Energetics of Hydrogen Storage Reactions: The Power of DFT. Jan Herbst Materials and Processes Laboratory GM R&D Center

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1 Energetics of Hydrogen Storage Reactions: The Power of DFT Jan Herbst Materials and Processes Laboratory GM R&D Center

2 ACKNOWLEDGEMENTS Fellow explorer: Lou Hector Sometime shipmate: Wes Capehart

3 Outline Challenge Motivation Methodology LaNi 5, LaNi 5 H 7 : benchmark results LaNi 5 H n, LaCo 5 H n : can DFT predict preferred H sites, filling sequence, maximum H concentration? LiNH 2 + LiH Li 2 NH + H 2 : energetics of a novel hydrogen storage reaction Summary

4 Challenge

5

6 CHALLENGE (cont d) Gravimetric Energy Density vs. Volumetric Energy Density of Fuel Cell Hydrogen Storage Systems System Energy per Unit Weight (MJ/kg) Compressed gas 10,000 psi Liquid hydrogen Minimum Performance Goal High-temperature hydride (e.g., MgH2) Medium-temperature hydride (e.g., NaAlH 4 ) Low-temperature hydride (e.g., LaNi 5 H 6 or FeTiH 2 ) Gasoline Ultimate Technology Goal System Energy per Unit Volume (MJ/liter)

7 CHALLENGE (cont d) HYDROGEN STORAGE PARAMETER GOALS METRIC GOAL System energy per unit weight for conventional > 6 MJ/kg vehicles with 300-mile range System energy per unit volume for conventional > 6 MJ/l vehicles with 300-mile range Usable energy consumed in releasing H 2 <5 % H 2 Release Temperature ~80 ºC Refueling Time <5 minutes H 2 Ambient Release Temp Range -40/+45 ºC Durability (to maintain 80% capacity) 150,000 miles

8 Motivation Assess the capability of density functional theory (DFT) for modeling properties of solid hydrides, including electronic structure, enthalpies of formation, hydrogen site preferences, and maximum hydrogen occupancy

9 Calculational Methodology (briefly!) Vienna ab initio simulation package (VASP) Projector-augmented wave (PAW) potentials

10 Benchmark Results: LaNi 5, LaNi 5 H 7

11 LaNi 5 and LaNi 5 H 7 Crystal Structures LaNi 5 hexagonal CaCu 5 P6/mmm (LaNi 5 H 7 ) 2 hexagonal P6 3 mc

12 LaNi 5 H 7 : Energy vs Volume E(V) -56 LaNi 5 H 7 E(V) (ev/lani 5 H 7 ) V/V expt

13 Crystal Structure Parameters for LaNi 5 and LaNi 5 H 7 LaNi 5 Calc Expt a (Å) c (Å) B (GPa) , 139 LaNi 5 H 7 Calc Expt Calc Expt Calc Expt La (2a) z H1 (2b) z a (Å) Ni1 (2b) z H2 (6c) x c (Å) Ni2 (2b) z z Ni3 (6c) x H3 (6c) x z z

14 4 LaNi 5 Band Structures of LaNi 5 and LaNi 5 H ε F Energy (ev) 4 2 Γ Γ Γ K M Γ A L H A LaNi 5 H ε F Γ Γ K M Γ A L H A Γ

15 δρ = ρ(lani 5 H 7 ) ρ(lani 5 H 0 ) - ρ (7H non-int) LaNi 5 H 7 (P6 3 mc) 8 [0001] 6 4 La H2 Ni1 H1 Ni3 H3 H1 Ni2 H2 La δρ(x)/å 3 2 Ni3 H3 (b) [1230]

16 LaNi 5 H 7 Electron Localization Function (ELF) LaNi 5 H 7 (P6 3 mc) 8 H2 Ni3 H1 1 ELF [0001] 4 La Ni1 H Ni2 La H1 Ni3 H [1230] (b)

17 ELF for NaCl 8 ELF 6 Na [001] Cl [100] 0

18 ELF for Na Metal h [001] Na Na ELF [110]

19 ELF for Diamond 4 ELF [001] 0 C C C [110]

20 Enthalpies of Formation Η Η(LaNi 5 H 7 ) = 2/7[E(LaNi 5 H 7 ) E(LaNi 5 ) ] E(H 2 ) = 40 kj/mole H 2 expt: other calcs: 57 (1998); 45 (2001) 1 kj/mole H 2 = 0.01 ev/h 2 Η(LaNi 5 ) = E(LaNi 5 ) E(La) 5 E(Ni) = 168 kj/mole LaNi 5 expt: 159 ± 8; 166

21 Elastic Constants of LaNi GPa LaNi5 (expt) LaNi5 (calc) 50 0 c11 c12 c13 c33 c44

22 Results: LaNi 5 H n, LaCo 5 H n

23 ??? For a given crystal structure, can DFT identify the sites preferred by hydrogen? establish the filling sequence of hydrogen sites? provide an estimate of the maximum hydrogen concentration?

24 LaCo 5 and LaCo 5 H 4 Crystal Structures LaCo 5 hexagonal CaCu 5 P6/mmm (LaCo 5 H 4 ) 2 base-centered orthorhombic Cmmm

25 Strategy Focus on LaNi 5 H n (P6 3 mc structure) and LaCo 5 H n (Cmmm structure) Calculate H(LaNi 5 H n ) = E(LaNi 5 H n ) E(LaNi 5 ) (n/2)e(h 2 ) H(LaCo 5 H n ) = E(LaCo 5 H n ) E(LaCo 5 ) (n/2)e(h 2 ) for various hydrogen configurations and occupancies Examined 38 hydrogen configurations in LaNi 5 H n, 93 configurations in LaCo 5 H n

26 Site-dependent Enthalpies of Formation in LaNi 5 H n 2a H(LaNi 5 H n ) (ev/hydrogen atom) a2b 2a2b 1 2b 2 2b 1 2b 2 2b 3 2b 2a6c 12d 2b12d LaNi 5 H n P6 3 mc structure 6c 1 6c 2 12d 2b 1 2b 2 6c 2b 1 2b 2 6c 1 6c 2 6c c 1 6c 2 2b6c 1 6c 2 6c 1 6c 2 6c 3 2b6c 1 6c 2 6c n in LaNi 5 H n

27 Site-dependent Enthalpies of Formation in LaCo 5 H n 1.5 4k H(LaCo 5 H n ) (ev/hydrogen atom) d 2b2d 2b 4l 4j 4g 4i 8p 8q 1 8q 2 4h 4e4h 4h16r 8o16r LaCo 5 H n Cmmm structure 4e4h 1 4h 2 8o 2b8o16r 4e8o16r 4e4h8o16r 2b4e8o16r n in LaCo 5 H n

28 Energetics of a Novel Hydrogen Storage Reaction: LiNH 2 + LiH Li 2 NH + H 2

29 Crystal Structures LiNH 2 amide tetragonal I-4 Li 2 NH imide orthorhombic Ima2

30 Densities of States Li amide Li imide 4 ε F 4 ε F 3 LiNH 2 3 Li 2 NH states/ev f.u H Li states/ev f.u H Li N N E (ev) E (ev)

31 ELF for LiNH 2 Å 6 4 Li H 1 ELF 2 0 Li H N H N H H N H Li Li Å

32 Li ELF for Li 2 NH Li L Å Li32N16H16 6 Li Li Li 1 ELF Li Li Li N H Li H Li N Å

33 T = 0: H 0 = H el + H ZPE Enthalpies of Formation H 0 (LiNH 2 ) = H el (LiNH 2 ) + H ZPE (LiNH 2 ) = [E el (LiNH 2 ) E el (Li) ½E el (N 2 ) E el (H 2 )] + [E ZPE (LiNH 2 ) E ZPE (Li) - ½E ZPE (N 2 ) E ZPE (H 2 )] T = 298K: H 298 = H 0 + δ H 298 δ H 298 (LiNH 2 ) = E ph (LiNH 2 ) E ph (Li) ½[7/2 kt + E vib (N 2 )] [7/2 kt +E vib (H 2 )]

34 Enthalpies of Formation H 298 and Reaction H R LiNH 2 LiH Li 2 NH H el H ZPE δ H H 298 kj/mole H 298 expt kj/mole LiNH 2 + LiH Li 2 NH + H 2 H R = H 298 (Li 2 NH) H 298 (LiNH 2 ) H 298 (LiH) H R (components, expt) = = 45 kj/mole H R (calc) = = 74 kj/mole H R (direct expt) = 66 kj/mole H 298 expt (Li 2 NH) = 222 kj/mole likely inaccurate

35 Summary DFT is capable of accurately describing properties of metallically-bonded hydrides such as LaNi 5 H n and LaCo 5 H n, as well as complex hydrides such as LiNH 2 and Li 2 NH Large, growing body of DFT results on other systems: binary hydrides, NaAlH 4, LiAlH 4, LiBH 4, etc. Session U14: Modeling Thursday 3/24 8a No question regarding the power of DFT for known hydrides ** Going forward: one goal is the imaginative use of DFT to spur discovery of technologically viable hydrogen storage materials