- Email: [email protected]
Atomic periodicity of 〈001〉 symmetric tilt boundary in molybdenum
Materials Science and Engineering A2344236 (1997) 1053%1056
Atomic periodicity
of (001) symmetric tilt boundary molybdenum
Koji Morita, Department
of Materials
Science
and Technology,
Graduate
Hideharu School
of Engineering
Nakashima Sciences,
Kyushu
in
* University,
Kasuga,
Fukuoka
816, Japan
Received 27 February 1997; received in revised form 1 April 1997
Abstract The grain boundary microstructure and its periodicity of [OOl] symmetric tilt boundary in molybdenum have been examined by applying the high-resolution transmission electron microscope (HRTEM) observation and the molecular dynamics (MD) method. As a result, it was found that the grain boundary structure consisted of the combination of structure units, which is based on the stable boundaries ((070) Cl and (110) Cl single crystals, and (130) C5 coincidence boundary), and the periodicity can be completely described in atomic-scale by the concept of structure unit model. Q 1997 Elsevier Science S.A. Keywords:
Molybdenum; Molecular dynamics; Structure unit model: Grain boundary energy
1. Introduction
2. Experimental procedures
In the case of a coincidence boundary [I], it is found that the grain boundary have a periodic structure of the coincidence site lattice (CSL) along the boundary. Moreover, the atomic structure between the CSL may have a particular periodicity, which is expected by structure unit model proposed by Sutton and Vitek [2]. In recent years, Penissonet al. [3] have presented that a low angle boundary of molybdenum can be described as a combination of two structure units. However, in our knowledge, no systematic investigation, which compared an expectation with a direct observation, has been carried out sufficiently. In the present work, in order to clarify the grain boundary microstructure in molybdenum, bicrystals with [OOI] symmetric tilt boundary have been observed by transmission electron microscopy (TEM) and compared with the results calculated by a molecular dynamics (MD) method. Moreover, micro-diffraction analysis was also conducted in order to determine the atomic periodicity of grain boundary structure units.
2.1. Specimens The molybdenum bicrystals with [OOl] symmetric tilt boundary were prepared by a r.f. floating-zone technique [4]. Here, the misorientation angle 4 was defined as the angle made by two (010) planes of adjacent crystals. In order to remove impurity atoms (C and 0), thin sheets (about 500 pm in thickness) were cut from the bicrystals perpendicular to the [OOl] tilt axis and purification treatments [4] were carried out at about 2300 K for 10.4 ks under wet-hydrogen and for 21.6 ks under dry-hydrogen. After purification, the impurities were determined by chemical analysis to be C < 5, 0 = 2.0 and N = 2.2 mass ppm, respectively. 2.2. Measurement of grain boundary energy During the purification treatment, boundary grooves with dihedral angle 2 B were formed on the surface by the balance between grain boundary energy ygb and surface energy ys. The relation of thermal balance between them may be expressed as follows ygb = 21/, cos 8
* Corresponding author. Tel.: + 81 92 5739611306; fax: + 81 92 5752318; e-mail: [email protected] 0921-5093/97/$17.00 0 1997 Elsevier Science S.A. All rights reserved. Pi1 SO921-5093(97)00306-7
(1)
By measuring the dihedral angles, the grain boundary energies relative to the surface energy can be obtained.
1054
K. Morita,
H. Nakashima
/Materials
Science
The details of thermal grooving method were described elsewhere [5]. 2.3. TEA4 observation For TEM observations, 3 mm disks were trepanned from the purified thin sheets by using the spark cutting machine and thinned by the twin-jet electropolishing technique. High resolution TEM (HRTEM) observations were conducted with a JEOL JEM-2000EX equipped with a top-entry goniometer stage. The microdiffraction analysis were conducted with a JEOL JEM2010 equipped with a field emission gun. Here, the analysis was carried out under edge-on conditions at thin area enough for HRTEM observation and converged the electron beam to about 3 nm in diameter. The diffraction pattern was taken by using the imagingplate recorded for 0.3 s.
3. Results and discussion 3.1. Misorientation energy
dependence of gruin boundary
Fig. la and b show misorientation dependence of grain boundary energy obtained by calculation and thermal grooving method, respectively [6]. For the calculation, MD method using Finnis-Sinclair type Nbody potential for molybdenum [7] has been applied. From the figures, it is found that grain boundary energy strongly depends on the misorientation angle. In Fig. la, two deep energy cusps are recognized at the misorientation angles of (130) and (120) x5 coincidence boundaries, and small energy cusps are recognized at the angles of (150) and (230) Cl 3 coincidence boundaries. In this study, the good agreements of misorientation dependence of the grain boundary energy are obtained between numerical and experimental studies. Moreover, these misorientation dependence of grain boundary energy for molybdenum agrees well with the result calculated by Wolf [S].
and Engineering
A234-236
(1997)
1053p1056
the so called favored boundary [2]. However, in the case of (130) x5 and (170) Cl favored boundaries, there is a difference of atomic arrangement in each units (e.g. B and B’ units for (120) x5 boundary), and its arrangement is translated into the [OOl] direction between the coplanar CSL shown by the large mark inside the open circle. Therefore, the structure units should be expressed as follows (OiO)~l(~=O”) (130)x5(@ = 36.87”) (lTO)Zl($ = 90°)
: : :
..IAl.. . IBB’I. . . $C’I.1
(2)
Here, B (or B’) unit in (130) C5 and C (or C’) unit in (170) Cl, which representing a half period of structure unit between the coplanar CSL, are called as a sub-unit. Fig. 3 shows the HRTEM image of near (130) Z5 coincidence boundary [6]. Periodic structure of CSL (arrows) and BB’ structure unit are observed as illustrated in the Fig. 3, and the structure corresponds well to the calculated one in atomic-scale. Fig. 4 shows a micro-diffraction pattern taken from the Fig. 3. Periodic extra reflections (arrows) are recognized around the fundamental reflections. The periodicity parallel
c 2.5 E A Tm 2.0
v1
0.1
k
2 0.08 -,-
-
t
-
-
r
-
_,-
-
t
-
-
+
-
-,-
-
-
-
3.2. Grain boundury structure I
--l--I_-L__I__I__L_-I--~--
Fig. 2 show some atomic structures of symmetric tilt boundaries relaxed by MD method [6]. Here, the open circles and the filled circles in the Fig. 2 represent atoms of two adjacent (002) planes, and large and small marks (inside the open circles) represent the CSL of two adjacent (002) planes on the boundary, respectively. By connecting the nearest-neighbor atoms, represented by the open and filled circle, specific atomic arrangements are observed along the boundary plane [9]. As these results, it is found that (130) C5 coincidence boundary consists of single structure unit. These boundaries are
-,-
-
7 - -
r
-
-,-
-
f
-
-;
-
_I-
t\
-
-l--
l Kk
I
I
0
10
I
I
I
I
I
I
20 30 40 50 60 70 Misorientation angle, + (deg)
I
80
90
Fig. 1. The misorientation dependence of grain boundary energy of [OOl] symmetric tilt boundary in molybdenum; (a) calculated by MD method and (b) measured as relative value by using thermal grooving method [6].
K. Morita,
c
H. Nakashima
-.-. I
G.B.
I I
/Materials
G.B.
I
(13O)I13(~=22.62’)
(2~0)~29
(4= 43.6’)
and Engineering
A234-236
(l?o,rs(4=53.l3~,
of [OOI] symmetric method [6].
tilt
boundaries
in
and perpendicular to the boundary agrees well with the results deduced from the atomic arrangement of BB’ structure unit. From the systematic calculations, it was found that all other boundaries which posses the intermediate misorientation angle between two favored boundaries consisted of a combination of two structure units as shown in Fig. 2 [6].
of a near [6].
[OOl](l?O)
C5
symmetric
tilt
pattern taken in Fig. 3[6].
from
the [OOl](l?O)
25 coinci-
For example, the grain boundaries with a range of 4 = O-36.87” (region I) consist of a combination of BB’ and A units. However, the ratio of structure units varied with misorientation angle. From the Fig. 2, the structures between the coplanar CSL of (150) 2 13 (4 = 22.62”) and (130) Xl7 (4 = 28.07”) coincidence boundaries can be represented as a ratio of 2:l (...IABAB’I...) and a ratio of 1:l (...IBAB’I...), respectively. Here, it is noted that a BB’ unit dissociate into two sub-units by a A unit. Fig. 5a and b show HRTEM images of near (150) Cl3 and near (140) X17 boundaries, respectively [6]. The periodic atomic arrangement are observed and correspond well to the calculated structures. On the other hand, in a range of 4 = 36.87-90” (region II), the structures consist of a combination of BB’ and CC’ units composing (130) X5 and (170) Cl favored boundaries. For example, (120) C5 (4 = 53.13”) coincidence boundary can be represented as a ratio of 1:l (...lBCl...). This periodicity of structure units agrees well with the result obtained by HRTEM observation as shown in Fig. 6 [6]. As a result, it is concluded that the structures of [OOl] symmetric tilt boundary in molybdenum can be described by the concept of structure unit model [2]. Consequently, symmetric tilt boundaries with (hk0) plane can be expressed by a simple rule as follows [lo] (hk0) = m(h,k,O)
Fig. 3. HRTEM image boundary of molybdenum
1055
1053-1056
(+=67.38’)
Fig. 4. Micro-diffraction dence tilt boundary
Fig. 2. The atomic structures molybdenum relaxed by MD
(1997)
I
(2%X13
(1~0)0)H17(#=28.07’)
Science
+ n(h*k20)
(3)
Here, the numbers tn and n are the ratio of structure units of two nearest favored boundaries (h,k,O) and (h&,0), respectively.
1056
K. Morita,
H. Nakashima
/Materials
Science
and Engineering
A2346236
Fig. 6. HRTEM image boundary of molybdenum
(1997)
1053- 1056
of a near [6].
[OOl](l?O)
25
symmetric
tilt
Acknowledgements The authors would like to express their thanks to Prof. N. Yoshida and Mr Y. Miyamoto, Institute of Applied Mechanics of Kyushu University, for their help for purification treatment, to Mr T. Manabe, HVEM LAB of Kyushu University, for his help for micro-diffraction analysis. The present work was financially supported by the Grant-in-Aid for Scientific Research, Ministry of Education, Science and Culture, Japan. This support is also very much appreciated. Fig. 5. HRTEM images [001](140) z17 symmetric
of (a) near [001](150) X13 and (b) near tilt boundaries of molybdenum [6].
[I] D.G. Brandon, Acta Metall. 12 (1964) 813; 14 (1966) 1479. [2] A.P. Sutton, V. Vitek, Phil. Trans. R. Sot. London A309 (1983)
4. Conclusion (1)
The grain boundary
misorient&ion
References
angle,
and
energy strongly depends on (130)
and
(120)
X5 coinci-
dence boundaries have lowest energy, and (150) and (230) Xl 3 coincidence boundaries have small energy cusps, respectively. (2) (130) C5 coincidence boundary is found to consist of single structure unit as well as single crystals. All other symmetric tilt boundaries are found to consist of the combination of two structure units based on the favored boundaries such as (070) Cl and (170) Cl single crystals, and (130) Z5 coincidence boundary.
[3] J.M.
Penisson,
T. Nowicki,
M. Biscondi,
Phil.
Mag.
A58 (1988)
947. [4] H. Kurishita, A. Oishi, H. Kubo, H. Yoshinaga, Trans. Jpn. Inst. Met. 26 (1985) 332. [5] S. Tsurekawa, T. Tanaka, H. Yoshinaga, Mat. Sci. Eng. Al76 (1994) 341. [6] K. Morita, M. Uehara, S. Tsurekawa, H. Nakashima, J. Jpn. Inst. Met. 61 (1997) 251. [7] M.W. Finnis, J.E. Sinclair, Phil. Mag. AS0 (1984) 45. [8] D. Wolf, Phil. Mag. A62 (1990) 447. [9] J.M. Penisson, M. Bacla, M. Biscondi, Phil. Mag. A73 (1996) 859. [lo] V.Yu. Gertsman, A.A. Nazarov, A.E. Romanov, R.Z. Valiev, V.I. Vladimirov, Phil. Mag. A59 (1989) 1113.
Atomic periodicity
of (001) symmetric tilt boundary molybdenum
Koji Morita, Department
of Materials
Science
and Technology,
Graduate
Hideharu School
of Engineering
Nakashima Sciences,
Kyushu
in
* University,
Kasuga,
Fukuoka
816, Japan
Received 27 February 1997; received in revised form 1 April 1997
Abstract The grain boundary microstructure and its periodicity of [OOl] symmetric tilt boundary in molybdenum have been examined by applying the high-resolution transmission electron microscope (HRTEM) observation and the molecular dynamics (MD) method. As a result, it was found that the grain boundary structure consisted of the combination of structure units, which is based on the stable boundaries ((070) Cl and (110) Cl single crystals, and (130) C5 coincidence boundary), and the periodicity can be completely described in atomic-scale by the concept of structure unit model. Q 1997 Elsevier Science S.A. Keywords:
Molybdenum; Molecular dynamics; Structure unit model: Grain boundary energy
1. Introduction
2. Experimental procedures
In the case of a coincidence boundary [I], it is found that the grain boundary have a periodic structure of the coincidence site lattice (CSL) along the boundary. Moreover, the atomic structure between the CSL may have a particular periodicity, which is expected by structure unit model proposed by Sutton and Vitek [2]. In recent years, Penissonet al. [3] have presented that a low angle boundary of molybdenum can be described as a combination of two structure units. However, in our knowledge, no systematic investigation, which compared an expectation with a direct observation, has been carried out sufficiently. In the present work, in order to clarify the grain boundary microstructure in molybdenum, bicrystals with [OOI] symmetric tilt boundary have been observed by transmission electron microscopy (TEM) and compared with the results calculated by a molecular dynamics (MD) method. Moreover, micro-diffraction analysis was also conducted in order to determine the atomic periodicity of grain boundary structure units.
2.1. Specimens The molybdenum bicrystals with [OOl] symmetric tilt boundary were prepared by a r.f. floating-zone technique [4]. Here, the misorientation angle 4 was defined as the angle made by two (010) planes of adjacent crystals. In order to remove impurity atoms (C and 0), thin sheets (about 500 pm in thickness) were cut from the bicrystals perpendicular to the [OOl] tilt axis and purification treatments [4] were carried out at about 2300 K for 10.4 ks under wet-hydrogen and for 21.6 ks under dry-hydrogen. After purification, the impurities were determined by chemical analysis to be C < 5, 0 = 2.0 and N = 2.2 mass ppm, respectively. 2.2. Measurement of grain boundary energy During the purification treatment, boundary grooves with dihedral angle 2 B were formed on the surface by the balance between grain boundary energy ygb and surface energy ys. The relation of thermal balance between them may be expressed as follows ygb = 21/, cos 8
* Corresponding author. Tel.: + 81 92 5739611306; fax: + 81 92 5752318; e-mail: [email protected] 0921-5093/97/$17.00 0 1997 Elsevier Science S.A. All rights reserved. Pi1 SO921-5093(97)00306-7
(1)
By measuring the dihedral angles, the grain boundary energies relative to the surface energy can be obtained.
1054
K. Morita,
H. Nakashima
/Materials
Science
The details of thermal grooving method were described elsewhere [5]. 2.3. TEA4 observation For TEM observations, 3 mm disks were trepanned from the purified thin sheets by using the spark cutting machine and thinned by the twin-jet electropolishing technique. High resolution TEM (HRTEM) observations were conducted with a JEOL JEM-2000EX equipped with a top-entry goniometer stage. The microdiffraction analysis were conducted with a JEOL JEM2010 equipped with a field emission gun. Here, the analysis was carried out under edge-on conditions at thin area enough for HRTEM observation and converged the electron beam to about 3 nm in diameter. The diffraction pattern was taken by using the imagingplate recorded for 0.3 s.
3. Results and discussion 3.1. Misorientation energy
dependence of gruin boundary
Fig. la and b show misorientation dependence of grain boundary energy obtained by calculation and thermal grooving method, respectively [6]. For the calculation, MD method using Finnis-Sinclair type Nbody potential for molybdenum [7] has been applied. From the figures, it is found that grain boundary energy strongly depends on the misorientation angle. In Fig. la, two deep energy cusps are recognized at the misorientation angles of (130) and (120) x5 coincidence boundaries, and small energy cusps are recognized at the angles of (150) and (230) Cl 3 coincidence boundaries. In this study, the good agreements of misorientation dependence of the grain boundary energy are obtained between numerical and experimental studies. Moreover, these misorientation dependence of grain boundary energy for molybdenum agrees well with the result calculated by Wolf [S].
and Engineering
A234-236
(1997)
1053p1056
the so called favored boundary [2]. However, in the case of (130) x5 and (170) Cl favored boundaries, there is a difference of atomic arrangement in each units (e.g. B and B’ units for (120) x5 boundary), and its arrangement is translated into the [OOl] direction between the coplanar CSL shown by the large mark inside the open circle. Therefore, the structure units should be expressed as follows (OiO)~l(~=O”) (130)x5(@ = 36.87”) (lTO)Zl($ = 90°)
: : :
..IAl.. . IBB’I. . . $C’I.1
(2)
Here, B (or B’) unit in (130) C5 and C (or C’) unit in (170) Cl, which representing a half period of structure unit between the coplanar CSL, are called as a sub-unit. Fig. 3 shows the HRTEM image of near (130) Z5 coincidence boundary [6]. Periodic structure of CSL (arrows) and BB’ structure unit are observed as illustrated in the Fig. 3, and the structure corresponds well to the calculated one in atomic-scale. Fig. 4 shows a micro-diffraction pattern taken from the Fig. 3. Periodic extra reflections (arrows) are recognized around the fundamental reflections. The periodicity parallel
c 2.5 E A Tm 2.0
v1
0.1
k
2 0.08 -,-
-
t
-
-
r
-
_,-
-
t
-
-
+
-
-,-
-
-
-
3.2. Grain boundury structure I
--l--I_-L__I__I__L_-I--~--
Fig. 2 show some atomic structures of symmetric tilt boundaries relaxed by MD method [6]. Here, the open circles and the filled circles in the Fig. 2 represent atoms of two adjacent (002) planes, and large and small marks (inside the open circles) represent the CSL of two adjacent (002) planes on the boundary, respectively. By connecting the nearest-neighbor atoms, represented by the open and filled circle, specific atomic arrangements are observed along the boundary plane [9]. As these results, it is found that (130) C5 coincidence boundary consists of single structure unit. These boundaries are
-,-
-
7 - -
r
-
-,-
-
f
-
-;
-
_I-
t\
-
-l--
l Kk
I
I
0
10
I
I
I
I
I
I
20 30 40 50 60 70 Misorientation angle, + (deg)
I
80
90
Fig. 1. The misorientation dependence of grain boundary energy of [OOl] symmetric tilt boundary in molybdenum; (a) calculated by MD method and (b) measured as relative value by using thermal grooving method [6].
K. Morita,
c
H. Nakashima
-.-. I
G.B.
I I
/Materials
G.B.
I
(13O)I13(~=22.62’)
(2~0)~29
(4= 43.6’)
and Engineering
A234-236
(l?o,rs(4=53.l3~,
of [OOI] symmetric method [6].
tilt
boundaries
in
and perpendicular to the boundary agrees well with the results deduced from the atomic arrangement of BB’ structure unit. From the systematic calculations, it was found that all other boundaries which posses the intermediate misorientation angle between two favored boundaries consisted of a combination of two structure units as shown in Fig. 2 [6].
of a near [6].
[OOl](l?O)
C5
symmetric
tilt
pattern taken in Fig. 3[6].
from
the [OOl](l?O)
25 coinci-
For example, the grain boundaries with a range of 4 = O-36.87” (region I) consist of a combination of BB’ and A units. However, the ratio of structure units varied with misorientation angle. From the Fig. 2, the structures between the coplanar CSL of (150) 2 13 (4 = 22.62”) and (130) Xl7 (4 = 28.07”) coincidence boundaries can be represented as a ratio of 2:l (...IABAB’I...) and a ratio of 1:l (...IBAB’I...), respectively. Here, it is noted that a BB’ unit dissociate into two sub-units by a A unit. Fig. 5a and b show HRTEM images of near (150) Cl3 and near (140) X17 boundaries, respectively [6]. The periodic atomic arrangement are observed and correspond well to the calculated structures. On the other hand, in a range of 4 = 36.87-90” (region II), the structures consist of a combination of BB’ and CC’ units composing (130) X5 and (170) Cl favored boundaries. For example, (120) C5 (4 = 53.13”) coincidence boundary can be represented as a ratio of 1:l (...lBCl...). This periodicity of structure units agrees well with the result obtained by HRTEM observation as shown in Fig. 6 [6]. As a result, it is concluded that the structures of [OOl] symmetric tilt boundary in molybdenum can be described by the concept of structure unit model [2]. Consequently, symmetric tilt boundaries with (hk0) plane can be expressed by a simple rule as follows [lo] (hk0) = m(h,k,O)
Fig. 3. HRTEM image boundary of molybdenum
1055
1053-1056
(+=67.38’)
Fig. 4. Micro-diffraction dence tilt boundary
Fig. 2. The atomic structures molybdenum relaxed by MD
(1997)
I
(2%X13
(1~0)0)H17(#=28.07’)
Science
+ n(h*k20)
(3)
Here, the numbers tn and n are the ratio of structure units of two nearest favored boundaries (h,k,O) and (h&,0), respectively.
1056
K. Morita,
H. Nakashima
/Materials
Science
and Engineering
A2346236
Fig. 6. HRTEM image boundary of molybdenum
(1997)
1053- 1056
of a near [6].
[OOl](l?O)
25
symmetric
tilt
Acknowledgements The authors would like to express their thanks to Prof. N. Yoshida and Mr Y. Miyamoto, Institute of Applied Mechanics of Kyushu University, for their help for purification treatment, to Mr T. Manabe, HVEM LAB of Kyushu University, for his help for micro-diffraction analysis. The present work was financially supported by the Grant-in-Aid for Scientific Research, Ministry of Education, Science and Culture, Japan. This support is also very much appreciated. Fig. 5. HRTEM images [001](140) z17 symmetric
of (a) near [001](150) X13 and (b) near tilt boundaries of molybdenum [6].
[I] D.G. Brandon, Acta Metall. 12 (1964) 813; 14 (1966) 1479. [2] A.P. Sutton, V. Vitek, Phil. Trans. R. Sot. London A309 (1983)
4. Conclusion (1)
The grain boundary
misorient&ion
References
angle,
and
energy strongly depends on (130)
and
(120)
X5 coinci-
dence boundaries have lowest energy, and (150) and (230) Xl 3 coincidence boundaries have small energy cusps, respectively. (2) (130) C5 coincidence boundary is found to consist of single structure unit as well as single crystals. All other symmetric tilt boundaries are found to consist of the combination of two structure units based on the favored boundaries such as (070) Cl and (170) Cl single crystals, and (130) Z5 coincidence boundary.
[3] J.M.
Penisson,
T. Nowicki,
M. Biscondi,
Phil.
Mag.
A58 (1988)
947. [4] H. Kurishita, A. Oishi, H. Kubo, H. Yoshinaga, Trans. Jpn. Inst. Met. 26 (1985) 332. [5] S. Tsurekawa, T. Tanaka, H. Yoshinaga, Mat. Sci. Eng. Al76 (1994) 341. [6] K. Morita, M. Uehara, S. Tsurekawa, H. Nakashima, J. Jpn. Inst. Met. 61 (1997) 251. [7] M.W. Finnis, J.E. Sinclair, Phil. Mag. AS0 (1984) 45. [8] D. Wolf, Phil. Mag. A62 (1990) 447. [9] J.M. Penisson, M. Bacla, M. Biscondi, Phil. Mag. A73 (1996) 859. [lo] V.Yu. Gertsman, A.A. Nazarov, A.E. Romanov, R.Z. Valiev, V.I. Vladimirov, Phil. Mag. A59 (1989) 1113.