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Effect of H absorption on the electronic structure Co3 Ti
Physica B 254 (1998) 202—206
Effect of H absorption on the electronic structure Co Ti Duan Suqing*, Liu Shaojun, Cai Jun, Ma Benkun Department of Physics, Beijing Normal University, Beijing 100875, People’s Republic of China Received 10 March 1998; received in revised form 26 June 1998
Abstract Electronic structure calculations based on the tight-binding linear muffin-tin orbital (TB-LMTO) method have been performed for Co Ti and its hydride Co TiH. The computed values of lattice constants and bulk moduli are in good agreement with the experiment data. The ab initio results show that (1) H atom has the tendency to stay in Co Ti, i.e., the hydrogen brittlement of Co Ti takes place very easily under hydrogen environment, (2) the number of p and d electrons in Co and Ti atomic spheres are increased due to hydrogen absorption, but the number of s electrons in these atomic spheres decreased, and (3) the ionicity of Co atomic spheres due to hydrogen absorption is changed from positive to negative. The changes of band structures due to hydrogenation are remarkable. 1998 Elsevier Science B.V. All rights reserved. PACS: 71.20; 73.40.j Keywords: Electronic structure; Absorption energy of hydrogen; Hydrogen brittlement
1. Introduction A great deal of interest has been shown in ¸1 type intermetallic compounds and alloys since they show a substantial increase in flow stress with increasing temperature [1—3]. However, the brittleness of this type of alloy has prevented it from being used as an alloy base for a structural material. T. Takasugi and Izumi had investigated the influence of a hydrogen environment on the mechanical properties of ¸1 type Co Ti compound. They found that Co Ti compound had an intrinsically good ductility over a wide range temperatures [4], but the hydrogen embrittlement was a common phenomenon in deformable ¸1 compounds [5]. * Corresponding author.
This paper is dedicated to understanding of the effects of hydrogen absorption on the total energies and the electronic structure of Co Ti. In this work, we report the ab initio results for Co Ti and Co TiH, using the self-consistent tight binding linear muffin-tin (TB-LMTO) method. The calculated values of the cohesive properties, such as equilibrium lattice constants and bulk moduli for ordered compounds Co Ti in ¸1 structure and its low H concentration hydride Co TiH, are com pared with the available experimental results. For the structure of Co Ti, there are two kinds of oc tahedral interstitial site [6] (see Fig. 1). One is the center of the octagon cage(O1) formed by the six nearest neighbor Co atoms, and the other is the center of octagon cage(O2) formed by four Co atoms and two Ti atoms. Our calculations show that the latter place(O2) is more stable for a
0921-4526/98/$ — see front matter 1998 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 8 ) 0 0 4 6 7 - 0
D. Suqing et al. / Physica B 254 (1998) 202—206
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the simple cubic Brillouin zone. The 3d4s electrons of Co, the 3d4s of Ti and the 1s electron of H are taken as the valence electrons. In ASA, the crystal is divided into space-filling, and therefore slightly over-lapping, spheres centred on each of the atomic sites. We choose t /r " 1.1 and 2 ! r /r " 0.5 according to the results of minimizing & ! the total energy of Co TiH. The calculated ground-state total energy E(r) are fitted to a Morse function as E(r) " A!2Ce\HP\P#Ce\HP\P, Fig. 1. The unit cell of Co Ti. The large black and open circles denote Ti and Co atoms, respectively. The small open circles denote two different octahedral interstitial sites.
hydrogen atom to stay. Band-structure results indicate that the number of p and d electrons in Co and Ti atomic spheres are increased due to hydrogen absorption, but the number of s electrons in these atomic spheres are decreased. In Co Ti the ionici ties of Co and Ti atomic spheres are positive and negative, respectively, while in Co TiH, the ionici ties of Co and Ti atomic spheres are negative, and that of H atomic sphere positive. H atoms are easily captured into O2. This ab initio calculation information of the electronic structures may be helpful to understand the hydrogen embrittlement and hydrogen diffusion in the intermetallic compound.
2. Computational details The conventional LMTO-ASA method [7,8] as well as its transformation to a localized representation (TB-LMTO) [9] are well described in the literature. Here we only give the relevant computational details. We have performed self-consistent calculations using the “frozen core” approximation and von Barth—Hedin [10] exchange-correlation potential. Spin-polarized as well as unpolarized calculations have been done for Co Ti, Co TiH(O1) and Co TiH(O2), using a minimal basis set consisting of s, p and d orbitals for Co, Ti and H. “Combined correction” has been taken into account. 165 K points have been used in the irreducible wedge of
(1)
where the independent parameter r is the Wigner—Seitz atomic radius related the volume per atom by the relation X " (4p/3)r, and A, C, j, and r are fitting parameters. For the compounds, we use an effective Wigner—Seitz radius, which is a weighted average of the constituent atomic radii. The absorption energy of hydrogen is defined as E
" E (Co TiH)!E (Co Ti)!E (H), (2) where E (Co TiH) and E (Co Ti) are to the ground-state energies of Co TiH and Co Ti per cell, respectively, and E (H) is the ground-state energy of a free-state hydrogen atom. The volume expansion of Co Ti due to hydrogen absorption is *X X !X ! 2 , " !2 & (3) X X ! 2 and X are the cell volume of where X ! 2 ! 2 & Co TiH and Co Ti, respectively. 3. Calculations and discussion Spin-polarized calculations show zero magnetic moment for Co Ti, Co TiH(O1) and Co TiH(O2) for the range of lattice parameters used by us. It may be noted that there is no experimental evidence for magnetic moments in these alloys. Thus, only the results of the unpolarised calculations is given here. Self-consistent total energies with various lattice constants are calculated for the ordered compounds Co Ti, Co TiH(O1) and Co TiH(O2). The variations of the total energies with lattice constant
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D. Suqing et al. / Physica B 254 (1998) 202—206
are shown in Fig. 2. Some cohesive properties are given in Table 1. It is evident from Table 1 that the computed equilibrium lattice constant of Co Ti are in excel lent agreement with the experiment (just 2% deviation) and the computed bulk moduli of Co Ti and Co TiH are consistently overestimated about 4—9%. The tabulated results reveal that the absorption energy of H both on the O1 site and on the O2 site are negative, and the absorption energy of H on the O2 site is lower than that to the O1 site. So hydrogen has the tendency to stay in Co Ti and it
prefers staying at the O2 sites to staying at the O1 sites. When a hydrogen atom is activated from an O2 site to an O1 site. Therefore, Co TiH(O2) is more stable than Co TiH(O1). On the other hand, one can see the lattice expansion of Co TiH is very small. We can notice that the results are different from those of Ni Al [4]: (i) the absorption energy of H in Co Ti is negative, but that in Ni Al is positive; (ii) the H atom in Co Ti prefers staying at the O2 sites to locating at the O1 sites, but the H atom in Ni Al prefers staying at the O1 sites to staying at the O2.
Fig. 2. The variations of total energy with lattice constants for Co Ti, Co TiH(O1) and Co TiH(O2).
Table 1 Cohesive properties of Co Ti and Co TiH
No. of valence electrons Lattice constant (nm) Experiment [11] Present Bulk modulus (GPa) Experiment [5] Present Total energy (Rydberg) Present Absorption energy of H E (ev) Present Volume expansion *X/X Present
Co Ti
Co TiH(O2)
Co TiH(O1)
31
32
32
0.3612 0.3621
— 0.3670
— 0.3670
0.25 0.26
0.22 0.24
0.23
!10054.5120
!10055.7608
!10055.7258
—
!3.38
!2.91
—
0.041
0.041
D. Suqing et al. / Physica B 254 (1998) 202—206
The negative absorption energy of H, and the small volume expansion in Co Ti may be used to explain why the hydrogen brittlement of Co Ti takes place very easily under a hydrogen environment. The integrated number of states (NOS) of the s, p and d partial waves at the Fermi energies are listed in Table 2. The total NOS of each atom is the sum of all the partial NOS. The effective charges of the atomic spheres *Q(e) due to charge transfer are also listed in Table 2. Table 2 shows that in Co TiH the effective charges of H atomic spheres due to charge transfer are positive, whereas those of Co and Ti are negative. So the ionicities of H atomic spheres are positive, whereas those of Co and Ti atomic spheres are negative. Therefore, ion H is attracted by ion Co and Ti in Co TiH. In Co Ti the ionicity of Co and Ti atomic spheres is positive and negative, respectively. The results reveal that the ionicity of Co atomic spheres due to hydrogen absorption is changed from the positive to the negative, but the ionicity of Ti atomic spheres remains constant. One can also notice that the NOS of p and d states of Co and Ti in Co TiH(O2) become larger than these in Co Ti, but the NOS of s states of Co and Ti in Co TiH become less than those in Co Ti, therefore the anisotropy of the valence charge densities of Co and Ti in Co TiH(O2) becomes stronger than that in Co Ti. It seems to us that the change of the ionicity of Co atomic spheres and the stronger
205
anisotropy of the valence charge densities of Co and Ti may be the main causes of the hydrogen embrittlement of Co Ti. Besides, one can see that the ionicity of H in Co TiH(O2) is stronger than that of H in Co TiH(O1). Fig. 3 is the calculated DOS of Co Ti, Co TiH(O1) and Co TiH(O2). One can see that the low-energy peaks and the high-energy antibonding peak become stronger, but the pseudogap remains still. The Fermi energies are below the pseudogaps of Co Ti and Co TiH, therefore the valence elec trons of Co Ti and Co TiH only occupy the bond ing states. The changes of the electronic structure of Co Ti due to hydrogen absorption are very obvious.
Table 2 Electronic structure parameters and charge transfers *Q(e)
NOS(E ) Co $
s p d Ti s p d H s p d *Q(e) Co Ti H
Co Ti
Co TiH(O1) Co TiH(O2)
0.681 0.740 7.558 0.640 0.866 2.559 — — — 0.022 !0.065 —
0.639 0.781 7.638 0.649 0.852 2.515 0.690 0.103 0.014 !0.058 !0.019 0.192
0.669 0.746 7.612 0.565 0.919 2.654 0.670 0.097 0.012 !0.064 !0.027 0.220
Fig. 3. Electronic DOS and Fermi energies of Co Ti, Co TiH(O1) and Co TiH(O2).
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D. Suqing et al. / Physica B 254 (1998) 202—206
4. Summary We have performed ab initio TB-LMTO calculations on the Co Ti and Co TiH compounds and obtained their total energies, cohesive properties and electronic structures. The theoretical cohesive properties like the equilibrium lattice constants and bulk moduli are in good agreement with experimental results. We observed a charge transfer from the H atom to the Co and Ti atoms, negative absorption energy of H, the change of the ionicities of Co atomic spheres and the increase of the NOS of p and d states and the decrease of the NOS of s state. We also observed the changes of electronic structures of Co Ti due to hydrogen absorption. Acknowledgements The authors are grateful to Prof. H. Skriver for providing TB-LMTO programs. The work is
supported by the Doctoral foundation of State Education Commission of China.
References [1] J.H. Westbook, Trans. Metal. Soc. A.I.M.E. 209 (1957) 898. [2] P.H. Thornton, R.G. Daries, T.L. Johnson, Metal. Tans. 1 (1970) 207. [3] D.M. Wee, O. Noguchi, Y. Oya, T. Suzuki, Japan Inst. Metals 21 (1980) 237. [4] T. Takasugi, O. Izumi, Acta Metal. 33 (1985) 39. [5] T. Takasugi, O. Izumi, Scripta Metal. 19 (1985) 903. [6] Xie Qian, Chen NanXian, Acta Matal. Sinica 7 (1994) 220. [7] O.K. Andersen, Phy. Rev. B 12 (1975) 3060. [8] H.L. Skriver, The LMTO Method Springer, Heidelberg, 1984. [9] O.K. Andersen, O. Jepsen, Phy. Rev. Lett. 53 (1984) 2571. [10] U. von Barth, L. Hedin, J. Phys. C 5 (1972) 1629. [11] T. Takasugi, O. Izumi, Acta Metal. 33 (1985) 33.
Effect of H absorption on the electronic structure Co Ti Duan Suqing*, Liu Shaojun, Cai Jun, Ma Benkun Department of Physics, Beijing Normal University, Beijing 100875, People’s Republic of China Received 10 March 1998; received in revised form 26 June 1998
Abstract Electronic structure calculations based on the tight-binding linear muffin-tin orbital (TB-LMTO) method have been performed for Co Ti and its hydride Co TiH. The computed values of lattice constants and bulk moduli are in good agreement with the experiment data. The ab initio results show that (1) H atom has the tendency to stay in Co Ti, i.e., the hydrogen brittlement of Co Ti takes place very easily under hydrogen environment, (2) the number of p and d electrons in Co and Ti atomic spheres are increased due to hydrogen absorption, but the number of s electrons in these atomic spheres decreased, and (3) the ionicity of Co atomic spheres due to hydrogen absorption is changed from positive to negative. The changes of band structures due to hydrogenation are remarkable. 1998 Elsevier Science B.V. All rights reserved. PACS: 71.20; 73.40.j Keywords: Electronic structure; Absorption energy of hydrogen; Hydrogen brittlement
1. Introduction A great deal of interest has been shown in ¸1 type intermetallic compounds and alloys since they show a substantial increase in flow stress with increasing temperature [1—3]. However, the brittleness of this type of alloy has prevented it from being used as an alloy base for a structural material. T. Takasugi and Izumi had investigated the influence of a hydrogen environment on the mechanical properties of ¸1 type Co Ti compound. They found that Co Ti compound had an intrinsically good ductility over a wide range temperatures [4], but the hydrogen embrittlement was a common phenomenon in deformable ¸1 compounds [5]. * Corresponding author.
This paper is dedicated to understanding of the effects of hydrogen absorption on the total energies and the electronic structure of Co Ti. In this work, we report the ab initio results for Co Ti and Co TiH, using the self-consistent tight binding linear muffin-tin (TB-LMTO) method. The calculated values of the cohesive properties, such as equilibrium lattice constants and bulk moduli for ordered compounds Co Ti in ¸1 structure and its low H concentration hydride Co TiH, are com pared with the available experimental results. For the structure of Co Ti, there are two kinds of oc tahedral interstitial site [6] (see Fig. 1). One is the center of the octagon cage(O1) formed by the six nearest neighbor Co atoms, and the other is the center of octagon cage(O2) formed by four Co atoms and two Ti atoms. Our calculations show that the latter place(O2) is more stable for a
0921-4526/98/$ — see front matter 1998 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 8 ) 0 0 4 6 7 - 0
D. Suqing et al. / Physica B 254 (1998) 202—206
203
the simple cubic Brillouin zone. The 3d4s electrons of Co, the 3d4s of Ti and the 1s electron of H are taken as the valence electrons. In ASA, the crystal is divided into space-filling, and therefore slightly over-lapping, spheres centred on each of the atomic sites. We choose t /r " 1.1 and 2 ! r /r " 0.5 according to the results of minimizing & ! the total energy of Co TiH. The calculated ground-state total energy E(r) are fitted to a Morse function as E(r) " A!2Ce\HP\P#Ce\HP\P, Fig. 1. The unit cell of Co Ti. The large black and open circles denote Ti and Co atoms, respectively. The small open circles denote two different octahedral interstitial sites.
hydrogen atom to stay. Band-structure results indicate that the number of p and d electrons in Co and Ti atomic spheres are increased due to hydrogen absorption, but the number of s electrons in these atomic spheres are decreased. In Co Ti the ionici ties of Co and Ti atomic spheres are positive and negative, respectively, while in Co TiH, the ionici ties of Co and Ti atomic spheres are negative, and that of H atomic sphere positive. H atoms are easily captured into O2. This ab initio calculation information of the electronic structures may be helpful to understand the hydrogen embrittlement and hydrogen diffusion in the intermetallic compound.
2. Computational details The conventional LMTO-ASA method [7,8] as well as its transformation to a localized representation (TB-LMTO) [9] are well described in the literature. Here we only give the relevant computational details. We have performed self-consistent calculations using the “frozen core” approximation and von Barth—Hedin [10] exchange-correlation potential. Spin-polarized as well as unpolarized calculations have been done for Co Ti, Co TiH(O1) and Co TiH(O2), using a minimal basis set consisting of s, p and d orbitals for Co, Ti and H. “Combined correction” has been taken into account. 165 K points have been used in the irreducible wedge of
(1)
where the independent parameter r is the Wigner—Seitz atomic radius related the volume per atom by the relation X " (4p/3)r, and A, C, j, and r are fitting parameters. For the compounds, we use an effective Wigner—Seitz radius, which is a weighted average of the constituent atomic radii. The absorption energy of hydrogen is defined as E
" E (Co TiH)!E (Co Ti)!E (H), (2) where E (Co TiH) and E (Co Ti) are to the ground-state energies of Co TiH and Co Ti per cell, respectively, and E (H) is the ground-state energy of a free-state hydrogen atom. The volume expansion of Co Ti due to hydrogen absorption is *X X !X ! 2 , " !2 & (3) X X ! 2 and X are the cell volume of where X ! 2 ! 2 & Co TiH and Co Ti, respectively. 3. Calculations and discussion Spin-polarized calculations show zero magnetic moment for Co Ti, Co TiH(O1) and Co TiH(O2) for the range of lattice parameters used by us. It may be noted that there is no experimental evidence for magnetic moments in these alloys. Thus, only the results of the unpolarised calculations is given here. Self-consistent total energies with various lattice constants are calculated for the ordered compounds Co Ti, Co TiH(O1) and Co TiH(O2). The variations of the total energies with lattice constant
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D. Suqing et al. / Physica B 254 (1998) 202—206
are shown in Fig. 2. Some cohesive properties are given in Table 1. It is evident from Table 1 that the computed equilibrium lattice constant of Co Ti are in excel lent agreement with the experiment (just 2% deviation) and the computed bulk moduli of Co Ti and Co TiH are consistently overestimated about 4—9%. The tabulated results reveal that the absorption energy of H both on the O1 site and on the O2 site are negative, and the absorption energy of H on the O2 site is lower than that to the O1 site. So hydrogen has the tendency to stay in Co Ti and it
prefers staying at the O2 sites to staying at the O1 sites. When a hydrogen atom is activated from an O2 site to an O1 site. Therefore, Co TiH(O2) is more stable than Co TiH(O1). On the other hand, one can see the lattice expansion of Co TiH is very small. We can notice that the results are different from those of Ni Al [4]: (i) the absorption energy of H in Co Ti is negative, but that in Ni Al is positive; (ii) the H atom in Co Ti prefers staying at the O2 sites to locating at the O1 sites, but the H atom in Ni Al prefers staying at the O1 sites to staying at the O2.
Fig. 2. The variations of total energy with lattice constants for Co Ti, Co TiH(O1) and Co TiH(O2).
Table 1 Cohesive properties of Co Ti and Co TiH
No. of valence electrons Lattice constant (nm) Experiment [11] Present Bulk modulus (GPa) Experiment [5] Present Total energy (Rydberg) Present Absorption energy of H E (ev) Present Volume expansion *X/X Present
Co Ti
Co TiH(O2)
Co TiH(O1)
31
32
32
0.3612 0.3621
— 0.3670
— 0.3670
0.25 0.26
0.22 0.24
0.23
!10054.5120
!10055.7608
!10055.7258
—
!3.38
!2.91
—
0.041
0.041
D. Suqing et al. / Physica B 254 (1998) 202—206
The negative absorption energy of H, and the small volume expansion in Co Ti may be used to explain why the hydrogen brittlement of Co Ti takes place very easily under a hydrogen environment. The integrated number of states (NOS) of the s, p and d partial waves at the Fermi energies are listed in Table 2. The total NOS of each atom is the sum of all the partial NOS. The effective charges of the atomic spheres *Q(e) due to charge transfer are also listed in Table 2. Table 2 shows that in Co TiH the effective charges of H atomic spheres due to charge transfer are positive, whereas those of Co and Ti are negative. So the ionicities of H atomic spheres are positive, whereas those of Co and Ti atomic spheres are negative. Therefore, ion H is attracted by ion Co and Ti in Co TiH. In Co Ti the ionicity of Co and Ti atomic spheres is positive and negative, respectively. The results reveal that the ionicity of Co atomic spheres due to hydrogen absorption is changed from the positive to the negative, but the ionicity of Ti atomic spheres remains constant. One can also notice that the NOS of p and d states of Co and Ti in Co TiH(O2) become larger than these in Co Ti, but the NOS of s states of Co and Ti in Co TiH become less than those in Co Ti, therefore the anisotropy of the valence charge densities of Co and Ti in Co TiH(O2) becomes stronger than that in Co Ti. It seems to us that the change of the ionicity of Co atomic spheres and the stronger
205
anisotropy of the valence charge densities of Co and Ti may be the main causes of the hydrogen embrittlement of Co Ti. Besides, one can see that the ionicity of H in Co TiH(O2) is stronger than that of H in Co TiH(O1). Fig. 3 is the calculated DOS of Co Ti, Co TiH(O1) and Co TiH(O2). One can see that the low-energy peaks and the high-energy antibonding peak become stronger, but the pseudogap remains still. The Fermi energies are below the pseudogaps of Co Ti and Co TiH, therefore the valence elec trons of Co Ti and Co TiH only occupy the bond ing states. The changes of the electronic structure of Co Ti due to hydrogen absorption are very obvious.
Table 2 Electronic structure parameters and charge transfers *Q(e)
NOS(E ) Co $
s p d Ti s p d H s p d *Q(e) Co Ti H
Co Ti
Co TiH(O1) Co TiH(O2)
0.681 0.740 7.558 0.640 0.866 2.559 — — — 0.022 !0.065 —
0.639 0.781 7.638 0.649 0.852 2.515 0.690 0.103 0.014 !0.058 !0.019 0.192
0.669 0.746 7.612 0.565 0.919 2.654 0.670 0.097 0.012 !0.064 !0.027 0.220
Fig. 3. Electronic DOS and Fermi energies of Co Ti, Co TiH(O1) and Co TiH(O2).
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4. Summary We have performed ab initio TB-LMTO calculations on the Co Ti and Co TiH compounds and obtained their total energies, cohesive properties and electronic structures. The theoretical cohesive properties like the equilibrium lattice constants and bulk moduli are in good agreement with experimental results. We observed a charge transfer from the H atom to the Co and Ti atoms, negative absorption energy of H, the change of the ionicities of Co atomic spheres and the increase of the NOS of p and d states and the decrease of the NOS of s state. We also observed the changes of electronic structures of Co Ti due to hydrogen absorption. Acknowledgements The authors are grateful to Prof. H. Skriver for providing TB-LMTO programs. The work is
supported by the Doctoral foundation of State Education Commission of China.
References [1] J.H. Westbook, Trans. Metal. Soc. A.I.M.E. 209 (1957) 898. [2] P.H. Thornton, R.G. Daries, T.L. Johnson, Metal. Tans. 1 (1970) 207. [3] D.M. Wee, O. Noguchi, Y. Oya, T. Suzuki, Japan Inst. Metals 21 (1980) 237. [4] T. Takasugi, O. Izumi, Acta Metal. 33 (1985) 39. [5] T. Takasugi, O. Izumi, Scripta Metal. 19 (1985) 903. [6] Xie Qian, Chen NanXian, Acta Matal. Sinica 7 (1994) 220. [7] O.K. Andersen, Phy. Rev. B 12 (1975) 3060. [8] H.L. Skriver, The LMTO Method Springer, Heidelberg, 1984. [9] O.K. Andersen, O. Jepsen, Phy. Rev. Lett. 53 (1984) 2571. [10] U. von Barth, L. Hedin, J. Phys. C 5 (1972) 1629. [11] T. Takasugi, O. Izumi, Acta Metal. 33 (1985) 33.