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Calculation of deuterium site occupancy in LaNi5D6.5, LaNi4AlD4.8 and LaNi4MnD5.9
Journal
of the Less-Common
Metals,
141
(1988)
163
- 167
163
CALCULATION OF DEUTERIUM SITE OCCUPANCY IN LaNisD,.s, LaNi4A1D,., AND LaNiaMnD,., YAN-BIN
WANG*
and DEREK
Department of Engineering N9B 3P4 (Canada) (Received
September
0. NORTHWOOD
Materials,
18, 1987;
University
of Windsor,
in revised form December
Windsor,
Ontario
14, 1987)
Summary By adopting our model for the calculation of the enthalpy of hydride formation, and by assuming that the number of bonds formed between the hydrogen and metal atoms in an alloy is proportional to the number of “broken” bonds for the metal atom, the interactive energy and site occupancy of deuterium in LaNi,D,.,, LaNi,A1D4., and LaNi4MnD,., are calculated and compared with experimental results. The agreement between the calculated and experimentally measured site occupancies is quite good with the exception that the occupation of the 3f and 4h sites in LaN&D,., and LaNi,MnD s.9 cannot be predicted. The enthalpies of deuterium sorption are also calculated for the three alloys. The addition of aluminium or manganese increases the enthalpy of sorption.
1. Introduction Several workers have proposed models for predicting the site occupancy of hydrogen atoms in hydrogen storage alloys. Shinar et al. [l] proposed an imaginary binary hydride model based on the method of Miedema [2,3] for the calculation of the heat of metal hydride formation. However, the success of this model in predicting hydrogen site occupancies has been questioned by Westlake [4] and Ivey and Northwood [5]. Although one of the coworkers of Shinar [l] has subsequently defended their model (Jacob [ 6]), the imaginary binary hydride model is not satisfactory because, among other things, it cannot explain the varied occupancy of the different types of site with the same atomic environment, such as the 12n and 120 sites in the LaNi, alloy. Westlake [4] proposed a geometric model based on hole size to explain the hydrogen capacity and site occupancy in hydrogen storage alloys, and successfully applied it to many alloys. We believe that there is a *Present address: Department Technology, Beijing, China. 0022-5088/88/$3.50
of Metal Physics,
0 Elsevier
Beijing
University
Sequoia/Printed
of Iron and Steel
in The Netherlands
164
need to consider properties other than the geometrical factors, and suggest that since, from the point of view of statistical thermodynamics, the site occupancy is associated with the interactive energy between hydrogen atoms and the interstitial sites, then the interactive energy is determined not only by the hole size but also by the atoms forming the interstitial site. Recently, we presented a modification of Miedema’s model for predicting the enthalpy of hydride formation and applied it to explain the site occupancy of hydrogen atoms in pure metals and some cubic Laves alloys [7, 81. In this paper we extend this work to LaNi, and alloys where aluminium or manganese are substituted for some of the nickel.
2. Analysis In refs. 7 and 8 we modified Miedema’s model and proposed that the electronegativity and electron density of a hydrogen atom would vary for interstitial sites of different size. To determine the interactive energy we proposed a method to calculate the number of bonds formed between a hydrogen atom and the metal atoms surrounding it. Once these calculations had been performed we could determine the hydrogen site occupancy in a similar manner as for the imaginary binary hydride model. In the imaginary binary hydride model, Shinar et al. [l] assumed that the number of bonds formed between a hydrogen atom and the different metal atoms surrounding it are the same [l]. However, this is probably not the case for hydrogen atoms in alloys. In this case the number of bonds, i.e. hydrogen-metal, can be realized by calculating the number of partly “broken” bonds between a metal atom and the metal atoms nearby. Thus it may be more reasonable to assume that the number of bonds formed between a hydrogen atom and a metal atom is proportional to the number of partly broken bonds between the metal atom and the other metal atoms forming the interstitial site. Then the equations (see eqn. (8) in ref. 8) for calculating the number of bonds formed between the hydrogen atom and the metal atoms surrounding it will be as follows D(Mi-H) = R(Mi, 1) + R(H, 1) - 0.6 log ci
(1)
D(Mi-Mj)
(2)
= R(Mi, 1) + R(Mj, 1) - 0.6 log(m, -xx)
Mi and Mj are metal atoms which form the interstitial site, D(Mi-H) is the distance between the hydrogen and Mi atoms, D(Mi-Mj) is the distance between metal atoms Mj and Mi in the metal hydride, R(Mi, l), R(Mj, l), R(H, 1) are the single bond radii of the Mi atom, the Mj atom and the hydrogen atom respectively. ci is the number of bonds formed between the hydrogen and Mi atoms, and is proportional to the partly broken bonds of the Mi atoms. mK is the number of bonds between Mi and Mj, and xx is the number of partly broken bonds after the hydrogen atom enters the interstitial site.
165
After obtaining the number of bonds formed between the hydrogen atom and the metal atoms surrounding it, we can calculate the interactive energy of the hydrogen atom in each kind of site and the site occupancy using the equations derived in refs. 7 and 8.
3. Results and discussion The calculated results for the interactive energy and site occupancy of deuterium in LaNi,D, 5, LaNi4A1D,_s and LaNbMnD,, 9 are given in Table 1. From Table 1, it can be seen that our calculations do not predict the occupation of the 3f and 4h sites. This results in a slightly higher number of deuterium atoms in the other sites. Westlake’s geometric model cannot predict the occupation of the 3f sites. This model is based on a minimum hole radius of 0.40 I%for hydrogen occupation of an interstice in a stable hydride, a minimum H-H distance of 2.10 A and the postulate that the larger interstices should fill first [9]. Because the radii of the 3f sites are much smaller TABLE
1
The interactive energy LaNisD6_s, LaNi4MDb.s
and site occupancy and LaNi~MnDs.9
of deuterium
atoms
in different
AllOY
Site
Atomic environment
In terac the energy @VI
Number of deuterium atoms (calculated)
LaNiD6.s
6m 12n 120 3f 4h
LazNiz LaNis LaNiJ LazNi4 Ni4
-0.1801
-0.1699 -0.1483 +0.2578 +0.0192
2.21 2.99 1.30 0 0
6m(a) 6m(b) 12n(a) 12n(b) 120(a) 120(b) 3f 4h
LazNi2 LazNiAl LaNi3 LaNi&l LaNis LaNiaAl LazNie NisAl
-0.2890 -0.2540 -0.2709 -0.0618 -0.2254 -0.0153 -to.0974 -0.0066
1.31 0.67 2.60 0 I 0.22 0 I 0 0
6m(a) 6m(b) 12n(a) l%(b) 120(a) 120(b) 3f 4h
LazNi2 LasNiMn LaNia LaNiaMn LaNi3 LaNisMn LazNi4 Ni3Mn
-0.1688 -0.2236 -0.2177 -0.2227 -0.1839 -0.1925 +0.1445 -0.0072
0.08 1.33 I 2.12 1.28 I 0.29 0.80
LaNi4AlDe.s
LaNi4MnDs
.a
sites
Number of deuterium atoms (experimental) IllI 1.91 2.14 1.29 0.64 0.52 2.06 2.74 0 0 0
2.06 2.48 0.81 0.35 0.20
in
166
than the size criterion of 0.4 A (0.3126 A, 0.2869 A and 0.3251 A for 3f sites in LaNi5D6.5, LaNi4A1D4.s and LaNi&InDSeg respectively), Westlake proposed that the occupation of the 3f sites was caused by diffusion, and gave the value of the occupation as 12n + 3f [lo]. If we adopt the value of 12n + 3f our results agree more satisfactorily with the experimental results. However, we do not think that diffusion is a satisfactory explanation. Although the deuterium atoms are in constant motion, from the point of view of statistical thermodynamics the time the deuterium atom remains in a certain site is determined by the interactive energy between the deuterium atom and the site. Deuterium atoms can only remain in 3f sites for a very short period of time as the energy is much lower than in other sites. Thus diffusion cannot explain the occupation of the 3f sites. The occupation of . . cannot be explained either. According to the exthe 4h sites m LaNi,D,., perimental results for 4h site occupation [ll], the interactive energy of deuterium with the 4h site must be more than -0.15 eV. It seems impossible for deuterium to have a higher interactive energy in a site formed by four nickel atoms (the 4h site) than in a site formed by one lanthanum atom and three nickel atoms (the 120 site). Further work is needed to explain satisfactorily the occupation of the 3f and 4h sites. Using the interactive energies and site occupancies given in Table 1, the enthalpies of deuterium sorption in each alloy can be calculated. These calculations have been performed and the results are listed in Table 2. The addition of aluminium or manganese increases the enthalpy of sorption. This agrees with the available experimental results [12,13]. TABLE 2 The enthalpy of deuterium sorption (&) Alloy
AH calculated (kJ (mol H2)-l)
AH experimental (kJ (mol Hz)-‘)
LaNisDgvs LaNi4AlDa.s LaNi4MnD5.9
32.6 52.4 42.4
31.8 47.7 48.5
Reference for experimental results
I121 1131 [I31
4. Conclusion Using our previous papers [7, 81 as a basis, the site occupancies and enthalpies of deuterium sorption in LaNisD6.s, LaNi4A1D,.s and LaNtare calculated. In the calculations the assumption is made that the MnD5.9 number of bonds formed between deuterium and a metal atom is proportional to the partly broken bonds between the metal atom and the other metal atoms forming the interstitial site. The calculated results agree quite well with published experimental results, with the exception that the occu-
167
pation of the 3f and 4h sites in LaNi,D,_, dicted. Further work is needed to explain sites.
and LaNi,MnD,., cannot be prethe occupation of the 3f and 4h
Acknowledgment This research was funded by the Natural Research Council of Canada (Grant A4391).
Sciences
and Engineering
References 1 J. Shinar, I. Jacob, D. Davidov and D. ShaItiel, in A. F. Andresen and A. J. Maeland (eds.), Proc. Int. Symp. on Hydrides for Energy Storage, Pergamon, Oxford, 1978, p. 337. 2 A. R. Miedema, F. R. Deboer and P. F. De Chatel, J. Phys. F, 3 (1973) 1558. 3 A. R. Miedema, J. Less-Common Met., 32 (1973) 117. 4 D. G. Westlake, in P. Jena and C. B. Satterthwaite (eds.), Electronic Structure and Properties of Hydrogen in Metals, Plenum, New York, 1983, p. 85. 5 D. Ivey and D. 0. Northwood, J. Less-Common Met., 115 (1986) 23. 6 I. Jacob, J. Less-Common Met., 130 (1987) 329. 7 Y. B. Wang and D. 0. Northwood, J. Less-Common Met., 135 (1987) 239. 8 Y. B. Wang and D. 0. Northwood, Mater. Sci. Technol., 4 (1988) 97. 9 D. G. Westlake, J. Less-Common Met., 105 (1985) 69. 10 D. G. Westlake, J. Less-Common Met., 91 (1983) 275. 11 A. Percheron-Guegan, C. Lartigue, J. C. Achard, P. Germi and F. Tasset, J. LessCommon Met., 74 (1980) 1. 12 H. H. van Mal, K. H. J. Buschow and A. R. Miedema, J. Less-Common Met., 35 (1974) 65. 13 A. Pasturel, C. ChatiRon-Colinet, A. Percheron-Guegan and J. C. Achard, J. LessCommon Met., 84 (1982) 73.
of the Less-Common
Metals,
141
(1988)
163
- 167
163
CALCULATION OF DEUTERIUM SITE OCCUPANCY IN LaNisD,.s, LaNi4A1D,., AND LaNiaMnD,., YAN-BIN
WANG*
and DEREK
Department of Engineering N9B 3P4 (Canada) (Received
September
0. NORTHWOOD
Materials,
18, 1987;
University
of Windsor,
in revised form December
Windsor,
Ontario
14, 1987)
Summary By adopting our model for the calculation of the enthalpy of hydride formation, and by assuming that the number of bonds formed between the hydrogen and metal atoms in an alloy is proportional to the number of “broken” bonds for the metal atom, the interactive energy and site occupancy of deuterium in LaNi,D,.,, LaNi,A1D4., and LaNi4MnD,., are calculated and compared with experimental results. The agreement between the calculated and experimentally measured site occupancies is quite good with the exception that the occupation of the 3f and 4h sites in LaN&D,., and LaNi,MnD s.9 cannot be predicted. The enthalpies of deuterium sorption are also calculated for the three alloys. The addition of aluminium or manganese increases the enthalpy of sorption.
1. Introduction Several workers have proposed models for predicting the site occupancy of hydrogen atoms in hydrogen storage alloys. Shinar et al. [l] proposed an imaginary binary hydride model based on the method of Miedema [2,3] for the calculation of the heat of metal hydride formation. However, the success of this model in predicting hydrogen site occupancies has been questioned by Westlake [4] and Ivey and Northwood [5]. Although one of the coworkers of Shinar [l] has subsequently defended their model (Jacob [ 6]), the imaginary binary hydride model is not satisfactory because, among other things, it cannot explain the varied occupancy of the different types of site with the same atomic environment, such as the 12n and 120 sites in the LaNi, alloy. Westlake [4] proposed a geometric model based on hole size to explain the hydrogen capacity and site occupancy in hydrogen storage alloys, and successfully applied it to many alloys. We believe that there is a *Present address: Department Technology, Beijing, China. 0022-5088/88/$3.50
of Metal Physics,
0 Elsevier
Beijing
University
Sequoia/Printed
of Iron and Steel
in The Netherlands
164
need to consider properties other than the geometrical factors, and suggest that since, from the point of view of statistical thermodynamics, the site occupancy is associated with the interactive energy between hydrogen atoms and the interstitial sites, then the interactive energy is determined not only by the hole size but also by the atoms forming the interstitial site. Recently, we presented a modification of Miedema’s model for predicting the enthalpy of hydride formation and applied it to explain the site occupancy of hydrogen atoms in pure metals and some cubic Laves alloys [7, 81. In this paper we extend this work to LaNi, and alloys where aluminium or manganese are substituted for some of the nickel.
2. Analysis In refs. 7 and 8 we modified Miedema’s model and proposed that the electronegativity and electron density of a hydrogen atom would vary for interstitial sites of different size. To determine the interactive energy we proposed a method to calculate the number of bonds formed between a hydrogen atom and the metal atoms surrounding it. Once these calculations had been performed we could determine the hydrogen site occupancy in a similar manner as for the imaginary binary hydride model. In the imaginary binary hydride model, Shinar et al. [l] assumed that the number of bonds formed between a hydrogen atom and the different metal atoms surrounding it are the same [l]. However, this is probably not the case for hydrogen atoms in alloys. In this case the number of bonds, i.e. hydrogen-metal, can be realized by calculating the number of partly “broken” bonds between a metal atom and the metal atoms nearby. Thus it may be more reasonable to assume that the number of bonds formed between a hydrogen atom and a metal atom is proportional to the number of partly broken bonds between the metal atom and the other metal atoms forming the interstitial site. Then the equations (see eqn. (8) in ref. 8) for calculating the number of bonds formed between the hydrogen atom and the metal atoms surrounding it will be as follows D(Mi-H) = R(Mi, 1) + R(H, 1) - 0.6 log ci
(1)
D(Mi-Mj)
(2)
= R(Mi, 1) + R(Mj, 1) - 0.6 log(m, -xx)
Mi and Mj are metal atoms which form the interstitial site, D(Mi-H) is the distance between the hydrogen and Mi atoms, D(Mi-Mj) is the distance between metal atoms Mj and Mi in the metal hydride, R(Mi, l), R(Mj, l), R(H, 1) are the single bond radii of the Mi atom, the Mj atom and the hydrogen atom respectively. ci is the number of bonds formed between the hydrogen and Mi atoms, and is proportional to the partly broken bonds of the Mi atoms. mK is the number of bonds between Mi and Mj, and xx is the number of partly broken bonds after the hydrogen atom enters the interstitial site.
165
After obtaining the number of bonds formed between the hydrogen atom and the metal atoms surrounding it, we can calculate the interactive energy of the hydrogen atom in each kind of site and the site occupancy using the equations derived in refs. 7 and 8.
3. Results and discussion The calculated results for the interactive energy and site occupancy of deuterium in LaNi,D, 5, LaNi4A1D,_s and LaNbMnD,, 9 are given in Table 1. From Table 1, it can be seen that our calculations do not predict the occupation of the 3f and 4h sites. This results in a slightly higher number of deuterium atoms in the other sites. Westlake’s geometric model cannot predict the occupation of the 3f sites. This model is based on a minimum hole radius of 0.40 I%for hydrogen occupation of an interstice in a stable hydride, a minimum H-H distance of 2.10 A and the postulate that the larger interstices should fill first [9]. Because the radii of the 3f sites are much smaller TABLE
1
The interactive energy LaNisD6_s, LaNi4MDb.s
and site occupancy and LaNi~MnDs.9
of deuterium
atoms
in different
AllOY
Site
Atomic environment
In terac the energy @VI
Number of deuterium atoms (calculated)
LaNiD6.s
6m 12n 120 3f 4h
LazNiz LaNis LaNiJ LazNi4 Ni4
-0.1801
-0.1699 -0.1483 +0.2578 +0.0192
2.21 2.99 1.30 0 0
6m(a) 6m(b) 12n(a) 12n(b) 120(a) 120(b) 3f 4h
LazNi2 LazNiAl LaNi3 LaNi&l LaNis LaNiaAl LazNie NisAl
-0.2890 -0.2540 -0.2709 -0.0618 -0.2254 -0.0153 -to.0974 -0.0066
1.31 0.67 2.60 0 I 0.22 0 I 0 0
6m(a) 6m(b) 12n(a) l%(b) 120(a) 120(b) 3f 4h
LazNi2 LasNiMn LaNia LaNiaMn LaNi3 LaNisMn LazNi4 Ni3Mn
-0.1688 -0.2236 -0.2177 -0.2227 -0.1839 -0.1925 +0.1445 -0.0072
0.08 1.33 I 2.12 1.28 I 0.29 0.80
LaNi4AlDe.s
LaNi4MnDs
.a
sites
Number of deuterium atoms (experimental) IllI 1.91 2.14 1.29 0.64 0.52 2.06 2.74 0 0 0
2.06 2.48 0.81 0.35 0.20
in
166
than the size criterion of 0.4 A (0.3126 A, 0.2869 A and 0.3251 A for 3f sites in LaNi5D6.5, LaNi4A1D4.s and LaNi&InDSeg respectively), Westlake proposed that the occupation of the 3f sites was caused by diffusion, and gave the value of the occupation as 12n + 3f [lo]. If we adopt the value of 12n + 3f our results agree more satisfactorily with the experimental results. However, we do not think that diffusion is a satisfactory explanation. Although the deuterium atoms are in constant motion, from the point of view of statistical thermodynamics the time the deuterium atom remains in a certain site is determined by the interactive energy between the deuterium atom and the site. Deuterium atoms can only remain in 3f sites for a very short period of time as the energy is much lower than in other sites. Thus diffusion cannot explain the occupation of the 3f sites. The occupation of . . cannot be explained either. According to the exthe 4h sites m LaNi,D,., perimental results for 4h site occupation [ll], the interactive energy of deuterium with the 4h site must be more than -0.15 eV. It seems impossible for deuterium to have a higher interactive energy in a site formed by four nickel atoms (the 4h site) than in a site formed by one lanthanum atom and three nickel atoms (the 120 site). Further work is needed to explain satisfactorily the occupation of the 3f and 4h sites. Using the interactive energies and site occupancies given in Table 1, the enthalpies of deuterium sorption in each alloy can be calculated. These calculations have been performed and the results are listed in Table 2. The addition of aluminium or manganese increases the enthalpy of sorption. This agrees with the available experimental results [12,13]. TABLE 2 The enthalpy of deuterium sorption (&) Alloy
AH calculated (kJ (mol H2)-l)
AH experimental (kJ (mol Hz)-‘)
LaNisDgvs LaNi4AlDa.s LaNi4MnD5.9
32.6 52.4 42.4
31.8 47.7 48.5
Reference for experimental results
I121 1131 [I31
4. Conclusion Using our previous papers [7, 81 as a basis, the site occupancies and enthalpies of deuterium sorption in LaNisD6.s, LaNi4A1D,.s and LaNtare calculated. In the calculations the assumption is made that the MnD5.9 number of bonds formed between deuterium and a metal atom is proportional to the partly broken bonds between the metal atom and the other metal atoms forming the interstitial site. The calculated results agree quite well with published experimental results, with the exception that the occu-
167
pation of the 3f and 4h sites in LaNi,D,_, dicted. Further work is needed to explain sites.
and LaNi,MnD,., cannot be prethe occupation of the 3f and 4h
Acknowledgment This research was funded by the Natural Research Council of Canada (Grant A4391).
Sciences
and Engineering
References 1 J. Shinar, I. Jacob, D. Davidov and D. ShaItiel, in A. F. Andresen and A. J. Maeland (eds.), Proc. Int. Symp. on Hydrides for Energy Storage, Pergamon, Oxford, 1978, p. 337. 2 A. R. Miedema, F. R. Deboer and P. F. De Chatel, J. Phys. F, 3 (1973) 1558. 3 A. R. Miedema, J. Less-Common Met., 32 (1973) 117. 4 D. G. Westlake, in P. Jena and C. B. Satterthwaite (eds.), Electronic Structure and Properties of Hydrogen in Metals, Plenum, New York, 1983, p. 85. 5 D. Ivey and D. 0. Northwood, J. Less-Common Met., 115 (1986) 23. 6 I. Jacob, J. Less-Common Met., 130 (1987) 329. 7 Y. B. Wang and D. 0. Northwood, J. Less-Common Met., 135 (1987) 239. 8 Y. B. Wang and D. 0. Northwood, Mater. Sci. Technol., 4 (1988) 97. 9 D. G. Westlake, J. Less-Common Met., 105 (1985) 69. 10 D. G. Westlake, J. Less-Common Met., 91 (1983) 275. 11 A. Percheron-Guegan, C. Lartigue, J. C. Achard, P. Germi and F. Tasset, J. LessCommon Met., 74 (1980) 1. 12 H. H. van Mal, K. H. J. Buschow and A. R. Miedema, J. Less-Common Met., 35 (1974) 65. 13 A. Pasturel, C. ChatiRon-Colinet, A. Percheron-Guegan and J. C. Achard, J. LessCommon Met., 84 (1982) 73.