3352
J. Phys. Chem. C 2009, 113, 3352–3358
Crystal Structures of Calcium Borohydride: Theory and Experiment E. H. Majzoub* Department of Physics and Astronomy, and Center for Nanoscience, UniVersity of Missouri, 503J Benton Hall, One UniVersity BlVd., St. Louis, Missouri 63121
E. Ro¨nnebro Sandia National Laboratories, 7011 East AVenue, LiVermore, California 94550 ReceiVed: July 21, 2008; ReVised Manuscript ReceiVed: NoVember 24, 2008
Calcium borohydride, containing almost 12 wt % of hydrogen, is one of the most promising and actively studied materials for hydrogen storage. However, experimental diffraction spectra indicate more than one crystal structure depending on the synthesis technique and temperature. Two structures, the ground-state in symmetry Fddd, or F2dd and one elevated temperature polymorph in symmetry P42/m, are presumed known. We identify three low energy crystal structure candidates for Ca(BH4)2 predicted by the methods of prototype electrostatic ground states (PEGS) and structure database searching. Two of the PEGS predicted crystal structures, C2/c, and P4j, appear to be observed in X-ray diffraction experiments and correspond to the groundstate and one of the metastable phases observed up to the decomposition temperature of approximately 330 °C. Database structure searching produces a low energy candidate in symmetry Pbca which produces diffraction peaks in agreement with a second elevated temperature polymorph denoted γ, recently reported in synchrotron diffraction experiments. First-principles calculations including lattice dynamical contributions to the free energy predict that C2/c is a competitive ground-state structure that is isoenergetic with the previously reported Fddd at T ) 0 K but possessing larger entropy and lower total free energy at all temperatures. These results indicate that the crystal structure of Ca(BH4)2, as a function of temperature, starts from this (R phase) in symmetry C2/c, F2dd, or Fddd, followed by a transition to symmetry P4j (β phase) at elevated temperatures. Rietveld refinements of powder X-ray diffraction data confirm the reported β phase structure has the predicted symmetry P4j, and that this symmetry has slightly lower Rietveld residuals than in symmetry P42/m. Although the structure in symmetry Pbca is calculated to be dynamically stable, the free energy indicates it should not be observed experimentally. I. Introduction Many state-of-the-art hydrogen storage materials are composed of groups containing covalently bonded Al-H and B-H complex anions such as AlH4-, AlH63-, and BH4-. These materials are generally superior to interstitial AB2 and AB5 metal hydrides when comparing H2 weight percent (e.g., LiBH4 at 18.5 wt % and the AB5 alloy LaNi5H6 at 1.38 wt %), and as such they are of intense interest for hydrogen storage applications. Recent experimental work has focused on the divalent metal borohydrides Mg(BH4)2 and Ca(BH4)2. These two materials, containing 15 and 12 wt % hydrogen, respectively, have been shown to be partially reversible at 400 bar and 270 °C1 and 700 bar and 450 °C2 and are at the forefront of hydrogen storage research. Recently, it was also shown that Ca(BH4)2 can be partially rehydrided from its decomposition products at lower pressures and temperatures around 100 bar and 350 °C.3,4 In order to improve the kinetics of hydrogen sorption and the reversibility of a hydride compound, it is necessary to fully understand the reaction mechanisms and thermodynamics governed by the underlying crystal structure(s). There are several reported experimental and theoretical structures for both Caand Mg-borohydride, indicating that different synthesis techniques, such as wet-chemical or solid-state, may affect the resultingcrystalstructure,i.e.,thecompoundsexhibitpolymorphism. * To whom correspondence should be addressed.
For example, in Mg(BH4)2, the observed low temperature structure contains 30 formula units in the space group P61, and the high-temperature structure (between 453-613 K) contains 64 formula units in the space group Fddd.5 These remarkably large unit cells were confirmed by a separate group which prepared Mg(BH4)2 samples using a different technique.6 Firstprinciples relaxations of the experimentally observed Mg(BH4)2 structure result in a slightly lower total energy (T ) 0 K) structure in the related space group P6122,7 while a PEGS search in Mg(BH4)2 produces a potentially new ground-state structure in the space group I4jm2 with lower total energy than all previously described structures, included those experimentally observed.8 In Ca(BH4)2, Miwa et al. first reported the low temperature (R phase) to possess orthorhombic symmetry in the space group Fddd.9 However, more recent in situ synchrotron diffraction experiments indicate three additional Ca(BH4)2 phases as a function of temperature.10,11 Evidently, Ca(BH4)2 is also polymorphic and may take on several related crystal structures as a function of temperature and pressure. In order to understand the thermodynamic pathways of desorption, and the kinetics of hydrogen sorption in this material, one must determine the relevant crystal structures yielding information on low energy surfaces that are likely exhibited during crystal growth and decomposition. It is necessary, therefore, to identify potential structures for comparison with experimental diffraction studies.
10.1021/jp8064322 CCC: $40.75 2009 American Chemical Society Published on Web 01/29/2009
Crystal Structures of Calcium Borohydride Hauback, et al.,10 have reported synchrotron diffraction results for Ca(BH4)2, heated in the temperature range from 40 to 500 °C. This sample was prepared using the wet-chemical synthesis technique of Fichtner et al. for Mg(BH4)2.12 Although there is no R phase (Fddd) present in this sample, there are two phases denoted γ and β present at 40 °C. The β phase is reported indexed on a tetragonal unit cell with lattice constants a ) 6.91 Å and c ) 4.34 Å, whereas the γ phase is indexed on an orthorhombic cell with lattice constants a ) 13.10 Å, b ) 7.52 Å, and c ) 8.40 Å. As the temperature is increased, γ phase gradually transforms to β phase up to 290 °C. There is a transition between 290 and 330 °C, in which the γ phase continues to transform, not to the β phase, but rather a new phase denoted δ. While the β phase decomposes at a temperature of 380 °C, the δ phase persists up to 400 °C and decomposes between 400 and 480 °C. This work was followed by a more complete treatment by Buchter, et al.,11 who report a structure solution for β phase in space group P42/m (#84), using a combination of Rietveld refinement with the structure solving program FOX.13 These authors also report the γ phase to be space group Pbca but were unable to determine atomic positions for this phase. Filinchuk, et al. performed in situ synchrotron diffraction data collected in the range 32-600 °C.14 Three structure candidates in this temperature range with symmetries F2dd, I4j2d, and P4j, were suggested for the observed phases and labeled R, R′, and β, respectively. The β phase structure in ref 14 in P4j was originally proposed as P42nm and was updated to P4j, based on the results obtained in this work. Temperature dependence of the a and c parameters revealed a second order transition from the F2dd to I4j2d phase. The Rietveld refined lattice parameters find the β phase to be 3.7-5.6% more dense than the R and R’ phases, depending on the temperature. The latter polymorphs transform into the stable β phase in the temperature range of 177-300 °C. From 32 °C up to decomposition, the unit cell parameters a and c and the unit cell volume of the β phase increased linearly with temperature. The β phase was shown to completely decompose between 382 and 387 °C. Hauback, et al. and Buchter, et al. did not observe the R′ phase, so the formation of the high-temperature R′ phase could be related to the heating rate, or solid-state sample preparation technique, thus allowing the formation of the intermediate R′ structure. FOX was used in each of these structure solutions, which will be discussed in more detail in section III. While these results point to a more complete picture of the structure of the polymorphs of Ca(BH4)2, they are not definitive. First, the program FOX solves crystal structures using a minimization procedure where the atomic coordinates are optimized in a predefined symmetry unit cell. The cost function for this minimization is defined by the difference between the calculated diffraction pattern of the resulting crystal and the diffraction from the experiment. FOX, however, contains no information on atomic interactions. Structures found by FOX must be checked using first-principles density functional theory (DFT) to determine if the structures are physically reasonable. For example, the structures must be checked for low total energy relative to competing structures, and dynamical stability by calculating phonon frequencies. While the authors did check the β phase structure in symmetry P42/m for dynamical stability, they checked the DFT total energy of competing structures only for four (P42, P42/m, P42nm, and P4jn2) out of eight candidate structures (P42, P4j, P42/m, P42212, P42nm, P4j21m, P4jn2, and P42/mmm), which by Rietveld refinement, showed small distortion of the B-H bonds in the BH4 tetrahedra. One of these
J. Phys. Chem. C, Vol. 113, No. 8, 2009 3353 structures (P4j) is identified in this work as an acceptable candidate for the β phase, with low B-H bond length distortion, isoenergetic total energy, and stable phonons. We present several previously unreported crystal structure candidates for Ca(BH4)2 predicted by database structure searching and a recently developed method of prototype electrostatic ground states (PEGS), which includes relevant interatomic interactions in complex hydrides.15 The crystal structures were investigated with first-principles calculations to ensure cohesive energies and lattice vibrations indicated low energy, dynamically stable structures. Two of these structures are clearly observed in X-ray diffraction experiments and correspond to the low temperature R phase and high temperature β phase (defined below) structures. We report a surprising potential ground-state structure for the R phase in space group C2/c, which is shown to be isoenergetic with the structure in Fddd near T ) 0 K, with larger entropy and lower total free energy at all temperatures. We also present a structure for the γ phase, which is in agreement with previous synchrotron diffraction data,10 and the Pbca symmetry proposed by Buchter, et al., which has calculated diffraction peaks in agreement with their synchrotron data. Atomic positions and lattice parameters for the predicted structures are given to provide useful structure-types for database searches. Section II will outline the experimental and theoretical methods employed in structure searching and verification. Comparison of the predicted structures with experimental data will be discussed in section III. Conclusions are given in section IV. II. Methods Sample Preparation. A pure sample of Ca(BH4)2 was prepared by heating a sample of Aldrich Ca(BH4)2(THF)2 at 150 °C in vacuum for several hours. All sample handling was performed in an argon-filled glovebox monitored to have O2 and H2O levels below 3 ppm. Phase identification was performed by collecting X-ray powder diffraction data on a model RU300 rotating anode Rigaku diffractometer with a Cu-target at 40 kV and 40 mA at 295 K. The powder was contained in a vacuum-grease sealed capillary of 0.7 mm diameter prepared in the glovebox. According to X-ray diffraction and differential scanning calorimetry, the solvent was completely removed to form a ratio of R and β Ca(BH4)2 polymorphs of 93:7. The white powder (650 mg) was mixed with 6 wt % of transition metal catalyst (for reversibility) and ball milled in a WC SPEX mill for 50 min with WC milling balls. The X-ray diffraction pattern shows a 50:50 ratio of R to β phase. Thereafter, the sample was placed in a sample holder attached to a Sievert’s apparatus and heated to 330 °C in vacuum to release hydrogen and then rehydrided at 120 bar of H2 pressure at the same temperature. Ab Initio Energetics. Crystal binding energies were calculated using the first-principles program Vienna Ab Initio Simulation Package (VASP).16,17 Projector augmented wave (PAW) pseudopotentials18,19 were used to represent the interactions between the ions and the valence electrons. Electron exchange-correlation interactions were treated in the generalized gradient approximation (GGA) using the exchange correlation functional of Perdew and Wang.20 Electronic states were expanded in plane wave basis with an energy cutoff of 600 eV. The Brillouin zone for each structure was sampled with a Monkhorst-Pack mesh21 using a k-point spacing of less than 0.05 Å-1. All structures were relaxed using the conjugate gradient algorithm until the atomic forces were less than 0.01 eV/Å and the stresses were below 0.05 kbar. Phonon frequencies
3354 J. Phys. Chem. C, Vol. 113, No. 8, 2009 were calculated using the supercell frozen phonon force constant method using the same PAW psuedopotentials and exchange correlation, and the same plane wave energy cutoff of 600 eV. A detailed description of this implementation can be found elsewhere.22 Bulk moduli were calculated by fitting the curve of total energy verses cell volume to the Murnaghan equation of state.23 The ionic positions were relaxed for each cell volume of the modulus calculation. ICSD Searching. The most popular method of structure searching employs a database such as the inorganic crystal structure database (ICSD). First-principles calculations of the total free energies of reasonable structure types from the database are compared. The lowest free energy structure is the assumed ground state. The database method requires an extensive database of trial structures. Although the method has proven successful,24 many complex structure types produce very few “hits” and limits the usefulness of this approach. A subset of the candidate Ca(BH4)2 structures we have searched has been previously performed and resulted in the identification of the Fddd BaMn2O8 structure which we also find.25 Additionally we find a low energy structure in symmetry Pbca which produces low angle diffraction peaks which agree with reports by both Hauback et al. and Buchter et al.10,11 In this work all structure types in the ICSD matching the string “AB2X8” were examined with Ca(BH4)2 chemistry. The following list gives the symmetries before structural relaxation: AgAu2F8 (P21/c), AuAu2F8 (P213), BaB2F8 (P21/c), BaAl2Cl8 (P2/c), BaAu2F8 (I4j), BaFe2Br8 (Pbca), BaMn2O8 (Fddd), BaMn2O8-2 (Fddd), BaMn2O8-3 (Fddd), BaTm2F8 (C2/m), BaY2F8 (C2/m), BeB2H8 (I41cd), CaAl2Cl8 (I41/acd), CaB2F8 (Pbca), CdAl2Cl8 (Pc), CdAu2F8 (P4/mcc), CeS2O8 (Pbca), CeSe2O8 (Pbca), CoAl2Cl8 (C2/c), CoAl2Cl8-2 (C2/c), CoCl2O8 (R3j ), CoRe2O8 (P3j ), CuAl2Cl8 (P21/c), CuAl2Cl8-2 (P1j ), CuCl2O8 (P2_1/c), CuGa2Cl8 (P21/c), ErAl2Cl8 (P2/c), ErAl2Cl8-2 (P2/c), HfMo2O8 (P3j 1c), HfMo2O8-2 (P3j 1c), HfMo2O8-3 (C2/c), HgAu2F8 (P4/mcc), ReK2F8 (Pnma), MgAl2Cl8 (C2/c), MgAl2H8 (P3jm1), MgAu2F8 (P21/c), MnB2F8 (Pnma), MnB2F8-2 (Pnma), MnRe2O8 (P3j), MoU2O8 (Pbam), MoV2O8 (C121), MoV2O8-2 (C2/m), MoV2O8-3 (Cmm2), NiAu2F8 (P21/c), NiAu2F8-2 (P21/c), NiCl2O8 (R3j), NiRe2O8 (P3j), PW2O8 (P2_12_12_1), PbRe2O8 (P31m), PdAl2Cl8 (P21/ c), PdAu2F8 (P21/c), PdGa2Br8 (C2/m), PdGa2I8 (C2/m), SmAl2Cl8 (P2/c), SrAl2Cl8 (Pbca), SrAl2Cl8-2 (I41/acd), SrAl2Cl8-3 (Pbca), SrAl2Cl8-4 (P2/c), TbCd2F8 (I4j), ThMo2O8 (P6j), ThMo2O8-2 (Pbca), ThMo2O8-3 (Pbca), ThMo2O8-4 (P6j), ThMo2O8-5 (Pbca), ThMo2O8-6 (P3j ), TiAl2Br8 (C2/c), TiAl2Br8-2 (Pnn2), TiAl2Cl8 (P21/c), TiAl2Cl8-2 (C2/c), UMo2O8 (Pban), UMo2O8-2 (Pban), UMo2O8-3 (Pban), UMo2O8-4 (P3), UMo2O8-5 (Pban), UMo2O8-6 (Pbca), UTa2O8 (P3j1m), UV2O8 (Pnma), UV2O8-2 (Pnma), UV2O8-3 (Pnma), UW2O8 (Pbca), WK2O8 (R3jc), WK2O8-2 (C2/m), WP2O8 (C2/m), WP2O8-2 (Pnma), YbAl2Cl8 (I41/acd), ZnAu2F8 (P2_1/c), ZnRe2O8 (P3j), ZrBa2F8 (Pnma), ZrBa2F8-2 (Pnma), ZrBa2F8-3 (Pnma), ZrBa2F8-4 (Pnma), ZrMo2O8 (P3j 1c), ZrMo2O8-2 (P3j 1c), ZrMo2O8-3 (C2/c), ZrMo2O8-4 (P3j1c), ZrMo2O8-5 (C2/m), ZrMo2O8-6 (Pmn21), ZrPb2F8 (Pnma), ZrS2O8 (Pnma), ZrS2O8-2 (Pnma), ZrW2O8 (P213), ZrW2O8-2 (P213), ZrW2O8-3 (P213), ZrW2O8-4 (P2_12_12_1), ZrW2O8-5 (P213). Many starting symmetries were identical or repeated multiple times in the database. The following list gives the resulting symmetry after full structural relaxation using first-principles DFT: AgAu2F8 (P21/c), BaB2F8 (P21/c), BaAl2Cl8 (P2/c), BaFe2Br8 (Pbca), BaMn2O8 (Fddd), BaTm2F8 (C2/m), BeB2H8 (I41cd), CaAl2Cl8 (I41/acd), CaB2F8 (Pbca), CdAl2Cl8 (Pc),
Majzoub and Ro¨nnebro CdAu2F8 (P4/mmm), CeS2O8 (Pbca), CeSe2O8 (Pbca), CoAl2Cl8 (C2/c), CoCl2O8 (R3j ), CuAl2Cl8 (P1j ), CuAl2Cl8 (P21/c), CuGa2Cl8 (P2_1/c), ErAl2Cl8 (P2/c), HfMo2O8 (C2/c), ReK2F8 (Pnma), MgAl2Cl8 (C2/c), MgAl2H8 (P3jm1), MgAu2F8 (P21/ c), MnB2F8 (Pnma), MoU2O8 (Pbam), MoV2O8 (Cmm2), NiAu2F8 (P21/c), PW2O8 (P2_12_12_1), PdAl2Cl8 (P21/c), PdAu2F8 (P21/c), PdGa2Br8 (C2/m), PdGa2I8 (C2/m), SmAl2Cl8 (P2/c), SrAl2Cl8 (P2/c), SrAl2Cl8 (Pbca), TbCd2F8 (I4j ), ThMo2O8 (Pbca), TiAl2Br8 (C2/c), TiAl2Cl8 (C2/c), TiAl2Cl8 (P21/c), UMo2O8 (Cmmm), UMo2O8 (Pbca), UMo2O8 (Pbca), UV2O8 (Pnma), UW2O8 (Pbca), WK2O8 (R3jc), WP2O8 (Pnma), WP2O8 (C2/m), ZnAu2F8 (P21/c), ZrMo2O8 (Fddd), ZrMo2O8 (P3jc1), ZrMo2O8 (C2/m), ZrMo2O8 (Pmn21), ZrPb2F8 (Pnma), ZrS2O8 (Pnma), ZrS2O8 (Pnma), ZrW2O8 (P213). PEGS Method. The prototype electrostatic ground state (PEGS) search method employs Metropolis Monte Carlo coupled with smoothing of the potential energy landscape to find the global minimum energy of a collection of complex anions charge balanced by positive cations, using a Hamiltonian consisting of the crystal electrostatic and soft-sphere repulsive energies:
∑ i
