Supplementary Online Materials: Formation of Stoichiometric CsF n Compounds

Size: px

Start display at page:

Download "Supplementary Online Materials: Formation of Stoichiometric CsF n Compounds"

Amos Jackson
6 years ago
Views:

1 Supplementary Online Materials: Formation of Stoichiometric CsF n Compounds Qiang Zhu, 1, a) Artem R. Oganov, 1, 2, 3 and Qingfeng Zeng 4 1) Department of Geosciences, Stony Brook University, Center for Materials by Design, Institute for Advanced Computational Science, Stony Brook University, NY 11794, USA 2) Department of Problems of Physics and Energetics, Moscow Institute of Physics and Technology, 9 Institutskiy lane, Dolgoprudny city, Moscow Region, 1417, Russia 3) School of Materials Science and Engineering, Northwestern Polytechnical University, Xi an,7172, China 4) Science and Technology on Thermostructural Composite Materials Laboratory, Northwestern Polytechnical University, Xi an, 7172, China (Dated: 16 June 214) I. STABILITY OF CSF UNDER PRESSURE Our detailed variable-composition structure searches between CsF and F, implicitly assume that CsF should be stable at all pressures. To check this, we also performed structure searches with up to 2 atoms for the entire composition space between Cs and F at and 1 GPa, respectively. As shown in Fig. S1, we found that (1) CsF is stable at both ranges; (2) most of the new stoichiometries are located between CsF and F. This assures that our search strategy is correct. 1 (a) GPa 1 Enthalpy of formation (ev/atom) CsF 5 2 CsF 2 CsF 3 3 CsF (b) 1 GPa FIG. S1. CsF 2 CsF CsF Composition ratio: F/(Cs+F) Relatively stabilities for all compounds in the Cs-F system at (a) GPa; and (b) 1 GPa, respectively. a) Electronic mail: qiang.zhu@stonybrook.edu

2 2 23 II. VIBRATIONS AND THERMODYNAMICS OF CSF n AT AMBIENT PRESSURE 24 A. Free energy of solids The calculated vibrational behaviors for CsF n (n=1,2,3,5) compounds under ambient pressures are given in Fig. S2. All of the dispersion curves have no imaginary phonon frequencies, indicating that they are all dynamically stable. The phonon densities of states were also calculated using a grid of wave vectors FIG. S2. Calculated phonon dispersion and density of states of (a) F m3m-csf; (b) I4/mmm-CsF 2; (c) R3m-CsF 3; (d) P 2 1-CsF 5 at ambient pressure The free energy of solid (such as CsF n compounds), can be expressed as, G(T, V ) = U(V ) + F elec + F vib, (1) where U is the internal lattice energy, while F elec and F vib denote the electronic and vibrational contributions. The electronic excitations are usually neglected, while vibrational contributions represents the phonon energy, which can be treated in the harmonic approximation, by summing over the normal modes frequencies, F vib = 1 2 n i=1 hv i [ ], (2) exp( hv i /kt ) 1 37 where k is Boltzmann constant, h is Planck constant.

3 3 38 B. Free energy of F 2 gas 39 On the other hand, the free energy of diatomic F 2 gas molecule can be expressed as: G(F 2 ) = U(F 2 ) k BT T S(F 2 ), (3) where the entropy S can be divided into there parts, namely, translation entropy S trans, rotational entropy S rot, vibrational entropy S vib and electronic entropy S elec. Again, S elec is neglected, while the other terms can be defined as, S vib = NkΘ vib( exp(θ vib /T ) 1 ) T S trans = 5 2 Nk + Nkln[ V N (2πmkT h 2 ) 3/2 ], S rot = Nk + Nkln T, 2Θ rot exp( Θ vib /T ) + Nkln( 1 exp( Θ vib /T ) ). (4) 43 Here, Θ rot and Θ vib are the characteristic rotational and vibrational temperatures, respectively. Θ rot = (h/2π)2, 2kI Θ vib = hv k, (5) where I is a molecular moment of inertia, v is the vibration frequency of F 2 molecule. To be consistent with the free energy calculation of solids, here we calculated the entropy of F 2 within the same functional. The relaxed F-F bond length in F 2 molecule is 1.43 Å, in satisfactory agreement with the experimental report (1.42 Å). The theoretical vibrational frequency for F-F stretching modes of F 2 is 3.1 THz, compared with the experimental value THz. Note that the vibrational component of the gas entropy here is very small (less than 1% of the total). The calculated temperature dependent S(F 2 ) is shown in Fig. S3. Compared to the experimental value (S expt (F 2 ) = 22.8 J/(mol K)) at standard conditions, our results are close Simulation Experiment Melting point Boiling point Entropy [J/(mol K)] Temperature [K] FIG. S3. The calculated entropy of F 2 gas at different temperatures. The melting point (53.48 K) and boiling point (85.3 K) are also shown for being consistent. 55

4 56 57 58 59 6 C. Thermochemistry of the suggested reactions By applying the eq. 1 and eq. 3, we obtain the formation energy of the suggested chemical reactions in Table 1.

4 C. Thermochemistry of the suggested reactions By applying the eq. 1 and eq. 3, we obtain the formation energy of the suggested chemical reactions in Table 1. The results are shown in S4. And the predicted decomposition temperatures are 491 K for CsF 2, 423 K for CsF 3, and 258 K for CsF 5, respectively. All of these temperatures are easily accessible, thus these materials are promising for reversible fluorine storage materials FIG. S4. The temperature dependence of free energy of the suggested chemical reactions (a)csf 2 CsF + 1 F2(g); (b) CsF3 2 CsF + F 2(g); (c) CsF 5 CsF + 2F 2(g) III. STABILITY OF CSF n (n>1) COMPOUNDS UNDER PRESSURE The detailed results for variable-composition structure searches between CsF and F, are shown in Fig. S5. There is clearly a general trend that the formation enthalpies of CsF n (n 1) compounds decrease with pressure, suggesting that the Cs atoms can be oxidized further. For the predicted stable high pressure phases, we calculated phonon frequencies throughout the Brillouin zone using the finite-displacement approach as implemented in the Phonopy code. As shown in Fig. S6, the absence of imaginary frequencies ensures that the obtained structures are dynamically stable. 75 IV. CRYSTALLOGRAPHIC DATA

5 5 Enthalpy of formation (ev/atom) CsF (a) GPa.4.2 CsF 3 CsF (b) 2 GPa CsF CsF (c) 5 GPa.4 (d) 1 GPa CsF.4 CsF CsF CsF 3 CsF Composition ratio: F/(Cs+F) Composition ratio: F/(Cs+F) FIG. S5. Relatively stabilities for all compounds in the CsF-F system at (a) GPa; (b) 2 GPa; (c) 5 GPa; and (d) 1 GPa, respectively.

6 6 FIG. S6. Phonon dispersion curves of CsFn compounds (a) P bam-csf2 at 5 GPa; (b) C2/c-CsF3 at 5 GPa; (c) C2/m-CsF4 at 2 GPa; (d) P 1-CsF4 at 5 GPa; (e) C2/m-CsF5 at 2 GPa; and (f) F dddm-csf4 at 5 GPa respectively.

7 7 TABLE S1. The detailed crystal structures of CsF n compounds at different pressures. Phase Pressure Space group Lattice parameters Atomic coordinates (GPa) CsF 2 I4/mmm a= Å Cs(4e) c= Å F1(4e) F2(4e) CsF 2 1 P bam a= Å Cs(4g) b= Å F1(4h) c= Å F2(4h) CsF 3 R3m a= Å Cs(3a)... c= Å F1(3b)...5 F2(6c) CsF 3 1 C2/c a= Å Cs(4c) b= Å F1(4e) c= Å F2(8f) β=1.65 CsF 4 2 C2/m a= 7.27 Å Cs1(2a)... b= 4.69 Å Cs2(2b)...5 c= Å F1(4i) β=58.43 F2(4i) F3(4i) F4(4i) CsF 4 5 P -1 a= 6.64 Å Cs1(1a)... b= 4.11 Å Cs2(1b) c= 4.31 Å F1(2i) α=88.68 F2(2i) β =84.76 F3(2i) γ=92.32 F4(2i) CsF 4 7 P -1 a= Å Cs1(2i) b= Å Cs2(2i) c= Å F1(2i) α=97.63 F2(2i) β =88.3 F3(2i) γ=89.31 F4(2i) F5(2i) F6(2i) F7(2i) F8(2i) CsF 5 P 2 1 a= Å Cs(2a) b= Å F1(2a) b= Å F2(2a) β= F3(2a) F4(2a) F5(2a) CsF 5 1 C2/c a= Å Cs(4e) b= 4.44 Å F1(4e) c= Å F2(8f) β= F3(8f) CsF 5 3 C2/m a= Å Cs(2a)... b= Å F1(2c)...5 b= Å F2(4i) β= 42.2 F3(4i) CsF 5 1 F dd2 a= Å Cs(8a) b= Å F1(8a) c= Å F2(16b) F3(16b)

I n general, for a given ionic compound AmBn, the stoichiometry reflects the ratio of valences (or the ratio of

I n general, for a given ionic compound AmBn, the stoichiometry reflects the ratio of valences (or the ratio of OPEN SUBJECT AREAS: ELECTRONIC STRUCTURE MATERIALS CHEMISTRY Received 10 September 2014 Accepted 15 December 2014 Published 22 January 2015 Correspondence and requests for materials should be addressed