- Email: [email protected]
Grain boundary segregation and diffusion in Ag-S solid solution
GRAIX BOUNDARY SEGREGATION AND DIFFWIOIt’ IN Ag-S SOLID SOLUTION B. AI..%‘IL~k’,F. CABM’%BR5iJTY Lboraroire
and J. CAB.Lt’E
5;~ Mtralhngie. ERZI t;j2. Facutte des Sciences et Techniqws (3X. Marseille fidex J. France (Recrired 23 Mnrch 1979; in rrvi.&Jorm
St J&r&e. rue H. PoincarS.
19 June I979)
4bstract-4 study is presented of grain boundary equilibrium segregation and diffttsion of sulphur :n high purity si!ve..r uii’ng the “S radiotracer. At S5WC: the segregation coefhcienr x = C,,,;‘C, does not depend on the bulk concentration C, for very low concentrations; it depends only on temperature: the energy for suiphur grain boundary interaction is AH = - 15,ooOcal~mole-r. For higher C,, z decreajss nhile the se!repared sulphur varies slightly. The simultaneous study of both equilibrium segregation and diffusion brings out the close relationship between these two phenomena. At a given temperature. the comples variations of rD,, are explained by the increase of &,-for very low bulk con~ntr~tjons and b:; a decrease of x fur higher ones. For C, constant, the grain boundary diffusion energ) Qyb (33,SO$catimole-’ ) 13 .- derived from the measured scrivation energy (Q,, + AH = IY.51Mcat~mole-~). R&m&-La segregation d’equilibre et la diffusion intergranuiaires du soufre, sent itudiees dans I’argent de haute purete. 6 (‘aide du radiotraceur 35S A 550°C, les variations du coefficient de segregation 2 = C, ‘C;. montrent qu’aux trts faibles concentrations z n’est pas fonction de C,; ii dtpend se&meat de la rempir;l:er: et I’6nergie &interaction soufrc-joint de grains est AH = - 15.000 cai. mold- r, Quand la concentration C,. augmente. x diminue tandis que la quantitt; de soufre segrege varie pw L’t:u& simulranee de 1~segregation d’tquilibre et de la diffusion met en tvidence les liens btroits entre ces deux ph&omt?nes. ‘4 temp&atur* i &onstante, ^ les variations complexes de xDj s’e.xpliquenr par une augmentation de Dj avec C, aux tres faibfes concentrations, par la diminution dz z aux concentrations pins e!ev&s. En maintenant C, Constant. i’tnergie &activation de diffusion intergranulaire Q: C33.500sai . mole_’ f est deduite de i’energie d’activation mesuree (Qj t AH = 15.500 cal*mote-‘1, Zusammenfassuog-Mit dem aktiven Isotop S3’ wurde die Gteichgewichtssegregation an Korngenzen und die Korn~enzdiffusion von Schwefel in hochreinem Silber untersucht. Bei 550°C ist der Sexesationskoeffizien: I = C&C, bei kleinen Konzentrationen C, konzentrationsunabhPngig: er hXngt nur van von Schwefel mit Korngrenzen ist AN = der Temperatur ab; die Wechseiwirkungsenergien - 15.000cal~~lo!c-‘. Bei grol3erem C, wird x kleiner; die Menge des segre$iertcn Schwefe!s Pnderr sich leicht. Die gleichzeitige Lintersuchung der Gleichgewichtssegregation und der Diffusion weist die enge Beziehung zwischen diesen beiden Erscheinungen auf. Bei konstanter Temperatur werden die komplexen Anderungen von x*Byb mit einem Anstieg von Dgbbei sehr kleinen Konzentrationen C,, und mit einer Verkicinerung von r bet hoherer Konzentration. Bei konstantem Cb wird die Aktivietungsenergie tir Korngrenzdiffusiun Qgb ~33,j~~~-~~ole-‘) aus der gemessenen ~kt~vierung~ner~e abgeteitet. I@, t AH = I J.-iifocal .
1. I~TRODZI’CXION In a solid at equilibrium. some elements in solution have a tendency to accumulate at dislocations[l J, grain boundaries [L] and free surfaces [3]: thus, for sulphur in copper. E. Maya measured a segregation coefficient z = C,, C, h %X0 at grain boundaries. This very important enrichment must be taken into account when grain boundary diffusion is studied; it can be done easily with the following assumptions: (i) an equilibrium is rapidly established near the grain boundary (the hypothesis being checked on the surface [3]): (ii) x and D,, (respectively segregation coefficient and grain boundary diffusion coefficient) only depend on temperature. Then the penetration curve derivated from the
Fick’s laws on11 leads to the product rD,,. Accordingly, the temperature dependence of this experimental parameter must be written
where Qgb is the activation energy for grain boundary diffusion and AH is the enthalpy variation related to the chemical equilibrium S* 72 Syb.
(2)
Sb representing the sulphur dissolved in the bulk. and S,, the sulphur segregated at the grain boundary. For suiphur in copper. E. Maya [?I found AH = - l3,000cal~molr-~ and Qgh= 3_;.OrX)cal. mole- f respectively. pointing out experimentally the im~rtant role plaved b) segregzion in a
1850
AUFRAY d at: G&41X BOW.DARY
SEGREGATIOX
AND DIFFUSIOW
Fig. 1. A ‘manufactured’ grain boundary (Scanning Electron Microscopy).
diffusion field. However the sulphur solubility in copper is always very low [J] (some 10T6 in weight), limited by the formation of copper sulphide: our field of investigation is therefore very narrow. From this point of view, the Ag-S system looks more interesting as solubility reaches some lo-’ in weight and the Ag(S) and Cu(S) solid solutions behave similarly [4,5]; the larger solubility in silver is mainly due to the lower stability of silver sulphide compared to copper sulphide [S]. In the present paper, segregation (z) and diffusion (zD,) of sulphur in silver are experimentally studied with regards to the bulk concentration to clarify the role played by equilibrium segregation on grain boundary diffusion.
2. EXPERIMENT.AL
PROCEDURES
These techniques are similar to those previously described [Z] for grain boundary studies in copper; so, we shall only describe here the typical points of our own procedures. All the samples are made from 99.999% Johnson Matthey silver which contains in fact some 10m6 at-at- ’ copper and iron [7] and some dissolved oxygen, the last impurity being removed by annealing under vacuum at 900°C. The preparation of the samples is somewhat different, according to their use. For segregation measurements, a silver platelet (20 x 20 x 0.05 mm) and a silver plate (20 x 20 x 1 mm) are heated. fastened together at 930°C under vacuum for about 20 h; then a single solid, presenting a quite plane interface parallel to the free surface at a distance of O.O5mm, is obtained.
Observed in the scanning electron microscope, this ‘manufactured’ interface appears to be like a set of grain boundaries with the same aspect as grown-in boundaries (Fig. 1). On the other hand, for diffusion measurements, silver rods are first heated at 700°C during 20h, in a very dilute H2-H$S mixture and then cold rolled to plates of about 2 mm thick. Then a 20 h recrystallization anneal is performed at 700°C in a mixture defined by p,&pH2 = 1.5 x 10e3. The fact that we introduce and maintain a small quantity of sulphur during these processes avoids a too rapid growth of the crystals which appear at 600°C in pure silver. In all cases, particular care is paid to the surface preparation by mechanical and chemical polishing. As for copper, the thermal treatments with sulphur are made in HI--H2S mixtures but our apparatus (Fig. 2) includes 3 furnaces instead of the two we had previously described in [2]. Thus, different radioactive and inactive HZ-H2S mixtures can be prepared in the circuits F,P,R,Rt and F2P2R,R,. and sent successively to the sample placed in F,. This process does not alter the sample temperature. After a rapid cooling, the samples are analyzed by alternative chemical dissolutions parallei to the free surface and superficial ‘?S activity measurements. 3. EQUILIBRIUM GRAEU BOUNDARY SEGREGATIOK 3.1 Segregation coefficient measurements Every sample with a Large grain boundary parallel to ?he free surface, is heated at 55o’C for 15 days in a
AUFRAY et af: GRAIN BOUNDARY
SEGREGATION
1851
AND DIFFUSION
Fig. 2. Apparatus for heat treatment in H,-H,S
mixtures.
(ii) For 0.04 < x c; 0.05 mm, the increase of activity comes from the silver screened fi rays emitted by the sulphur segregated at the ‘manufactured’ grain boundary. (iii) For x = 0.05 mm, the rapid fall in activity shows that the grain boundary has just been passed over. If A,,,,, is the maximum activity and A, the bulk activity near the boundary, the activity A, of the segregated sulphur is given by
HZ-H2 “S mixture; the sulphur 1eveI concentration then remains approximately equal to a depth of about 0.06 mm and, according to the mixture composition, it varies in weight fraction from 0 to 100 x 10-6. The depth dependence of the superficial 35S activity measurements is represented in Fig. 3; it can be divided into three different parts: (i) For x x 0.04 mm and x > 0.05 mm, the small decrease of activity is a result of bulk diffusion. For each step the con~ntration C, can be derived from the A”, value corresponding to the known solubility (5) and the slope of the penetration curve. It can also be calculated if the standard activity A, of a sulphur chemisorbed monolayer (39 x 10-sg-cm-2 from [8]), is measured; constant
A@b = A,,-
A,.
It is related to the sulphur grain boundary concentration Cgb by
Agb 1 cgb = r-$39
x
10-9,
1
C* = -$;39
x 10-9,
with 6 the width of the grain boundary. and (4), we find
n with p the absorption coefficient for sulphur /I rays by silver (3,400 cm-‘), p the silver specific mass and Ab the bulk activity.
-.A
l l
I 20
r I: (A,,, - Ab) t_ Ab
-m-*s I 40
I
20
Using (3)
30
X,
L.__*_ I
I
50
60
*---•70
pm
Fig. 3. “S activity as a function of depth in a segregated sample: for .X= 0, A = AO,and A=A_.
(5)
for x =
%prn.
1852
AUFRAY et al: GRAIN BOUNDARY
SEGREGATION
AND DIFFUSION
Table 1. Segregation results
(
X:b6) 0.35 * 0.02 2
11.400 * 500
fJ P/,
0.35 * 0.02 9700~1cQo
5
0.6 f 0.2 11$00+500
4.5
6.4 + 1 4900~600
9
7.4 + 1
23 + 2
3100 + 500
42
1400 + IGOO
31
92 + 4 900 * 300
44
-100
u is the percentage of monolayer in the grain boundary, derived from Cb and z.
It is difficult to calculate errors in a, although those of activity measurements (A,,,, AJ are approximately known; in fact, one must take into account the quality of the ‘manufactured’ grain boundary and the parallelism of the slices; especially as shown on Fig. 1, the flatness of this grain boundary is not rigorous, that is why the activity fall near 0.05 mm spreads over some micrometers. At last the reproducibility of the results seems to be the best way to test and trust our measurements. 3.2 Segregation results: isotherm at 550°C The results obtained at 550°C according to the bulk concentration are represented in Table 1. For very low levels, the segregation coefficient remains approximately constant: subsequently the grain boundary concentration increases linearly (Fig. 4). In this field, the bulk and the grain boundary concentrations are both small and the equilibrium constant related to the segregation equilibrium (2) is expressed by a=
c
AH
b=aoexp-=. Cb
For sulphur in copper we have z,, = 1.5, in agreement with MacLean’s assumption [8] a0 ‘c 1’; using the same approximation, our results lead to AH = - 15,OOOcal*mole-’ which is the segregation enthalpy or the interaction energy between the dissolved sulphur and the grain boundary. When the bulk level increases to the solubility Ii&, the segregation coefficient quickly decreases; in this field, the grain boundary concentration remains constant for 2 x 10e6 < Cb < 23 x 10s6 (Fig. 4), then increases again and the quantity of segregated sulphur is about a superficial monolayer at the solubility limit.
. ,/--
3.104-
Due to lack of experimentation, it is difficult to clarify the behaviour of the grain boundary in this last field. 4. GRAIN BOUNDARY 4.1 Measurement
DIFFUSION
of the diflusion parameter rD,,
A polycrystalline sample prepared as described above, is raised to the diffusion temperature under a hydrogen atmosphere in the furnace F, (Fig. 2). There, it is submitted to the following treatment: firstly, a long anneal in a H,-H,S mixture (PHJpH2 = 1.5 x 10m3); a homogeneous solid solution Ag-S is then found to a depth of about 0.1 mm. Then secondly, a short diffusion anneal in an equivalent radioactive mixture: the radiotracer then penetrates the solid with no change of its chemical composition. This procedure actually gives access to the impurity (sulphur) self diffusion. The experiment is stopped by a rapid cooling followed by sample analysis of the depth x. The concentration curve C = f(x) is derived from the activity measurements A = f(x) using Gruzin’s method [lo]. With Whipple’s solution [ 111 for the Fick’s law integration and Leclaire’s approximation [12], the diffusion parameter is calculated from either A = f(x) or C = f(x) (Fig. 5)
valid for fl> 5 B =with 6 the apparent
adD,b t&,&t
width of the grain boundary
___--________~----_--
"0 /'
l
", 2.104 1' 3 I IO4 -I I t I
I IO
I 20
I 30
c, x I06
Fig. 4. Grain boundary concentration
C,, as a function of bulk concentration
(C,): isotherm at 55O’C.
AUFRAY er al: GRAIN BOUNDARY
x %
SEGREGATION
AND DIFFUSION
-I2 I-
Fig. 5. Penetration curve log A = f(~~~~),for grain troundary diffusion.
t
I
I
I2
I3
104/i; Fig.
(generahy taken equaf to 5 x tO-scm in metals); 4 the bulk diffusion coefficient; t the length of the diffusion anneal. Because of the reproducibility of our results, we can approximately evaluate the errors of a&, to 15%.
I li
7.
K-’
Temperature dependence of XI),,.
and for very low bulk concentrations is represented by
the segregation
Sb r? S,, with Cpcl= Cb exp ------. Rf
(8)
4.2 Resufrs Bulk c~~centr~tj~n effect, In Fig. 6, diRitsion parameters measured at 480°C are plotted vs bulk concentration. Despite the small number of experiments, there seems to be a good concordance between these results and those obtained by Gas and Bernasdini for tin diffusion in Ag-Sn alioys [13]. When CI, increases, the diffusion parameter increases rapidly for low bulk concentrations and then decreases quite rapidly. Temperuture effect. From (I), the influence of temperature can easily be explained as long as E and Deb anly depend on temperature, but a gfance at Fig. 6 shows that this is not obvious: Dgbdepends essentialfy on the ex~rimenta1 conditions (C,, C,,). Indeed, the sulphur bulk solubihty in H,-H$ mixtures is given by [S] H, s Sb + HZ with C, = 1.5 ‘xexp
- 1F
(7)
That is to say
In the end, C,, hardly varies with temperature when the mixture composition (PH9/pH2)stays the same. In our procedures, the ratio pHS,:pH2 is I.5 x 10m3. By (7), we can see that the bulk solubilities are then contained between 0.2 and 1.6 x 10e6 when temperature varies from 478 to 698°C; according to the isotherm, this is the case where z is independent of bulk concentration and only changes with tem~rature. In Fig. 7, we have represented z& variations with the reverse temperature. This allows us to write Deba = 5.8 exp -
18,500 RT
PH2
Using (8), we obtain D,
33,500 RT
= 5.8exp - -.
Let us recall our results for segregation at SST. At very low bulk concentrations, we have a rapid increase of the grain boundary concentration joined to a constant segregation coeffcient; in this field, there is no interaction between the sulphur atoms: Henry’s law is followed in the bulk and in the boundary. But when C* increases and is near the solubility limit, we observe a decrease of the segregation coeEicient 0: while the segregated quantity increases slowly and almost attains a monolayer.
lSj-1
AUFRAY et al: GRAIN BOUNDARY SEGREGATION AND DIFFUSION
As far as grain boundary segregation depends on the relative crystallographic orientation, an experimental result obtained on a set of various grain boundaries seems to be a mean value difficult to explain at the atomic scale. For instance, it is difficult to define precisely the limit between the 2 domains described above or to give an exact definition of saturation. Anyhow it is obvious that S-S interactions appear far below the solubility and also that, as a free surface [8][3], the grain boundary becomes saturated. We can extend our results to other temperatures, with the following fair assumptions (i) for very low concentrations, z only depends on temperature; and (ii) the maximum segregated quantity weakly depends on temperature. These assumptions allow us to clearly explain the ‘complicated’ variation of rD,, with the sulphur bulk concentration, this evolution being directly related to the shape of the segregation isotherm. In Fig 6, the first part where a.D,(, increases, corresponds to some extent to the field where z is constant; in this case, D,, increases with C,,. In the second part, the grain boundary becomes saturated and C,, is quite constant so that the diffusion coefficient no longer varies when rl decreases. The diffusion parameter aD,, roughly varies as the inverse of the bulk concentration. When C,, remains constant and small, the influence of temperature on the diffusion coefficient gives an activation energy higher than expected for grain boundary diffusion in metals, and rather close to the activation energy for bulk diffusion
should then consider that the small difference between Q”,(,and Qsbis a consequence of the decrease of the formation enthalpy of defects compensated for by a significant increase of the migration enthalpy included in the total activation energy. CONCLUSION
This study about grain boundary equilibrium segregation in !S-Ag solid solutions leads us to clarify the effect of bulk concentration on sulphur segregated in the boundary: it is obvious that grain boundaries are quite saturated for very low bulk concentrations, far below the solubility limit. The simultaneous study of equilibrium segregation and grain boundary diffusion stresses the close relationship existing between these phenomena: this leads to the real grain boundary diffusion coefficient, clarifies the apparently complicated dependence of zD,, on the bulk concentration and also explains why the activation energy is higher than expected. In fact, this work is based on a set of grain boundaries with various crystallographic data. This puts a limit to our explanations; the segregation measurements do indeed represent a mean value while the diffusion ones especially concern the boundaries with high diffusivity. For all these reasons. this work is now going on in our laboratory with bicrystals. REFERENCES
F. Moya, G. E. Moya-Gontier and F. Cabane-Brouty, Phys. Star. Sol. (a) 2, 101 (1970). 2. F. Moya and G. E. Moya-Gontier, J. Phys. 36 C4, 157 [14] sulphur diffusion in silver (1975). 3. P. Petrino, F. Moya and F. Cabane-Brouty, J. Solid Q”,, = 33,500 Cal- mole - ’ State Chem. 2,439 (1970). Qt = 37,100 cal-mole-’ 4. F. Moya, G. E. Moya-Gontier, F. Cabane-Brouty and J. Oudar, Acta metall. 19, 1189 (1971). [ 151 self diffusion 5. N. Barbouth and J. Oudar, C.r. Acad. Sci. Paris, 267, 644 (1968). Q,“b’= 20,000 cal.mole-’ 6. F. D. Richardson and J. H. E. Jeffes, J. iron Steel Inst. Qt* = 46,000 cal.mole-’ II161 171, 165 (1952). 7. G. Mathieu, S. Guiot and J. Le Hericy. Mem. scient. Revue M&all. 4, 281 (1976). The noticeable differences usually observed 8. J. Benard. J. Oudar and F. Cabane-Brouty, Surface Sci. 3, 359 (1965). between Qgband Qb can be explained by an important 9. D. MacLean, Grain Boundaries in Metals pp. 143, 117. decrease of the formation enthalpy of point defects, Clarendon Press (1957). due to the boundary structure. But as far as we can 10. G. Seibel, Int. J. appl. Rad. Isotopes 15, 679 (1964). compare sulphur with metallic impurities, another 11. R. T. P. Whinnle, Phil. Mau. 45, 1225 (1954). point of view must be retained, i.e. the great tendency 12. A. D. Le Claire, Brit. J. appl. Phys. 14,.351 (1963). 13. P. Gas and J. Bernardini. Surface Sci. 72. 365 (1978). of sulphur to accumulate at the grain boundary, as14. J. Ladet, B. Aufray and’ F. Maya, Me&l Se;. 4, 195 sociated with the fact that S-Ag are more strongly (1978). stuck together in the boundary than in the bulk, the 15. G. Martin and B. Peraillon, J. Phys. 36 C4, 165(1975). result being a greater difficulty for sulphur to jump in 16. J. Bernardini and J. Cabane, Acra metal/. 21, 1561 (1973). a grain boundary than in a bulk concentration. We 1.
and J. CAB.Lt’E
5;~ Mtralhngie. ERZI t;j2. Facutte des Sciences et Techniqws (3X. Marseille fidex J. France (Recrired 23 Mnrch 1979; in rrvi.&Jorm
St J&r&e. rue H. PoincarS.
19 June I979)
4bstract-4 study is presented of grain boundary equilibrium segregation and diffttsion of sulphur :n high purity si!ve..r uii’ng the “S radiotracer. At S5WC: the segregation coefhcienr x = C,,,;‘C, does not depend on the bulk concentration C, for very low concentrations; it depends only on temperature: the energy for suiphur grain boundary interaction is AH = - 15,ooOcal~mole-r. For higher C,, z decreajss nhile the se!repared sulphur varies slightly. The simultaneous study of both equilibrium segregation and diffusion brings out the close relationship between these two phenomena. At a given temperature. the comples variations of rD,, are explained by the increase of &,-for very low bulk con~ntr~tjons and b:; a decrease of x fur higher ones. For C, constant, the grain boundary diffusion energ) Qyb (33,SO$catimole-’ ) 13 .- derived from the measured scrivation energy (Q,, + AH = IY.51Mcat~mole-~). R&m&-La segregation d’equilibre et la diffusion intergranuiaires du soufre, sent itudiees dans I’argent de haute purete. 6 (‘aide du radiotraceur 35S A 550°C, les variations du coefficient de segregation 2 = C, ‘C;. montrent qu’aux trts faibles concentrations z n’est pas fonction de C,; ii dtpend se&meat de la rempir;l:er: et I’6nergie &interaction soufrc-joint de grains est AH = - 15.000 cai. mold- r, Quand la concentration C,. augmente. x diminue tandis que la quantitt; de soufre segrege varie pw L’t:u& simulranee de 1~segregation d’tquilibre et de la diffusion met en tvidence les liens btroits entre ces deux ph&omt?nes. ‘4 temp&atur* i &onstante, ^ les variations complexes de xDj s’e.xpliquenr par une augmentation de Dj avec C, aux tres faibfes concentrations, par la diminution dz z aux concentrations pins e!ev&s. En maintenant C, Constant. i’tnergie &activation de diffusion intergranulaire Q: C33.500sai . mole_’ f est deduite de i’energie d’activation mesuree (Qj t AH = 15.500 cal*mote-‘1, Zusammenfassuog-Mit dem aktiven Isotop S3’ wurde die Gteichgewichtssegregation an Korngenzen und die Korn~enzdiffusion von Schwefel in hochreinem Silber untersucht. Bei 550°C ist der Sexesationskoeffizien: I = C&C, bei kleinen Konzentrationen C, konzentrationsunabhPngig: er hXngt nur van von Schwefel mit Korngrenzen ist AN = der Temperatur ab; die Wechseiwirkungsenergien - 15.000cal~~lo!c-‘. Bei grol3erem C, wird x kleiner; die Menge des segre$iertcn Schwefe!s Pnderr sich leicht. Die gleichzeitige Lintersuchung der Gleichgewichtssegregation und der Diffusion weist die enge Beziehung zwischen diesen beiden Erscheinungen auf. Bei konstanter Temperatur werden die komplexen Anderungen von x*Byb mit einem Anstieg von Dgbbei sehr kleinen Konzentrationen C,, und mit einer Verkicinerung von r bet hoherer Konzentration. Bei konstantem Cb wird die Aktivietungsenergie tir Korngrenzdiffusiun Qgb ~33,j~~~-~~ole-‘) aus der gemessenen ~kt~vierung~ner~e abgeteitet. I@, t AH = I J.-iifocal .
1. I~TRODZI’CXION In a solid at equilibrium. some elements in solution have a tendency to accumulate at dislocations[l J, grain boundaries [L] and free surfaces [3]: thus, for sulphur in copper. E. Maya measured a segregation coefficient z = C,, C, h %X0 at grain boundaries. This very important enrichment must be taken into account when grain boundary diffusion is studied; it can be done easily with the following assumptions: (i) an equilibrium is rapidly established near the grain boundary (the hypothesis being checked on the surface [3]): (ii) x and D,, (respectively segregation coefficient and grain boundary diffusion coefficient) only depend on temperature. Then the penetration curve derivated from the
Fick’s laws on11 leads to the product rD,,. Accordingly, the temperature dependence of this experimental parameter must be written
where Qgb is the activation energy for grain boundary diffusion and AH is the enthalpy variation related to the chemical equilibrium S* 72 Syb.
(2)
Sb representing the sulphur dissolved in the bulk. and S,, the sulphur segregated at the grain boundary. For suiphur in copper. E. Maya [?I found AH = - l3,000cal~molr-~ and Qgh= 3_;.OrX)cal. mole- f respectively. pointing out experimentally the im~rtant role plaved b) segregzion in a
1850
AUFRAY d at: G&41X BOW.DARY
SEGREGATIOX
AND DIFFUSIOW
Fig. 1. A ‘manufactured’ grain boundary (Scanning Electron Microscopy).
diffusion field. However the sulphur solubility in copper is always very low [J] (some 10T6 in weight), limited by the formation of copper sulphide: our field of investigation is therefore very narrow. From this point of view, the Ag-S system looks more interesting as solubility reaches some lo-’ in weight and the Ag(S) and Cu(S) solid solutions behave similarly [4,5]; the larger solubility in silver is mainly due to the lower stability of silver sulphide compared to copper sulphide [S]. In the present paper, segregation (z) and diffusion (zD,) of sulphur in silver are experimentally studied with regards to the bulk concentration to clarify the role played by equilibrium segregation on grain boundary diffusion.
2. EXPERIMENT.AL
PROCEDURES
These techniques are similar to those previously described [Z] for grain boundary studies in copper; so, we shall only describe here the typical points of our own procedures. All the samples are made from 99.999% Johnson Matthey silver which contains in fact some 10m6 at-at- ’ copper and iron [7] and some dissolved oxygen, the last impurity being removed by annealing under vacuum at 900°C. The preparation of the samples is somewhat different, according to their use. For segregation measurements, a silver platelet (20 x 20 x 0.05 mm) and a silver plate (20 x 20 x 1 mm) are heated. fastened together at 930°C under vacuum for about 20 h; then a single solid, presenting a quite plane interface parallel to the free surface at a distance of O.O5mm, is obtained.
Observed in the scanning electron microscope, this ‘manufactured’ interface appears to be like a set of grain boundaries with the same aspect as grown-in boundaries (Fig. 1). On the other hand, for diffusion measurements, silver rods are first heated at 700°C during 20h, in a very dilute H2-H$S mixture and then cold rolled to plates of about 2 mm thick. Then a 20 h recrystallization anneal is performed at 700°C in a mixture defined by p,&pH2 = 1.5 x 10e3. The fact that we introduce and maintain a small quantity of sulphur during these processes avoids a too rapid growth of the crystals which appear at 600°C in pure silver. In all cases, particular care is paid to the surface preparation by mechanical and chemical polishing. As for copper, the thermal treatments with sulphur are made in HI--H2S mixtures but our apparatus (Fig. 2) includes 3 furnaces instead of the two we had previously described in [2]. Thus, different radioactive and inactive HZ-H2S mixtures can be prepared in the circuits F,P,R,Rt and F2P2R,R,. and sent successively to the sample placed in F,. This process does not alter the sample temperature. After a rapid cooling, the samples are analyzed by alternative chemical dissolutions parallei to the free surface and superficial ‘?S activity measurements. 3. EQUILIBRIUM GRAEU BOUNDARY SEGREGATIOK 3.1 Segregation coefficient measurements Every sample with a Large grain boundary parallel to ?he free surface, is heated at 55o’C for 15 days in a
AUFRAY et af: GRAIN BOUNDARY
SEGREGATION
1851
AND DIFFUSION
Fig. 2. Apparatus for heat treatment in H,-H,S
mixtures.
(ii) For 0.04 < x c; 0.05 mm, the increase of activity comes from the silver screened fi rays emitted by the sulphur segregated at the ‘manufactured’ grain boundary. (iii) For x = 0.05 mm, the rapid fall in activity shows that the grain boundary has just been passed over. If A,,,,, is the maximum activity and A, the bulk activity near the boundary, the activity A, of the segregated sulphur is given by
HZ-H2 “S mixture; the sulphur 1eveI concentration then remains approximately equal to a depth of about 0.06 mm and, according to the mixture composition, it varies in weight fraction from 0 to 100 x 10-6. The depth dependence of the superficial 35S activity measurements is represented in Fig. 3; it can be divided into three different parts: (i) For x x 0.04 mm and x > 0.05 mm, the small decrease of activity is a result of bulk diffusion. For each step the con~ntration C, can be derived from the A”, value corresponding to the known solubility (5) and the slope of the penetration curve. It can also be calculated if the standard activity A, of a sulphur chemisorbed monolayer (39 x 10-sg-cm-2 from [8]), is measured; constant
A@b = A,,-
A,.
It is related to the sulphur grain boundary concentration Cgb by
Agb 1 cgb = r-$39
x
10-9,
1
C* = -$;39
x 10-9,
with 6 the width of the grain boundary. and (4), we find
n with p the absorption coefficient for sulphur /I rays by silver (3,400 cm-‘), p the silver specific mass and Ab the bulk activity.
-.A
l l
I 20
r I: (A,,, - Ab) t_ Ab
-m-*s I 40
I
20
Using (3)
30
X,
L.__*_ I
I
50
60
*---•70
pm
Fig. 3. “S activity as a function of depth in a segregated sample: for .X= 0, A = AO,and A=A_.
(5)
for x =
%prn.
1852
AUFRAY et al: GRAIN BOUNDARY
SEGREGATION
AND DIFFUSION
Table 1. Segregation results
(
X:b6) 0.35 * 0.02 2
11.400 * 500
fJ P/,
0.35 * 0.02 9700~1cQo
5
0.6 f 0.2 11$00+500
4.5
6.4 + 1 4900~600
9
7.4 + 1
23 + 2
3100 + 500
42
1400 + IGOO
31
92 + 4 900 * 300
44
-100
u is the percentage of monolayer in the grain boundary, derived from Cb and z.
It is difficult to calculate errors in a, although those of activity measurements (A,,,, AJ are approximately known; in fact, one must take into account the quality of the ‘manufactured’ grain boundary and the parallelism of the slices; especially as shown on Fig. 1, the flatness of this grain boundary is not rigorous, that is why the activity fall near 0.05 mm spreads over some micrometers. At last the reproducibility of the results seems to be the best way to test and trust our measurements. 3.2 Segregation results: isotherm at 550°C The results obtained at 550°C according to the bulk concentration are represented in Table 1. For very low levels, the segregation coefficient remains approximately constant: subsequently the grain boundary concentration increases linearly (Fig. 4). In this field, the bulk and the grain boundary concentrations are both small and the equilibrium constant related to the segregation equilibrium (2) is expressed by a=
c
AH
b=aoexp-=. Cb
For sulphur in copper we have z,, = 1.5, in agreement with MacLean’s assumption [8] a0 ‘c 1’; using the same approximation, our results lead to AH = - 15,OOOcal*mole-’ which is the segregation enthalpy or the interaction energy between the dissolved sulphur and the grain boundary. When the bulk level increases to the solubility Ii&, the segregation coefficient quickly decreases; in this field, the grain boundary concentration remains constant for 2 x 10e6 < Cb < 23 x 10s6 (Fig. 4), then increases again and the quantity of segregated sulphur is about a superficial monolayer at the solubility limit.
. ,/--
3.104-
Due to lack of experimentation, it is difficult to clarify the behaviour of the grain boundary in this last field. 4. GRAIN BOUNDARY 4.1 Measurement
DIFFUSION
of the diflusion parameter rD,,
A polycrystalline sample prepared as described above, is raised to the diffusion temperature under a hydrogen atmosphere in the furnace F, (Fig. 2). There, it is submitted to the following treatment: firstly, a long anneal in a H,-H,S mixture (PHJpH2 = 1.5 x 10m3); a homogeneous solid solution Ag-S is then found to a depth of about 0.1 mm. Then secondly, a short diffusion anneal in an equivalent radioactive mixture: the radiotracer then penetrates the solid with no change of its chemical composition. This procedure actually gives access to the impurity (sulphur) self diffusion. The experiment is stopped by a rapid cooling followed by sample analysis of the depth x. The concentration curve C = f(x) is derived from the activity measurements A = f(x) using Gruzin’s method [lo]. With Whipple’s solution [ 111 for the Fick’s law integration and Leclaire’s approximation [12], the diffusion parameter is calculated from either A = f(x) or C = f(x) (Fig. 5)
valid for fl> 5 B =with 6 the apparent
adD,b t&,&t
width of the grain boundary
___--________~----_--
"0 /'
l
", 2.104 1' 3 I IO4 -I I t I
I IO
I 20
I 30
c, x I06
Fig. 4. Grain boundary concentration
C,, as a function of bulk concentration
(C,): isotherm at 55O’C.
AUFRAY er al: GRAIN BOUNDARY
x %
SEGREGATION
AND DIFFUSION
-I2 I-
Fig. 5. Penetration curve log A = f(~~~~),for grain troundary diffusion.
t
I
I
I2
I3
104/i; Fig.
(generahy taken equaf to 5 x tO-scm in metals); 4 the bulk diffusion coefficient; t the length of the diffusion anneal. Because of the reproducibility of our results, we can approximately evaluate the errors of a&, to 15%.
I li
7.
K-’
Temperature dependence of XI),,.
and for very low bulk concentrations is represented by
the segregation
Sb r? S,, with Cpcl= Cb exp ------. Rf
(8)
4.2 Resufrs Bulk c~~centr~tj~n effect, In Fig. 6, diRitsion parameters measured at 480°C are plotted vs bulk concentration. Despite the small number of experiments, there seems to be a good concordance between these results and those obtained by Gas and Bernasdini for tin diffusion in Ag-Sn alioys [13]. When CI, increases, the diffusion parameter increases rapidly for low bulk concentrations and then decreases quite rapidly. Temperuture effect. From (I), the influence of temperature can easily be explained as long as E and Deb anly depend on temperature, but a gfance at Fig. 6 shows that this is not obvious: Dgbdepends essentialfy on the ex~rimenta1 conditions (C,, C,,). Indeed, the sulphur bulk solubihty in H,-H$ mixtures is given by [S] H, s Sb + HZ with C, = 1.5 ‘xexp
- 1F
(7)
That is to say
In the end, C,, hardly varies with temperature when the mixture composition (PH9/pH2)stays the same. In our procedures, the ratio pHS,:pH2 is I.5 x 10m3. By (7), we can see that the bulk solubilities are then contained between 0.2 and 1.6 x 10e6 when temperature varies from 478 to 698°C; according to the isotherm, this is the case where z is independent of bulk concentration and only changes with tem~rature. In Fig. 7, we have represented z& variations with the reverse temperature. This allows us to write Deba = 5.8 exp -
18,500 RT
PH2
Using (8), we obtain D,
33,500 RT
= 5.8exp - -.
Let us recall our results for segregation at SST. At very low bulk concentrations, we have a rapid increase of the grain boundary concentration joined to a constant segregation coeffcient; in this field, there is no interaction between the sulphur atoms: Henry’s law is followed in the bulk and in the boundary. But when C* increases and is near the solubility limit, we observe a decrease of the segregation coeEicient 0: while the segregated quantity increases slowly and almost attains a monolayer.
lSj-1
AUFRAY et al: GRAIN BOUNDARY SEGREGATION AND DIFFUSION
As far as grain boundary segregation depends on the relative crystallographic orientation, an experimental result obtained on a set of various grain boundaries seems to be a mean value difficult to explain at the atomic scale. For instance, it is difficult to define precisely the limit between the 2 domains described above or to give an exact definition of saturation. Anyhow it is obvious that S-S interactions appear far below the solubility and also that, as a free surface [8][3], the grain boundary becomes saturated. We can extend our results to other temperatures, with the following fair assumptions (i) for very low concentrations, z only depends on temperature; and (ii) the maximum segregated quantity weakly depends on temperature. These assumptions allow us to clearly explain the ‘complicated’ variation of rD,, with the sulphur bulk concentration, this evolution being directly related to the shape of the segregation isotherm. In Fig 6, the first part where a.D,(, increases, corresponds to some extent to the field where z is constant; in this case, D,, increases with C,,. In the second part, the grain boundary becomes saturated and C,, is quite constant so that the diffusion coefficient no longer varies when rl decreases. The diffusion parameter aD,, roughly varies as the inverse of the bulk concentration. When C,, remains constant and small, the influence of temperature on the diffusion coefficient gives an activation energy higher than expected for grain boundary diffusion in metals, and rather close to the activation energy for bulk diffusion
should then consider that the small difference between Q”,(,and Qsbis a consequence of the decrease of the formation enthalpy of defects compensated for by a significant increase of the migration enthalpy included in the total activation energy. CONCLUSION
This study about grain boundary equilibrium segregation in !S-Ag solid solutions leads us to clarify the effect of bulk concentration on sulphur segregated in the boundary: it is obvious that grain boundaries are quite saturated for very low bulk concentrations, far below the solubility limit. The simultaneous study of equilibrium segregation and grain boundary diffusion stresses the close relationship existing between these phenomena: this leads to the real grain boundary diffusion coefficient, clarifies the apparently complicated dependence of zD,, on the bulk concentration and also explains why the activation energy is higher than expected. In fact, this work is based on a set of grain boundaries with various crystallographic data. This puts a limit to our explanations; the segregation measurements do indeed represent a mean value while the diffusion ones especially concern the boundaries with high diffusivity. For all these reasons. this work is now going on in our laboratory with bicrystals. REFERENCES
F. Moya, G. E. Moya-Gontier and F. Cabane-Brouty, Phys. Star. Sol. (a) 2, 101 (1970). 2. F. Moya and G. E. Moya-Gontier, J. Phys. 36 C4, 157 [14] sulphur diffusion in silver (1975). 3. P. Petrino, F. Moya and F. Cabane-Brouty, J. Solid Q”,, = 33,500 Cal- mole - ’ State Chem. 2,439 (1970). Qt = 37,100 cal-mole-’ 4. F. Moya, G. E. Moya-Gontier, F. Cabane-Brouty and J. Oudar, Acta metall. 19, 1189 (1971). [ 151 self diffusion 5. N. Barbouth and J. Oudar, C.r. Acad. Sci. Paris, 267, 644 (1968). Q,“b’= 20,000 cal.mole-’ 6. F. D. Richardson and J. H. E. Jeffes, J. iron Steel Inst. Qt* = 46,000 cal.mole-’ II161 171, 165 (1952). 7. G. Mathieu, S. Guiot and J. Le Hericy. Mem. scient. Revue M&all. 4, 281 (1976). The noticeable differences usually observed 8. J. Benard. J. Oudar and F. Cabane-Brouty, Surface Sci. 3, 359 (1965). between Qgband Qb can be explained by an important 9. D. MacLean, Grain Boundaries in Metals pp. 143, 117. decrease of the formation enthalpy of point defects, Clarendon Press (1957). due to the boundary structure. But as far as we can 10. G. Seibel, Int. J. appl. Rad. Isotopes 15, 679 (1964). compare sulphur with metallic impurities, another 11. R. T. P. Whinnle, Phil. Mau. 45, 1225 (1954). point of view must be retained, i.e. the great tendency 12. A. D. Le Claire, Brit. J. appl. Phys. 14,.351 (1963). 13. P. Gas and J. Bernardini. Surface Sci. 72. 365 (1978). of sulphur to accumulate at the grain boundary, as14. J. Ladet, B. Aufray and’ F. Maya, Me&l Se;. 4, 195 sociated with the fact that S-Ag are more strongly (1978). stuck together in the boundary than in the bulk, the 15. G. Martin and B. Peraillon, J. Phys. 36 C4, 165(1975). result being a greater difficulty for sulphur to jump in 16. J. Bernardini and J. Cabane, Acra metal/. 21, 1561 (1973). a grain boundary than in a bulk concentration. We 1.