[PPT] - DFT study of anisotropic elastic property of LiCoO2 during lithium PowerPoint Presentation

SLIDE 1

DFT study of anisotropic elastic property

f LiCoO2 during lithium intercalation and

deintercalation process

Lingbin Meng

Department of Mechanical and Energy Engineering Indiana University - Purdue University Indianapolis (IUPUI)

MSE 69700 Project Report, 12/06/2018

SLIDE 2

Introduction

Lithium cobalt oxide (LiCoO2) is a popular

cathode material of lithium-ion batteries due to its excellent electrochemical properties [1].

LiCoO2 consists of layers of lithium that lie

between slabs of octahedron formed by cobalt and oxygen atoms.

During charging-discharging, LiCoO2

becomes LixCoO2 while x ranges from 0 (discharging) to 1 (charging).

2

Unit cell of LiCoO2, with small black balls being Li, small white balls being O and big grey balls being Co [2].

[1] B. Huang, Y. I. Jang, Y. M. Chiang, and D. R. Sadoway, “Electrochemical evaluation of LiCoO2 synthesized by decomposition and intercalation of hydroxides for lithium-ion battery applications,” J. Appl. Electrochem. 28, 1365–1369 (1998). [2] L. Wu, J. Zhang, “Ab initio study of anisotropic mechanical properties of LiCoO2 during lithium intercalation and deintercalation process,” J. Appl. Phys. 118, 225101 (2015).

SLIDE 3

Motivations

Performance of LiCoO2 are sensitive to number of charge-discharge

cycles and working environment.

Large volume expansion, phase transition, and associated Li diffusion-induced

stresses within electrode materials can lead to their fracture and failure, which result in battery capacity loss and power fade [2].

From experiment, it is reported that the mechanical properties of LiCoO2 will

degrade after dozens of charge-discharge cycles [3, 4].

To insure the performance of LiCoO2 based lithium-ion batteries, it is

imperative to understand the mechanical properties of LiCoO2 during lithium intercalation and deintercalation process.

3

[2] L. Wu, J. Zhang, “Ab initio study of anisotropic mechanical properties of LiCoO2 during lithium intercalation and deintercalation process,” J. Appl. Phys. 118, 225101 (2015). [3] W.-S. Yoon, K.-B. Kim, M.-G. Kim, M.-K. Lee, H.-J. Shin, J.-M. Lee et al., “Oxygen contribution on Li-ion intercalation-deintercalation in LiCoO2 investigated by O K-edge and Co L-edge x-ray absorption spectroscopy,” J. Phys. Chem. B 106, 2526–2532 (2002). [4] H. Wang, Y. I. Jang, B. Huang, D. R. Sadoway, and Y. M. Chiang, “TEM study of electrochemical cycling-induced damage and disorder in LiCoO2 cathodes for rechargeable lithium batteries,” J. Electrochem. Soc. 146, 473–480 (1999).

SLIDE 4

Objective

Test the hypothesis that the anisotropic elastic behavior of LixCoO2

will be alleviated with higher lithium concentration

Obtain initial unit cell structures of CoO2 and LiCoO2 from literature
Fully relax the unit cells using VASP
Compute their elastic constants, and using nanoMATERIALS

SeqQuest DFT

Compare the ratio of and between CoO2 and LiCoO2
Test the hypothesis that LDA tends to predict harder bond than GGA
Use both LDA and GGA, and compare final results

4

SLIDE 5

Initial structures of LiCoO2 from literature

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Cell Vectors [2]: 2.4595121500000000 -1.4200000000000000 0.0000000000000000 0.0000000000000000 2.8400000000000000 0.0000000000000000 0.0000000000000000 0.0000000000000000 14.1600000000000000 Atomic Structure (Fractional) [2]: Li 0.0000000000000000 0.0000000000000000 -0.0000000000000000 Li 0.6666666666666643 0.3333333333333357 0.3333333333333357 Li 0.3333333333333357 0.6666666666666643 0.6666666666666643 O 0.0000000000000000 0.0000000000000000 0.2390065962445188 O 0.6666666666666643 0.3333333333333357 0.5723399295778544 O 0.3333333333333357 0.6666666666666643 0.9056732629111830 O -0.0000000000000000 -0.0000000000000000 0.7609934037554813 O 0.6666666666666643 0.3333333333333357 0.0943267370888169 O 0.3333333333333357 0.6666666666666643 0.4276600704221455 Co 0.0000000000000000 0.0000000000000000 0.5000000000000000 Co 0.6666666666666643 0.3333333333333357 0.8333333333333357 Co 0.3333333333333357 0.6666666666666643 0.1666666666666643

[2] L. Wu, J. Zhang, “Ab initio study of anisotropic mechanical properties of LiCoO2 during lithium intercalation and deintercalation process,” J. Appl. Phys. 118, 225101 (2015).

SLIDE 6

Initial structures of CoO2 from literature

6

Cell Vectors [2]: 2.883956181 0.000000000 0.000000000

1.416978091 2.484278046 0.000000000

0.000000000 0.000000000 4.596576611 Atomic Structure (Fractional) [2]: O 0.3333333333333357 0.6666666666666643 0.2037769783220773 O 0.6666666666666643 0.3333333333333357 0.7962230216779227 Co -0.0000000000000000 0.0000000000000000 0.0000000000000000

[2] L. Wu, J. Zhang, “Ab initio study of anisotropic mechanical properties of LiCoO2 during lithium intercalation and deintercalation process,” J. Appl. Phys. 118, 225101 (2015).

SLIDE 7

Relaxation

Using VASP to fully relax the structure
VASP predicts more accurate lattice parameters, which can be seen later. This

helps us start with reliable unit cell structures

For CoO2, number of K-points in all directions is 12.
For LiCoO2, number of K-points in x, y, z directions is 6, 6, 2, respectively.
The INCAR file is shown below
ISIF = 3 means both cell shape and cell volume are allowed to change to minimize the

total energy

ENCUT is the KE cutoff in eV

7

SLIDE 8

Relaxation (cont.)

Insert initial structure, GGA potentials, number of kpoints into

POSCAR, POTCAR and KPOINTS files in correct format, and use the INCAR in the previous slide, the computation can be started in VASP

Read results in CONTCAR:

8

SLIDE 9

Lattice parameters of LiCoO2 comparison

The result is similar to experimental result and other DFT results.

9

a & b (Å) c (Å) V (Å3) This work (GGA) 2.85 14.04 33.02 Experiment [5] 2.82 14.05 32.23 Wu et al. (GGA) [2] 2.84 14.16 32.96 Xiong et al. (GGA) [6] 2.84 14.17 32.99 Qi et al. (HSE06) [7] 2.80 14.07 31.84

[2] L. Wu, J. Zhang, “Ab initio study of anisotropic mechanical properties of LiCoO2 during lithium intercalation and deintercalation process,” J. Appl. Phys. 118, 225101 (2015). [5] T. Motohashi, Y. Katsumata, T. Ono, R. Kanno, M. Karppinen, and H. Yamauchi, “Synthesis and properties of CoO2, the x ¼ 0 end member of the LixCoO2 and NaxCoO2 systems,” Chem. Mater. 19, 5063–5066 (2007).

[6] F. Xiong, H. J. Yan, Y. Chen, B. Xu, J. X. Le, and C. Y. Ouyang, “The atomic and electronic structure changes upon delithiation of LiCoO2: From first principles calculations,” Int. J. Electrochem. Sci. 7, 9390 (2012). [7] Y. Qi, L. G. Hector, C. James, and K. J. Kim, “Lithium concentration dependent elastic properties of battery electrode materials from first principles calculations,” J. Electrochem. Soc. 161, F3010–F3018 (2014).

SLIDE 10

Input geometry

The rest of the project will based on nanoMATERIALS SeqQuest DFT

[8] tool at https://nanohub.org/tools/nmst_dft.

The input geometries are shown below:

10

[8] R. P. Kumar Vedula, G. Bechtol, Benjamin. P. Haley, A. Strachan (2016), "nanoMATERIALS SeqQuest DFT," https://nanohub.org/resources/nmst_dft. (DOI: 10.4231/D3K931744).

SLIDE 11

Energy expression

The following image shows the setting for LiCoO2. For CoO2, change

the number of K-points to 12-12-12.

11

SLIDE 12

k-points convergence test

The next step is to compute the elastic constants by applying some strain

to the structure and computing for stress or energy.

To make sure that the current K-point set is reliable, it is necessary to test

the total energy and stress of the system will converge at current K-point set (12, 12, 12 for CoO2 and 6, 6, 2 for LiCoO2).

The 6-6-2 k-point set for LiCoO2 converges well, whereas the 12-12-12 K-

point set still has small fluctuation. But more k-points will lead to out-of- memory issue in the tool.

12

LiCoO2 Stress (GPa) Energy (Ryd) xx yy zz zy zx yx kpoints 3-3-1

7.4195 -8.5868 -6.4538 -0.2781 0.1605

1.0230

848.8639

kpoints 5-5-2

7.4735 -8.3797 -6.4120 0.1356 -0.0783 0.7824
848.8667

kpoints 6-6-2

7.4611 -8.3973 -6.3796 0.1324 -0.0765 0.8075
848.8665

kpoints 8-8-3

7.4554 -8.3980 -6.3850 0.1364 -0.0787 0.8137
848.8665

CoO2 Stress (GPa) Energy (Ryd) xx yy zz zy zx yx kpoints 3-3-3

5.3889
4.0528
4.5506
0.2212
0.1100

2.9322

281.7845

kpoints 5-5-5

3.9842
5.1338
6.0261

0.0378

0.4830

0.5706

281.7831

kpoints 8-8-8

4.0614
5.0113
5.5457
0.3226

0.0950 0.8454

281.7842

kpoints 10-10-10

4.0903
5.0065
5.5160
0.3808

0.1945 0.9046

281.7844

kpoints 12-12-12

4.0788
5.0507
5.5647
0.3195

0.0769 0.8485

281.7843

SLIDE 13

Comments on nanoMATERIALS SeqQuest DFT

The results indicate that the GGA potential in the tool tends to predict

larger lattice parameters than literature in our case. For current structure, the computed stress components, , and , are negative, which means that the lattice parameters after relaxation in this tool will be larger than current structure. And since current structure is similar to those in literature, it means that this tool tends to predict larger lattice parameters. But since elastic property is not sensitive to small initial stress (it bases on the difference of stress), it’s acceptable to resume with current structure.

13

LiCoO2 Stress (GPa) Energy (Ryd) xx yy zz zy zx yx kpoints 3-3-1

7.4195 -8.5868 -6.4538 -0.2781 0.1605

1.0230

848.8639

kpoints 5-5-2

7.4735 -8.3797 -6.4120 0.1356 -0.0783 0.7824
848.8667

kpoints 6-6-2

7.4611 -8.3973 -6.3796 0.1324 -0.0765 0.8075
848.8665

kpoints 8-8-3

7.4554 -8.3980 -6.3850 0.1364 -0.0787 0.8137
848.8665

CoO2 Stress (GPa) Energy (Ryd) xx yy zz zy zx yx kpoints 3-3-3

5.3889
4.0528
4.5506
0.2212
0.1100

2.9322

281.7845

kpoints 5-5-5

3.9842
5.1338
6.0261

0.0378

0.4830

0.5706

281.7831

kpoints 8-8-8

4.0614
5.0113
5.5457
0.3226

0.0950 0.8454

281.7842

kpoints 10-10-10

4.0903
5.0065
5.5160
0.3808

0.1945 0.9046

281.7844

kpoints 12-12-12

4.0788
5.0507
5.5647
0.3195

0.0769 0.8485

281.7843

SLIDE 14

Apply strain

According to generalized Hooke’s Law, to obtain

, and . So

.
To obtain

, , . So

.

14

Generalized Hooke’s Law:

SLIDE 15

Apply strain (cont.)

in this example screenshot.
Click simulate to start computation
Read results in “Data”

15

SLIDE 16

Stress-strain method

According to the following stress-strain curve, for LiCoO2,

=344.81 GPa, =249.71 GPa. For CoO2, =354.4 GPa, =153.05 GPa.

16

y = 344.81x - 6.9245 y = 354.4x - 3.6648

12
8
4

4 8 12 0.01 0.02 0.03 0.04 0.05 0.06

σxx (GPa)

εxx

LiCoO2 CoO2 Linear (LiCoO2) Linear (CoO2)

y = 249.71x - 6.3004 y = 153.05x - 5.3323

8
4

4 8 0.01 0.02 0.03 0.04 0.05 0.06 0.07

σzz (GPa)

εzz

LiCoO2 CoO2 Linear (LiCoO2) Linear (CoO2)

SLIDE 17

Anisotropic elastic property

The ratio of

and

f LiCoO2 is 344.81/249.71=1.381.
The ratio of CoO2 is 354.4/153.05=2.316.
This result indicates that the anisotropic elastic behavior of LixCoO2

will be alleviated with higher lithium concentration. The hypothesis is verified.

In reference [2], the ratios of

and

f LiCoO2 and CoO2 are 1.508

and 3.444, respectively, which leads to the same conclusion.

According to [2], the reason of this phenomenon is that the layers of

CoO2 are weakly bonded by van der Waals forces without the Li ions.

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[2] L. Wu, J. Zhang, “Ab initio study of anisotropic mechanical properties of LiCoO2 during lithium intercalation and deintercalation process,” J. Appl. Phys. 118, 225101 (2015).

SLIDE 18

Energy-strain method

The internal energy can be expressed as

, with , and

. The

elastic constant can be obtained by a polynomial fit to strain energy density with respect to the deforming strain component [8].

The elastic constant can be computed from
.

18

[9] K.B. Panda, K.S. Ravi Chandran, “First principles determination of elastic constants and chemical bonding of titanium boride (TiB) on the basis of density functional theory,” Acta Materialia 54, 1641– 1657 (2006).

SLIDE 19

Energy-strain method (cont.)

For LiCoO2,
×.
×.
. For CoO2,
.

This leads to the same conclusion.

19

y = 8.0336x2 - 0.321x - 7E-05 y = 2.4286x2 - 0.1071x + 6E-06

0.004
0.003
0.002
0.001

0.000 0.001 0.002 0.003 0.004 0.005 0.01 0.02 0.03 0.04 0.05 0.06

ΔE (Ryd)

εxx

LiCoO2 CoO2

Poly. (LiCoO2)
Poly. (CoO2)

y = 5.3393x2 - 0.3581x - 3E-05 y = 1.2381x2 - 0.1007x + 1E-05

0.007
0.006
0.005
0.004
0.003
0.002
0.001

0.000 0.001 0.01 0.02 0.03 0.04 0.05 0.06 0.07

ΔE (Ryd)

εzz

LiCoO2 CoO2

Poly. (LiCoO2)
Poly. (CoO2)

SLIDE 20

LDA results

The computation of

and

f LiCoO2 in stress-strain method is

conducted again but using LDA potential this time.

The predicted

=411.14 GPa, =262.04 GPa, both larger than the GGA results, respectively. This verifies that LDA tends to predict harder bond than GGA.

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y = 411.14x + 14.198 y = 262.04x + 12.139

4

4 8 12 16 20

0.05
0.04
0.03
0.02
0.01

0.01 0.02

σ (GPa)

ε

xx zz Linear (xx) Linear (zz)

SLIDE 21

Conclusions

The anisotropic elastic property of LiCoO2 has been studied by

comparing the ratio of and between LiCoO2 and CoO2.

The ratio decreases with increasing lithium concentration, indicating that the

anisotropic elastic behavior of LixCoO2 will be alleviated with higher lithium

concentration. The hypothesis is verified.
A comparison between GGA and LDA is conducted by comparing the

predicted elastic constants of the same structure.

LDA predicts larger elastic constants, indicating that it tends to predict harder

bond than GGA.

21

SLIDE 22

References

[1] B. Huang, Y. I. Jang, Y. M. Chiang, and D. R. Sadoway, “Electrochemical evaluation of LiCoO2 synthesized by decomposition and intercalation of hydroxides for lithium-ion battery applications,” J. Appl. Electrochem. 28, 1365–1369 (1998). [2] L. Wu, J. Zhang, “Ab initio study of anisotropic mechanical properties of LiCoO2 during lithium intercalation and deintercalation process,” J. Appl. Phys. 118, 225101 (2015). [3] W.-S. Yoon, K.-B. Kim, M.-G. Kim, M.-K. Lee, H.-J. Shin, J.-M. Lee et al., “Oxygen contribution on Li-ion intercalation-deintercalation in LiCoO2 investigated by O K-edge and Co L-edge x-ray absorption spectroscopy,” J. Phys. Chem. B 106, 2526–2532 (2002). [4] H. Wang, Y. I. Jang, B. Huang, D. R. Sadoway, and Y. M. Chiang, “TEM study of electrochemical cycling-induced damage and disorder in LiCoO2 cathodes for rechargeable lithium batteries,” J. Electrochem. Soc. 146, 473–480 (1999). [5] T. Motohashi, Y. Katsumata, T. Ono, R. Kanno, M. Karppinen, and H. Yamauchi, “Synthesis and properties of CoO2, the x ¼ 0 end member of the LixCoO2 and NaxCoO2 systems,” Chem. Mater. 19, 5063–5066 (2007). [6] F. Xiong, H. J. Yan, Y. Chen, B. Xu, J. X. Le, and C. Y. Ouyang, “The atomic and electronic structure changes upon delithiation of LiCoO2: From first principles calculations,” Int. J. Electrochem. Sci. 7, 9390 (2012). [7] Y. Qi, L. G. Hector, C. James, and K. J. Kim, “Lithium concentration dependent elastic properties of battery electrode materials from first principles calculations,” J. Electrochem. Soc. 161, F3010–F3018 (2014). [8] R. P. Kumar Vedula, G. Bechtol, Benjamin. P. Haley, A. Strachan (2016), "nanoMATERIALS SeqQuest DFT," https://nanohub.org/resources/nmst_dft. (DOI: 10.4231/D3K931744). [9] K.B. Panda, K.S. Ravi Chandran, “First principles determination of elastic constants and chemical bonding of titanium boride (TiB)

n the basis of density functional theory,” Acta Materialia 54, 1641–1657 (2006).

22