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Secondary ordering in Pt-rich Pt–Mn binary alloys and CuMnPt6 ternary alloy
ARTICLE IN PRESS
Physica B 385–386 (2006) 130–132 www.elsevier.com/locate/physb
Secondary ordering in Pt-rich Pt–Mn binary alloys and CuMnPt6 ternary alloy Miwako Takahashia,, Ananda Kumar Dasa,1, Timbangen Sembiringb, Hiroshi Iwasakic, Ken-ichi Ohshimaa a Institute of Materials Science, University of Tsukuba, Tsukuba 305-8573, Japan Department of Physics, Faculty of Mathematics and Natural Science, University of Sumatera Utara, Medan, Indonesia c Synchrotron Radiation Center, Ritsumeikan University, Kusatsu 525-8577, Japan
b
Abstract Using pulsed-neutron diffraction technique, we performed in situ measurements of structural ordering in Pt-rich Pt–Mn binary alloys and CuMnPt6 ternary alloy. The observed diffraction patterns at various temperatures have revealed two ordered phases in these alloys. Below the order–disorder transition temperature, a Cu3 Au type ordered structure is formed as an ordering within the fundamental facecentered cubic lattice to subdivide the lattice into two sublattices formed by face-centered sites (first sublattice) and corner sites (second sublattice). At low temperature, an ABC6 type ordered structure is formed as an ordering within the second sublattice to subdivide the lattice further into two sublattices formed by alternating (1 1 1) planes. A secondary ordering in the alloys is discussed in terms of two order parameters in the ABC6 type structure utilizing the method of static concentration waves originally proposed by Khachaturyan. It is shown that the degree of order for the secondary ordering is rather low for the CuMnPt6 ternary alloy. r 2006 Elsevier B.V. All rights reserved. PACS: 61.12.Ld; 61.66.Dk; 64.60.Cn Keywords: Secondary ordering; ABC6 type ordered structure; In situ neutron diffraction
It is known that most of the Pt-based binary alloys having the composition Pt3 M (M ¼ 3d elements) have the Cu3 Au type ordered structure, one of the common ordered structures in binary alloy system. For Pt-rich Pt–Mn binary alloys, the phase diagram shows that the alloys have a facecentered cubic (FCC) fundamental structure above the order–disorder transition temperature T c and below T c they form a Cu3 Au type ordered structure in a composition range of 17–37 at.% Mn [1]. However, the phase diagram for the alloys with the Mn composition less than 17 at.% has remained unclear. Our X-ray diffraction studies have shown coexistence of the two kinds of atomic correlations in the Pt–Mn alloys with this concentration region: one is
Corresponding author.
E-mail address: [email protected] (M. Takahashi). On leave from Bangladesh Atomic Energy Commission, Dhaka 1000, Bangladesh. 1
0921-4526/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2006.05.298
of the Cu3 Au type ordered structure and the other is of the layered structure of alternate (1 1 1) planes. The alloy Pt3 Cu behaves somewhat differently from other Pt3 M alloys in that it does not form the Cu3 Au type ordered structure and Schneider & Esch proposed an orthorhombic ordered structure derived from FCC structure [2]. On the other hand, Tang has proposed a different structure model of the ABC6 type ordered structure for the Pt-72.5 at.% Cu [3]. The structure is unique in that the unit cell is as large as 2 2 2 the fundamental FCC cell, the largest cubic unit cell found in the ordered FCC alloy. The unit cell is divided into three sublattices A, B and C, as shown in Fig.1. The structure is regarded as a layered structure consisting of alternate (1 1 1) planes, one containing the A- and C-sublattice sites and the other containing the B- and C-sublattice sites. In the reciprocal space, superlattice reflections appear at both X- and L-points of the FCC Brillouin zone in the ABC6 type ordered structure, while they appear only at X-point in the
ARTICLE IN PRESS M. Takahashi et al. / Physica B 385–386 (2006) 130–132
131
5.0x10-2 0.14
C
Fig. 1. Structure of the ABC6 type order.
0.10 3.0 0.08
0.06
0.04
MnPt7 100 3/2 1/2 1/2 1.0
0.02 200 (a)
400 600 800 Temperature (°C ) 5.0x10-2
0.7 4.0
0.6
Intensity (arb.units)
Cu3 Au type ordered structure. The Pt–Cu has been the only binary alloy to possess the ABC6 type ordered phase. Khachaturyan, with his static concentration wave theory, predicted that the structure is a secondary ordered superlattice and arises from the non-stoichiometric hightemperature superlattice with the Cu3 Au type structure [4]. Since the ABC6 type structure consists of the three sets of cubic sublattice, it is more appropriate to regard it as the ordered structure proper to the three component system. The present study is motivated choosing Pt-rich Pt–Mn binary alloys and CuMnPt6 ternary alloys for investigating their ordered structures and ordering behavior. In this paper, we report the results of in situ pulsed-neutron diffraction measurements on MnPt7 binary alloy [5] and CuMnPt6 ternary alloy [6]. Single crystals were grown using the Bridgman technique at the Institute for Materials Research, Tohoku University. The crystals utilized in the present measurements are cylindrical with about 10 mm height and 7 mm diameter for MnPt7 and 15 mm height and 12 mm diameter for CuMnPt6 . Prior to the measurements, the samples were annealed to achieve high degree for the low temperature ordered structure for more than 1 month. Neutron diffraction measurements were performed on a time-of flight Laue-type diffractometer at beam line H1 of the Neutron Science Laboratory in KEK [7]. For the measurements at high temperatures, the samples were sealed in a vacuum silica tube to avoid oxidation and set in a furnace with MoSi2 heaters [8]. Diffraction patterns of the ð0 1¯ 1Þ plane were recorded in the temperature range from 25 to 1050 C. Fig. 2(a) shows temperature variations of the intensities for the X-point (1 0 0) and L-point ð32 12 12Þ superlattice reflections of the MnPt7 sample. Temperatures at which superlattice reflections vanish are different for the X- and L-point reflections; 792 C for the former and 668 C for the latter. Since superlattice reflections only at the X-points correspond to a Cu3 Au type ordered structure, the former temperature is the transition temperature between the disordered FCC phase and the Cu3 Au type ordered phase and designated here as T c . The latter temperature is the transition temperature between the Cu3 Au type ordered phase and a new ordered phase and designated as T cl .
2.0
Intensity (arb.units)
B
4.0
0.5 3.0 0.4 0.3 0.2 0.1
2.0 CuMnPt6 100 3/2 1/2 1/2
Intensity (arb.units)
A
Intensity (arb. units)
0.12
1.0
0.0 200 (b)
400 600 800 Temperature (°C )
1000
Fig. 2. Temperature dependences of the intensities of (1 0 0) and ð32 12 12Þ superlattice reflections for: (a) MnPt7 and (b) CuMnPt6 . The arrows indicate T cl and T c , respectively.
Results of the measurements carried out on the CuMnPt6 sample are similar to those for the MnPt7 sample. Fig. 2(b) shows temperature dependences of the intensities at the X-point (1 0 0) and the L-point ð32 12 12Þ of the CuMnPt6 sample. The intensity at (1 0 0) disappears at 968 C while that at ð32 12 12Þ disappears at 746 C. The observations clearly show a double-step ordering in the present alloys. On the basis of the Tang’s model with the ABC6 type ordered structure, we regard the ordered structure forming at temperatures below T cl as PtMnPt6 for the binary MnPt7 alloy, and as the ABC6 type order with real three component system for the CuMnPt6 ternary
ARTICLE IN PRESS M. Takahashi et al. / Physica B 385–386 (2006) 130–132
132
alloy. We have also investigated a Pt–Mn alloy with 14.5 at.% Mn and found the double-step ordering at T c ¼ 969 C and T cl ¼ 682 C in the alloy. They are the first alloys that exhibit the secondary ordering with the FCCbased lattice. Using the theory of static concentration waves developed by Khachaturyan [4], the atomic arrangement of the ABC6 type ordered structure is described with two independent order parameters, S 1 and S 2 by the equation na ðrÞ ¼ ca þ g1a S 1 ðe2pib1 r þ e2pib2 r þ e2pib3 r Þ þ g2a S 2 fepiðb1 þb2 þb3 Þr þ epiðb1 þb2 þb3 Þr þ epiðb1 b2 þb3 Þr þ epiðb1 þb2 b3 Þr g,
ð1Þ
where a represents Mn in the MnPt7 and Mn or Cu atom in the CuMnPt6 ; ca is the concentration of the a atom in the alloy and is 18 for the present alloys with the stoichiometric composition; b1 , b2 , and b3 are the reciprocal lattice vectors of the fundamental FCC lattice; S 1 and S2 are the order parameters; and g1a , g2a are symmetry coefficients determined by normalization and are given as
where bMn , bCu and bPt are scattering amplitudes for Mn, Cu, and Pt, respectively. In MnPt7 , the structure factors are obtained simply by replacing bCu by bPt in Eq. (4). From the observed neutron intensities at fundamental reflections and superlattice reflections at the X-point and L-point, the two order parameters S 1 and S 2 are estimated using Eq. (4) for the present alloys. They are S1 ¼ 0:9 and S2 ¼ 0:7 for MnPt7 and S1 ¼ 0:9 and S 2 ¼ 0:3 for CuMnPt6 . The low value for S 2 in the ternary alloy is due to difficulties in the interchange of Mn and Cu atoms which are next-nearest neighbors to each other. In the binary alloy the interchange is only between Mn and Pt atoms, which makes the secondary ordering much easier. In summary, we have observed a double step ordering of FCC ! Cu3 Au type ! ABC6 type in Pt–Mn binary alloys and CuMnPt6 ternary alloy. The formation of the ABC6 type order in these alloys are the first examples of a secondary ordering for the alloys with FCC-based lattice.
g1Mn ¼ g2Mn ¼ 1=8, g1Cu ¼ g2Cu ¼ 1=8.
(2)
In Eq. (1), we assume that the order parameters take the same values for Mn and Cu atoms in the ternary alloys. In other words, the two atoms contribute to the orderings in the same way. The function na ðrÞ takes three values na ðrA Þ ¼ 1=8 þ 3g1a S 1 þ 4g2a S 2 ,
Acknowledgements We would like to thank Mr. T. Sugawara of IMR, Tohoku University for growing the crystals. The present work was supported by a Grant-in-Aid for Young Scientists (B) (KAKENHI, No. 15760487) of Japan Society for the Promotion of Science.
na ðrB Þ ¼ 1=8 þ 3g1a S1 4g2a S 2 , na ðrC Þ ¼ 1=8 g1a S 1 ,
(3)
on sites of A, B and C sublattices, respectively. Eq. (3) clearly shows that S1 and S 2 are related to the difference in probability of finding a atom between A, B and C sublattices and between A and B sublattices, respectively. With this concentration wave, the structure factors for CuMnPt6 are given as F ¼ 4fðbMn þ bCu þ 6bPt Þg Fundamental, F ¼ 4fS1 ðbMn bPt Þ þ S1 ðbCu bPt Þg X-point, F ¼ 4fS2 ðbMn bPt Þ S 2 ðbCu bPt Þg L-point,
ð4Þ
References [1] T.B. Massalski, H. Okamoto, P.R. Subramanian, L. Kacprzak, Binary Alloy Phase Diagrams, second ed., ASM International, 1990. [2] A. Schneider, U. Esch, Z. Elektrochem. 50 (1944) 290. [3] Y. Tang, Acta Cryst. 4 (1951) 377. [4] A.G. Khachaturyan, Prog. Mater. Sci. 22 (1978) 1. [5] M. Takahashi, T. Sembiring, M. Yashima, T. Shishido, K. Ohshima, J. Phys. Soc. Japan 71 (2002) 681. [6] M. Takahashi, A.K. Das, R. Nakamura, H. Iwasaki, T. Shishido, K. Ohshima, J. Phys. Soc. Japan 75 (2006) 013601. [7] M. Takahashi, ICNAS-XV, in: S. Itoh, J. Suzuki (Eds.), Proceedings of the 15th Meeting of the International Collaboration on Advanced Neutron Sources, KEK Proceedings 2000-22/JAERI-Conf 2001–002, 2001, vol. 1, p. 492. [8] M. Yashima, T. Oketani, O. Yokota, Y. Hatoyama, R. Ali, T. Nogami, S. Utsumi, H. Sugawara, M. Ohashi, K. Ohoyama, Y. Yamaguchi, in: S. Sato, N. Tawata, N. Takesue, H. Yoshizawa (Eds.), Activity Report on Neutron Scattering Research, Shinsen Kogyo, 1999, vol. 6, p. 74.
Physica B 385–386 (2006) 130–132 www.elsevier.com/locate/physb
Secondary ordering in Pt-rich Pt–Mn binary alloys and CuMnPt6 ternary alloy Miwako Takahashia,, Ananda Kumar Dasa,1, Timbangen Sembiringb, Hiroshi Iwasakic, Ken-ichi Ohshimaa a Institute of Materials Science, University of Tsukuba, Tsukuba 305-8573, Japan Department of Physics, Faculty of Mathematics and Natural Science, University of Sumatera Utara, Medan, Indonesia c Synchrotron Radiation Center, Ritsumeikan University, Kusatsu 525-8577, Japan
b
Abstract Using pulsed-neutron diffraction technique, we performed in situ measurements of structural ordering in Pt-rich Pt–Mn binary alloys and CuMnPt6 ternary alloy. The observed diffraction patterns at various temperatures have revealed two ordered phases in these alloys. Below the order–disorder transition temperature, a Cu3 Au type ordered structure is formed as an ordering within the fundamental facecentered cubic lattice to subdivide the lattice into two sublattices formed by face-centered sites (first sublattice) and corner sites (second sublattice). At low temperature, an ABC6 type ordered structure is formed as an ordering within the second sublattice to subdivide the lattice further into two sublattices formed by alternating (1 1 1) planes. A secondary ordering in the alloys is discussed in terms of two order parameters in the ABC6 type structure utilizing the method of static concentration waves originally proposed by Khachaturyan. It is shown that the degree of order for the secondary ordering is rather low for the CuMnPt6 ternary alloy. r 2006 Elsevier B.V. All rights reserved. PACS: 61.12.Ld; 61.66.Dk; 64.60.Cn Keywords: Secondary ordering; ABC6 type ordered structure; In situ neutron diffraction
It is known that most of the Pt-based binary alloys having the composition Pt3 M (M ¼ 3d elements) have the Cu3 Au type ordered structure, one of the common ordered structures in binary alloy system. For Pt-rich Pt–Mn binary alloys, the phase diagram shows that the alloys have a facecentered cubic (FCC) fundamental structure above the order–disorder transition temperature T c and below T c they form a Cu3 Au type ordered structure in a composition range of 17–37 at.% Mn [1]. However, the phase diagram for the alloys with the Mn composition less than 17 at.% has remained unclear. Our X-ray diffraction studies have shown coexistence of the two kinds of atomic correlations in the Pt–Mn alloys with this concentration region: one is
Corresponding author.
E-mail address: [email protected] (M. Takahashi). On leave from Bangladesh Atomic Energy Commission, Dhaka 1000, Bangladesh. 1
0921-4526/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2006.05.298
of the Cu3 Au type ordered structure and the other is of the layered structure of alternate (1 1 1) planes. The alloy Pt3 Cu behaves somewhat differently from other Pt3 M alloys in that it does not form the Cu3 Au type ordered structure and Schneider & Esch proposed an orthorhombic ordered structure derived from FCC structure [2]. On the other hand, Tang has proposed a different structure model of the ABC6 type ordered structure for the Pt-72.5 at.% Cu [3]. The structure is unique in that the unit cell is as large as 2 2 2 the fundamental FCC cell, the largest cubic unit cell found in the ordered FCC alloy. The unit cell is divided into three sublattices A, B and C, as shown in Fig.1. The structure is regarded as a layered structure consisting of alternate (1 1 1) planes, one containing the A- and C-sublattice sites and the other containing the B- and C-sublattice sites. In the reciprocal space, superlattice reflections appear at both X- and L-points of the FCC Brillouin zone in the ABC6 type ordered structure, while they appear only at X-point in the
ARTICLE IN PRESS M. Takahashi et al. / Physica B 385–386 (2006) 130–132
131
5.0x10-2 0.14
C
Fig. 1. Structure of the ABC6 type order.
0.10 3.0 0.08
0.06
0.04
MnPt7 100 3/2 1/2 1/2 1.0
0.02 200 (a)
400 600 800 Temperature (°C ) 5.0x10-2
0.7 4.0
0.6
Intensity (arb.units)
Cu3 Au type ordered structure. The Pt–Cu has been the only binary alloy to possess the ABC6 type ordered phase. Khachaturyan, with his static concentration wave theory, predicted that the structure is a secondary ordered superlattice and arises from the non-stoichiometric hightemperature superlattice with the Cu3 Au type structure [4]. Since the ABC6 type structure consists of the three sets of cubic sublattice, it is more appropriate to regard it as the ordered structure proper to the three component system. The present study is motivated choosing Pt-rich Pt–Mn binary alloys and CuMnPt6 ternary alloys for investigating their ordered structures and ordering behavior. In this paper, we report the results of in situ pulsed-neutron diffraction measurements on MnPt7 binary alloy [5] and CuMnPt6 ternary alloy [6]. Single crystals were grown using the Bridgman technique at the Institute for Materials Research, Tohoku University. The crystals utilized in the present measurements are cylindrical with about 10 mm height and 7 mm diameter for MnPt7 and 15 mm height and 12 mm diameter for CuMnPt6 . Prior to the measurements, the samples were annealed to achieve high degree for the low temperature ordered structure for more than 1 month. Neutron diffraction measurements were performed on a time-of flight Laue-type diffractometer at beam line H1 of the Neutron Science Laboratory in KEK [7]. For the measurements at high temperatures, the samples were sealed in a vacuum silica tube to avoid oxidation and set in a furnace with MoSi2 heaters [8]. Diffraction patterns of the ð0 1¯ 1Þ plane were recorded in the temperature range from 25 to 1050 C. Fig. 2(a) shows temperature variations of the intensities for the X-point (1 0 0) and L-point ð32 12 12Þ superlattice reflections of the MnPt7 sample. Temperatures at which superlattice reflections vanish are different for the X- and L-point reflections; 792 C for the former and 668 C for the latter. Since superlattice reflections only at the X-points correspond to a Cu3 Au type ordered structure, the former temperature is the transition temperature between the disordered FCC phase and the Cu3 Au type ordered phase and designated here as T c . The latter temperature is the transition temperature between the Cu3 Au type ordered phase and a new ordered phase and designated as T cl .
2.0
Intensity (arb.units)
B
4.0
0.5 3.0 0.4 0.3 0.2 0.1
2.0 CuMnPt6 100 3/2 1/2 1/2
Intensity (arb.units)
A
Intensity (arb. units)
0.12
1.0
0.0 200 (b)
400 600 800 Temperature (°C )
1000
Fig. 2. Temperature dependences of the intensities of (1 0 0) and ð32 12 12Þ superlattice reflections for: (a) MnPt7 and (b) CuMnPt6 . The arrows indicate T cl and T c , respectively.
Results of the measurements carried out on the CuMnPt6 sample are similar to those for the MnPt7 sample. Fig. 2(b) shows temperature dependences of the intensities at the X-point (1 0 0) and the L-point ð32 12 12Þ of the CuMnPt6 sample. The intensity at (1 0 0) disappears at 968 C while that at ð32 12 12Þ disappears at 746 C. The observations clearly show a double-step ordering in the present alloys. On the basis of the Tang’s model with the ABC6 type ordered structure, we regard the ordered structure forming at temperatures below T cl as PtMnPt6 for the binary MnPt7 alloy, and as the ABC6 type order with real three component system for the CuMnPt6 ternary
ARTICLE IN PRESS M. Takahashi et al. / Physica B 385–386 (2006) 130–132
132
alloy. We have also investigated a Pt–Mn alloy with 14.5 at.% Mn and found the double-step ordering at T c ¼ 969 C and T cl ¼ 682 C in the alloy. They are the first alloys that exhibit the secondary ordering with the FCCbased lattice. Using the theory of static concentration waves developed by Khachaturyan [4], the atomic arrangement of the ABC6 type ordered structure is described with two independent order parameters, S 1 and S 2 by the equation na ðrÞ ¼ ca þ g1a S 1 ðe2pib1 r þ e2pib2 r þ e2pib3 r Þ þ g2a S 2 fepiðb1 þb2 þb3 Þr þ epiðb1 þb2 þb3 Þr þ epiðb1 b2 þb3 Þr þ epiðb1 þb2 b3 Þr g,
ð1Þ
where a represents Mn in the MnPt7 and Mn or Cu atom in the CuMnPt6 ; ca is the concentration of the a atom in the alloy and is 18 for the present alloys with the stoichiometric composition; b1 , b2 , and b3 are the reciprocal lattice vectors of the fundamental FCC lattice; S 1 and S2 are the order parameters; and g1a , g2a are symmetry coefficients determined by normalization and are given as
where bMn , bCu and bPt are scattering amplitudes for Mn, Cu, and Pt, respectively. In MnPt7 , the structure factors are obtained simply by replacing bCu by bPt in Eq. (4). From the observed neutron intensities at fundamental reflections and superlattice reflections at the X-point and L-point, the two order parameters S 1 and S 2 are estimated using Eq. (4) for the present alloys. They are S1 ¼ 0:9 and S2 ¼ 0:7 for MnPt7 and S1 ¼ 0:9 and S 2 ¼ 0:3 for CuMnPt6 . The low value for S 2 in the ternary alloy is due to difficulties in the interchange of Mn and Cu atoms which are next-nearest neighbors to each other. In the binary alloy the interchange is only between Mn and Pt atoms, which makes the secondary ordering much easier. In summary, we have observed a double step ordering of FCC ! Cu3 Au type ! ABC6 type in Pt–Mn binary alloys and CuMnPt6 ternary alloy. The formation of the ABC6 type order in these alloys are the first examples of a secondary ordering for the alloys with FCC-based lattice.
g1Mn ¼ g2Mn ¼ 1=8, g1Cu ¼ g2Cu ¼ 1=8.
(2)
In Eq. (1), we assume that the order parameters take the same values for Mn and Cu atoms in the ternary alloys. In other words, the two atoms contribute to the orderings in the same way. The function na ðrÞ takes three values na ðrA Þ ¼ 1=8 þ 3g1a S 1 þ 4g2a S 2 ,
Acknowledgements We would like to thank Mr. T. Sugawara of IMR, Tohoku University for growing the crystals. The present work was supported by a Grant-in-Aid for Young Scientists (B) (KAKENHI, No. 15760487) of Japan Society for the Promotion of Science.
na ðrB Þ ¼ 1=8 þ 3g1a S1 4g2a S 2 , na ðrC Þ ¼ 1=8 g1a S 1 ,
(3)
on sites of A, B and C sublattices, respectively. Eq. (3) clearly shows that S1 and S 2 are related to the difference in probability of finding a atom between A, B and C sublattices and between A and B sublattices, respectively. With this concentration wave, the structure factors for CuMnPt6 are given as F ¼ 4fðbMn þ bCu þ 6bPt Þg Fundamental, F ¼ 4fS1 ðbMn bPt Þ þ S1 ðbCu bPt Þg X-point, F ¼ 4fS2 ðbMn bPt Þ S 2 ðbCu bPt Þg L-point,
ð4Þ
References [1] T.B. Massalski, H. Okamoto, P.R. Subramanian, L. Kacprzak, Binary Alloy Phase Diagrams, second ed., ASM International, 1990. [2] A. Schneider, U. Esch, Z. Elektrochem. 50 (1944) 290. [3] Y. Tang, Acta Cryst. 4 (1951) 377. [4] A.G. Khachaturyan, Prog. Mater. Sci. 22 (1978) 1. [5] M. Takahashi, T. Sembiring, M. Yashima, T. Shishido, K. Ohshima, J. Phys. Soc. Japan 71 (2002) 681. [6] M. Takahashi, A.K. Das, R. Nakamura, H. Iwasaki, T. Shishido, K. Ohshima, J. Phys. Soc. Japan 75 (2006) 013601. [7] M. Takahashi, ICNAS-XV, in: S. Itoh, J. Suzuki (Eds.), Proceedings of the 15th Meeting of the International Collaboration on Advanced Neutron Sources, KEK Proceedings 2000-22/JAERI-Conf 2001–002, 2001, vol. 1, p. 492. [8] M. Yashima, T. Oketani, O. Yokota, Y. Hatoyama, R. Ali, T. Nogami, S. Utsumi, H. Sugawara, M. Ohashi, K. Ohoyama, Y. Yamaguchi, in: S. Sato, N. Tawata, N. Takesue, H. Yoshizawa (Eds.), Activity Report on Neutron Scattering Research, Shinsen Kogyo, 1999, vol. 6, p. 74.