- Email: [email protected]
Ti quasiperiodic superlattices
Journal of Magnetism and Magnetic Materials 156 (1996) 49-50
of • HJeurnal magnetism
A l l and magnetic ~ H materials
ELSEVIER
X-ray diffraction study of W/Ti quasiperiodic superlattices F.M. Pan, J.W. Feng, G.J. Jin, A. Hu, S.S. Jiang * National Laboratory of Solid State Microstructures and Center)or Advanced Studies in Science and Technology of Microstructures, Nanjing University, Nanjing 210093. China
Abstract W / T i quasiperiodic superlattices with a Fibonacci sequence have been fabricated by magnetron sputtering. X-ray diffraction has been used to characterize the microstructures of these superlattices. Numerical calculations are performed to fit the experimental results, and quantitative agreement is obtained.
This paper reports an investigation of W / T i quasiperiodic superlattices (QS) with a Fibonacci sequence. X-ray diffraction is used to characterize the microstructures of these QS, and numerical calculations are performed to compare with the experimental results. The Fibonacci sequence can be obtained by repeated operations starting with an A, and repeatedly applying the substitution rules A ~ AB, B ~ A, i.e. A ~ AB ~ ABA ABAAB ~ ABAABABA ~ • • •. The corresponding superlattice is produced by attaching a basis to each A and B in order to separate the two neighbouring A's in the sequence. The W / T i QS (samples 1 and 2) were fabricated on glass substrates by dual-target magnetron sputtering. The vacuum system was initially pumped down to below 10 6 Tom and the sputtering pressure was 7.5 × 10-3 Torr of argon gas. The building blocks A and B in sample 1 consisted of (8.6 A tungsten)-(22.1 ,~ titanium) and (8.6 ,~ tungsten)-(10.4 A titanium), respectivelyo. In sample 2 the blocks A and B were designed as (6.8 A tungsten)-(14.5 ,~ titanium) and (6.8 ,~ tungsten)-(25.4 ,~ titanium). In sample 1 the thickness ratio d A / d B is ~-, which is the golden mean ratio, while in sample 2 the thickness ratio is the reciprocal of 7". The multilayer films were characterized using X-ray diffractometry. A 12 kW Rigaku rotating anode X-ray source (a Cu anode in the high brilliance 0.22 × 2 mm 2 spot mode and a symmetric graphite (002) monochromator) was used. The X-ray measurements were performed both near the Bragg peaks of W and Ti, and at grazing angles of incidence (0.5 ° < 20_< 10°). The scattering vector was kept normal to the film surface for these diffraction patterns, with an X-ray wavelength of 1.5418 ,~.
* Corresponding author. Fax: [email protected].
+ 86-25-3300535;
email:
In the high-angle region, the main diffraction peaks for the two samples were found at the same position. These peaks correspond to the 2.238 A spacing of the (110) planes in bcc tungsten, and to the 2.244 A spacing of the (110) planes in bcc titanium. Because the difference in lattice parameters between W and Ti is very small ( = 0.006 A), the Bragg peaks of W and Ti can hardly be distinguished in the spectra. No other main peaks are present. From this, the W / T i QS are dominated by crystalline W and Ti with W(110) and Ti(110) textures. On both sides of the main peak there are some satellite peaks originating from the superstructure of the W / T i QS. In comparison with the main diffraction peak from the W / T i periodic superlattices (to be shown in another paper), the main peak in the W / T i QS is much sharper. It is suggested that the W / T i QS are much less affected by discrete fluctuations in a layer than the periodic samples [1,2]. Meanwhile, the small lattice parameter difference between W(110) and T i ( l l 0 ) leads to the sharpness of high-angle diffraction peak [1,2]. The thickness ratio in the Fibonacci sequence is usually chosen to be 7-, as in sample 1. For d A / d B ve 7 (sample 2), the quasiperiodic properties are preserved due to the topological equivalence between a square and a rectangle in the projection method. This can be proved by use of projection on a rectangular lattice with basis vectors a and ~Ta (T/# 0,1), if the projection angle 0 satisfies cot 0 = r/~-, where d A / d n = ~/cot 0 [3]. By changing the layer thickness, it is often possible to optimize the desired properties of the system. In reciprocal lattice space the relation between the diffraction vectors and the average modulation wavelength is as follows: K ( m , n ) = 2~r(m + r t T " ) O --1 , (l) where m and n are integers, and D is the average modulation wavelength ( = 7"dA +dB). Figs. l and 2 show the X-ray diffraction spectra of the two samples in the low-an-
0304-8853/96/$15.00 © 1996 Elsevier Science B.V. All rights reserved SSD10304-8853(95)00751-2
50
F.M. Pan et al. // Journal o f Magnetism and Magnetic Materials 156 (1996) 4 9 - 5 0
I °~11(1,1)
Table 1 Indices, 20 angles and scattering vectors of some of the diffraction peaks shown in Figs. 1 and 2. Here K~ = 4arA-~ sin 0, and
(
I i
o)
A i
K 2 = 2 ~ r D - I ( m + n'r)
(1,1)
I 0.5
6.0
3.0
12.0
9.0
20 (degree) Fig. 1. 0 - 2 0 scan of X-ray diffraction in the low-angle region for sample 1. d A = 8.6 .& (dw)+22.1 ,~ (dTi), d B = 8.6 ,& ( d w ) + 10.4 A (dTi).
gle region. Each peak is indexed by (m,n). Their indices, peak positions and scattering vectors are listed in Table 1. The experimental values of the scattering vectors ( K = 4wA 1sin 0) are in good agreement with the calculated values derived from Eq. (1). Because of the refraction correction, the smaller the angle, the greater is the deviation between the experimental and calculated values. Furthermore, from Table 1 it is clear that K(a,~+2,an+l)=K(an+,,an)+K(a,,
a.
1)
(2)
is satisfied, where a , are Fibonacci numbers, a n + 2 = an + l + a n, a 2 = 1, a I = 0. This reflects the self-similarity of the reciprocal lattice. Comparing the spectra of the two Fibonacci samples, it
(o'1)
(I,2)
Indices
Sample 1
(m,n)
20
Kl
K2
20
KI
K2
(deg)
(A ')
(A- ~)
(deg)
(,~- ')
(,~- ' )
1.56 2.26 2.80 3.52 4.30 4.78 5.60
0.111 0.161 0.199 0.250 0.306 0.340 0.398
0.094 0.153 0.189 0.247 0.305 0.341 0.399
1.56 2.04 2.66 3.42 4.20 4.64 5.44
0.111 0.145 0.189 0.243 0.298 0.330 0.387
0.091 0.144 0.183 0.240 0.295 0.330 0.386
(1,0) (0,1) (2,0) (1,1) (0,2) (2,1) (1,2)
Sample 2
is noted that in Fig. 2 the peaks with high relative intensities are concentrated in the region close to zero angle, in contrast with the case of Fig. 1. For instance, the intensity of the peak labelled (1,2) in Fig. 2 is more than 20 times that of the same peak in Fig. 1, although these two peaks are at about the same angle in the spectra. The thickness ratio has a large influence on the X-ray diffraction spectra of these QS. This phenomenon has serious implications for the use of W / T i QS as reflectors of soft X-rays [4]. The X-ray diffraction patterns have been numerically simulated in the low-angle region, and the model for the compositionally modulated multilayer was used for the simulation. The calculation method was the same as that used for a periodic T a / A I multilayer [5], but the sequence is different. The experimental data are consistent with the numerical calculations for both the scattering intensities and the peak positions. Acknowledgements: This work has been supported by the National Natural Science Foundation of China and the Provincial Natural Science Foundation of Jiangsu. References
i
(0,2) ,0'11 0,5
3.0
(,,1
6.0
9.0
12.0
20 (degree) Fig. 2. 0 - 2 0 scan of X-ray diffraction in the low angle region for sample 2. d A =6.8 ,& ( d w ) + 14.5 ,& (dTi), d B =6.8 ,& ( d w ) + 25.4 A (dTi).
[1] E.E. Fullerton, I.K. Schuller, H. Vanderstraeten and Y. Bruynseraede, Phys. Rev. B 45 (1992) 9292. [2] J.-P. Locquet, D. Neerinck, L. Stockman, Y. Bruynseraede and I.K. Schuller, Phys. Rev. B 39 (1989) 13338. [3] A. Hu, C. Tien, X.J. Li, Y.H. Wang and D. Feng, Phys. Lett. A 119 (1986) 313. [4} R.W. Peng, A. Hu and S.S. Jiang, Appl. Phys. Lett. 59 (1991) 2512. [5] S.S. Jiang, A. Hu, H. Chen, W. Liu, Y.X. Zhang, Y. Qiu and D. Feng, J. Appl. Phys. 66 (1989) 5258.
of • HJeurnal magnetism
A l l and magnetic ~ H materials
ELSEVIER
X-ray diffraction study of W/Ti quasiperiodic superlattices F.M. Pan, J.W. Feng, G.J. Jin, A. Hu, S.S. Jiang * National Laboratory of Solid State Microstructures and Center)or Advanced Studies in Science and Technology of Microstructures, Nanjing University, Nanjing 210093. China
Abstract W / T i quasiperiodic superlattices with a Fibonacci sequence have been fabricated by magnetron sputtering. X-ray diffraction has been used to characterize the microstructures of these superlattices. Numerical calculations are performed to fit the experimental results, and quantitative agreement is obtained.
This paper reports an investigation of W / T i quasiperiodic superlattices (QS) with a Fibonacci sequence. X-ray diffraction is used to characterize the microstructures of these QS, and numerical calculations are performed to compare with the experimental results. The Fibonacci sequence can be obtained by repeated operations starting with an A, and repeatedly applying the substitution rules A ~ AB, B ~ A, i.e. A ~ AB ~ ABA ABAAB ~ ABAABABA ~ • • •. The corresponding superlattice is produced by attaching a basis to each A and B in order to separate the two neighbouring A's in the sequence. The W / T i QS (samples 1 and 2) were fabricated on glass substrates by dual-target magnetron sputtering. The vacuum system was initially pumped down to below 10 6 Tom and the sputtering pressure was 7.5 × 10-3 Torr of argon gas. The building blocks A and B in sample 1 consisted of (8.6 A tungsten)-(22.1 ,~ titanium) and (8.6 ,~ tungsten)-(10.4 A titanium), respectivelyo. In sample 2 the blocks A and B were designed as (6.8 A tungsten)-(14.5 ,~ titanium) and (6.8 ,~ tungsten)-(25.4 ,~ titanium). In sample 1 the thickness ratio d A / d B is ~-, which is the golden mean ratio, while in sample 2 the thickness ratio is the reciprocal of 7". The multilayer films were characterized using X-ray diffractometry. A 12 kW Rigaku rotating anode X-ray source (a Cu anode in the high brilliance 0.22 × 2 mm 2 spot mode and a symmetric graphite (002) monochromator) was used. The X-ray measurements were performed both near the Bragg peaks of W and Ti, and at grazing angles of incidence (0.5 ° < 20_< 10°). The scattering vector was kept normal to the film surface for these diffraction patterns, with an X-ray wavelength of 1.5418 ,~.
* Corresponding author. Fax: [email protected].
+ 86-25-3300535;
email:
In the high-angle region, the main diffraction peaks for the two samples were found at the same position. These peaks correspond to the 2.238 A spacing of the (110) planes in bcc tungsten, and to the 2.244 A spacing of the (110) planes in bcc titanium. Because the difference in lattice parameters between W and Ti is very small ( = 0.006 A), the Bragg peaks of W and Ti can hardly be distinguished in the spectra. No other main peaks are present. From this, the W / T i QS are dominated by crystalline W and Ti with W(110) and Ti(110) textures. On both sides of the main peak there are some satellite peaks originating from the superstructure of the W / T i QS. In comparison with the main diffraction peak from the W / T i periodic superlattices (to be shown in another paper), the main peak in the W / T i QS is much sharper. It is suggested that the W / T i QS are much less affected by discrete fluctuations in a layer than the periodic samples [1,2]. Meanwhile, the small lattice parameter difference between W(110) and T i ( l l 0 ) leads to the sharpness of high-angle diffraction peak [1,2]. The thickness ratio in the Fibonacci sequence is usually chosen to be 7-, as in sample 1. For d A / d B ve 7 (sample 2), the quasiperiodic properties are preserved due to the topological equivalence between a square and a rectangle in the projection method. This can be proved by use of projection on a rectangular lattice with basis vectors a and ~Ta (T/# 0,1), if the projection angle 0 satisfies cot 0 = r/~-, where d A / d n = ~/cot 0 [3]. By changing the layer thickness, it is often possible to optimize the desired properties of the system. In reciprocal lattice space the relation between the diffraction vectors and the average modulation wavelength is as follows: K ( m , n ) = 2~r(m + r t T " ) O --1 , (l) where m and n are integers, and D is the average modulation wavelength ( = 7"dA +dB). Figs. l and 2 show the X-ray diffraction spectra of the two samples in the low-an-
0304-8853/96/$15.00 © 1996 Elsevier Science B.V. All rights reserved SSD10304-8853(95)00751-2
50
F.M. Pan et al. // Journal o f Magnetism and Magnetic Materials 156 (1996) 4 9 - 5 0
I °~11(1,1)
Table 1 Indices, 20 angles and scattering vectors of some of the diffraction peaks shown in Figs. 1 and 2. Here K~ = 4arA-~ sin 0, and
(
I i
o)
A i
K 2 = 2 ~ r D - I ( m + n'r)
(1,1)
I 0.5
6.0
3.0
12.0
9.0
20 (degree) Fig. 1. 0 - 2 0 scan of X-ray diffraction in the low-angle region for sample 1. d A = 8.6 .& (dw)+22.1 ,~ (dTi), d B = 8.6 ,& ( d w ) + 10.4 A (dTi).
gle region. Each peak is indexed by (m,n). Their indices, peak positions and scattering vectors are listed in Table 1. The experimental values of the scattering vectors ( K = 4wA 1sin 0) are in good agreement with the calculated values derived from Eq. (1). Because of the refraction correction, the smaller the angle, the greater is the deviation between the experimental and calculated values. Furthermore, from Table 1 it is clear that K(a,~+2,an+l)=K(an+,,an)+K(a,,
a.
1)
(2)
is satisfied, where a , are Fibonacci numbers, a n + 2 = an + l + a n, a 2 = 1, a I = 0. This reflects the self-similarity of the reciprocal lattice. Comparing the spectra of the two Fibonacci samples, it
(o'1)
(I,2)
Indices
Sample 1
(m,n)
20
Kl
K2
20
KI
K2
(deg)
(A ')
(A- ~)
(deg)
(,~- ')
(,~- ' )
1.56 2.26 2.80 3.52 4.30 4.78 5.60
0.111 0.161 0.199 0.250 0.306 0.340 0.398
0.094 0.153 0.189 0.247 0.305 0.341 0.399
1.56 2.04 2.66 3.42 4.20 4.64 5.44
0.111 0.145 0.189 0.243 0.298 0.330 0.387
0.091 0.144 0.183 0.240 0.295 0.330 0.386
(1,0) (0,1) (2,0) (1,1) (0,2) (2,1) (1,2)
Sample 2
is noted that in Fig. 2 the peaks with high relative intensities are concentrated in the region close to zero angle, in contrast with the case of Fig. 1. For instance, the intensity of the peak labelled (1,2) in Fig. 2 is more than 20 times that of the same peak in Fig. 1, although these two peaks are at about the same angle in the spectra. The thickness ratio has a large influence on the X-ray diffraction spectra of these QS. This phenomenon has serious implications for the use of W / T i QS as reflectors of soft X-rays [4]. The X-ray diffraction patterns have been numerically simulated in the low-angle region, and the model for the compositionally modulated multilayer was used for the simulation. The calculation method was the same as that used for a periodic T a / A I multilayer [5], but the sequence is different. The experimental data are consistent with the numerical calculations for both the scattering intensities and the peak positions. Acknowledgements: This work has been supported by the National Natural Science Foundation of China and the Provincial Natural Science Foundation of Jiangsu. References
i
(0,2) ,0'11 0,5
3.0
(,,1
6.0
9.0
12.0
20 (degree) Fig. 2. 0 - 2 0 scan of X-ray diffraction in the low angle region for sample 2. d A =6.8 ,& ( d w ) + 14.5 ,& (dTi), d B =6.8 ,& ( d w ) + 25.4 A (dTi).
[1] E.E. Fullerton, I.K. Schuller, H. Vanderstraeten and Y. Bruynseraede, Phys. Rev. B 45 (1992) 9292. [2] J.-P. Locquet, D. Neerinck, L. Stockman, Y. Bruynseraede and I.K. Schuller, Phys. Rev. B 39 (1989) 13338. [3] A. Hu, C. Tien, X.J. Li, Y.H. Wang and D. Feng, Phys. Lett. A 119 (1986) 313. [4} R.W. Peng, A. Hu and S.S. Jiang, Appl. Phys. Lett. 59 (1991) 2512. [5] S.S. Jiang, A. Hu, H. Chen, W. Liu, Y.X. Zhang, Y. Qiu and D. Feng, J. Appl. Phys. 66 (1989) 5258.