grain boundary thickness defined by Fisher's model /4/ as an homogeneous thin slab of material where the diffusion coeffirient Dgb (T) is constant and large compared to D. In this so-called type C kinetic regime , diffusion takes only place inside the grain boundary without any diffusion of the atoms from the grain boundary towar6 the lattice. It should thus be possible to measure directly the grain boundary diffusion coefflrient without any assumption on the grain boundary thiclcness ar,d on the lattice diffusion coefficient.
Let us remind that in the classical type B kinetic regime defined as:
with grain size, the grain boundary diffusion coefficient is obtaj-ned through a penetrat-ion curve which mainly takes into account the diffusion of the tracer from the grain boundary inside the lattice. This experimental approach only leads to the value of a parameter
B
= Dgb.6/2D.(Dt)0.a /5/function of the l-attice diffusion coefficient and of the gb thickness. The gh diffusion coefficient, which may he e>:tracted from these experimental data is thus strongly linked to the diffusion model chosen /4/ 2nd to the value of the lattice diffusion coefficient at the temperature where the experiment is done
(which is generally not properly known hut extrapolated from high temperature measurements) .
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1990174
Cl-478 COLLOQUE DE PHYSIQUE
The purpose of the present paper is to check the possibilities and
difficulties of grain boundary diffusion measurements in conditions close to those known as type C kinetics. This means:
1: To show that experimental penetration profiles typical of type C kinetics can be obtained,
2: To study the passage from type B to type C kinetics, and the validity of the gb diffusion coefficients deduced from the two approaches.
To reach this goal we chose to study silver gb self-diffusion. Lattice and gb silver self-diffusion have been the object of a large number of publications.
In both cases, the diffusion has been explained by a vacancy mechanism /6-10/.
From a practical point of view, silver is a very convenient material since it is not reactive and can be obtained at a high purity level /11/. Diffusion studies can be performed with the radioactive tracer 1'OAg (gamma emittor, half life: 253 days) which is readily available and easy to use. It should thus be possible to compare type B and type C kinetics in a wide range of temperatures and of lattice penetration depths.
I1 - EXPERIMENTAL TECHNIQUES AND RESULTS a) Material and heat treatments
The initial material was 5N Johnson Matthey silver. In order to decrease its oxygen and volatil impurity content, silver was first melted in dynamic vacuum
(10-6 Torc) in a high purity graphite crucible. Platelets, about 20x15 mm2 are then obtained from the rods by rolling and cutting. Different grain sizes were obtained by varying the rolling purcentage and the recrystallisation
temperature. Samples with a mean grain diameter of 400pm were obtained by annealing at 680°C for 20 hours, there were used for the experiments conducted at high temperature. Samples with a mean grain diameter of about 100 pm were obtained after heavy rolling and annealing at 350°C for 17 hours. These samples with a high density of grain boundaries were used for the experiments conducted at low temperature.
Before the thermal diffusion treatments, -samples underwent a pre-anneal at the diffusion temperature with time chosen long enough to reach thermodynamic equilibrium with respect to point defects and grain boundaries.
llOAg was then electroplated on the polished sample surface. The diffusi.on annealing was done (as any o t k r heat treatment) in a flow of purified N60 hydrogen, the furnace temperature was cant-rolled to about +/-1°C. After these annealings, the'back and the edges of the sample were aroilnded to eliminate the activity which might have diffused inwards from the sides of the sample.
The concentrat-ion profiles of the radioactive tracer were deternined by a serial sectioning technique. Layers were removed using electro-chemical dissolution. The radiotracer concentrations were measured by counting the residual activity of the sample and the activity of the slices with a G e g ~ spectrometer. Tha 658 and 885 Rev radiations were monitored, long counting times (t>12 hours) were necessary in order to get significant measurements at low activity levels.
b) Penetration profiles
llOAg gh self-diffusion has been studied between 15F°C and 6320C for periods of time ranging between 1 (632OC) and 1919 (187OC) hours. In these conditions penetration depths (D.t)0.5 (with D = 1 exp
-
23000/T) /12/ varied between 0.01 and 2571 nn. These large variations both in temperatures and in lattice penetrat5.0~ depth allow us to coppare the "OAQ penetration profiles from conditions typical of tyge B kinktics to conditions severer than those defined by Harrisson for type C kineti.cs. Moreover a comparative study of thediffusion coefficients extracted from both approaches and of their dependance on tenperature should be possible.
Figure 1 presents a plot of the lcgarithm pf the M 0 A g activity (log A) as a function of depth !X) ohtaFned after a diffusion treatment at 333OC for 119.64 hours. The calculeted penetration dcgth is 37.7 nm and one can notice that the logarithn of the activity varies almost lin:+arely with depth. T5is profile is typical of gb diffusion studi-es performed in type B conditions / 5 / and in the present case similar to any profile cbtained with a lattice penetration depth larger than 50 am.
The same representation (log A vs X) is used in Figure 2 to present a profile obtained after diffusion at 203OC for 78 hours. In this case, the lattice penetration depth can be calculated as 0.04 nm and three things have to be noticed:
a) the profile is not linear but presents a small negative curvature, b) the tracer penetration can be followed on distances such as 60 pm which means 1.5~106 times the lattice penetration depth.
C) the activity at the surface shows a rapid drop. This should not be
interpreted as lattice penetration but is more likely the combined result of the surface imperfection of the sample and of the slicing process.
Equival.ent profiles (with a more or less pronounced curvature) have been obtained for lattice penetration depth lower than 0.5 nm.
FIG. 1
-
Penetration profile of "OAg FIG. 2-
Penetration profile of ll0Ag after a heat treatment at 333OC for after a heat treatment at 203OC for 76119.62 hr. hr.
I11
-
DISCUSSIONa) Analysis of diffusion profiles and grain boundary diffusion coefficients
In type B kinetic conditions the grain boundary is not an isolated medium and the rapid penetration along gb is characterized by the lattice diffusion from the grain boundary inside th,e grain. The grain boundary diffusivity (P = Dgb 6) is thus defined by the well known system of equations involving Dgb (grain boundary diffusion coefficient); D (lattice diffusion coefficient) and 6
(grain boundary thickness) and may be extrapolated from the profile using the Suzuoka solution /13/:
In this expression, A is the activity of the tracer at the depth X , D is the lattice diffusion coefficient, t the annealing time. Because P=P/2D.(Dt)'/*, the grain boundary diffusivity Dgb.6 has to be calculated by an interaction procedure.
Expression (3) shows that in type B conditions a plot of the logarithm of the activity as a function of the 6/5th power of the depth should be linear.
In type C conditions, the grain boundary may be considered as an isolated diffusion medium, the gb diffusion coefficient Dgb is then directly deduced from FFck's second law and is given by /6/:
In that case, the logarithm of the activity decreases as the square of the depth as expected for diffusion by a single mechanism from an instantaneous smirce.
C 1-480 CoLLOQUE DE PHYSIQUE
Two criteria can thus be used to check from a penetration profile, the validity of type C kinetics:
-
the quality of the log A vs X2 fit,-
the value of the gb diffusion coefficient deduced from this plot.Figure 3 (a) presents the same diffusion profile as figure 2, but plotted on a log A vs X2 representation, the fit is quite good and characterized by a quality factor = 0.998. The gb diffusion coefficient which can be deduced from this plot is Dgb = 1.5 10 - 1 0 cm2/s. It should be stressed that Yhis gb
diffusion coefficient is not dependent on any gb diffusion model and is thus of crucial importance for gb diffusion studies. Its validity has however to be checked. This is done in figure 3 (b) where the same experimental points have been plotted on a logA vs X 6 / = representation only valid for type B kinetics.
Surprisingly enough the fit is not too bad, the quality factor is 0.993 and leads to a'gb diffusivity P = Dgb.6 = 7.8 10-19 cm3/s (calculated assuming D = 1 10-*l cmZ/s). If one takes the usual assumption of a grain boundary
thickness 6=0.5nm, one gets Dgb = 1.56 10-1"m2/s, a value which is not too different from the value deduced from the logA vs X2 plot. These values are reported on table 1 together with the values deduced from three other
experiments with a penetration depth lower than 0.5nm (Harrisson's criterium for type C diffusibn). One can see from this table that the "absolute" values of the gb diffusion coefficients are not very helpfull to establish if type C
kinetics are really observed.
The situation is thus the following:
-
diffusion profiles do not indicate clearly the limit between type B and type C kinetics.-
gb diffusion coefficients deduced from the two approaches are not too different, specially if one takes into account the fact that gb diffusion coefficients deduced from type C kinetics depend on two values:-
the gb thickness which is not known,-
the lattice diffusion coefficient from the grain boundary which is very poorly known at temperatures as low as 150°C.FIG. 3
-
Same penetration profile as on FIG 2 but respectively plotted on a log A vs X2 graph (a) and on a log A vs X615 graph (b).b) Variations with temperature,
If it is difficult to deduce the validity of the type C kinetic approach from an isothermal study, one may expect that some informations may be deduced from the variation with temperature of the gb diffusion coefficients when
experimental conditions are evolving toward the type C livit.
Figure 4 is an Arrhenius representation log Dgb = f(l/T) of the silver gb self-diffusion coefficients. On this figure:
- I represent gb diffusion coefficients calculated using equation (3) (type B ) when the lattice penetration depth is larger than 10 nm,
-
m represent gb diffusion coefficients calculated using equation (3) when the lattice penetration depth is smaller than 10 nm,- +
represent gb diffusion coefficients calculated using equation 1 4 ) (type C) when the lattice penetration depth is smaller than 0.5 nm. In that case, a teach temperature one has two gh dZffu.sion coefficiects, one calculat.ed
assuming type B kinetic ( o ) , the other calculated assuming typc C kinetic ( + l .
- S 1 1
CI .I
m I
P
FIG. 4
-
Arrhenius plot of the.
- 7 - 11oAg grain boundary diffusionB
coefficients in silver, (m)W coefficients deduced from
-9
-
equation (3) (type B) witht
penetration depths higher thand
lOnm, (e) equation ( 3 ) andab -=, -
penetration dapths lower thand 10 nm, ( + l equation (4) (type
C) and genetration depths lower
- x 3 4 than 0.5 nm.
1 1 15 1 9 2 3
It appears that:
a) if one supposes type B kinetics (m! and e):
- the Arrhenius plot cannot be correctly fitted by a straight line through the whole temperature doaain,
-
the gb diffusion coefficients deduced from experiments with penetration depth larger than 10 nm (m) follow the Arrhenius equation:D g b (cn2/s) = 0.074 exp (-9712/T) (5)
-
the gb diffusion coefficients deduced from experiments with penetration depths smaller than 7.0 nm (m) are all located below this Arrhenius line.b) if one supposes type C kinetics ! + ) :
- the gb diffusion coefficients agree with equation (5) when lattice penetration depths are lower than 0.1 nm,
- in the two other cases (penetration depths included betwesn 0.1 and 0.5 nm), the gb dtffusion coefficients are below this Arrhenius line.
Table 1: "OAg Grain boundary self-8iffusion coefficients deduced from experi~ents approaching the type C linit.
( a > pe~etraticn depths calculated assuming D (cmZ/s) = l exp (-23000/T)
( b ) cal.cu:ated from equation (4) which assilmes that type C kinetics are valid.
( C ) calculated from equatien (3) which assinmes that type R kinetics are valid,
6 is taken as: 0.5 nm and D (cm2/s) as: 1 exp (-23OOO/T(R)).
: c ) extrapolated from high temperature measurements done in type R conditions
using equation (5)
.
C 1-482 COLLOQUE DE PHYSIQUE
This representation shows which are experimentally the limits of type B or type C kinetic conditions for gb diffusion sti- dies:
-
type B conditions are fulfilled for lattice penetration depths larger than 1 0 ~ 7 , below this limit g h diffusion coefficients deduced from a type Bapproach are undarestinated,
- type C conditions appear to be fulfilled for lattice penetration depth lower or equal to 0.1 nn; over this Linit gb diffusion ccefficients deduced fro3 a type C approach are underastinateb.
-
nhsa type B or type C conditions are fulfilled, there is a good agreement bet-ween the values of the diffusion coefficients deduced from both approaches.Tt is imaortant to mention that this agreement is based on the two assuzptinns:
-
that the gb is correctly represented by a uniform slab of material with thickness E = 0.5 nm,-
that the l a t t i c e diffusion fron the grain boucdary is correctly represented by the expression: D = l exp !-23000/T).CONCLUSIONS
1) C r ~ i n houndary self-di.ffusion of silver has been studied in experimental conditions soing from pure type B kinetics (.IDt>>SOnrn) to condi'tions expected to give type C kinetics (dDt<0.5nm).
2) Even with very low lattice penetration depths (JDt<O.Snm) the distinction between X 6 / 5 and X2 depth profiles is not obvious. It is thus difficult to deduce from penetration plots which kinetic of diffusion explains the
penetration along grain boundaries. The grain boundary diffusion coefficients deduced from the two plots differ by less than one order of magnitude.
3 ) A study of the variations of the gb diffusion coefficients with terc.perat.ure gives more information and shows that the variation of tbe gb self-diffusion coefficients between 630 and 150°C is correctly represented by: Dgb = 0.074 exp
-
97L2/T. This expression is valid for experiments conducted in type B conditions when penetration depths are higher than lOnm, as well as for experiments conducted in type C conditions when aenetration depths are lower than 0.1 nm.4 ) Betwern these t w o values (0,3<JDtclO am) both kinetic regines are wrong and
lead to underestimated diffusion coefficients.
5) The usual assumption 6=0.5 nm used to calculate the gb diffusion coefficient appears to be correct.
6 ) A l l these conclusions are based on the value of the lattice penetratton
depth. The validsty of this criterium at low temperature and when penetration depth becomes very small (<0.5nm) is still an open question.
REFERENCES
/l/ P. Gas, S. Poize, J. Bernardini, and F. Cabane, Acta Metall. 37 (1988) 17.
/2/ P. Gas, Applied Surface Science, 38 (1989) 178.
/3/ L.G. Rarrisson. Trans. Faraday Soc. 57 (1961) 1191.
/4/ J.C. Fisher, J. Appl. Phys. 22 (1951) 74.
/5/ J. Philibert, D i f f u s i o n e t t r a n s p o r t d a n s l e s s o l i d e s , (Ed. de Physique, Les Ulis, France, 1985).
/6/ Y. Adda and J. Philibert, La d i f f u s i o n d a n s l e s s o l i d e s , (Presses Universitaires de France, Paris, 1966).
/7/ F. Kaut and W. Gust, F u n d a m e n t a l s of G r a i n and I n t e r p h a s e B o u n d a r y
D i f f u s i o n (Ziegler Press, Stuttgart, 1988), p. 72/73.
/8/ G. Martin and B. Perraillon, J. Phys. C 4 , 36 (1975) 165.
/9/ G. Martin, D. A. Blackburn, and Y. Adda, Phys. Stat. Sol., 23 (1967) 223.
/10/J.T. Robinson and N.L. Petersson, Surf. Sci., 33 (3972) 586, and Acta Metal., 21 (1973) 1181.
/11/G. Mathieu, S. Guyot, and J. Le Hericy, Mem. Sci. Revue Metall., 73 (1976) 281.
/12/P. Gas and J. Bernardini, Surface Science, 72 (1978) 365 /13/T. Suzuoka, Trans. Jap. Inst. Met. 2, 25 (1961).
