Commentson determining diffusion parameters on the basis of measurements of spreading kinetics of extrinsic grain boundary dislocations

Scripta METALLURGICA

Vol. 20, pp. 545-549, 1986 Printed in the U.S.A.

COT~ENTS ON DETERMINING

DIFFUSION

OF SPREADING KINETICS H.Garbacz

PARAMETERS

OF EXTRINSIC

Pergamon Press Ltd. All rights reserved

ON THE BASIS OF ~ A S U R E ~ E N T S

GRAIN BOUNDARY DISLOCATIONS

, K.J.Kurzydlowski

, J.W.Wyrzykowski

Institute

of Materials Science and Engineering Warsaw Technical University Narbutta 85, 02-524 Warsaw, Poland (Received November 25, 1985) (Revised January 27, 1986)

Investigations of EGBD spreading kinetics make it possible to determine characteristic parameters of the Drocess, in particular the spreading time /td/ at a given temperature /Td/. EGBDs disappear on a boundary at a different rate in a wide range of temperatures [I]. Varin [I] and Swlatnicki [2] used formulae of the Johannesson-Th~len model 13S and Lojkowski-Grabski model [4] for calculating the enthalpy of GB self-d~f~usion /Hg/. The same procedure can be applied to the Pumphrey-Gleiter model [5]. The formulae are presented in Table I. The formulae from Table I differ, which becomes expecially vivid after transforming them into the following forms:

g

HP_G =

~t d

RTdln

11/

D°

GV

HgL-G =

HgJ-T =

HP-Gg + RTdl n

H P-G + g G V TdkS m

RTdln

+ RTdln ~ TdkS m

+ RTdln ~

b I, 5

121 IO

=

HL_ G + RTdln g

IOb

131

I, 5

/As regards the comparison between the J-T model and the others, the formula employed is of formal character due to different significance of the parameter Sm/ where: R - 6as constant, T d - spreading temperature, t d spreadlng time, D~ - GB self-dlffusion coefficient, S~ - width of dislocation core /the P-G and L-G models/ distance between dissoclated dislocations /the J-T model/, ~ - width of boundary, G - shear modulus, V - atomic volume, k - the Boltzmann constant, b - the Burgers vector. Allowing for the fact that I O b ~ 1,5~, it can be stated that the formulae of LoJkowski-Grabski and Johannesson-Th~len are very similar. The Pumphrey-Gleiter formula, however, differs distinctly. And yet, all of them appear in the literature. This raises some doubt as to the legitimacy of using any of them to calculate Hg. Therefore it is necessary to decide which of the presented formulae is most adequate. Such a decision can be made by means of testing the formulae with different types of testing techniques. So far the question about the formulae remains unanswered. Therefore, these formulae can be used without ambiguity only when they lead to quantatively insignificant differences in results. The calculatlons made by Varin [I] for austenitic stainless steel may serve as an example Provided that the appropriate formula is choosen, the errors committed during determining H~ can be divided into two groups: systematic errors and accidental errors. The~first group includes a possible error in choosing the formula on td, using wrong values of the parameters G, V etc. The second group includes

545 0036-9748/86 $3.00 + .00 Copyright (c) 1986 Pergamon Press Ltd.

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EXTRINSIC GBDS

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errors committed during measuring the time, t d and temperature, T d The main potential sources of systematic errors are different'values of D~ and Sm, which have not been unequivocally and precisely fixed in the available literature. It is convenient to analyse the effect of Sm and D~ values u s e d i n calculating Hg parallel to the analysis of errors in T and t m~asurement. The effect of the accuracy of T and t measurement and the accuracy of the adopted D~ and S m values can be analysed by means of error calculation method /tables II and III/. Errors for the selected FCC metals /nickel, austenitic steel and aluminium/ - Tables IV-VI were calculated for cases of extreme inaccuracy. Data presented in Tables II-IV show that temperature and time have the greatest effect on the precision of the calculated Hg values. It can be noticed, however, that measurement of EGBD spreading temperature with an accuracy of 30 K /which seems to be an exaggerated inaccuracy/ results in a maximum 10% error in the calculated GB self-diffusion enthalpy. It has to be pointed out that both temperature and time in the process of EGBD spreading are.parameters whose measurements are relatively accurate, especially when Varin s procedure is employed [1]. This means that the measurements of temperature and time of EGBD spreading, which are relatively accurate, can be excluded as a potential source of error in evaluating Hg. From the Tables II-IV it follows also that errors in D~ and Sm cause minor charges in the value of GB self-diffusion enthalpy. Therefore, measurements of EGBD spreading kinetics, with all the above reservations concerning the choice of the model, make it possible, in the case of many materials, to adequately assess the value of H e. The above analysis rationalizes unexpected pre~ision obtained in Hg calculations by means of EGBD spreading parameters [1, 3] References I. Varin R.A.: Z. Metallkde. Bd. 73H, 10, 653, /1982/. 2. Swiatnicki W.A., Lojkowski W., Grabski M.W.: submitted to Acta Met., /1985/. 3. Lojkowski W., Grabski M.W.: in: "Deformation of Polycrystals Mechanisms and ~.~crostructures" eds: N.Hansen et all. 2nd Ris~ Int. Symp. on Metallurgy and Mater. Sci., 329, /1981/. 4. Johannesson Y., ThNlen A.: Met. Sci., 189, /1972/. 5. Pumphrey P.H., Gleiter H.: Phil. Mag., 30, 593, /1974/. 6. Kurzydlowski K.J., Wyrzykowski J.W., Pakiela Z. and Grabski M.W.: Met. Sci. and Eng., 72, L13, /1985/. 7. Lojkowski W., Grabski M.W.: S~ripta Metall., 13,511, /1979/. 8. Brown A.M., Ashby M.F.: Acta ~letallurgica Vol. 28, 1085, /1980/. Table I Activation enthalpy of grain boundary self-diffusion derived from different models of EGBD spreading

The Pumphrey-Gleiter model

Hg =

RTdlU

Sm

I~-QI The LoJkowski-Grabski model

t~ D ° a2

Rg =

RT dln

Hg =

RTdln

~L-G/

td G ~ V

DRo T d 1Ok S 3 m

td G b V D ° The Johannesson-Th~len model

IJ-~l

Td 1 , 5 k S 3 m

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547

Table II Expressions describing absolute errors in determining

Hg

3 Hg A T

At

At RT d , td

RAT Ln

J-T

RT d

. ,

Hg

Sm

tdD~

sF

td

Tdl OkS3m

At

tdD ~ G b V

ASm

ASm RTd

D~

-2RT d Sm

RAT( td QV _ I)

~t L-G

o

5~

td

P-G

Hg

Hg

-

ASm RTd

o Dg

-3RT d

o

-3RT d

Sm

1)

ASm

RT d

RTd

'"

td

Dg

Sm

Table III Expressions describing relative errors in determining Hg, resulting from inaccurate measurements of EGBD spreading temperature Hg/Hg

0 H~ AT I Hg O Td AT

P-G

Td AT L-G

AT A

Td

Td

AT

AT

Td

Td

J -T

where:

R AT A = -~-g A-->O

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Table IV Relative error in Hg value caused by inaccurate measurements of Td,t d and Sm,D ~ /the data have Been taken from [8,6]/ NICKEL

~H@t

HgA T

Model

/

0t d

/ He

0 Td

sm

[%]

[%1 i

Accepted aeas~ing error

& t = 60 s

,

,

i

~Sm,, 1 -10"8n

~T= 30K

P-G

8,0

6,1

0,1

1,5

L-G

8,8

5,9

O,1

2,2

J-T

8,4

5,9

0,1

2,1

AUSTENIT

~HgAt Model

HgAT

/ Hg

Ot d

STEEL

IC

/ Hg

Td

0H Sm / Hg

Do /Hg

"D s m

o 0,1 D~ ~Dg=

~Sm= 1.10-8m

4,1

O,1

0,1

7,5

4,5

0,1

0,2

7,2

4,3

0,1

0,2

Accepted .easuring e r r o r

~ t = 60 s

P - g

6,8

L - G

J - T

&T = 30K

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549

Table V o Relative error in Hg value caused by i n a c c u r a t e measurements of Td,t d and Sm, Dg /calculated for T d = 295 K, t d = 30s/ A L U M I N I U M

Model

DBg~t

Dtd Accepted aeasuring error

I Hs

I Hs

~

HgASm / Hg sm

&T= 30K

t = 60 s

=]~= o,1 D;

~.S== 1 "10-8m

P-G

8,4

10,1

0,2

0,1

L-G

9,7

9,7

0,3

0,1

J-T

9,7

9,7

0,2

0,1

Table VI Relative error in ~ v a l u e caused by inaccurate measurements /the data have been taken from [7,81/

Model

tel

Accepted neasuring error

A t = 60 s

P - G

0,2

o / Hs

/ Hg

I Hs

,

~HgASm / Hg sm

Td

£ T = 30K

of Td,t d and Sm, Dgo

&D~ =

0,1 D~

&Sin= 1.10-8m

10,2

0,2

0,1

,,,,

L - g

0,3

9,8

0,2

0,1

J-T

0,2

9,8

0,2

0,1