J. Mater. Sci. Technol. ›› 2018, Vol. 34 ›› Issue (9): 1699-1712.DOI: 10.1016/j.jmst.2018.01.007
• Orginal Article • Previous Articles
Guoliang Liuab, Demin Chena*(), Yuanming Wanga*(), Ke Yanga
Received:
2017-10-23
Revised:
2017-12-02
Accepted:
2017-12-27
Online:
2018-09-20
Published:
2018-09-25
Contact:
Chen Demin,Wang Yuanming
Guoliang Liu, Demin Chen, Yuanming Wang, Ke Yang. Experimental and computational investigations of LaNi5-xAlx (x = 0, 0.25, 0.5, 0.75 and 1.0) tritium-storage alloys[J]. J. Mater. Sci. Technol., 2018, 34(9): 1699-1712.
Fig. 1. X-ray diffraction patterns of LaNi5-xAlx (x = 0, 0.25, 0.5 and 0.75) alloys. (a) Curves of experimental lattice parameters a, c, unit cell volume V, and a/c ratio vs. Al content (x) in LaNi5-xAlx (x = 0, 0.25, 0.5 and 0.75) (b).
Fig. 2. Hydrogen and deuterium absorption/desorption PC isotherms of LaNi5-xAlx (x = 0, 0.25, 0.5, 0.75 and 1.0) alloys: LaNi5 (a), (b); LaNi4.75Al0.25 (c), (d); LaNi4.5Al0.5 (e), (f); LaNi4.25Al0.75 (g), (h); LaNi4Al [26] (i).
Fig. 3. Experimental curves of vs. (Van’t Hoff relation) for LaNi5-xAlx (x = 0 (a), 0.25 (b), 0.5 (c) and 0.75 (d)) alloys. The equilibrium pressure PQ was measured at the midpoint of each platform in Fig. 2.
Fig. 4. Schematic (1 × 1 × 2) supercell of LaNi4.5Al0.5, whose structure was established according to Ref. [34]. The La, Ni and Al atoms are represented by light blue, black blue and pink balls, respectively. Their Wyckoff positions in this structure are denoted by 1a, 2c, 3g0 and 3g1. Among them, the light blue La atoms are at 1a site in unit cells I and II, the black blue Ni atoms are at 2c, 3g1 sites in unit cell I and 2c, 3g0, 3g1 sites in unit cell II, and the pink Al atom is at 3g0 site in unit cell I.
Compound | Space group | a (?) | c (?) | a/c | V (?3) | ΔE (kJ/mol) |
---|---|---|---|---|---|---|
LaNi5 Cal. | P6/mmm | 5.095 | 3.978 | 1.281 | 89.431 | -164.2 |
This study Exp. | 5.018 | 3.980 | 1.261 | 86.759 | ||
Ref. [ | 5.020 | 3.977 | 1.262 | 86.791 | ||
LaNi5H Cal. | Cmm2 | 5.035 | 4.040 | 1.246 | 92.655 | -185.3 |
LaNi5D Cal. | 5.034 | 4.041 | 1.246 | 92.951 | -185.3 | |
LaNi5T Cal. | 5.034 | 4.041 | 1.246 | 92.653 | -185.3 | |
LaNi4.75Al0.25 Cal. | Fmmm | 5.085 | 4.014 | 1.267 | 90.540 | -194.3 |
This study Exp. | 5.027 | 3.995 | 1.258 | 87.436 | ||
Ref. [ | 5.021 | 3.981 | 1.261 | 86.930 | ||
LaNi4.75Al0.25H Cal. | C2 | 5.047 | 4.036 | 1.250 | 93.249 | -216.0 |
LaNi4.75Al0.25D Cal. | 5.046 | 4.036 | 1.250 | 93.241 | -216.0 | |
LaNi4.75Al0.25T Cal. | 5.045 | 4.036 | 1.250 | 93.263 | -216.0 | |
LaNi4.5Al0.5 Cal. | Immm | 5.083 | 4.044 | 1.257 | 91.373 | -225.7 |
This study Exp. | 5.040 | 4.020 | 1.254 | 88.434 | ||
Ref. [ | 5.038 | 4.007 | 1.257 | 88.073 | ||
LaNi4.5Al0.5H Cal. | C2 | 5.052 | 4.059 | 1.245 | 94.261 | -251.6 |
LaNi4.5Al0.5D Cal. | 5.052 | 4.059 | 1.245 | 94.266 | -251.6 | |
LaNi4.5Al0.5T Cal. | 5.052 | 4.058 | 1.245 | 94.228 | -251.6 | |
LaNi4.25Al0.75 Cal. | Fmmm | 5.087 | 4.048 | 1.257 | 92.202 | -252.0 |
This study Exp. | 5.053 | 4.052 | 1.247 | 89.579 | ||
Ref. [ | 5.045 | 4.050 | 1.246 | 89.262 | ||
LaNi4.25Al0.75H Cal. | C2 | 5.069 | 4.062 | 1.248 | 95.234 | -281.2 |
LaNi4.25Al0.75D Cal. | 5.069 | 4.062 | 1.248 | 95.210 | -281.2 | |
LaNi4.25Al0.75T Cal. | 5.068 | 4.062 | 1.248 | 95.230 | -281.2 | |
LaNi4Al Cal. | Cmmm | 5.092 | 4.049 | 1.258 | 93.058 | -282.3 |
Ref. [ | 5.055 | 4.064 | 1.244 | 89.930 | ||
LaNi4AlH Cal. | P2 | 5.078 | 4.047 | 1.255 | 96.203 | -317.2 |
Table 1 Comparison of experimental and first-principles (GGA) calculated lattice parameters, unit cell volumes of LaNi5-xAlx and LaNi5-xAlxH (D or T) as well as their space groups. The first-principles calculated formation energies at T = 0 K are defined as (Q = H, D or T), ΔEM = Etotal[LaNi5-xAlx] - (Et[La] + (5 - x)Et[Ni] + xEt[Al]), Etotal or Et is the total energy of substance in the bracket. Et[Q2] is the total energy of an isolated H2 (D2 or T2) molecule.
Compound | Space group | a (?) | c (?) | a/c | V (?3) | ΔE (kJ/mol) |
---|---|---|---|---|---|---|
LaNi5 Cal. | P6/mmm | 5.095 | 3.978 | 1.281 | 89.431 | -164.2 |
This study Exp. | 5.018 | 3.980 | 1.261 | 86.759 | ||
Ref. [ | 5.020 | 3.977 | 1.262 | 86.791 | ||
LaNi5H Cal. | Cmm2 | 5.035 | 4.040 | 1.246 | 92.655 | -185.3 |
LaNi5D Cal. | 5.034 | 4.041 | 1.246 | 92.951 | -185.3 | |
LaNi5T Cal. | 5.034 | 4.041 | 1.246 | 92.653 | -185.3 | |
LaNi4.75Al0.25 Cal. | Fmmm | 5.085 | 4.014 | 1.267 | 90.540 | -194.3 |
This study Exp. | 5.027 | 3.995 | 1.258 | 87.436 | ||
Ref. [ | 5.021 | 3.981 | 1.261 | 86.930 | ||
LaNi4.75Al0.25H Cal. | C2 | 5.047 | 4.036 | 1.250 | 93.249 | -216.0 |
LaNi4.75Al0.25D Cal. | 5.046 | 4.036 | 1.250 | 93.241 | -216.0 | |
LaNi4.75Al0.25T Cal. | 5.045 | 4.036 | 1.250 | 93.263 | -216.0 | |
LaNi4.5Al0.5 Cal. | Immm | 5.083 | 4.044 | 1.257 | 91.373 | -225.7 |
This study Exp. | 5.040 | 4.020 | 1.254 | 88.434 | ||
Ref. [ | 5.038 | 4.007 | 1.257 | 88.073 | ||
LaNi4.5Al0.5H Cal. | C2 | 5.052 | 4.059 | 1.245 | 94.261 | -251.6 |
LaNi4.5Al0.5D Cal. | 5.052 | 4.059 | 1.245 | 94.266 | -251.6 | |
LaNi4.5Al0.5T Cal. | 5.052 | 4.058 | 1.245 | 94.228 | -251.6 | |
LaNi4.25Al0.75 Cal. | Fmmm | 5.087 | 4.048 | 1.257 | 92.202 | -252.0 |
This study Exp. | 5.053 | 4.052 | 1.247 | 89.579 | ||
Ref. [ | 5.045 | 4.050 | 1.246 | 89.262 | ||
LaNi4.25Al0.75H Cal. | C2 | 5.069 | 4.062 | 1.248 | 95.234 | -281.2 |
LaNi4.25Al0.75D Cal. | 5.069 | 4.062 | 1.248 | 95.210 | -281.2 | |
LaNi4.25Al0.75T Cal. | 5.068 | 4.062 | 1.248 | 95.230 | -281.2 | |
LaNi4Al Cal. | Cmmm | 5.092 | 4.049 | 1.258 | 93.058 | -282.3 |
Ref. [ | 5.055 | 4.064 | 1.244 | 89.930 | ||
LaNi4AlH Cal. | P2 | 5.078 | 4.047 | 1.255 | 96.203 | -317.2 |
H sites | H—Ni at 2c in Cell I | H—Ni at 3g1 in Cell I | H—La in Cell I | H—Al at 3g0 in Cell I | H—Ni at 3g0 in Cell II | |||||
---|---|---|---|---|---|---|---|---|---|---|
BO | BL | BO | BL | BO | BL | BO | BL | BO | BL | |
12na in Cell I | 0.280 | 1.669 | 0 | 3.543 | -0.220 | 2.605 | 0.050 | 2.467 | 0.310 | 1.624 |
12 nb in Cell I | 0.280 | 1.688 | 0.300 | 1.682 | -0.245 | 2.556 | 0 | 3.310 | 0 | 3.560 |
Table 2 Bond orders (BO) and bond lengths (BL) between H—Ni, H—La and H—Al in LaNi4.5Al0.5H in which a hydrogen atom is at the preferable 12na or 12nb site in Cell I, with reference to Fig. 5(b).
H sites | H—Ni at 2c in Cell I | H—Ni at 3g1 in Cell I | H—La in Cell I | H—Al at 3g0 in Cell I | H—Ni at 3g0 in Cell II | |||||
---|---|---|---|---|---|---|---|---|---|---|
BO | BL | BO | BL | BO | BL | BO | BL | BO | BL | |
12na in Cell I | 0.280 | 1.669 | 0 | 3.543 | -0.220 | 2.605 | 0.050 | 2.467 | 0.310 | 1.624 |
12 nb in Cell I | 0.280 | 1.688 | 0.300 | 1.682 | -0.245 | 2.556 | 0 | 3.310 | 0 | 3.560 |
Compound | H at 12nb in Cell I | Ni at 2c in Cell I | Ni at 3g1 in Cell I | La in Cell I | Al at 3g0 in Cell I | Ni at 3g0 in Cell II |
---|---|---|---|---|---|---|
LaNi4.5Al0.5H | -0.240 | -0.390 | -0.370 | 2.010 | -0.060 | -0.440 |
Table 3 Average net charges (ANCs) on H, Ni, La and Al in LaNi4.5Al0.5H.
Compound | H at 12nb in Cell I | Ni at 2c in Cell I | Ni at 3g1 in Cell I | La in Cell I | Al at 3g0 in Cell I | Ni at 3g0 in Cell II |
---|---|---|---|---|---|---|
LaNi4.5Al0.5H | -0.240 | -0.390 | -0.370 | 2.010 | -0.060 | -0.440 |
Fig. 5. Schematic diagram of (2 × 2 × 2) supercell (a) of LaNi4.5Al0.5H used for calculating BO, BL and ANC, where only the pink Al atoms at 3g0 sites in I, IV, V, VIII unit cells were shown. The (1 × 1 × 2) supercells ((b), (c)) are composed of unit cells I and II, in which the La atoms, Ni atoms, H atoms possible to put in the interstitial sites and Al atom are represented by light blue, black blue, white and pink balls, respectively. The possible interstitial sites of 12na, 12nb, 6ma and 6mb are also labeled.
Fig. 6. Relationship between formation energy difference ΔEM-H - ΔEM of LaNi5-xAlxH (x = 0, 0.25, 0.5 and 0.75) and . In this figure is the average of BOH-Ni/BLH-Ni values between H and Ni at 2c and 3g1 around H.
Fig. 7. Total density of states (TDOS) (1) (a) and (b) and the enlarged partial density of states (PDOS) (2) (a) and (b) for LaNi5H (D or T) and LaNi4.5Al0.5H (D or T), where Ef (Fermi level) is referenced as zero.
Compound | Supercell | (kJ/mol) | (kJ/mol) | Hvib (T) (kJ/mol) | S (T) (J/mol/K) |
---|---|---|---|---|---|
H2 | 1 × 1 × 1 | 28.3 | 28.3 | 1.8 | 139.2 |
D2 | 1 × 1 × 1 | 20.8 | 20.8 | 2.9 | 153.5 |
T2 | 1 × 1 × 1 | 18.8 | 18.8 | 4.1 | 161.2 |
LaNi5 | 2 × 2 × 2 | 20.1 | -144.1 | 40.3 | 213.2 |
LaNi5H | 2 × 2 × 2 | 40.1 | -145.2 | 42.5 | 217.6 |
LaNi5D | 2 × 2 × 2 | 34.1 | -151.2 | 43.8 | 223.4 |
LaNi5T | 2 × 2 × 2 | 32.4 | -152.9 | 43.9 | 220.8 |
LaNi4.75Al0.25 | 2 × 2 × 2 | 21.7 | -172.6 | 40.7 | 207.6 |
LaNi4.75Al0.25H | 2 × 2 × 2 | 38.6 | -177.4 | 43.1 | 223.2 |
LaNi4.75Al0.25D | 2 × 2 × 2 | 33.1 | -182.9 | 44.3 | 228.7 |
LaNi4.75Al0.25T | 2 × 2 × 2 | 30.8 | -185.2 | 45.1 | 231.7 |
LaNi4.5Al0.5 | 2 × 2 × 2 | 21.4 | -204.3 | 39.6 | 201.5 |
LaNi4.5Al0.5H | 2 × 2 × 2 | 37.6 | -214.0 | 43.8 | 221.3 |
LaNi4.5Al0.5D | 2 × 2 × 2 | 33.4 | -218.2 | 44.2 | 217.9 |
LaNi4.5Al0.5T | 2 × 2 × 2 | 30.0 | -221.6 | 45.6 | 228.6 |
LaNi4.25Al0.75 | 2 × 2 × 2 | 21.7 | -230.3 | 39.3 | 199.1 |
LaNi4.25Al0.75H | 2 × 2 × 2 | 39.4 | -241.8 | 42.7 | 219.9 |
LaNi4.25Al0.75D | 2 × 2 × 2 | 33.8 | -247.4 | 43.8 | 224.9 |
LaNi4.25Al0.75T | 2 × 2 × 2 | 31.7 | -249.5 | 44.4 | 226.7 |
Table 4 List of all compounds in LaNi5-xAlx-H2 (D2 or T2) system considered in this work and first-principles T = 0 K calculated ZPE, ΔE + ZPE, as well as vibrational energies Hvib (T) and entropies S (T) at T = 400 K. The standard entropies of H2, D2 and T2 at T = 400 K are obtained by looking up Thermochemical Data of Pure Substances [49]. The second column gives the supercell sizes used in our frozen phonon calculations. Eight H (D or T) atoms were put at eight 12nb sites in each 2 × 2 × 2 supercell in our phonon calculations.
Compound | Supercell | (kJ/mol) | (kJ/mol) | Hvib (T) (kJ/mol) | S (T) (J/mol/K) |
---|---|---|---|---|---|
H2 | 1 × 1 × 1 | 28.3 | 28.3 | 1.8 | 139.2 |
D2 | 1 × 1 × 1 | 20.8 | 20.8 | 2.9 | 153.5 |
T2 | 1 × 1 × 1 | 18.8 | 18.8 | 4.1 | 161.2 |
LaNi5 | 2 × 2 × 2 | 20.1 | -144.1 | 40.3 | 213.2 |
LaNi5H | 2 × 2 × 2 | 40.1 | -145.2 | 42.5 | 217.6 |
LaNi5D | 2 × 2 × 2 | 34.1 | -151.2 | 43.8 | 223.4 |
LaNi5T | 2 × 2 × 2 | 32.4 | -152.9 | 43.9 | 220.8 |
LaNi4.75Al0.25 | 2 × 2 × 2 | 21.7 | -172.6 | 40.7 | 207.6 |
LaNi4.75Al0.25H | 2 × 2 × 2 | 38.6 | -177.4 | 43.1 | 223.2 |
LaNi4.75Al0.25D | 2 × 2 × 2 | 33.1 | -182.9 | 44.3 | 228.7 |
LaNi4.75Al0.25T | 2 × 2 × 2 | 30.8 | -185.2 | 45.1 | 231.7 |
LaNi4.5Al0.5 | 2 × 2 × 2 | 21.4 | -204.3 | 39.6 | 201.5 |
LaNi4.5Al0.5H | 2 × 2 × 2 | 37.6 | -214.0 | 43.8 | 221.3 |
LaNi4.5Al0.5D | 2 × 2 × 2 | 33.4 | -218.2 | 44.2 | 217.9 |
LaNi4.5Al0.5T | 2 × 2 × 2 | 30.0 | -221.6 | 45.6 | 228.6 |
LaNi4.25Al0.75 | 2 × 2 × 2 | 21.7 | -230.3 | 39.3 | 199.1 |
LaNi4.25Al0.75H | 2 × 2 × 2 | 39.4 | -241.8 | 42.7 | 219.9 |
LaNi4.25Al0.75D | 2 × 2 × 2 | 33.8 | -247.4 | 43.8 | 224.9 |
LaNi4.25Al0.75T | 2 × 2 × 2 | 31.7 | -249.5 | 44.4 | 226.7 |
Compound | Supercell | (kJ/mol Q2) | (J/mol/K Q2) | ΔHExp. (kJ/mol Q2) | ΔSExp. (J/mol/K Q2) | ||
---|---|---|---|---|---|---|---|
Ads. | Des. | Ads. | Des. | ||||
LaNi5H | 2 × 2 × 2 | -27.8 | -130.4 | -27.9; -30.8a | 28.9 | -99.9; -108.0a | 101.1 |
LaNi5D | 2 × 2 × 2 | -30.8 | -133.1 | -28.8 | 32.3 | -104.3 | 112.0 |
LaNi5T | 2 × 2 × 2 | -33.2 | -146.0 | ||||
LaNi4.75Al0.25H | 2 × 2 × 2 | -34.8 | -108.0 | -31.4; -31.5b | 32.9 | -101.2; -100.8b | 102.4 |
LaNi4.75Al0.25D | 2 × 2 × 2 | -37.0 | -111.3 | -33.9 | 36.4 | -110.3 | 113.7 |
LaNi4.75Al0.25T | 2 × 2 × 2 | -39.2 | -113.0 | ||||
LaNi4.5Al0.5H | 2 × 2 × 2 | -41.0 | -99.6 | -39.4; -37.3b | 40.7 | -113.2; -102.7b | 114.2 |
LaNi4.5Al0.5D | 2 × 2 × 2 | -42.2 | -120.7 | -40.9 | 43.1 | -118.8 | 122.3 |
LaNi4.5Al0.5T | 2 × 2 × 2 | -45.4 | -107.0 | ||||
LaNi4.25Al0.75H | 2 × 2 × 2 | -46.2 | -97.6 | -43.1; -41.4b | 45.2 | -111.6; -106.0b | 115.1 |
LaNi4.25Al0.75D | 2 × 2 × 2 | -48.8 | -101.9 | -44.1 | 46.8 | -116.6 | 121.3 |
LaNi4.25Al0.75T | 2 × 2 × 2 | -51.0 | -106.0 | -46.2c | -127.2c |
Table 5 Comparison of the first-principles (GGA) T = 400 K calculated enthalpy changes ΔH, entropy changes ΔS and the experimental ΔHExp., ΔSExp. of LaNi5-xAlxH (D or T) in absorption/desorption processes, deduced using Van’t Hoff Eqs. (1) and (2).
Compound | Supercell | (kJ/mol Q2) | (J/mol/K Q2) | ΔHExp. (kJ/mol Q2) | ΔSExp. (J/mol/K Q2) | ||
---|---|---|---|---|---|---|---|
Ads. | Des. | Ads. | Des. | ||||
LaNi5H | 2 × 2 × 2 | -27.8 | -130.4 | -27.9; -30.8a | 28.9 | -99.9; -108.0a | 101.1 |
LaNi5D | 2 × 2 × 2 | -30.8 | -133.1 | -28.8 | 32.3 | -104.3 | 112.0 |
LaNi5T | 2 × 2 × 2 | -33.2 | -146.0 | ||||
LaNi4.75Al0.25H | 2 × 2 × 2 | -34.8 | -108.0 | -31.4; -31.5b | 32.9 | -101.2; -100.8b | 102.4 |
LaNi4.75Al0.25D | 2 × 2 × 2 | -37.0 | -111.3 | -33.9 | 36.4 | -110.3 | 113.7 |
LaNi4.75Al0.25T | 2 × 2 × 2 | -39.2 | -113.0 | ||||
LaNi4.5Al0.5H | 2 × 2 × 2 | -41.0 | -99.6 | -39.4; -37.3b | 40.7 | -113.2; -102.7b | 114.2 |
LaNi4.5Al0.5D | 2 × 2 × 2 | -42.2 | -120.7 | -40.9 | 43.1 | -118.8 | 122.3 |
LaNi4.5Al0.5T | 2 × 2 × 2 | -45.4 | -107.0 | ||||
LaNi4.25Al0.75H | 2 × 2 × 2 | -46.2 | -97.6 | -43.1; -41.4b | 45.2 | -111.6; -106.0b | 115.1 |
LaNi4.25Al0.75D | 2 × 2 × 2 | -48.8 | -101.9 | -44.1 | 46.8 | -116.6 | 121.3 |
LaNi4.25Al0.75T | 2 × 2 × 2 | -51.0 | -106.0 | -46.2c | -127.2c |
Fig. 8. Two-dimensional transformation schematics from P6/mmm to Cmm2 for (1 × 2 × 1) (a) and (3 × 2 × 1) (b) supercells, where only the white H atoms in each supercell are shown.
Fig. 9. Calculated densities of phonon states (pDOSs) for LaNi5H with 2 × 1 × 1 (a), 2 × 2 × 1 (b), 2 × 2 × 2 (c), 1 × 2 × 1 (d) and 3 × 2 × 1 (e) supercells. H was located at 12 nb site in each unit cell of input supercells, with reference to Fig. 5(b).
Compound | Space group | Supercell | ΔE (kJ/mol) | ZPE (kJ/mol) | (kJ/mol H2) | ΔS (J/mol/K H2) |
---|---|---|---|---|---|---|
LaNi5H | P6/mmm | 2 × 1 × 1 | -185.9 | 40.6 | -28.8 | -141.0 |
2 × 2 × 1 | -185.7 | 39.3 | -29.2 | -120.0 | ||
2 × 2 × 2 | -185.3 | 40.1 | -27.8 | -130.4 | ||
1 × 2 × 1 | -185.9 | 46.9 | -19.6 | -168.0 | ||
3 × 2 × 1 | -186.0 | 39.2 | -33.4 | -133.8 |
Table 6 Relations of the first-principles calculated formation energies ΔE, ZPE at T = 0 K, and enthalpy changes ΔH, entropy changes ΔS at T = 400 K with respect to the supercell size for LaNi5H in which H was located at 12 nb site in each unit cell with P6/mmm as shown in Fig. 8. The second column gives the space group of input unit cell of LaNi5H.
Compound | Space group | Supercell | ΔE (kJ/mol) | ZPE (kJ/mol) | (kJ/mol H2) | ΔS (J/mol/K H2) |
---|---|---|---|---|---|---|
LaNi5H | P6/mmm | 2 × 1 × 1 | -185.9 | 40.6 | -28.8 | -141.0 |
2 × 2 × 1 | -185.7 | 39.3 | -29.2 | -120.0 | ||
2 × 2 × 2 | -185.3 | 40.1 | -27.8 | -130.4 | ||
1 × 2 × 1 | -185.9 | 46.9 | -19.6 | -168.0 | ||
3 × 2 × 1 | -186.0 | 39.2 | -33.4 | -133.8 |
Fig. 10. Calculated densities of phonon states (pDOSs) (b) and (c) in (1), (2), (3) and (4), and partial densities of phonon states (ppDOSs) (a) in (1), (2), (3) and (4) for LaNi5-xAlxH (D and T) (x = 0 (1), 0.25 (2), 0.5 (3) and 0.75 (4)) with 2 × 2 × 2 supercell. In all phonon calculations, H (D or T) was put at 12nb site in each unit cell of 2 × 2 × 2 supercell, with reference to Fig. 5(b).
Fig. 11. Curves of calculated ΔH and experimental -ΔHExp. in the hydrogen desorption process vs. hydrogen storage capacity for LaNi5Hy (y = 1, 2, 3 and 4) and LaNi4AlHy (y = 1, 2 and 3). The calculation parameters including selected supercell size, preferable sites occupied by H are listed in Table 7.
Compound | Supercell | y | H sites | (kJ/mol H2) | (J/mol/K H2) | (kJ/mol H2) |
---|---|---|---|---|---|---|
LaNi5Hy | 2 × 2 × 2 | 1 | 12 nb | -27.8 | -130.4 | 24.4 |
2 | 12nb*2 | -32.5 | -132.5 | 20.5 | ||
3 | 12nb*2 + 6m | -34.4 | -134.6 | 19.4 | ||
4 | 12nb*2 + 12na + 6m | -28.3 | -137.9 | 26.7 | ||
LaNi4AlHy | 2 × 2 × 2 | 1 | 12 nb | -56.5 | -127.9 | -5.3 |
2 | 12nb*2 | -57.3 | -130.1 | -5.3 | ||
3 | 12nb*2 + 6mb | -49.8 | -133.1 | 3.4 |
Table 7 First-principles and frozen phonon calculated enthalpy changes ΔH, entropy changes ΔS and Gibbs free energy changes ΔG at T = 400 K for LaNi5Hy (y = 1, 2, 3 and 4) and LaNi4AlHy (y = 1, 2 and 3) using 2 × 2 × 2 supercell. The preferable sites occupied by the H atoms (y) are listed in forth column, with reference to Fig. 5(b).
Compound | Supercell | y | H sites | (kJ/mol H2) | (J/mol/K H2) | (kJ/mol H2) |
---|---|---|---|---|---|---|
LaNi5Hy | 2 × 2 × 2 | 1 | 12 nb | -27.8 | -130.4 | 24.4 |
2 | 12nb*2 | -32.5 | -132.5 | 20.5 | ||
3 | 12nb*2 + 6m | -34.4 | -134.6 | 19.4 | ||
4 | 12nb*2 + 12na + 6m | -28.3 | -137.9 | 26.7 | ||
LaNi4AlHy | 2 × 2 × 2 | 1 | 12 nb | -56.5 | -127.9 | -5.3 |
2 | 12nb*2 | -57.3 | -130.1 | -5.3 | ||
3 | 12nb*2 + 6mb | -49.8 | -133.1 | 3.4 |
Fig. 12. Relationships between ΔZPE + ΔHvib (the sum of zero-point energy difference at T = 0 K and vibration enthalpy difference at T = 400 K in LaNi5-xAlx-H (D or T) system) and (square root of molar mass of atom Q) for each LaNi5-xAlxQ (x = 0, 0.25, 0.5 and 0.75, Q = H, D, T).
Fig. 13. Linear relations of the absolute value of calculated ΔHM-Q listed in Table 5 and experimental vs. (mQ is the molar mass of atom Q) at temperatures of 313, 333 and 353 K for LaNi4.75Al0.25Q (Q = H, D, T). Semi-solid blue triangles, red circles and pink rhombuses represent the experimental s, and solid blue triangles, red circles and pink rhombuses represent the predicted s. Each experimental was measured at the midpoint of each platform at 313, 333 and 353 K in Fig. 2(c), (d) for LaNi4.75Al0.25 alloy.
Alloy | T (K) | Predicted | Exp. | Predicted | Exp. | Predicted |
---|---|---|---|---|---|---|
LaNi4.75Al0.25 | 313 | 0.116 | 0.119 | 0.288 | 0.237 | 0.325 |
333 | 0.855 | 0.861 | 1.029 | 1.035 | 1.121 | |
353 | 1.491 | 1.482 | 1.678 | 1.711 | 1.772 |
Table 8 Comparison between the predicted , , and the experimental , for LaNi4.75Al0.25 alloy. The experimental PH and PD were measured in the midpoint of platform at 313, 333 and 353 K for LaNi4.75Al0.25Q as shown in Fig. 2(c) and (d).
Alloy | T (K) | Predicted | Exp. | Predicted | Exp. | Predicted |
---|---|---|---|---|---|---|
LaNi4.75Al0.25 | 313 | 0.116 | 0.119 | 0.288 | 0.237 | 0.325 |
333 | 0.855 | 0.861 | 1.029 | 1.035 | 1.121 | |
353 | 1.491 | 1.482 | 1.678 | 1.711 | 1.772 |
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