The structural, elastic and electronic properties of BiI3 ...

Physica B 407 (2012) 735–739

Contents lists available at SciVerse ScienceDirect

Physica B journal homepage: www.elsevier.com/locate/physb

The structural, elastic and electronic properties of BiI3: First-principles calculations Xiao-Xiao Sun a, Yan-Ling Li a,b,n, Guo-Hua Zhong c, Hua-Ping Lu¨ a, Zhi Zeng b a

Department of Physics, Xuzhou Normal University, Xuzhou 221116, People’s Republic of China Key Laboratory of Materials Physics, Institute of Solid State Physics, Chinese Academy of Sciences, Hefei 230031, People’s Republic of China c Center for Photovoltaics and Solar Energy, Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen 518055, People’s Republic of China b

a r t i c l e i n f o

abstract

Article history: Received 18 July 2011 Received in revised form 21 November 2011 Accepted 2 December 2011 Available online 8 December 2011

The structural, elastic and electronic properties of BiI3 are investigated using the first-principles pseudopotential calculations within the framework of density functional theory. The calculated equilibrium structural parameters agree well with the experimental values. The results show that rhombohedral R-3 structure is low enthalpy structure at zero pressure. R-3 structure will transform into SbI3-type structure (space group P21/c) at about 7.0 GPa. At zero pressure, BiI3 with R-3 symmetry meets the mechanical stability criteria, but BiI3 with P-31 m symmetry is an unstable one mechanically. For R-3 structure, the obtained bulk, shear, and Young’s moduli are 25.6, 15.3 and 38.3 GPa, respectively. BiI3 presents large elastic anisotropy. Debye temperature of R-3 structure calculated is 181 K. The metallization pressure of R-3 structure is about 133 GPa and that of predicted high pressure phase P21/c structure is about 61 GPa, indicating BiI3’s potential application as a nuclear radiation detector under high pressure environment. & 2011 Elsevier B.V. All rights reserved.

Keywords: Elastic constant Phase transition Density functional theory Metallization

1. Introduction Bismuth tri-iodide (BiI3), a layered semiconductor, with its distinct properties of strong intrinsic optical anisotropy, wide band gap and heavy atoms constituents, is mainly used as a candidate material for a room temperature gamma-ray detector or an x-ray digital imaging sensor [1–3]. Layered BiI3 crystal is considered to be the three-layered stacking structure, where bismuth atom planes are sandwiched between iodide atom planes, which form the sequence I–Bi–I planes. The periodic stacking of three layers forms rhombohedral BiI3 crystal with R-3 symmetry [4,5]. Layers are relative shifted horizontally, without which BiI3 crystal is one-layered periodic stacking structure. The successive stacking of one I–Bi–I layer forms hexagonal structure with P-31m symmetry [6,7]. The intralayer is strong ionic bonding, while interlayers are weak van der Waals bonding, making that BiI3 presents optic anisotropy. A single crystal of BiI3 has been synthesized by Nason and Keller [8]. However, no sufficiently large sized single crystals may be obtained for nuclear radiation detectors. Thus, further investigation about related physical properties of the material is highly necessary.

n Corresponding author at: Xuzhou Normal University, Department of Physics, Xuzhou 221116, China. Tel./fax: þ86 516 83500484. E-mail address: [email protected] (Y.-L. Li).

0921-4526/$ - see front matter & 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2011.12.011

Many studies of BiI3 focused on its structural [5], electronic [6,7] and optical [9–12] properties up to now. Keller and Nason [12] pointed out that the lattice parameters of BiI3 are a¼7.519270.0003 A˚ and c¼ 20.72170.004 A˚ at room tempera¨ et al. [7] calculated the electronic band structure of ture. Schluer hexagonal BiI3 crystal using the empirical pseudopotential method. Krylova et al. [13] measured the absorption and luminescence spectra of BiI3 crystals under the low temperature (1.6–77 K). Lifshitz and Bykov [14] also reported the luminescence properties of BiI3. Adopting dependent temperature optical absorption measuring method, Kaifu and Komatsu [10] observed the edge absorption spectrum of BiI3. Yorikawa and Muramatsu [6] studied the structural and electronic properties of BiI3, and then explained the disagreement between experimental and theoretical results relating to a direct or indirect band gap. Despite the technological importance in applications, few theoretical works have been done to study its fundamental physical property, in particular, elastic and electronic properties at high pressure. To more fully understand of BiI3 crystal, we have used first-principles method to further investigate physical properties of this material. Firstly structural and elastic properties were discussed at zero pressure. We readdressed the structural stability of BiI3 by means of low enthalpy criterion and mechanical stability criterion. A structural phase transition from R-3 structure to P21/c structure is predicted by compressibility analysis, and then confirmed by low enthalpy calculations. Secondly, the elastic property of stable phase at zero pressure

736

X.-X. Sun et al. / Physica B 407 (2012) 735–739

was discussed in detail. Lastly, electronic property at zero and high pressure was explored. We found that semiconducting BiI3 can transform into metal at high pressure.

1=BR ¼ ð2S11 þS33 Þ þ 2ðS12 þ2S13 Þ

ð7Þ

15=GR ¼ 4ð2S11 þ S33 Þ4ðS12 þ 2S13 Þ þ3ð2S44 þ S66 Þ:

ð8Þ

In Eqs. (3), (4), (7) and (8), the Sij are the elastic compliance constants. Generally, according to Hill average [16], bulk modulus B and shear modulus G are obtained by formulae:

2. Theoretical methods Calculations were performed by the CASTEP code using ab initio pseudopotentials based on density functional theory within the general gradient approximation with the exchange-correlation functional of Perdew Burke Ernzerhof [15]. In the structural geometrical optimization, lattice parameters and atomic coordinates were optimized simultaneously. All the possible structures were optimized by BFGS algorithm, which provides a fast way of finding the lowest energy structure and supports cell optimization in the CASTEP code. The interaction between the ions and the electrons is described by using Vanderbilt’s ultra-soft pseudopotentials (USPP). The calculations were carried out using cut-off energy of 300 eV. During the geometry optimization, the convergence threshold is 5.0 10 6 eV/atom for the maximum energy change and 0.01 eV/A˚ for the maximum force. All the stress components are converged to less than 0.02 GPa, and the dis˚ The placement of all the atoms is less than 5.0 10 4 A. convergence threshold in self-consistent field (SCF) calculation is 5.0 10 7 eV/atom. A 4 4 2 K-point mesh was used to yield convergence. The elastic constants were calculated by using the finite strain technique within the framework of the linear response theory. In general, BV and GV represent the Voigt bulk modulus and the Voigt shear modulus, respectively. BR and GR represent the Reuss bulk modulus and the Reuss shear modulus, respectively. For the Voigt approximation, BV and GV are 9BV ¼ ðC 11 þ C 22 þ C 33 Þ þ2ðC 12 þ C 23 þ C 31 Þ

ð1Þ

15GV ¼ ðC 11 þ C 22 þC 33 ÞðC 12 þC 23 þ C 31 Þ þ3ðC 44 þ C 55 þ C 66 Þ:

ð2Þ

For the Reuss approximation, BR and GR are defined as 1=BR ¼ ðS11 þ S22 þ S33 Þ þ2ðS12 þ S23 þ S31 Þ

ð3Þ

15=GR ¼ 4ðS11 þ S22 þS33 Þ4ðS12 þS23 þ S31 Þ þ 3ðS44 þ S55 þ S66 Þ:

ð4Þ

For rhombohedral lattice, BV, GV, BR and GR can be described as follows: BV ¼ ð2C 11 þC 33 þ 2C 12 þ 4C 13 Þ=9

ð5Þ

5GV ¼ ð2C 11 þ C 33 ÞðC 12 þ 2C 13 Þ þ 3ð2C 44 þ ðC 11 C 12 Þ=2Þ

ð6Þ

G ¼ ðGR þGV Þ=2,B ¼ ðBR þ BV Þ=2:

ð9Þ ’

Further, the Young modulus E and Poisson s ratio n can be given using B and G by the following equations: E¼

9BG , 3B þ G

u¼

3B2 G : 6B þ 2G

ð10Þ

3. Results and discussions 3.1. Structural properties For BiI3, the reported structures include rhombohedral R-3 and hexagonal P-31m symmetries. Both two structures have two bismuth atoms and six iodine atoms in the primitive cell, and each bismuth atom is surrounded by six iodine atoms to form the octahedral structure (see Fig. 1). The optimized equilibrium volume per molecule, lattice constants, density, and relative enthalpy per molecule for two phases of BiI3, i.e., P-31m, and R-3, are displayed in Table 1. It is shown in Table 1 that the calculated equilibrium parameters agree well with the experimental values. The calculations of enthalpy for two phases at zero pressure show that the ground state of BiI3 has R-3 symmetry, in which six bismuth atoms occupy 6c Wyckoff site (0, 0, 0.1705) (z is close to experimental value of 0.1667), and eighteen iodine atoms hold 18f Wyckoff site (0.3256,0.3244,0.0858) (experimental value is (0.3415, 0.3395, 0.0805)). For P-31m structure, two bismuth atoms occupy site 2c

Table 1 The equilibrium crystal structural parameters for BiI3 obtained from the GGA calculations. a and c are lattice parameters. V0 is unit cell volume. r is the density. DH is the single molecular relative enthalpy, referenced to the R-3 phase. Space group

DH(eV)

V0 (A˚ 3)

˚ a (A)

P-31m

0.0571

165.0 168.1

7.430 7.50

R-3

0

168.9 176.2

7.511 7.516

r (g/cm3)

Ref.

6.904 6.90

5.93 5.64

This work Expt. [10]

21.636 20.72

5.56 5.64

This work Expt. [11]

˚ c (A)

Fig. 1. Conventional unit cells of (a) R-3, (b) P-31m, (c) Pnma and (d) P21/c. The red balls represent the bismuth atoms and the green balls represent the iodide atoms.


(0.3333, 0.6667, 0) and six iodine atoms hold 6k site (0.6667, 0, 0.2571). The densities obtained are 5.93 g/cm3 and 5.56 g/cm3 for P-31m and R-3 structure, respectively, which agree well with the experimental values. It is well known that lattice constants are overestimated when using the GGA’s exchange-correlation function. However, the situation for BiI3 is different. It is worthy to note that optimized lattice constant a values are slightly smaller than experimental ones for two phases of BiI3. In order to illustrate the compressibility of BiI3 quantitatively, we observe the changes in length of crystallographic axes a and c when exerting the static pressure on BiI3. That is, we calculate the c/a ratios as a function of pressure. The results show that c/a ratio decrease with increasing pressure for BiI3 (Fig. 2(a)). From Fig. 2(a), it can be seen that a-axis is the most difficult to be compressed compared with c axis at 10 GPa below. The difference in compressibility along different directions originates from the different electronic repulsion in nature. Besides, axis compression shows elastic anisotropy for R-3 phase, as is discussed later. Also it is interesting that c/a ratio has a point of minimum at 20 GPa. This unusual feature can be an indication of structural phase transition. For this reason, we investigate the structural phase transition of BiI3 at high pressure by plotting relative enthalpy per formula unit as a function of pressure (Fig. 2(b)), in which only four competing structures are shown (see also Fig. 1). One can see that R-3 structure transforms into SbI3-type structure (space group P21/c) at about 7 GPa, in which four Bi atoms occupy 4e Wyckoff site (0.0223,0.7743,0.1378) and twelve I atoms hold other three Wyckoff 4e sites (0.2267,1.0652,0.1884), ( 0.2276,0.9337,0.3310), and (0.3592,0.7443,0.4658). At 7GPa, the optimized lattice para˚ respectively. meters a, b and c are 6.7398, 9.3619 and 8.0786 A, Besides, interior free parameter angle beta of P21/c phase is 107.131 at 7 GPa.

3.2. Elastic properties Elastic properties of a solid are related to various physical properties, such as interatomic potentials, phonon spectra and equation of states [17]. The elastic constants determine the stiffness of a crystal against an externally applied strain [18]. For a stable structure, elastic constants should satisfy the wellknown Born–Huang stability criteria [19]. Hexagonal crystal has

five independent elastic constants, i.e., C11, C33, C44, C12 and C13. Mechanical stability leads to restrictions on the elastic constants, which for hexagonal crystals are C 11 40,C 33 4 0,ðC 11 C 12 Þ 40,C 44 4 0,ðC 11 þC 12 ÞC 33 2C 213 4 0: ð11Þ For rhombohedral crystal, there are six independent elastic constants, i.e., C11, C33, C44, C12, C13 and C14. The requirement of mechanical stability results in the following restrictions on the elastic constants: C 33 40,C 44 4 0,C 11 9C 12 9 40,ðC 11 þ C 12 ÞC 33 2C 213 4 0,ðC 11 C 12 ÞC 44 2C 214 4 0:

ð12Þ

The calculated elastic constants, bulk modulus B, shear modulus G, the Young’s modulus E and Poisson’s ratio n are listed in Table 2. Obviously, the calculated elastic constants for hexagonal P-31m phase dissatisfy the mechanical stability criteria, signaling its mechanical instability. The elastic constants of rhombohedral R-3 phase match all the mechanical stability criteria, showing its stability mechanically. Combining enthalpy and elastic constants calculations, it can be concluded that rhombohedral R-3 structure is the most stable structure at zero pressure, while P-31m structure is unstable one due to its mechanical instability. The small elastic modulus of BiI3 is due to weaker interatomic interactions (discussed later). Young’s modulus and Poisson’s ratio are essential for technological and engineering applications of solids. Young’s modulus is used to provide a measure of the stiffness of the material. The calculated E value is 38.3 GPa, which means that BiI3 is slightly stiff. Poisson’s ratio is related to the volume change during uniaxial deformation. If n ¼0.5, no volume change occurs during elastic deformation [17]. Our result n ¼0.25 indicates that a large volume change is associated with its Table 2 The calculated zero-pressure elastic constants Cij (GPa), the isotropic bulk modulus B (GPa), shear modulus G (GPa), Young’ modulus E (GPa), Poisson’s ratio n, and Debye temperature yD (K) for the P-31m and R-3 phases of BiI3. C11

C33

C44

C12

C13

C14

B

G

E

n

yD (K)

P-31m 14.0 48.2 24.4 58.1 28.4 0 – – – – – R-3 48.8 37.5 18.4 13.0 17.4 7.9 25.6 15.3 38.3 0.25 181

0.6

2.90 R-3

2.88

0.4

Relative Enthalpy (eV/f.u.)

2.86 2.84 2.82

c/a

737

2.80 2.78 2.76 2.74

0.2 0.0 -0.2 -0.4

R-3 P-31m Pnma P21 /c

-0.6

2.72

-0.8

2.70 0

5

10

15

20

Pressure (GPa)

25

30

0

5

10

15

20

Pressure (GPa)

Fig. 2. (a) The c/a ratio of R-3 phase as a function of pressure for BiI3. (b) Enthalpy per chemical formula unit of four competing structures as a function of pressure, referenced to the R-3 phase.

738


deformation. The calculated value B/G is 1.67, indicating that BiI3 in R-3 structure is brittle. It is well known that the elastic anisotropy of crystals is correlated with the hardness and the possibility to induce microcracks in the materials. Hence it is important to analyze elastic anisotropy so as to understand the mechanical properties of crystals. The elastic anisotropy arises from both shear and compression anisotropy. For hexagonal lattice, shear anisotropy can be determined by the value of C44/C66 and compression anisotropy can be identified by Bc =Ba ¼ ðC 11 þ C 12 2C 13 Þ=ðC 33 C 13 Þ ratio, where Bc and Ba represent bulk modulus along c-axis and a-axis direction, respectively. The calculated value of C44/C66 is 1.031, indicating higher shear anisotropy. From Bc/Ba ¼1.34 obtained, it is concluded that a-axis has stronger incompressibility than c-axis, that is, a-axis is more difficult to be compressed than c-axis, which again confirm the conclusion obtained by analyzing change of c/a ratio with increasing pressure above (see Fig. 2(a)). Most recently, Ranganathan and Ostioja-Starzewski introduced a concept of universal anisotropy index to measure the single crystal elastic anisotropy [20]. The universal anisotropy index is defined as AU ¼ 5

GV B V þ 6: GR BR

ð13Þ

A value of zero for AU represents locally isotropic single crystals and the departure of AU from zero denotes the extent of single crystal anisotropy. The calculated value of Au is 1.053 for BiI3 with R-3 symmetry, suggesting again its stronger anisotropy, which is characterized predominantly by weak van der Waals bonding between adjacent planes. Debye temperature yD correlates many physical properties with thermodynamic properties, e.g. specific heat, thermal expansion, and thermal conductivity. The Debye temperature can be estimated from the averaged sound velocity by the equation [21]: h 3n NA r 1=3 yD ¼ vm , ð14Þ k 4p M where h is Planck’s constant; k is Boltzmann’s constant; NA is Avogadro’s number; n is the number of atoms in the molecule; r is the density; M is the molecular weight, and nm is the averaged wave velocity. The calculated Debye temperature yD is 181 K for R-3 phase of BiI3.

Fig. 3. (a) The charge density distribution of R-3 phase. (b) Scale. (c) The white panel showing plotted plane in (a).

3.3. Electronic property To understand the correlation between the electronic properties and the mechanical properties, we present the electron density distributions, band energy and density of states (DOS). The bonding type takes responsibility for the elastic property of materials. For resisting either plastic or elastic deformation, highly directional bonding is prior to highly ionic or metallic bonding. In order to unravel the bonding properties of BiI3, we plot the charge density distribution in Fig. 3. It is clearly seen that there is no strong bonding between Bi–I atoms as there is no accumulation of charges than the background charge density of the plane. From the charge density distributions, charge concentrates and surrounds at each atom in which no obvious hybridization or overlay is observed. At the same time, the charge density around I atom is obviously larger than that around Bi atom (that is, there is charge transfer from Bi atom to I atom). It appears that the Bi–I atoms bonding is predominantly ionic in BiI3. The ionic characteristic in BiI3 can also been observed by atomic population analysis. The calculated charges of I and Bi atoms are 0.18e and þ0.55e, respectively, pointing to existence of strong ionic bonding between I and Bi. The intralayer ionic bonding contributes to the lower bulk modulus of BiI3 and thus its large compressibility. On the other hand, we also noticed that the layer space along c

˚ while the intralayer bond lengths between direction is 3.700 A, ˚ This strong layered structure and large Bi–I atoms is 3.029 A. atomic distance also imply the existence of weak interaction such as interlayer van der Waals force and intralayer ionic bond. This implies that there is a stronger electron density in ab-plane than that along c-direction, resulting in stronger electronic repulsion along a-axis or b-axis than c-axis. Thus, the incompressibility along c-axis is much lower than that along a-axis or b-axis at lower pressure, i.e. compression anisotropy, as given in Fig. 2(a). Band structure calculations show that the rhombohedral BiI3 is an indirect band-gap semiconductor with 2.48 eV of band gap at zero pressure, which is higher than experimental value (2.008 eV) given by Kaifu and Komatsu [10]. Near the valence band top, electronic band structure dispersion is less, which shows the electron distribution is local relatively. The same result can be obtained from the corresponding density of states calculation. The total DOS and partial atomic DOS (PDOS) for R-3 structure at zero pressure and P21/c structure at phase transition pressure (7 GPa) are shown in Figs. 4(a) and (b), respectively. The electronic distribution of two phases presents similar behavior. Both R-3 and P21/c phases have obvious band gap, presenting semiconducting behavior. The bottom of the conduction band is predominantly Bi-p and I-p states.


739

2.5 8

R-3

0GPa: Bi-s 0GPa: Bi-p

6

2.4 2.3

0 30

0GPa: I- s 0GPa: I- p

20 10

2.2 2.0 Band gap (eV)

2

Band gap (eV)

DOS (states/eV/cell)

4

2.1 2.0

0 30

Total

1.9

20 10

P21/c

1.5 1.0 0.5 0.0

0

10

0 -12

-10

-8

-6

-4

-2

0

2

4

6

30

40

50

60

Pressure (GPa)

1.8

0

20

5

8

10

15

20

25

30

Pressure (GPa)

Energy (eV) Fig. 5. Change of band gaps for R-3 and P21/c phases with increasing pressure.

15 7GPa: Bi-s 7GPa: Bi-p

DOS (states /eV/ cell)

10

theory. The calculated structural parameters are in good agreement with experimental values. Both enthalpy and elastic constants calculations confirmed that rhombohedral R-3 phase of BiI3 is the most stable structure at zero pressure. It is found that R-3 phase of BiI3 has higher elastic anisotropy. We predicted that R-3 structure transforms into P21/c structure at about 7 GPa. The predicted metallization of BiI3 indicates that it has potential application as an electronic device at high pressure environment.

5 0 7GPa: I- s 7GPa: I- p

20 10 0

Acknowledgments

Total

20 10 0 -14 -12 -10

-8

-6

-4

-2

0

2

4

6

8

10

Energy (eV) Fig. 4. Total and projected atomic density of states for BiI3. Vertical dotted lines indicate the highest occupation level. (a) R-3 phase at zero pressure. (b) P21/c phase at 7 GPa.

The electrons from the I-p states and a small quantity of Bi-s states dominate the top of the valence band (from 2 eV to 0 eV). Near the top of valence band, the weak hybridization between Bi-s and I-p electrons indicates weak covalent bonding of Bi–I, which contributes to low bulk modulus. The weak hybridization between Bi-s and I-p is consistent with the idea of little charge accumulation of electrons between the Bi–I atoms noted in Fig. 3. Additionally, as is shown in Fig. 5, we found that the band gap of R-3 structure decreases with increasing pressure and is closed at about 133 GPa. As for the predicted high pressure phase, P21/c structure, its band gap is about 1.54 eV at phase transition pressure ( 7 GPa) and is closed at about 61 GPa. This transition from semiconductor to metal indicates that there should be another potential structure phase transition at 61 GPa below.

4. Conclusions The structural, elastic, and electronic properties of BiI3 are performed using first-principles based on density functional

YL is grateful to Prof. H.Q. Lin for discussions and comments. This work was supported by the National Natural Science Foundation of China (Grant no. 11047013). Part of the calculations was performed in Center for Computational Science of CASHIPS.

References [1] G.E. Jellison, J.O. Ramey, L.A. Boatner, Phys. Rev. B 59 (1999) 9718. ˜ a, I. Aguiar, A. Gancharov, M. Pe´rez, L. Fornaro, Cryst. Res. Technol. 39 [2] A. Cun (2004) 899. ˜ a, A. Noguera, E. Saucedo, L. Fornaro, Cryst. Res. Technol. 39 (2004) 912. [3] A. Cun [4] K. Watanabe, T. Karasawa, T. Komatsu, Y. Kaifu, J. Phys. Soc. Jpn. 55 (1986) 897. [5] R.W.G. Wyckoff, Crystal Structures, 2nd ed., Inc. New York, 1964. [6] H. Yorikawa, S. Muramatsu, J. Phys.: Condens. Matter 20 (2008) 325220. ¨ [7] M. Schluter, M.L. Cohen, S.E. Kohn, C.Y. Fong, Phys. Status Solidi B 78 (1976) 737. [8] D Nason, L. Keller, J. Cryst. Growth 156 (1995) 221. [9] Y. Kaifu, J. Lumin. 42 (1988) 61. [10] Y. Kaifu, T. Komatsu, J. Phys. Soc. Jpn. 40 (1976) 1377. [11] Z.G. Pinsker, Phase Transition 38 (1992) 127. [12] L. Keller, D. Nason, Powder Diffr. 11 (1996) 91. [13] N.O. Krylova, R.I. Shekhmametev, M.Yu. Gurgenbekov, Opt. Spectrosc. 38 (1975) 545. [14] E. Lifshitz, L. Bykov, J. Phys. Chem. 99 (1995) 4894. [15] M.D. Segall, P.J.D. Lindan, M.J. Probert, C.J. Pickard, P.J. Hasnip, S.J. Clark, M.C. Payne, J. Phys.: Condens. Matter 14 (2002) 2717. [16] R. Hill, Proc. Phys. Soc. London 65 (1952) 349. [17] P. Ravindran, L. Fast, P.A. Korzhavvi, B. Johansson, J. Wills, O. Eriksson, J. Appl. Phys. 84 (1998) 4891. [18] O. Beckstein, J.E. Klepeis, G.L.W. Hart, O. Pankratov, Phys. Rev. B 63 (2001) 134112. [19] M. Born, K. Huang, Dynamical Theory of Crystal Lattices, Clarendon, Oxford, 1956. [20] S.I. Ranganathan, M. Ostoja-Starzewski, Phys. Rev. Lett. 101 (2008) 055504. [21] O.L. Anderson, J. Phys. Chem. Solids 24 (1963) 909.