First-principles study of the structural, electronic, dynamical, and thermodynamic properties of Li5AlO4

Journal of Nuclear Materials 465 (2015) 170e176

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First-principles study of the structural, electronic, dynamical, and thermodynamic properties of Li5AlO4 Qiushi Guan a, b, Xiaojun Chen a, Tao Gao b, Chengjian Xiao a, Linjie Zhao a, Jianchao He a, Xinggui Long a, * a b

Institute of Nuclear Physics and Chemistry, China Academy of Engineering Physics, Mianyang 621903, PR China Institute of Atomic and Molecular Physics, Sichuan University, Chengdu 610065, PR China

a r t i c l e i n f o

a b s t r a c t

Article history: Received 20 January 2015 Received in revised form 18 March 2015 Accepted 25 May 2015 Available online 2 June 2015

Pentalithium aluminate, Li5AlO4, has attracted increasing attention for its high lithium density and potential uses in tritium breeding materials and thermal batteries. In this work, the structural, electronic, lattice dynamical, and thermodynamic properties of a- and b-phase Li5AlO4 were investigated using firstprinciples density functional theory. The optimized structural parameters were consistent with the experimental values, with the absolute deviation being less than 2.5%. The indirect band gaps of a- and bLi5AlO4 were 4.82 and 5.16 eV, respectively, showing that they are insulators. In addition, the vibrational properties of a- and b-Li5AlO4 were computed using density functional perturbation theory. By adding Born effective charges into the phonon calculations, the longitudinal opticaletransverse optical (LO-TO) splittings were calculated. The optical modes at the G point were categorized as Raman- and IR-active modes. Our results show that b-Li5AlO4 is more polar and anisotropic than a-Li5AlO4. Furthermore, their thermodynamic functions were determined using the calculated phonon density of states. The results were in good agreement with those of previous theoretical studies. The data presented in this work will help in the further characterization of Li5AlO4, which may be valuable for future experimental studies. © 2015 Elsevier B.V. All rights reserved.

Keywords: Li5AlO4 Tritium breeding material Lithium ceramics First-principles

1. Introduction Tritium breeders play a significant role in fusion reactors, maintaining the supply of tritium to ensure its “self-sufficiency” during deuteriumetritium reactions [1e3]. Lithium ceramics are widely recognized as promising tritium breeder candidates; they release tritium through the reaction 6Li þ nf / 3T þ 4He. Therefore, one of the major requirements of tritium breeding materials is high lithium density, which leads to the formation of more tritium. Li5AlO4 has been proposed by Guggi et al. as a tritium breeding material owing to its high rate of tritium release at moderate temperatures (about 770 K) [4]; in addition, it is stable from room temperature to 1320 K, which is compatible with the temperature

Abbreviations: BZ, Brillouin zone; CBM, conduction bands minimum; DFPT, density functional perturbation theory; DFT, density functional theory; LO, longitudinal optical; PDOS, partial density of states; TO, transverse optical; TDOS, total density of states; VB, valance band; VBM, valence band maximum. * Corresponding author. E-mail address: [email protected] (X. Long). http://dx.doi.org/10.1016/j.jnucmat.2015.05.015 0022-3115/© 2015 Elsevier B.V. All rights reserved.

window of the breeding blanket [5]. Furthermore, the lithium density of Li5AlO4 is 0.62 g/cm3, which is higher than that of most tritium breeder materials, except for Li2O and Li8ZrO6. Thus, Li5AlO4 may be more suitable as a tritium breeder material than g-LiAlO2. In addition, Li5AlO4 can be used as a CO2 sorbent to reduce global warming owing to its high CO2 chemisorption capacity [6,7], or employed as a solid electrolyte for thermal battery applications [8e10]. Several experimental studies have been carried out on the synthesis and characterization of Li5AlO4 [11e17]. Notably, Li5AlO4 exists in two phases: a- and b-Li5AlO4 [12,13]. The a-phase, which is stable from room temperature to about 1100 K, undergoes a phase transformation into b-Li5AlO4 at high temperature [18]. The hightemperature b-phase is stable from room temperature to 1320 K, at which it decomposes. Guggi et al. investigated the tritiumreleasing properties of Li5AlO4 in a series of studies [4,11]. In contrast to the large number of reported experimental studies, only a few theoretical investigations have been carried out. In particular, Kulkarni [19] optimized the thermodynamic parameters of the Li2OeAl2O3 system, which includes Li5AlO4, using the

Q. Guan et al. / Journal of Nuclear Materials 465 (2015) 170e176

available thermodynamic data and assessed the phase-diagram data. However, to the best of our knowledge, the electronic, vibrational, and thermodynamic properties of Li5AlO4 have not been systematically investigated. To address this issue, we calculated herein the band structure and density of states of the two phases of Li5AlO4 using firstprinciples density functional theory (DFT). Their stability (especially dynamical) properties were studied, and the Born effective charges and macroscopic static dielectric tensors were computed to investigate the optical phonon frequencies, including Raman- and IR-active modes at the G point. Based on the phonon density of states, the following thermodynamic functions were determined: entropy(S), internal energy(E), constant-volume specific heats(Cv), and Helmholtz free energies(F). 2. Computational details All calculations were carried with the Vienna ab initio simulation package [20,21], which is based on first-principles DFT. The projector-augmented wave pseudopotential [22,23] was used to describe the interactions of electrons and ions. The generalized gradient approximation within the PerdeweWang scheme [24] was employed. Preliminary tests allowed us to determine the kinetic energy cut-offs and the k-point sampling grids. The total energies at different kinetic energy cut-offs and k-points are presented in Fig. 1. For a- and b-Li5AlO4, the oscillations in the total energy after 450 and 400 eV, respectively, were slight, within 0.1 eV (Fig. 1(a)). Thus, it is sufficient to set the kinetic energy cut-offs at 450 and 400 eV for a- and b-Li5AlO4, respectively, to expand the plane wave. The k-point sampling grids were set as n  n  n using the Monkhorst-Pack method [25], and when n greater than 4 for aLi5AlO4 and 6 for b-Li5AlO4, the corresponding total energies converges very well. Consequently, the k-point sampling grids were set as 4  4  4 and 6  6  6 for the a- and b-phases, respectively. The optimized structures were obtained by relaxing both the lattice constants and the internal coordinates. The energy bands were plotted along the high-symmetry point in the Brillouin zone (BZ); 1  2  1 and 1  1  2 supercells were created for a- and b-Li5AlO4, respectively, from the optimized structures for the phonon calculations. The Born effective charges and the dielectric constants were also calculated based on density functional perturbation theory (DFPT) [26e28]. The phonon frequencies were calculated using the

171

PHONOPY software package [29] combined with ab initio DFPT. The longitudinal opticaletransverse optical (LO-TO) splittings at the G point and the vibrational spectra, containing IR- and Raman-active modes, were also studied. Finally, the thermodynamic properties as a function of temperature were evaluated according to the phonon density of states. 3. Results and discussion 3.1. Structure and optimization The crystal structures of the two phases are shown in Fig. 2; the calculated lattice parameters (and a comparison with the experimental data) are listed in Table 1 a-Li5AlO4 is isotopic with aLi5GaO4, having orthorhombic crystals in space group Pbca (No.61); its lattice constants a, b, and c are 9.08, 8.94, and 9.12 Å, respectively. It has eight formula units in each unit cell, and the occupied Wyckoff positions are 8c for Li, O, and Al. b-Li5AlO4 also has an orthorhombic structure with space group PmmnZ (No.59); its lattice parameters a, b, and c are 6.424, 6.305, and 4.623 Å, respectively. There are two formula units in each unit cell, and the Wyckoff positions are 2a for Al, 4e and 4f for O, and 8g and 2b for Li. In both phases, Al and O are connected tetrahedrally, and are surrounded by Li atoms. The optimized and experimental atomic fractional coordinates are listed in Table 2. The optimized AleO bonds in a-Li5AlO4 are reduced from their experimental lengths; the average value of these bonds changes from 1.816 to 1.787 Å. The AlO4 tetrahedron becomes more regular after optimization because the variances of the optimized AleO bond lengths and the bond angles are smaller for b-Li5AlO4. The largest deviations from the experimental values for a- and bLi5AlO4 are 0.44% and 2.1%, respectively. Overall, the calculated results are sufficient to confirm the validity of our computational approach. 3.2. Electronic properties The band structures of a- and b-Li5AlO4 are displayed in Fig. 3. The Fermi energy level was assumed to be zero and used as a reference. Both a- and b-Li5AlO4 have an indirect band gap, because the conduction band minimum (CBM) and the valence band maximum (VBM) lie at different high-symmetry points. For aLi5AlO4, the indirect band gap is 4.82 eV; the width of the valance band (VB) is 3.82 eV (from 3.89 to 0.07 eV). For b-Li5AlO4, the indirect band gap is 5.16 eV; the width of the VB is 3.86 eV (from 3.92 to 0.06 eV). According to Duan [30], the DFTcalculated band gaps are usually smaller than the experimental ones. Therefore, the experimental measurements should be higher than our DFT results. The values of the band gaps show that the materials are insulators. For both a- and b-Li5AlO4, a smaller and lower VB is located at 15 eV, with widths of 0.88 and 0.90 eV, respectively (data not shown). Fig. 4 shows the total density of states (TDOS) and partial density states (PDOS) values of Li, O, and Al for the two phases of Li5AlO4. In both cases, the Li-s and Li-p orbitals have the largest contributions to the conduction bands. The upper VB has the largest contributions from the O-p and Li-p orbitals. Al-s and O-p contribute to the lower part of the VB. 3.3. Dynamical properties

Fig. 1. The calculated total energies of a- and b-Li5AlO4 (a) as a function of kinetic energy cut-offs and (b) as a function of k-point sampling grids (n  n  n).

The calculated phonon dispersion curves and phonon density of states values are shown in Fig. 5. There are 80 and 20 atoms in the unit cells of a- and b-Li5AlO4, respectively; therefore, these systems contain 240 and 60 phonon branches, respectively. Both the

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Fig. 2. Crystal structures of a- and b-Li5AlO4. Blue, red, and purple spheres represent Li, O, and Al atoms, respectively: (a) a-Li5AlO4 and (b) b-Li5AlO4. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Table 1 Experimental and optimized crystal structural parameters of the two phases of Li5AlO4.

a-Li5AlO4 Pbca (No. 61) Z ¼ 8 b-Li5AlO4 PmmnZ (No. 59) Z ¼ 2

a b

Experimentala,b

Optimized

Deviations

a ¼ 9.087 b ¼ 8.947 c ¼ 9.120 a ¼ 6.424 b ¼ 6.305 c ¼ 4.623

a ¼ 9.113 b ¼ 8.986 c ¼ 9.150 a ¼ 6.288 b ¼ 6.357 c ¼ 4.590

0.29% 0.44% 0.33% 2.12% 0.82% 0.71%

þ 5Au

Ref [12]. Ref [13].

structures of a-Li5AlO4 (No.61) and b-Li5AlO4 (No.59) have orthorhombic symmetry, with the corresponding point group D2h. Consequently, the irreducible representations of a- and b-Li5AlO4 at the center of the BZ are:

Gaco ¼ B1u þ B2u þ B3u

for a­ and b­Li5 AlO4 ;

Gopt ¼ 30Ag þ 30B1g þ 30B2g þ 30B3g þ 29B1u þ 29B2u þ 29B3u þ 30Au

Gopt ¼ 9Ag þ 5B1g þ 8B2g þ 8B3g þ 8B1u þ 7B2u þ 7B3u

for a­Li5 AlO4 ;

for b­Li5 AlO4 :

Parameter Gaco represents the three acoustic modes: B1u, B2u, and B3u. In the optical modes (Gopt), the active modes include Ag, B1g, B2g, B3g, B1u, B2u, and B3u; Au is a silent mode, which is inactive. Ag, B1g, B2g, and B3g are Raman active, whereas B1u, B2u, and B3u are IR active. Therefore, there are 120 and 30 Raman-active modes, 87 and 22 IR-active modes, and 30 and 5 silent modes for a- and bLi5AlO4, respectively. Fig. 5 shows the LO-TO splittings [31]; Table 3 lists selected calculated phonon frequencies at the G point of the two phases, including Raman- and IR-active modes, with large LOTO splittings. We also calculated the Born effective charges and the macroscopic static dielectric tensors in order to study the polar properties of Li5AlO4. The diagonal element eigenvalues of the Born effective charges of nonequivalent atoms of a- and b-Li5AlO4 and their average eigenvalues are listed in Table 4. Since a- and b-Li5AlO4 are orthorhombic, the off-diagonal values of the macroscopic static dielectric tensor are zero; the diagonal elements are εxx ¼ 2.875, εyy ¼ 2.814, and εzz ¼ 2.775 for a-Li5AlO4, and εxx ¼ 2.731, εyy ¼ 2.826, and εzz ¼ 2.723 for b-Li5AlO4. Notably, both the macroscopic static dielectric tensors and Born effective charges include the local field effects of the crystals. As shown in Table 4, the

Table 2 Optimized and experimental atomic fractional coordinates of the two phases of Li5AlO4.

a-Li5AlO4 Pbca (No. 61) Z ¼ 8

b-Li5AlO4 PmmnZ (No. 59) Z ¼ 2

a b

Ref [12]. Ref [13].

Atom

Site

Expta,b

Al O(1) O(2) O(3) O(4) Li(1) Li(2) Li(3) Li(4) Li(5) Al O(1) O(2) Li(1) Li(2)

8c 8c 8c 8c 8c 8c 8c 8c 8c 8c 2a 4e 4f 8g 2b

(0.145, (0.250, (0.038, (0.012, (0.246, (0.093, (0.131, (0.356, (0.398, (0.364, (0.250, (0.250, (0.018, (0.065, (0.250,

Optimized 0.117, 0.119) 0.012, 0.005) 0.002, 0.243) 0.242, 0.037) 0.236, 0.244) 0.153, 0.409) 0.085, 0.661) 0.093, 0.347) 0.164, 0.609) 0.124, 0.883) 0.250, 0.230) 0.017, 0.000) 0.250, 0.416) 0.026, 0.764) 0.750, 0.757)

(0.144, (0.247, (0.037, (0.015, (0.248, (0.114, (0.118, (0.373, (0.394, (0.352, (0.250, (0.250, (0.013, (0.011, (0.250,

0.116, 0.994, 0.000, 0.239, 0.232, 0.139, 0.102, 0.098, 0.167, 0.131, 0.250, 0.016, 0.250, 0.447, 0.750,

0.123) 0.010) 0.243) 0.038) 0.243) 0.398) 0.659) 0.355) 0.619) 0.879) 0.226) 0.015) 0.432) 0.746) 0.793)

Q. Guan et al. / Journal of Nuclear Materials 465 (2015) 170e176

Fig. 3. Calculated electronic band structures and total density of states (TDOS) values: (a) a-Li5AlO4 and (b) b-Li5AlO4.

Fig. 4. Calculated TDOS and partial density of states (PDOS) of each element: (a) a-Li5AlO4 and (b) b-Li5AlO4.

Fig. 5. Calculated phonon dispersion curves with LO-TO splitting: (a) a-Li5AlO4 and (b) b-Li5AlO4.

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Q. Guan et al. / Journal of Nuclear Materials 465 (2015) 170e176

Table 3 Phonon frequencies at the G points of a- and b-Li5AlO4. Infrared

a-Li5AlO4 Pbca (No. 61) Z ¼ 8

b-Li5AlO4 PmmnZ (No. 59) Z ¼ 2

Raman

B1u

B2u

B3u

Ag

B1g

B2g

B3g

181.13/180.68 317.22/318.05 400.3/398.63 492.9/486.89 617.75/634.43 772.49/779.52 372.27/376.41 396.41/398.14 517.79/541.04 742.95/743.64 749.23/749.02

290.64/291.32 345.69/354.15 430.09/432.5 496.33/498.01 534.9/535.31 683.4/688.75 224.70/230.97 274.93/275.83 497.10/505.36 592.75/596.93 732.47/735.91

203.92/205.18 373.41/374.44 517.93/519.27 580.48/584.72 617.75/634.43 818.65/823.69 354.07/364.79 467.81/470.58 510.50/517.79 649.00/654.28 755.34/827.66

151.76 275.28 387.13 457.6 611.15 736.42 236.57 290.80 341.30 390.27 444.88

164.35 294.64 372.23 466.95 578.94 788.42 246.08 329.43 371.25 494.75 585.96

186.45 271.34 378.86 487.42 569.74 790.55 234.56 310.88 334.82 464.02 493.26

161.38 270.51 384.73 477.99 576.08 788.85 168.16 263.34 320.48 379.10 461.91

atoms of a-Li5AlO4 tend to be more isotropic than those of bLi5AlO4. The absolute values of the effective charges of Li, O, and Al are lower than those of their formal charges, i.e., 1, 2, and 3 for Li, O, and Al, respectively. 3.4. Thermodynamic functions Based on the DFPT and phonon density of states results, we calculated the thermodynamic properties of the two phases of Li5AlO4. Within the harmonic approximation, the phonon contribution to the thermodynamic functions, including F, E, Cv, and S, are defined as follows [31]:

ZuL DF ¼ 3nkB T 0

ZuL DE ¼ 3nN

Z 2 0

  Zu gðuÞdu ln 2 sinh 2kB T

(1)

  Zu gðuÞdu u coth 2kB T

(2)

ZuL  Cv ¼ 3nNkB 0

   Zu Zu csc h2 gðuÞdu 2kB T 2kB T

(3)

  Zu Zu Zu coth  ln 2 sinh gðuÞdu 2kB T 2kB T 2kB T

ZuL  S ¼ 3nkB 0

(4)

where g(u) is the normalized phonon density of states, kB is the Table 4 Born effective charges of a- and b-Li5AlO4. Atom

Z1

Z2

Z3

Zaver

0.91 1.00 1.02 0.94 0.97 1.71 1.84 1.72 1.77 2.22 0.92 1.05 1.77 1.69 2.22

0.92 1.06 0.85 1.02 1.00 1.81 1.79 1.80 1.78 2.33 0.98 1.06 1.69 1.89 2.24

1.09 0.88 0.91 0.94 1.00 1.81 1.66 1.77 1.74 2.19 0.97 0.86 1.74 1.67 2.12

0.97 0.98 0.93 0.97 0.99 1.78 1.76 1.76 1.76 2.24 0.96 0.99 1.74 1.75 2.19

a-Li5AlO4 Pbca (No. 61) Z ¼ 8

b-Li5AlO4 PmmnZ (No. 59) Z ¼ 2

Li1(8c) Li2(8c) Li3(8c) Li4(8c) Li5(8c) O1(8c) O2(8c) O3(8c) O4(8c) Al(8c) Li1(8g) Li2(2b) O1(4e) O2(4f) Al(2a)

Boltzmann constant, n is the number of atoms per unit cell, N is the number of unit cells, - is the reduced Planck constant, and u is the phonon frequency. The calculated thermodynamic parameters of the two phases of Li5AlO4 as a function of temperature are displayed in Fig. 6. Since aLi5AlO4 is stable from room temperature to ~1100 K, the temperature ranges for a- and b-Li5AlO4 are 0e1100 and 0e1350 K, respectively. At absolute zero (0 K), from Eqs. (1) and (2), we obtain DE ¼ DF ¼ 77.96 kJ/mol for a-Li5AlO4 and 78.23 kJ/mol for b-Li5AlO4. The data shown in Fig. 6(b) confirm that E increases almost linearly with temperature, tending to display kBT behavior. Fig. 6(c) shows the S values as a function of temperature; the calculated value for bLi5AlO4 at 298 K is 132.87 J/K$mol. Kulkarni and Besmann [20] optimized the thermodynamic parameters in the Li2OeAl2O3 system, obtaining a value of 124.4 J/K$mol. The 6.37% deviation may originate from the two different methods and systems used. The data in Fig. 6(d) show that at low temperature, Cv is proportional to T3, whereas at high temperature, Cv tends to attain a constant value. According to the classical equipartition law, Cv ¼ 3NkB (where N is the number of particles per unit cell) at high temperatures. In this case, Li5AlO4 contains 10 atoms, i.e., 10NA particles (where NA is the Avogadro constant), which means that the theoretical value of Cv should be 249.23 J/K$mol. However, in our results, the calculated Cv values for a- and b-Li5AlO4 are 241.78 and 244.28 J/K$mol, affording deviations of 1.99 and 2.99%, respectively. Table 5 lists the calculated Cv values for b-Li5AlO4 at selected temperatures and previously determined values for the specific heat at constant pressure, Cp [32]. The relationship between Cp and Cv is defined as follows:



vV Cp ¼ Cv þ T vT

  p

vP vT

    V

¼ Cv þ a2 BVT

(5)

V¼V0 ðTÞ

where B is the bulk modulus, a is the volume thermal expansion coefficient, V is the volume, and T is the absolute temperature. The calculation of Cp is more complicated than that of Cv and it is necessary to deduce the value of a; the calculation of this value is currently in progress. 4. Conclusions The structural, electronic, dynamical, and thermodynamic properties of the two phases of Li5AlO4 were investigated using first-principles DFT calculations. The optimized lattice parameters and atomic fractional coordinates of a- and b-Li5AlO4 were consistent with the experimental values. The band structures of aand b-Li5AlO4 showed some similarities; for example, both materials are insulators. The Li-s and Li-p orbitals mainly contribute to the conduction bands, and the O-p orbital mostly contributes to the

Q. Guan et al. / Journal of Nuclear Materials 465 (2015) 170e176

175

Fig. 6. Calculated thermodynamic properties of a- and b-Li5AlO4: (a) Helmholtz free energy F; (b) internal energy E; (c) entropy S; and(d) specific heat at constant volume Cv.

VB. The band gaps between the CBM and VBM are 4.82 and 5.16 eV for a- and b-Li5AlO4, respectively. The dynamical properties were further studied using DFPT combined with the PHONOPY package. The phonon dispersion curves and the Born effective charges were calculated. The phonon frequencies at the G point categorized as Raman- and IR (including LO-TO splitting) -active modes were listed. Finally, thermodynamic properties such as the S, F, and Cv values

of a- and b-Li5AlO4 were studied as a function of temperature under the harmonic approximation. The Cv values obtained at different temperatures were also compared with those of previous theoretical studies. The thermodynamic properties of the two phases of Li5AlO4 were quite similar. The experimental values of the thermodynamic functions could not be determined. Thus, the calculated data can support future experimental work. Acknowledgement

Table 5 Previously calculated Cv and Cp values of b-Li5AlO4. T(K)

Cv(calc.)

Cp ¼ a þ bT þ CT 2 þ dT 2 þ eT 1 ðJ=mol$KÞa a

298 300 400 500 600

172.77 173.34 200.51 215.92 225.23

700 800 900 1000 1100 1200 1300

231.22 235.26 238.11 240.19 241.75 242.95 243.89

a

Ref [20].

This work was supported by the National Magnetic Confinement Fusion Science Program (2013GB110004, 2014GB111001).

225.405

b  103

33.387

c  106

d  105

e  103

26.283

55.947

0

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249.793

26.858

68.064

67.767

0

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