The effects of hydrostatic pressure on mbh4 (m = k, na) structures - Do Phu Manh

Journal of Science and Technology 54 (1A) (2016) 323-329 THE EFFECTS OF HYDROSTATIC PRESSURE ON MBH4 (M = K, Na) STRUCTURES Do Phu Manh * , Le Tuan School of Engineering Physics, Hanoi University of Science and Technology, 1 Dai Co Viet Str., Hanoi, Vietnam * Email: dophumanh@gmail.com Received: 17 September 2015; Accepted for publication: 20 October 2015 ABSTRACT In recent decades, a lot of efforts has been spent on investigation of metal borohydrides, which can potentially serve as advanced hydrogen storage materials for mobile applications. In this research, we investigate the structure changes under high pressure of the compounds MBH4 (M = K, Na) as important borohydrides in hydrogen technologies, using ABINIT simulation package based on density functional theory (DFT) and the generalized gradient approximation (GGA). The pressure is in a wide range of 0 GPa to 40 GPa. Structural analysis indicates the phase transformation in the examined range of pressure, which is evidenced by the interaction between metal cations and BH4 - , interactive behavior of BH4 tetrahedron in the simulated cells, change of volume, distance between B and H ions, and enthalpy difference. Keywords: DFT, KBH4, NaBH4, pressure, phase. 1. INTRODUCTION Hydrogen, a popular element on the Earth, is an energy carrier that has great potential in future applications. Unlike traditional fossil energy sources (e.g., oil, coal, etc.), hydrogen has a clean reaction with oxygen, which does not create products that cause the greenhouse effect. It also has a high performance ratio energy/mass. There are examples of current and future applications where hydrogen is used either in fuel cells to provide electricity for electric motors, or used in mobile combustion engines. In the last decade, research in the both of theoretical and experimental fields has been done in order to look for ideal hydrogen-containing structures. KBH4, NaBH4 are compounds that contain elements that are widely available in nature, easily synthesized, and stable in cubic phase at normal conditions. They can contain respectively 7.4 % and 10.6 % hydrogen [1] by weight. For NaBH4, phase transition from cubic to tetragonal structures were observed under pressure between 5.4 and 6.3 GPa [2], or near 6.8 GPa [3], and the next phase transition to orthorhombic structure occur above 8.9 GPa [2], or near 10 GPa [4]. With KBH4, previous studies show that when it is under pressure, structural phase transition from cubic structures to tetragonal structures occurred at 3.8 GPa [4], and then to orthorhombic structure about 6.2 and 10 GPa [4]. Do Phu Manh, Le Tuan 324 However, the clear and commonly recognized picture of phase transitions of MBH4 (M = K, Na) over the range of pressure is still not available at the present. By using computational simulation method, we have investigated the influence of pressure in the range from 0 GPa to 40 GPa on borohydride structures, which is wider than one previously reported, e.g., up to 20GPa for KBH4 [2], and up to 30 GPa [5], 17 GPa [6], or 11.2 GPa [7] for NaBH4. By choosing a larger range of pressure and a comparison with experimental data reported recently, we hope to make a more conclusive study on the properties of borohydride structures MBH4 (M = K, Na) under high pressure. 2. COMPUTATIONAL METHODS Lattice structures and total energy were calculated by using density functional theory (DFT) within the generalized gradient approximation (GGA) by using ABINIT program. We used exchange interactive potential that was built by Perdew, Burke, Ernzerfhof (PBE). We used k- momentum grids (Monkhost-Pack) as followings, in the first Brillouin zone: 3×3×3 with cubic structures, 4x4x3 with tetragonal structures, and 4×6×5 with orthorhombic structures. The relaxation of structures was estimated by Broyden-Fletcher-Goldfarb-Shanno minimization method and comparing minimization of both force and stress tensor. Structures were relaxed when the value force/stress < 10 -5 Ha/Bohr. In all calculations, structures were stressed in all directions form 0 to 40 GPa with step 5 GPa at 0 K. Values of volumes as a funtion of pressure were extracted from Calculated relaxation results. Space group of those structures were determined by FINDSYM, figures of structures were ploted by VESTA. Distance between B and H ions in BH4 tetrahedral with each pressure value was extracted by VESTA. 3. RESULTS AND DISCUSSION Firstly, to built calculation models, we used data of lattice constants, Wickoff positions were taken from experiment reports as the following: α - NaBH4 (cubic phase Fm-3m) [8] β - NaBH4 (tetragonal phase P42mn/c) [8] γ - NaBH4 (orthorhombic phase Pnma) [2] α - KBH4 (cubic phase Fm-3m) [8] β - KBH4 (tetragonal phase P42mn/c) [8] γ - KBH4 (orthorhombic phase Pnma) [9] Since α, β, γ phases for KBH4 and NaBH4 compounds have the similar space groups, then in Figure 1 we plot only the structure for KBH4 phases. In Figure 1 potassium atoms are symbolized by big violet balls, boron atoms – by green balls and hydrogen atom – by smallest balls. After the data analysis we collected some initial information that shows a picture about the changes of structures under pressure. When being stressed in all directions, the size of structure is likely to decrease. Figure 2 shows the calculation results of volume of KBH4 as a funtion of pressure which are compared with experimental data from Reference [9]. The volume is taken for the structure cell containing 24 atoms (4 formula units). The comparison between theoretical calculation and experimental data shows a good matching. The effects of hydrostatic pressure on MBH4 (M=K, Na) structures 325 Figure 1. KBH4 phases, (a) cubic phase Fm-3m, (b) tetragonal phase P42mn/c, (c) orthorhombic phase Pnma. Figure 2. Volume pressure diagram of KBH4 in pressure range from 0 GPa to 40 GPa. Figure 3. Volume pressure diagram of NaBH4 in pressure range from 0 GPa to 40 GPa. Similar to KBH4, the calculation results of volume of NaBH4 as a function of pressure were also compared to experimental data from Reference [5], and shown in Figure 3. In difference from the case of KBH4, the volume of NaBH4 was taken in formula unit. As shown, the results also proved the agreement between theoretical calculation and experiment. To have futher understanding about the effects of hydrostatic pressure on structures, lattice constants and distance between B and H were analyzed. The following tables show calculated data of lattice constants and compared to experiment data in published reports. The tolerance of calculated data about lattice constants is under 5 %, compared with experimental data. This shows an agreement between theory and experiment. Do Phu Manh, Le Tuan 326 Table 1. Compare calculated results about lattice constant with experiment data of NaBH4. NaBH4 Calculated results Experiment Cubic 6.1039 Å (at 0 GPa) 6.150 Å [2] (at 0 GPa) Tetragonal 4.2585 Å (at 5 GPa) 6.1096 Å 4.086 Å [2] (at 6.3 GPa) 5.597 Å [2] Orthorhombic 7.2698 Å (at 10 GPa) 4.1130 Å 5.5902 Å 7.389 Å [2] (at 8.9 GPa) 4.166 Å [2] 5.633 Å [2] Table 2. Compare calculated results about lattice constant with experiment data of KBH4. KBH4 Calculated results Experiment Cubic 6.3266 Å (at 0 GPa) 6.6897 Å [9] (at 0.5 GPa) Tetragonal 4.4124 Å (at 5 GPa) 6.2046 Å 4.4754 Å [9] (at 4 GPa) 6.363 Å [9] Orthorhombic 7.1466 Å (at 20 GPa) 4.6059 Å 5.4893 Å 6.976 Å [9] (at 20 GPa) 4.933 Å [9] 5.111 Å [9] The calculated distance between B and H atoms in tetrahedral is about 1.1 - 1.4 Å. When pressure is increasing, BH4 tetrahedron was deformed. The symmetry of BH4 decreases when the compounds are stressed under high pressure. The B-H distance in NaBH4 cubic phase is 1.4668 Å at 0 GPa compared with experiment is 1.19 Å at 200 K [10], in orthorhombic phase is 1.2063 Å at 10 GPa compared with experiment is 1.17 Å at 11.2 GPa [7]; in KBH4 cubic phase is 1.4494 Å at 0 GPa compared with experiment is 1.09 Å at 293 K[11]. The distance between M-B atoms in NaBH4 are as followings: for cubic structure, it is 3.05198 Å at 0 GPa compared with 3.065 Å obtained experimently at 200 K [12], for tetragonal one - it is 3.0548 Å at 5 GPa compared with 2.976-3.091 Å in experiment at 180 K [12], for orthorhombic phase, it is 2.7974 Å at 10 GPa compared with 2.763 - 2.849 Å in experiment at 11.2 GPa [12]. For KBH4: in cubic structure, it is 3.1633 Å at 0 GPa compared with 3.364 Å in experiment [13]. At high pressure, the symmetry of the structures decreased from highest symmetry phase, which is cubic, to tetragonal and to orthorhombic ones. Changes of structures under pressure is mostly in M-B distance. B-H distance doesn't change much. The enthalpy values of phases were calculated to get a general view about change of energy of structures. Enthalpy was Calculated by the following fomula : The effects of hydrostatic pressure on MBH4 (M=K, Na) structures 327 H = E + PV with H is enthalpy, E is total energy, P is pressure, V is volume of structures, then enthalpy values were divided by the number of atom use in program. Results show enthalpy of KBH4 is lower than enthalpy of NaBH4 ~75 eV/atom with similar structures. With KBH4, we cannot observe phase transition between cubic phase and tetragonal phase. The same conclusion is shown in a previous report [14], also as between tetragonal phase and orthorhombic phase. Enthalpy diagram of KBH4 is shown in Figure 4. Figure 4. Diagram of enthalpy as a funtion of pressure of KBH4 in pressure range from 0 GPa to 40 GPa. Figure 5. Diagram of enthalpy as a funtion of pressure of NaBH4 in pressure range from 0 GPa to 40 GPa. Similar to KBH4 case, we do not observe phase transition between cubic phase and tetragonal phase in NaBH4 structures. However, phase transition between tetragonal phase and orthorhombic phase can be observed. At 10 GPa, we can see the diffrence between two enthalpy lines of tetragonal phase and orthorhombic phase clearly. This completly matches with experiment reported before. The enthalpy diagram of NaBH4 is shown in Figure 5. We can see some differences between sodium and potassium in four figures above. In both theoretical calculation and experiment, sodium compound always shows different behaviors from potassium and other alkali metals. The very similar structures and phase relations of NaBH4 and KBH4 at atmospheric pressure suggest that the behaviors at high pressure should also be similar but it is not the case. It should be noted that the cubic to tetragonal transformation in NaBH4 gives thermal conductivity measurements rise to large anomalies, involving a step change by 25 percent [4]. In theoretical calculation, Lee et al., have made an attempt to calculate the slope of this phase line using DFT, but the theoretical slope exceeds what found experimentally by a large factor [4]. Experimental values of vibrations by Raman measurement are: 1.83 for sodium compound, 1.79 for potassium, rubidium and cesium compound [15]. In experiments with activation energy, NaBH4 also shows large anomalies than those with KBH4 [16]. So, the difference of NaBH4 structure behavior likely may be explained due to the relatively distinguished proportion of ion mass/size in the chain of alkali elements. This factor likely leads to the difference of interaction between (Na +δ , K + δ ) ions and BH4 - δ tetrahedrals (e.g., charge distribution, interact distance, etc.) in NaBH4 and KBH4 compounds, and therefore, their different behaviors. Do Phu Manh, Le Tuan 328 4. CONCLUSIONS The effects of pressure on MBH4 (M = Na, K) structures was studied by using density functional theory (DFT) in a range of pressure from 0 GPa to 40 GPa at 0 K. Volume of structures in phases were calculated and matched with experimental data. Analysis of lattice cell data indicates that at high pressure, symmetry degree of the investigated structures decreases. Although the enthalpy diagram of structures reflects only the phase transition between tetragonal and orthorhombic phases of NaBH4, it can contribute an evidence for the phase transition of the studied structures. Further research is needed to better address this issue. REFERENCES 1. Yang Song - New perspectives on potential hydrogen storage materials using high pressure, Phys. Chem. Chem. Phys. 15 (2013) 14524-14547. 2. Kumar R. S., Cornelius A. L. - Structural transitions in NaBH4 under pressure, Appl. Phys. Lett. 87 (2005) 2619161-2619163. 3. Sihachakr D., André R. and Loubeyre P. - Proceedings on Joint 20th AIRAPT and on 43rd EHPRG Confenference on High Pressure Science and Technology, Karlsruhe 2005, edited by E. Dinjus and N. Dahmen, Forschungszentrum Karlsruhe (2005). 4. Sundqvist B. - Pressure-Temperature Phase Relations in Complex Hydrides, Solid State Phenomena 150 (2009) 175-195. 5. Eunja Kim, Ravhi Kumar, Philippe F. Weck, Andrew L. Cornelius, Malcolm Nicol, Sven C. Vogel, Jianzhong Zhang, Monika Hartl, Ashley C. Stowe, Luke Daemen, and Yusheng Zhao - Pressure-Driven Phase Transitions in NaBH4: Theory and Experiments, J. Phys. Chem. B 111 (2007) 13873-13876. 6. Lyci George, Vadym Drozd, Helene Couvy, Jiuhua Chen, and Surendra K. Saxena - An extended high pressure – temperature phase diagram of NaBH4, J. Chem. Phys. 131 (2009) 0745051-0745057. 7. Filinchuk Y., Talyzin A. V., Chernyshov D., and Dmitriev V. - High pressure phase of NaBH4: crystal structure from synchrotron powder diffraction data, Physical Rewiew B 76 (2007) 0921041-0921044. 8. Vajeeston P. , Ravindran P., Kjekshus A., Fjellvg H. - Structural stability of kali boron tetrahydrides ABH4 (A=Li, Na, K, Rb, Cs) from first principle calculation, Journal of Alloys and Compounds 387 (2005) 97–104. 9. Ravhi S. Kumar, Eunja Kim, and Andrew L. Cornelius - Structural phase transitions in the potential hydrogen storage compound KBH4 under compression, J. Phys. Chem. C 112 (22) (2008) 8452–8457. 10. Filinchuk Hagemann - Structures and properties of NaBH4·2H2O and NaBH4, Eur. J. Inorg. Chem. 2008 (20) (2008) 3127-3133. 11. Luck, R. L.; Schelter, E. J., - potassium borohydride, Acta Cryst. C. 55 (1999) IUC9900151. 12. Yaroslav Filinchuk, Dmitry Chernyshov, Vladimir Dmitriev - boron hydrides, high potential hydrogen storage materials, ed. U.B. Demirci & P. Miele, Nova publishers, (2010) 138-164. The effects of hydrostatic pressure on MBH4 (M=K, Na) structures 329 13. Renaudin G., Gomes S., Hagemann H., Keller L., Yvon K. - Structural and spectroscopic studies on the alkali borohydrides MBH4 (M = Na, K, Rb, Cs). J. Alloys Compd. 375 (2004) 98-106. 14. Le Tuan, Cuong Kieu Nguyen and Tran Doan Huan, - First-principles prediction for the stability of LiK(BH4)2, Phys. Status Solidi B 251 (8) (2014) 1539–1544. 15. Gomes S., Hagemann H., Keller L., Yvon K., Renaudin G. - Structural and spectroscopic studies on the alkali borohydrides MBH4 (M = Na, K, Rb, Cs), Journal of Alloys and Compounds 375 (2004) 98–106. 16. Nina Verdal, Michael R. Hartman, Timothy Jenkins, Daniel J. DeVries, John J. Rush, and Terrence J. Udovic, - Reorientational dynamics of NaBH4 and KBH4, J. Phys. Chem. C 114 (2010) 10027–10033. TÓM TẮT N N N LÊN MBH4 (M = K, Na) Đỗ hú Mạnh*, Lê uấn Viện Vật lý kỹ thuật, Trường Đại học Bách khoa Hà Nội, số 1 Đại Cồ Việt, Hà Nội. * Email: dophumanh@gmail.com Trong những h niên gần đây, một lượng lớn nghiên cứu đã được thực hiện trên các cấu trúc borohydride kim loại với vai trò v t liệu tiên tiến lưu trữ hydro nhằm sử dụng trên các hương tiện di động. Chúng tôi trình bày nghiên cứu biến đổi cấu trúc của các hợp chất mang tầm quan trọng về công nghệ lưu trữ Hydro MBH4 (M = K, Na) dưới ảnh hưởng của áp suất cao. Trong nghiên cứu này, chúng tôi khảo sát borohydride kim loại MBH4 bị nén dưới áp suất từ 0 đến 40 GPa, sử dụng chương trình mô phỏng Abinit trên cơ sở lý thuyết hàm m t độ và sử dụng phép xấp xỉ gradient tổng quát. Các phân tích cấu trúc đã chỉ rõ các biến đổi pha được nh n thấy trong khoảng áp suất khảo sát, với các biểu hiện qua ương tác giữa các ion kim loại và BH4 - , và ương tác trong tứ diện BH4, sự thay đổi thể tích, khoảng cách các ion B-H, chênh lệch enthalpy. Từ khóa: lí huyế h độ, KBH4, NaBH4, uấ , pha.