@article{840e65815cde4ecea588b18ab25b5ef5,
title = "Electronic and vibrational properties of nickel sulfides from first principles",
abstract = "We report the results of first-principles calculations (generalized gradient approximation-Perdew Wang 1991) on the electronic and vibrational properties of several nickel sulfides that are observed on Ni-based anodes in solid oxide fuel cells (SOFCs) upon exposure to H2 S contaminated fuels: heazlewoodite Ni3 S2, millerite NiS, polydymite Ni3 S4, and pyrite Ni S2. The optimized lattice parameters of these sulfides are within 1% of the values determined from x-ray diffraction. The electronic structure analysis indicates that all Ni-S bonds are strongly covalent. Furthermore, it is found that the nickel d orbitals shift downward in energy, whereas the sulfur p orbitals shift upward with increasing sulfur content; this is consistent with the decrease in conductivity and catalytic activity of sulfur-contaminated Ni-based electrodes (or degradation in SOFC performance). In addition, we systematically analyze the classifications of the vibrational modes at the point from the crystal symmetry and calculate the corresponding vibrational frequencies from the optimized lattice constants. This information is vital to the identification with in situ vibrational spectroscopy of the nickel sulfides formed on Ni-based electrodes under the conditions for SOFC operation. Finally, the effect of thermal expansion on frequency calculations for the Ni3 S2 system is also briefly examined.",
author = "Wang, {Jeng Han} and Zhe Cheng and B{\'r}das, {Jean Luc} and Meilin Liu",
note = "Funding Information: This work was supported by the US Department of Energy (DOE) Solid State Energy Conversion Alliance (SECA) Core Technology Program (Grant No. DE-FC26-04NT42219), DOE Office of Basic Energy Sciences, Catalysis Science Program (Grant No. DE-FG02-06ER15837), and by the National Science Foundation (NSF) under the Chemistry Research Instrumentation and Facilities (CRIF) Award CHE-0443564. It was performed using the Molecular Science Computing Facility (MSCF) in Environmental Molecular Sciences Laboratory (EMSL), a national scientific user facility sponsored by the U.S. DOE Office of Biological and Environmental Research (DOE/OBER) and located at Pacific Northwestern National Laboratory (PNNL). Table I. The crystal parameters, internal atomic distances, and angles of Ni 3 S 2 , NiS, Ni 3 S 4 , and Ni S 2 in the units of {\AA} and deg. Ni 3 S 2 (healzlewoodite, R 32 ) a Computational results Experimental results ( a , γ ) (4.09, 89.4) (4.08, 89.5); b (4.07, 89.5); c (4.06, 89.6) d Ni–S (2.26, 2.29) (2.27, 2.27); b (2.25, 2.29) d Ni–Ni (2.51, 2.55) (2.52, 2.52); b (2.50, 2.53) d S–S (3.55, 4.09) (3.50, 4.08); b (3.51, 4.07) d < S – Ni – S (100.7, 127.7) (100.7, 127.8); b (100.8, 127.3) d < Ni – Ni – Ni (60.0, 98.9, 108.0, 149.0) (60.0, 99.2, 108.6, 147.9); b (60.0, 99.0, 108.1, 148.7) d < Ni – S – Ni (114.9, 127.7) (112.6, 127.8); b (114.5, 127.3) d NiS (millerite, R 3 m ) ( a , c ) (9.62, 3.15) (9.62, 3.15); e (9.59, 3.17); f (9.61, 3.14) g Ni–S (2.26, 2.38) (2.26, 2.38); e (2.26, 2.37) g Ni–Ni 2.55 2.53; e 2.53 g S–S 3.22 3.15; e 3.14 g < S – Ni – S (85.3, 90.6, 95.8, 111.1) (85.4, 91.6, 95.7, 110.6); e (85.4, 91.2, 95.6, 111.8) g < Ni – Ni – Ni 60.0 60.0; e 60.0 g Ni 3 S 4 (polydymite, F d 3 m ) a 9.49 9.48; h 9.49; i 9.46; j 9.41 k Ni S 2 (pyrite, P a 3 ) a 5.69 5.69; h 5.67; k 5.68; l 5.62 m Ni–S 2.40 2.39 l S–S 2.08 2.07 l S–Ni–S 93.5 93.5 l S–S–Ni 104.3 104.6 l a Nickel sulfide composition (crystal structure, space group). b Reference 8 . c Reference 9 . d Reference 10 . e Reference 11 . f Reference 12 . g Reference 13 . h Reference 14 . i Reference 15 . j Reference 16 . k Reference 17 . l Reference 18 . m Reference 19 . Table II. Bader charges of Ni 3 S 2 , NiS, Ni 3 S 4 , and Ni S 2 . Ni 3 S 2 Ni(3) S(2) 0.41 − 0.62 NiS Ni(1) S(1) 0.48 − 0.48 Ni 3 S 4 Ni(1) Ni(2) S(4) 0.54 0.62 − 0.45 Ni S 2 Ni(1) S(2) 0.60 − 0.30 Table III. The classification of Ni 3 S 2 , NiS, Ni 3 S 4 , and Ni S 2 crystal vibrations at the Γ point. Ni 3 S 2 NiS Ni 3 S 4 Ni S 2 Formula units 1 3 2 4 Dimension representations 15 18 42 36 Irreducible representations 2 A 1 + 3 A 2 + 5 E 4 A 1 + 2 A 2 + 6 E A 1 g + E g + F 1 g + 3 F 2 g + 2 A 2 u + 2 E u + 5 F 1 u + 2 F 2 u A g + E g + 3 F g + 2 A u + 2 E u + 6 F u Raman active modes 2 A 1 + 4 E 3 A 1 + 5 E A 1 g + E g + 3 F 2 g A g + E g + 3 F g IR active modes 2 A 2 + 4 E 3 A 1 + 5 E 4 F 1 u F u Translations A 2 + E A 1 + E F 1 u F u Table IV. Calculated and experimentally observed Raman frequencies ( cm − 1 ) of Ni 3 S 2 , NiS, Ni 3 S 4 , and Ni S 2 . Ni 3 S 2 Modes E ( 1 ) A 1 ( 1 ) E ( 2 ) E ( 3 ) E ( 4 ) A 1 ( 2 ) Calc. 367 367 320 317 316 241 241 204 203 201 Ref. 27 351 324 305 223 201 190 NiS Modes A 1 ( 1 ) E ( 1 ) A 1 ( 2 ) A 1 ( 3 ) E ( 2 ) E ( 3 ) E ( 4 ) E ( 5 ) Calc. 356 341 341 290 277 252 251 231 230 201 201 148 148 Ref. 21 372 350 301 283 246 222 181 142 Ref. 22 369 349 300 283 244 144 Ref. 23 376 355 305 251 239 204 154 Ref. 27 370 349 300 246 Ni 3 S 4 Modes A 1 g ( 1 ) T 2 g ( 1 ) T 2 g ( 2 ) E g ( 1 ) T 2 g ( 3 ) Calc. 388 339 338 338 284 284 283 208 207 206 206 205 Ref. 23 383 338 288 224 208 Ref. 27 375 335 285 222 Ni S 2 Modes T g ( 1 ) A g ( 1 ) T g ( 2 ) E g ( 1 ) T g ( 3 ) Calc. 462 462 461 446 342 341 341 285 285 278 278 277 Ref. 24 490 480 285 274 Ref. 25 488 478 281 Ref. 26 487 480 285 272 Table V. Calculated Raman frequencies ( cm − 1 ) of Ni 3 S 2 before and after thermal expansion correction. Modes E ( 1 ) A 1 ( 1 ) E ( 2 ) E ( 3 ) E ( 4 ) A 1 ( 2 ) Uncorrected, 0 K 367 367 320 317 316 241 241 204 203 201 300 K 366 366 319 314 314 234 234 204 204 202 600 K 360 360 321 308 308 228 228 206 206 201 900 K 359 359 320 300 300 222 222 204 204 196 FIG. 1. (Color online) Crystal structures of Ni 3 S 2 , NiS, Ni 3 S 4 , and Ni S 2 from different perspectives. Blue and yellow balls are represented as Ni and S atoms, respectively. FIG. 2. DOS analysis for (a) Ni 3 S 2 , (b) NiS, (c) Ni 3 S 4 , and (d) Ni S 2 . The total and partial DOS of sulfur p and nickel d orbitals are shown in the top, middle, and bottom figures, respectively). The solid and dashed lines in Ni(d) of Ni 3 S 4 represent the two types of Ni I and Ni II atoms, respectively. FIG. 3. (Color online) Comparison of the partial DOS for the (a) nickel d orbitals and (b) sulfur p orbitals. FIG. 4. (Color online) Ni 3 S 2 : vibrational mode analysis and related frequencies ( cm − 1 ) of the primitive cell. Blue and yellow balls represent Ni and S atoms, respectively. FIG. 5. (Color online) NiS: vibrational mode analysis and related frequencies ( cm − 1 ) of the primitive cell. Blue and yellow balls represent Ni and S atoms, respectively. FIG. 6. (Color online) Ni 3 S 4 : vibrational mode analysis and related frequencies ( cm − 1 ) of the primitive cell. Blue and yellow balls represent Ni and S atoms, respectively. FIG. 7. (Color online) Ni S 2 : vibrational mode analysis and related frequencies ( cm − 1 ) of the primitive cell. Blue and yellow balls represent Ni and S atoms, respectively. ",
year = "2007",
doi = "10.1063/1.2801985",
language = "English",
volume = "127",
journal = "Journal of Chemical Physics",
issn = "0021-9606",
publisher = "American Institute of Physics Publising LLC",
number = "21",
}