Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://www.issp.ac.ru/libm/papers/158.pdf Äàòà èçìåíåíèÿ: Wed Dec 28 12:47:23 2005 Äàòà èíäåêñèðîâàíèÿ: Tue Oct 2 01:51:54 2012 Êîäèðîâêà: Ïîèñêîâûå ñëîâà: m 103

Acta Materialia 53 (2005) 247­254 www.actamat-journals.com

Faceting of R3 and R9 grain boundaries in Cu­Bi alloys
B.B. Straumal
a

a,*

, S.A. Polyakov

a,b

, E. Bischoff b, W. Gust b, B. Baretzky

b

Laboratory of Interfaces in Metals, Institute of Solid State Physics, Institutskii prospect 15, 142432 Chernogolovka, Moscow District, Russia b Max-Planck-Institut fur Metallforschung and Institut fur Metallkunde, Heisenbergstr. 3, 70569 Stuttgart, Germany ¨ ¨ Received 11 March 2004; received in revised form 11 August 2004; accepted 13 August 2004

Abstract The faceting of R3 and R9 tilt grain boundaries (GBs) has been studied in bicrystals of pure Cu and Cu­Bi alloys containing 2.5 · 10þ3, 10 · 10þ3 and 16 · 10þ3 at.% Bi. The R3(1 0 0), R9(1 0 0), R9(þ1 1 0), and R9(þ1 2 0) facets and non-CSL R3 82° 9R facet were observed, where R is the inverse density of coincidence sites. The ratio between GB energy, rGB, and surface energy, rsur, was measured by atomic force microscopy using the GB thermal-groove method. The GB energy and thermal-groove deepening rate increased slightly between 0 and 10 · 10þ3 at.% Bi for all facets studied. However, between 10 · 10þ3 and 16 · 10þ3 at.% Bi the GB energy increased dramatically [from a factor 2 for the R9(1 1 0) facet to 15 times larger for the R3(1 0 0) facet]. The thermalgroove deepening rate also increased by a factor of 10 in this concentration range. This change corresponds well with the GB solidus line (i.e., the formation of a stable layer of a liquid-like GB phase called GB prewetting) observed previously. Wulff diagrams were constructed using measured rGB/rsur values. ñ 2004 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
Keywords: Grain boundaries; Faceting; Roughening; Cu; Cu­Bi alloys; Prewetting; Phase diagrams

1. Introduction The faceting of low-R grain boundaries (GBs), where R is the inverse density of coincidence sites, plays a special role in polycrystals. In certain materials the number of low-R GBs, especially R3 and R9 GBs, is surprisingly high [1]. An increase in R3 and R9 GBs is accompanied by a marked improvement of the properties, particularly a decrease in GB corrosion rate [2]. Faceting is a characteristic feature for GBs with misorientation angles close to the coincidence misorientation, hR. The presence of GB faceting correlates also with the phenomenon of abnormal grain growth [3]. Faceting may be regarded as a phase transition in which a flat (single phase) interface is transformed into a faceted structure consisting of
Corresponding author. Tel.: +7 09652 22957; fax: +7 095 2382326/ 1117067. E-mail address: straumal@issp.ac.ru (B.B. Straumal).
*

two or more facet types (phases) which coexist along the line of intersection [4]. Another important class of GB phase transformations are GB wetting, prewetting, and premelting transitions, which can drastically change the properties of polycrystals, especially those of nanocrystalline materials. If a GB wetting phase transition proceeds during heating within the two-phase liquid + solid area of the bulk phase diagram (Fig. 1), then the liquid phase forms at the GBs, and replaces them completely since the GB cannot exist in the equilibrium with the melt. The GB solidus in the single-phase S area may be regarded as a continuation of the GB wetting tie-lines which are present in the two-phase liquid + solid area. The GB solidus line is defined as labeled in Fig. 1. GB properties such as GB diffusivity, segregation, mobility, brittleness, plasticity, and electrical conductivity change drastically at GB solidus ([5] and references therein).

1359-6454/$30.00 ñ 2004 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2004.08.015


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1400

L

1300 Segregation 1200

Prewetting

(Cu)+ S
1100 Temperature, K S 1000

(Cu)+

L

S+L

900 Precipitation 800

Tw,max

700 Cu

(Cu)+ L+L
50 100 150 Bi concentration, 10 -4 at.%

Tw,min
200

Fig. 1. Cu-rich side of the Cu­Bi phase diagram. The thick curve is the (retrograde) bulk solidus line [7]. The thin retrograde curve is the GB solidus line obtained for the Cu­Bi polycrystals [7]. The GB wetting phase transition tie-lines at Tw,max and Tw,min in the two-phase S + L area are constructed from the data of [15]. The broken line denotes the annealing temperature of 1293 K. The black squares denote the Bi concentration in the samples (0, 25, 100 and 160 at.ppm Bi).

The discontinuity of the temperature dependence of the GB energy at the GB solidus line in the Cu­Bi system reveals a first order GB prewetting (premelting) phase transition [6]. The coupling of GB faceting and wetting­prewetting phase transitions is of primary importance since it can influence interface-controlled processes in two- and multicomponent polycrystals, like superplasticity, liquid-phase and activated sintering, liquid phase penetration, welding, soldering, penetration of melts and fluids in rocks, etc. [5]. Cu­Bi alloys present a good opportunity to study this coupling since the formation of GB phases was studied recently [5­7], and the influence of Bi additions on GB faceting in Cu is also well documented in the literature [8­10].

formed between them. The (1 1 1)/(1 1 5) inclination of the R9 GB is unstable against the dissociation reaction: R9 ! R3 + R3. Therefore, multiple elongated twins (Fig. 2) with well-developed R3 GBs appear during the growth of a bicrystal instead of {1 1 1}1 /{1 1 5}2 or R9(1 1 0) facets (the subscripts 1 and 2 correspond to the grains 1 and 2) [5]. The [1 1 0] axes in both grains are parallel to the growth axis. Therefore, the R3 [1 1 0] tilt GB in the sample contains all crystallographically possible inclinations. 2.5 mm thick circular platelets were cut from the bicrystal perpendicularly to the growth axis and etched. Next, the vapor transfer method was used to introduce Bi into the Cu platelets. Different annealing times for a vapor transfer from a Cu­0.3 at.% Bi alloy vapor source were chosen in order to produce samples with different Bi content (2.5 · 10þ3, 10 · 10þ3 and 16 · 10þ3 at.% Bi). All samples were homogenized at 1123 K for 168 h in evacuated (5 · 10þ4 Pa) silica ampules without a Bi source. The alloyed and pure platelets were annealed then in a 80% Ar + 20% H2 gas mixture at 1293 K and 2 · 104 Pa for 48 h. During the annealing the GB migrates slowly towards the center of the bicrystal permitting equilibrium facets to develop. The GB shape and geometry of facets were analyzed and photographed in polarized light in bright and dark field with the aid of a Zeiss Axiophot optical microscope and by a Topometrix 2000 Explorer atomic force microscope operating in the contact mode. The samples were then carefully repolished and annealed again for 48 h to form GB thermal grooves. In order to determine the ratio between GB energy, rGB, and surface energy, rsur, the profiles of the GB thermal grooves were analyzed with the aid of atomic force microscopy (AFM). Typically, a 50 lm · 50 lm field containing 500 · 500 pixels was analyzed. For the analysis, 10 neighboring profiles were used to obtain a

2. Experimental details For the investigation of GB faceting, a cylindrical, coaxial Cu bicrystal was grown by the Bridgman technique from 99.999 wt% purity Cu [11]. Grain 1 is completely surrounded by a grain 2 and a R9 [1 1 0] tilt GB

Fig. 2. Micrograph of multiple twins between grain 1 and grain 2 with R9 misorientation. The common [1 1 0] axis is perpendicular to the micrograph plane.


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249

mean profile (Fig. 3). The diameter of the individual experimental points shown in Fig. 3 is larger than the error of AFM height measurements. The rGB/rsur ratio

1,0 0,8 Height, µm 0,6 0,4 0,2 <1 at.ppm Bi 0,0 0 10 20 30

(a)
40

1,0 0,8 Height, µm 0,6 0,4 0,2 25 at.ppm Bi 0,0 10
1,0 0,8 Height, µm 0,6 0,4 0,2 100 at.ppm Bi 0,0 10 20 30 40

(b)
30 40 50

20

was calculated using the measured values for the GB groove angles. To determine the groove angle, full groove profile was used for pure Cu and Cu with 2.5 · 10þ3 and 10 · 10þ3 at.% Bi (Figs. 3(a)­(c)) as proposed in [6]. These profiles can be good approximated by the standard Mullins solution. The profile part from one ``Mullins hillock'' to another one containing about 250­300 experimental points was used for the fitting. The AFM needle used is very fine. Therefore, only 2­4 experimental points at the groove tip had to be excluded from the fitting procedure. Before the AFM method became available, the GB groove profiles were measured using the optical interferometer. In those measurements the distorted area at the groove tip, not usable for the fitting, was about five times larger ([12] and references therein). Each side of the GB groove profile was fitted separately and the tip location was calculated [6]. Polynoms of first, second, fourth, sixth and eighth order were compared. The transition from first to fourth order improved the results drastically. Since further extension of polynoms did not change the results, the fourth order polynoms were used for the approximation. The derivatives for both halves of the groove profile were determined in the intersection point. Their sum delivered the groove angle. For Cu containing 16 · 10þ3 at.% Bi the GB groove was very deep, asymmetric and faceted (Fig. 3(d)). Since it cannot be approximated by the Mullins solution, the groove tip angle was measured in a linear approximation. The local misorientation was determined with a commercially available system (OIMe, by TSL). The deviation of misorientation angle from ideal R3 and R9 misorientations was below 2°.

3. Results The Cu­Bi phase diagram is shown in Fig. 1. The thick curve is the (retrograde) bulk solidus line [7]. The thin retrograde curve is the GB solidus line obtained in Cu­Bi polycrystals [7]. To the left of the GB solidus the conventional segregation layer US is present in GBs. The GB prewetting phase transition occured at the GB solidus line and a thin layer of the Bi-rich GB phase UL formed in between the GB and bulk solidus lines [7]. The occurrence of GB Bi-rich layer between the GB and bulk solidus lines was observed by high-resolution electron microscopy (HREM) [13,14]. Computer modeling also revealed that specific interfacial phases form in the Cu­Bi system [14]. The GB wetting phase transition tie-lines at Tw,max and Tw,min in the two-phase solid + liquid area are constructed based on the data [15]. Above Tw,max all high-angle GBs are wetted by the melt. Below Tw,min no GB wetting occurs in twophase (Cu) + L polycrystals. Above the GB wetting tie-line the energy of two solid/liquid interfaces 2rSL is lower than the GB energy rGB. The resulting energy gain

(c)
50

5 4 Height, µm 3 2 1 160 at.ppm Bi 0 0 5 10 Width, µm 15 20

(d)

Fig. 3. AFM profiles of the thermal groove for the R9(þ1 1 0) facet at various Bi concentrations. Note the different height scale for 160 at.ppm Bi.


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Dr = 2rSL þ rGB is also present in the one-phase area of the bulk phase diagram where only the solid solution is in equilibrium. The energy difference, Dr, can stabilize a thin GB layer with a thermodynamically defined liquidus composition in the single-phase area (Fig. 1). As a result, a tie-line of the GB wetting phase transition can continue in the S area of the bulk phase diagram. The broken line in Fig. 1 denotes the annealing temperature of 1293 K. The black squares denote the Bi concentration in the samples (0, 2.5 · 10þ3, 10 · 10þ3 and 16 · 10þ3 at.% Bi). Three samples (0, 2.5 · 10þ3 and 10 · 10þ3 at.% Bi) were in the (Cu) + US area, and one sample with 16 · 10þ3 at.% Bi was between the GB and bulk solidus lines. At temperature T = 1293 K = 0.95Tm the R3 GB contains two facets, namely symmetric R3 twins [(1 1 1)1/ (1 1 1)2 or R3(1 0 0) facets] and non-CSL facets forming the angle of 82° with the R3(1 0 0) facets. Therefore, the twin plates in Cu are not rectangular. HREM studies revealed that this 82° facet has a so-called 9R structure forming a plate of body-centered cubic GB phase in the face-centered cubic matrix [12]. Such R3(1 0 0) and 82° 9R facets on the R3 twin plate are also clearly seen in our samples in Fig. 2. The same two R3(1 0 0) and 82° 9R facets are present at T = 1293 K in alloys with 2.5 · 10þ3, 10 · 10þ3 and 16 · 10þ3 at.% Bi. No additional facets appear at T = 1293 K both in (Cu) + US and (Cu) + UL areas of the Cu­Bi phase diagram. The (1 1 1)1/(1 1 5)2 or R9(1 1 0) facets are unstable against the dissociation reaction: R9 ! 2R3 at all Bi concentrations studied. R9 GBs in pure Cu contain two CSL facets R9(þ110) and R9(þ120) at T = 1293 K. These facets are present at all Bi concentrations studied. Two additional CSL facets R9(þ410) and R9(þ2 3 0) appear at the highest Bi concentration of 16 · 10þ3 at.%. This corresponds to the observation that the fraction of faceted GBs in polycrystals increases with increased Bi content [8­10]. The R9(1 0 0) facet becomes stable in pure Cu between 0.8 and 0.95Tm [11]. It also becomes stable in Cu­Bi alloys between 10 · 10þ3 and 16 · 10þ3 at.% Bi. Nevertheless, it was possible to measure the GB groove shape at 0.95Tm for low Bi concentrations at the inclination angle corresponding to the R9(1 0 0) facet, where the GB is only slightly curved. The AFM profiles of the thermal groove at the R9(þ1,1,0) facet at various Bi concentrations are shown in Fig. 3. At 0, 2.5 · 10þ3 and 106 · 10þ3 at.% Bi. [i.e. in the (Cu) + US area of the Cu­Bi phase diagram] the groove profiles correspond to the Mullins equations when groove growth is surface diffusion controlled. At 16 · 10þ3 at.% Bi in the (Cu) + UL area of the Cu­Bi phase diagram the shape of GB groove changes drastically, (Fig. 3(d)) becoming very deep (about 5 lm instead of 0.6­0.9 lm at low Bi concentrations), asymmetric, and faceted. The groove penetration rate along GB drastically increases in the (Cu) + UL area of

the Cu­Bi phase diagram in comparison with (Cu) + US area (Fig. 4). This means that the presence of GB phase between GB and bulk solidus lines enhances the kinetics of GB grooving. The dependence of the rGB/rsur ratio on the bulk Bi concentration for (a) R3(1 0 0) and 9R R3 facets and (b) R9(1 0 0), R9(þ1 1 0) and R9(þ1 2 0) facets is shown in Fig. 5. The R9(1 0 0) facet flattens only between 10 · 10þ3 and 16 · 10þ3 at.% Bi. Therefore, the GB groove shape at low Bi concentrations has been meas-

Penetration rate, 10

-12

m/s

3

9 (110) facet

2

1

0

0

50

100
-4

150

Bi concentration, 10 at.%
Fig. 4. Dependence of the groove penetration rate on the bulk Bi concentration for the R9(1 1 0) facet.

1,5 (a)
3 9R facet

1,0

GB/su

r

0,5
3 (100) facet

0,0
1,0 (b) 0,8

9 (100) facet

(120)

GB/

sur

0,6

0,4

9 (110) facet

0,2 0 50 100 -4 Bi concentration, 10 at.% 150

Fig. 5. Dependence of ratio rGB/rsur on bulk Bi concentration for (a) R3(1 0 0) and 9R R3 facets and (b) R9(1 0 0), R9(þ110) and R9(þ120) facets.


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ured at the inclination angle corresponding to the facet R9(1 0 0) on the slightly curved GB. In all five cases the addition of Bi (up to 10 · 10þ3 at.% Bi), i.e. in the one-phase S area slightly increases the rGB/rsur ratio. However, the rGB/rsur ratio increased drastically after intersection of the GB solidus line between 10 · 10þ3 and 16 · 10þ3 at.% Bi. The rGB/rsur value increases by a factor of 15 for symmetric twin GBs R3(1 0 0), and by a factor of 3 for the R9(1 0 0) facet.

4. Discussion In the case of ordinary coexistence of two bulk phases a large inclusion of one phase may remain in stable equilibrium inside of the second phase (matrix). The average shape of the inclusion is then determined by strictly thermodynamic considerations based on the Gibbs energy minimum for the creation of the necessary interfacial boundary. If both coexisting phases are isotropic (e.g. fluids), the shape of the inclusion is spherical. If one or both are crystalline or otherwise anisotropic, interfaces of some orientations are preferred over those of the other orientations, and the ``equilibrium crystal shape'' (ECS) of the inclusion is non-spherical and can exhibit varying complexity. Wulff first proposed the following construction (see Fig. 6(a)) [16]. When the interface Gibbs energy per unit area f(m) is drawn as a polar plot (Wulff plot sometimes called c-plot), the crystal shape is given as the interior envelope of the family of perpendicular planes passing through the end of radius vectors m. Such a crystal shape corresponds to the minimum of the Gibbs energy. Andreev [17] first pointed

(100)
0.3

0. 1

0.2



GB r su

9R

Fig. 6. Wulff diagram for [1 1 0] tilt R3 GBs in Cu at 1273 K constructed using the data [12]. Open circles denote the ratio rGB/rsur of non-relaxed GBs with different inclinations produced by diffusion bonding. The solid circles denote rGB/rsur after relaxation (i.e. after decomposition into low-energy facets) The circles denote the scale of the rGB/rsur ratio.

out that the Wulff construction is simply the geometrical version of a two-dimensional Legendre transformation between the Gibbs energy, f(m), and the crystal shape, r(h), where h is the facet orientation relative to crystal axes. Thus, knowing the Gibbs energy one can reconstruct the equilibrium crystal shape and vice versa. Until now only anisotropic inclusion and isotropic second phase were considered. This corresponds to the crystal surfaces. What happens when both the ``matrix'' and ``inclusion'' are crystalline and, therefore, anisotropic? Grain boundaries as interfaces between two identical but misoriented lattices represent the simplest case. Therefore, the approach developed for description of ECS for crystal surfaces can also be used for GBs. If the flat surface (or interface) has an inclination between two energetic minima in Gibbs energy it would transform into a faceted structure consisting of two facet types (phases) which coexist along the lines of intersection [4]. The Wulff construction, that permits Gibbs energy estimation the energy of such faceted interfaces, would predict a circle between neighboring f(m) minima. The Wulff diagram for [1 1 0] tilt R3 GBs in Cu at 1273 K is shown in Fig. 6 constructed using the data ([12] and references therein). Open circles denote the ratio rGB/ rsur of non-relaxed GBs with different inclinations produced by diffusion bonding. Solid circles denote rGB/rsur after relaxation (i.e. after decomposition into low-energy facets). Solid circles are positioned along the circle segments drawn between the minima for the R3(1 0 0) and 82° 9R facets. The circles denote the scale of the rGB/rsur ratio. The Wulff plot is shown in Fig. 7(a) for R3 GBs at 1293 K and 10 · 10þ3 at.% Bi constructed using the rGB/rsur ratios measured with the aid of AFM (see Fig. 5). The low energy of coherent R3(1 0 0) facets determines the platelet-like form of twins in Cu. However, the difference between rGB/rsur values for R3(1 0 0) and 82° 9R facets is only about 15% at 16 · 10þ3 at.% Bi and, therefore, the ECS for twin becomes broader and less like the platelet. The inclination angle, /(h), schematically shown in Fig. 7(a) determines the angular intervals for the of R3(1 0 0) and 82° 9R facets. Wulff plots are shown in Figs. 7(b) and (c) for R9 GBs at 2.5 · 10þ3 and 10 · 10þ3 at.% Bi. The R9(1 1 0) facet is unstable against the dissociation into two R3 GBs. Therefore, the point with doubled R3(1 0 0) energy appears at the R9 Wulff plot instead of the R9(1 1 0) facet energy. The point at inclination corresponding to the (1 0 0)R9CSL facet position has been measured at curved (rough) GB. No minima appeared in the f(m) energy dependence at this inclination, since the R9(1 0 0) facet appears only at 16 · 10þ3 at.% Bi. The R9(þ1 2 0) facets are stable in pure Cu [11], but they become metastable at 2.5 · 10þ3 and 10 · 10þ3 at.% Bi. The presence of the R9(þ1 2 0) facets in the sample reveal the existence of the energetic minima on the Wulff plot f(m). However,




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B.B. Straumal et al. / Acta Materialia 53 (2005) 247­254

(100)

r(h)
0

m

f(m

)

0.1 0.2

h

9R GB /sur

(a)
0) (11 9
B Gr su

) 20 (-1 9

0) -11 9 (

9 (110)

3(100)+3(100)

(b)
0) (11 9
0. 2 0. 1

it follows from Figs. 7(b) and (c) that these minima are not deep enough to allow the corresponding facets to be stable. The theoretical picture of the thermal evolution of ECS for a typical crystal surrounded by the vacuum or fluid is given in [18]. As T increases, facets shrink and eventually disappear, each at its own characteristic roughening (``faceting'') temperature TR(h). At sufficiently high temperatures the ECS becomes smoothly rounded everywhere (unless, of course, the system first undergoes a bulk phase change, such as melting). The observed R3(1 0 0)/82° 9R ridges of the twin plates are sharp. In other words, the roughening temperature TR for R3(1 0 0) and 9R facets is higher than the melting temperature Tm. In case of R9 GBs the situation is more complicated. For example, the GB with an inclination corresponding to the R9(1 0 0) facet remains rough (rounded) at 0, 2.5 · 10þ3 and 10 · 10þ3 at.% Bi (Figs. 7(b) and (c)). However, between the lines of the GB and bulk solidus the R9(1 0 0) facet becomes flat, i.e. between 10 · 10þ3 and 16 · 10þ3 at.% Bi the GB roughening transition occurs for the R9(1 0 0) facet. However, the Wulff diagram shows that the R9(1 0 0) facet remains metastable at 16 · 10þ3 at.% Bi. In other words, although a minimum is present on the f(m) curve at the R9(1 0 0) inclination, this minimum remains too shallow to contribute to the ECS. The phase diagram for R3 facets is shown in Fig. 8 for /(h) according to the approach proposed in [18] for ECS. Instead of the temperature, the Bi concentration c is plotted as the ordinate. No fields corresponding to the rough phases are present in this diagram. Open

0. 1

0. 2





0. 3





GB

0) -11 9 (

150
Bi concentration, 10 at.%

-4

100

9 (110)

3(100)+ 3(100)

3(100)
50

9R

(c)
Fig. 7. Wulff energy f(m) and resulting ECS r(h) in a plane section perpendicular to the [1 1 0] tilt axis for the (a) R3 GBs in Cu­100 at.ppm Bi alloy; (b) R9 GBs in Cu­25 at.ppm Bi alloy and (c) R9 GBs in Cu­100 at.ppm Bi alloy. The open circles represent the GB energy rGB for various facets measured with the aid of AFM. The values rGB/ rsur = 0.1, 0.2 and 0.3 are marked in polar coordinates. h and / are the angular variables which measure the interfacial orientation (m) and crystal shape (h), respectively.

0 0 20 40 60 80 Inclination (h), deg
Fig. 8. Bi concentration vs. inclination for plotted according to the approach of [18]. angular variable which measures the crystal section of the full three-dimensional phase dicular to the [1 1 0] tilt axis. The (c,/) phase outline of the faceted areas of GB shape. R3 [1 1 0] tilt GBs in Cu The inclination / is the shape (h) in an equatorial diagram which is perpendiagram plots the angular

9R

(-12 9

(100)

0. 3

0)


B.B. Straumal et al. / Acta Materialia 53 (2005) 247­254

253

squares at / = 0° and 82° denote the R3(1 0 0) and 9R facets observed at all studied Bi concentrations. If one intentionally produce a flat GB with intermediate inclination (for example, / = 45°) and than anneals it at T = 0.95Tm the GB would decompose into the grid of R3(1 0 0) and 9R facets, as it was observed experimentally in [18]. Fig. 6 shows the Wulff diagram for this case. The lines in Fig. 8 mark the angular areas /(h) for the ECS. The circles mark the / values where R3(1 0 0) and 9R facets intersect. The same circles mark the / values where 9R and 9R facets intersect. The / values were obtained from the experimentally measured Wulff diagrams for different c values. The 9R/9R ridges lie at / = 90°. With increasing Bi concentration, c, the 9R area becomes broader at the cost of R3(1 0 0) area up to 10 · 10þ3 at.% Bi. Between 10 · 10þ3 and 16 · 10þ3 at.% Bi the R3(1 0 0) area shrinks again. The phase diagram for R9 facets is shown in Fig. 9 for /(h), the c is plotted as the ordinate. Open squares denote the stable facets and crosses denote the metastable facets. The lines mark the the angular areas /(h) for the respective ECS facets. With increasing c the R9(þ4 1 0) area becomes broader on the cost of 2R3(1 0 0) areas up to 10 · 10þ3 at.% Bi. Between 10 · 10þ3 and 16 · 10þ3 at.% Bi the R3(1 0 0) area shrinks and two new facets R9(þ4 1 0) and R9(þ23 0) appear. The facet R9(þ1 2 0) becomes metastable between 0 and 2.5 · 10þ3 at.% Bi. Therefore, the GB prewetting phase transition increases the number of stable R9 facets between 10 · 10þ3 and 16 · 10þ3 at.% Bi. This fact explains the early data obtained in the Cu­Bi polycrystals [9,10]. The number of faceted GBs in Cu­ 3 · 10þ3 at.% Bi [10] and Cu­9 · 10þ3 at.% Bi [9] polycrystalline alloys was low since the Bi content in these

alloys is below the GB solidus concentration. However, the number of faceted GBs in Cu­30 · 10þ3 at.% Bi alloys was very high [9] because this concentration is well above the GB solidus.

5. Conclusions 1. Cylindrical tilt R3 and R9 GBs in Cu bicrystals containing the full spectrum of inclinations become faceted at 0.95Tm in the solid-solution area of the Cu­Bi phase diagram (i.e. from 0 to 16 · 10þ3 at.% Bi). 2. No rough corners between R3(1 0 0) and 82° 9R facets were observed indicating that Tm is lower than the facets roughening temperature in pure Cu and Cu­ Bi alloys. 3. The ratio between GB energy, rGB, and surface energy, rsur, was measured by atomic force microscopy using the GB thermal-groove method for tilt R3 and R9 GBs. Between 0 and 10 · 10þ3 at.% Bi the rGB/rsur ratio and deepening rate of thermal groove slightly increased with increasing Bi concentration, c. By intersecting of the GB solidus line (about 11 · 10þ3 at.% Bi), both rGB/rsur ratio and deepening rate of the thermal groove drastically increased. 4. Wulff diagrams constructed using the measured rGB/ rsur values reveal that the R9(þ1 2 0) facet that is stable at low c values becomes metastable at high c values. On the contrary, the R9(1 1 0) facet which is rough (unstable) at low c values becomes metastable at high c values.

Acknowledgements
9(100)= = 3(100)

150
Bi concentration, 10 at.%

Investigations were partly supported by the German Federal Ministry for Education and Research (project WTZ RUS 04/014), INTAS (contract 03-51-3779), Russian Foundation for Basic Research RFBR (contract 0403-32800) and NATO Linkage grant (contract PST.CLG.979375).

(010) (-410) (-210) (-230) (-110)

-4

100

2 3 (100)
50

(-230)

(010)

(-100)

(100)

2 3 (100)

References
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) 10 (- 2

0 0 40

80
Inclination (h), deg

120

160

Fig. 9. Bi concentration vs. inclination for R9 [1 1 0] tilt GBs in Cu plotted according to the approach of [18].


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