Lattice dynamics and vibrational spectra of the orthorhombic ......2015/09/25 · Lattice dynamics...

Lattice dynamics and vibrational spectra of the orthorhombic,

tetragonal and cubic phases of methylammonium lead iodide

Federico Brivio,1 Jarvist M. Frost,1 Jonathan M. Skelton,1 Adam J.

Jackson,1 Oliver J. Weber,1 Mark T. Weller,1 Alejandro R. Goni,2

Aurelien M. A. Leguy,3 Piers R. F. Barnes,3 and Aron Walsh1, 4, ∗

1Centre for Sustainable Chemical Technologies and Department of Chemistry,

University of Bath, Claverton Down, Bath BA2 7AY, UK

2ICREA, Passeig Lluıs Companys 23, E-08010 Barcelona,

Spain; Institut de Ciencia de Materials de Barcelona (ICMAB-CSIC),

Campus UAB, E-08193 Bellaterra, Spain

3Department of Physics, Imperial College London, SW7 2AZ, UK

4Global E3 Institute and Department of Materials Science and Engineering,

Yonsei University, Seoul 120-749, Korea

(Dated: September 25, 2015)

1

I. SUPPLEMENTAL MATERIAL

A. Comparison of calculated and measured crystal structures

Figure 1. Calculated powder diffraction patterns of structural models for each phase of

CH3NH3PbI3 developed from neutron powder diffraction data collected on the D20 instrument

at ILL, Grenoble1 and from the equilibrium PBEsol/DFT structures reported in the main text.

Generated using CrystalDiffract CrystalMaker Software Ltd.

B. Tabulated Phonon and Molecular Vibration Data

Data are presented for the phonon frequencies, Raman activity and Infrared activity of

the cubic, tetragonal and orthorhombic phases of MAPbI3.

Raman intensity is estimated from the change in polarisability upon following the eigen-

mode of the phonon using Vasp-Raman.2 This value comes from the derivative of the

electronic-polarisation component of the dielectric tensor (the high frequency component of

the dielectric function). This is calculated from a finite-difference method with two explicit

calculations forwards and backwards along each eigenmode displacement. The dielectric

2

tensor is reduced to a scalar in the far-from-resonance Raman approximation. Infrared ac-

tivity is estimated by projecting the phonon eigenmode against the Born effective charges

of the initial structure.

Computer readable files of these data, and the starting structures and VASP3,4 and

Phonopy5,6 input files are provided in a GitHub repository.7

3

Phonon Mode Wavelength (cm−1) Frequency (THz) i.r. activity Raman intensity

1 3209.16 96.21 0.4996 3087

2 3106.69 93.14 1.714 840.3

3 3098.09 92.88 0.6011 6046

4 3084.96 92.48 0.005823 969.8

5 3077.70 92.27 0.1006 842.9

6 2983.39 89.44 0.006279 1394

7 1564.15 46.89 0.2461 2.552

8 1548.44 46.42 0.1417 272.3

9 1468.95 44.04 0.1987 251

10 1430.89 42.90 0.01116 77

11 1423.38 42.67 0.02558 74.81

12 1383.28 41.47 0.01256 280.2

13 1237.18 37.09 0.001075 21.49

14 1218.69 36.54 0.02127 856.4

15 1007.57 30.21 0.009019 90.33

16 913.13 27.37 0.03994 7.78

17 879.38 26.36 0.05012 675.5

18 317.65 9.52 0.0007563 43.1

19 133.98 4.02 0.08169 3.013

20 129.68 3.89 0.006312 17.78

21 117.79 3.53 0.05354 20.29

22 91.91 2.76 0.0213 52.17

23 81.33 2.44 0.2316 3.235

24 75.02 2.25 0.2622 198

25 69.37 2.08 0.2338 285.6

26 67.84 2.03 0.06232 2.175

27 52.28 1.57 0.03675 25.22

28 33.98 1.02 0.01263 422.7

29 33.43 1.00 0.006817 19.93

30 33.26 1.00 0.01038 296.2

31 30.69 0.92 0.01096 184.2

32 26.71 0.80 0.001683 299.5

33 19.14 0.57 0.006464 15.46

34 0.77 0.02 8.356E − 05 0.01388

35 1.63 0.05 8.31E − 06 0.06414

36 2.53 0.08 2.778E − 05 0.3813

Table I: Phonons in the cubic phase of MAPbI3.

4


1 3229.82 96.83 0.04797 51.4

2 3227.42 96.76 1.221 6838

3 3224.49 96.67 0.1859 2234

4 3222.81 96.62 0.3512 2467

5 3109.97 93.23 1.142 237.1

6 3107.69 93.17 2.452 444.5

7 3092.95 92.72 0.6583 3439

8 3091.87 92.69 0.7217 1914

9 3086.54 92.53 1.487 6202

10 3085.20 92.49 0.7841 1562

11 3083.61 92.44 0.1002 129

12 3083.38 92.44 0.2274 123.2

13 3079.20 92.31 0.172 11770

14 3078.32 92.29 0.07283 497.4

15 3077.04 92.25 0.1161 263.2

16 3076.78 92.24 0.06272 135.4

17 3073.12 92.13 0.4584 2518

18 3072.60 92.11 0.5603 2634

19 3070.63 92.06 0.4692 2953

20 3069.20 92.01 0.8809 2669

21 2979.51 89.32 0.001334 4780

22 2978.90 89.31 0.009879 39.64

23 2978.32 89.29 0.008205 1162

24 2978.06 89.28 0.002011 18.8

25 1562.85 46.85 0.01531 39.26

26 1562.14 46.83 0.006076 4.009

27 1557.53 46.69 0.001154 1.012

28 1556.78 46.67 0.1664 124.7

29 1534.22 45.99 0.7533 109.6

30 1533.75 45.98 0.7248 72.85

31 1532.73 45.95 0.0609 19.9

32 1532.23 45.93 0.01943 51.01

33 1458.10 43.71 0.1032 99.27

34 1456.32 43.66 0.09715 1330

35 1452.96 43.56 0.117 66.87

36 1452.31 43.54 0.08018 40.38

37 1429.02 42.84 0.0137 61.96

38 1428.37 42.82 0.0006682 28.51

39 1427.40 42.79 0.0005263 30.14

40 1426.70 42.77 0.05691 41.98

41 1423.80 42.68 0.01971 8.807

42 1423.71 42.68 0.02181 85.28

43 1423.37 42.67 0.0004379 93.33

Table II: (Tetragonal phase, continued)

5


44 1423.30 42.67 0.003042 10.06

45 1374.25 41.20 0.07101 261.4

46 1373.71 41.18 0.02292 451.3

47 1373.55 41.18 0.05785 30.73

48 1372.77 41.15 0.002207 9.847

49 1234.52 37.01 0.04212 17.7

50 1234.09 37.00 0.03204 7.66

51 1233.25 36.97 0.01672 95.56

52 1233.12 36.97 0.01039 30.58

53 1228.22 36.82 0.00607 681.5

54 1227.38 36.80 0.002512 231.9

55 1225.10 36.73 0.004345 720.3

56 1223.67 36.68 0.0002986 45.99

57 1009.52 30.26 0.01796 199.3

58 1008.93 30.25 0.01098 62.08

59 1008.32 30.23 0.02429 97.36

60 1007.84 30.21 0.021 55.29

61 906.42 27.17 0.02459 15.17

62 906.07 27.16 0.06459 44.73

63 904.08 27.10 0.06341 45.26

64 903.69 27.09 0.08659 62.72

65 891.10 26.71 0.07416 468.2

66 889.69 26.67 0.05425 118.9

67 886.19 26.57 0.0113 14.28

68 884.00 26.50 0.1859 438.2

69 309.62 9.28 0.0006686 40.9

70 308.88 9.26 0.02902 119.6

71 303.54 9.10 0.004784 33.5

72 301.96 9.05 0.01748 122.3

73 172.43 5.17 0.04361 2.594

74 171.23 5.13 0.09551 3.164

75 167.79 5.03 0.05951 3.33

76 167.01 5.01 0.104 6.066

77 138.67 4.16 0.02347 5.693

78 132.00 3.96 0.04715 202.2

79 129.63 3.89 0.09213 64.68

80 129.08 3.87 0.06865 93.8

81 116.20 3.48 0.01654 22.25

82 114.90 3.44 0.0284 47.36

83 113.89 3.41 0.01378 5.492

84 113.30 3.40 0.02674 48.67

85 111.65 3.35 0.001147 6.409

86 109.86 3.29 0.00909 26.3


6


87 108.58 3.26 0.02438 19.33

88 107.54 3.22 0.07923 58.55

89 105.53 3.16 0.0606 8.356

90 103.56 3.10 0.01004 22.33

91 101.23 3.03 0.04541 13.27

92 98.77 2.96 0.07767 44.5

93 98.37 2.95 0.002222 12.93

94 98.13 2.94 0.002387 94.1

95 97.49 2.92 0.00864 18.25

96 94.66 2.84 0.006435 1.582

97 93.18 2.79 0.02255 51.12

98 90.75 2.72 0.008559 0.402

99 81.67 2.45 0.03079 3.895

100 80.97 2.43 0.05127 2.153

101 80.24 2.41 0.005113 21.22

102 79.43 2.38 0.03232 21.38

103 75.76 2.27 0.02447 12.64

104 74.55 2.23 0.04086 29.58

105 73.63 2.21 0.02408 7.482

106 73.09 2.19 0.07055 3.98

107 72.73 2.18 0.04121 6.97

108 69.64 2.09 0.03558 0.5877

109 66.73 2.00 0.3491 4.793

110 65.66 1.97 0.5081 14.12

111 65.07 1.95 0.7109 1.971

112 64.33 1.93 0.03268 1.099

113 63.16 1.89 0.6911 27.45

114 59.27 1.78 0.00973 23.02

115 51.47 1.54 0.004845 0.2237

116 46.30 1.39 0.01916 441.6

117 44.40 1.33 0.005416 232.4

118 43.79 1.31 0.0005969 6.334

119 43.36 1.30 0.005424 244.6

120 42.13 1.26 0.001729 11.89

121 39.91 1.20 0.002021 1.734

122 39.52 1.18 0.02086 72.31

123 38.52 1.15 0.003202 82.61

124 37.60 1.13 5.369E − 05 1.749

125 36.60 1.10 0.02153 9.93

126 36.04 1.08 0.002995 29.85

127 34.95 1.05 0.0579 40.06

128 34.01 1.02 0.001718 4.683

129 33.52 1.00 0.0193 5.423


7


130 31.57 0.95 0.0359 22.58

131 30.58 0.92 0.01841 17.56

132 29.53 0.89 0.04276 5.007

133 28.70 0.86 0.03096 40.88

134 27.66 0.83 0.0007514 1.388

135 27.13 0.81 0.002491 15.3

136 26.48 0.79 0.0007249 1.107

137 26.08 0.78 0.003126 15.55

138 24.08 0.72 0.003662 5.562

139 23.17 0.69 3.506E − 05 0.3476

140 17.73 0.53 0.0004512 1.115

141 17.41 0.52 0.0001654 0.8277

142 0.71 0.02 8.99E − 06 0

143 1.03 0.03 6.122E − 06 0

144 1.33 0.04 8.159E − 05 0

Table II: Phonons in the tetragonal phase of MAPbI3.

8


1 3138.94 94.10 7.548E − 07 2904

2 3130.91 93.86 6.155 0.4683

3 3130.49 93.85 0.0003957 982.7

4 3129.34 93.82 1.374E − 05 0.04791

5 3124.56 93.67 7.541 0.1477

6 3122.22 93.60 0.9806 1.214

7 3122.10 93.60 1.232E − 05 18850

8 3121.71 93.59 0.0003912 3011

9 3086.74 92.54 0.03273 3.853

10 3086.59 92.53 6.551E − 05 1607

11 3086.52 92.53 4.75E − 06 7840

12 3084.82 92.48 1.214 0.03087

13 3074.28 92.16 0.0009936 0.3824

14 3074.18 92.16 2.152E − 08 0.07841

15 3073.28 92.13 3.163E − 06 2154

16 3073.22 92.13 8.824E − 08 1879

17 3071.25 92.07 6.918E − 05 7182

18 3071.09 92.07 2.062E − 07 235.5

19 3070.68 92.06 0.001342 0.04717

20 3070.63 92.06 0.07945 4.85

21 2972.26 89.11 4.733E − 07 7352

22 2971.87 89.09 1.038E − 06 741.6

23 2971.53 89.08 0.01149 0.3687

24 2971.45 89.08 0.0008958 0.3931

25 1560.82 46.79 0.04564 0.03482

26 1560.70 46.79 1.132E − 06 1043

27 1560.44 46.78 1.323E − 07 47.82

28 1558.89 46.73 0.009325 0.5779

29 1551.98 46.53 1.243E − 12 0.5364

30 1548.13 46.41 8.183E − 10 15.59

31 1545.51 46.33 5.853E − 08 120.4

32 1544.99 46.32 0.004793 0.5004

33 1431.19 42.91 6.725E − 06 1965

34 1428.05 42.81 0.2497 0.4477

35 1423.95 42.69 0.009817 0.04111

36 1423.58 42.68 4.415E − 08 0

37 1423.57 42.68 0.006353 554.4

38 1423.54 42.68 0.1159 29.54

39 1423.02 42.66 2.374E − 05 425.5

40 1422.43 42.64 3.074E − 06 12.55

41 1422.21 42.64 2.084E − 06 416.1

42 1422.20 42.64 6.183E − 08 20.31

43 1421.66 42.62 0.06856 0.4492

Table III: (Orthorhombic phase, continued)

9


44 1421.63 42.62 0.08266 0.1024

45 1380.36 41.38 3.269E − 06 416.4

46 1380.06 41.37 4.858E − 06 153.2

47 1379.47 41.36 0.02271 0.03165

48 1378.82 41.34 0.02345 0.564

49 1244.11 37.30 5.07E − 06 114.3

50 1243.73 37.29 1.758E − 05 55.78

51 1243.60 37.28 0.01094 0.08196

52 1243.56 37.28 0.1013 0.02431

53 1237.66 37.10 6.174E − 05 126.4

54 1237.44 37.10 1.429E − 06 0.2614

55 1237.39 37.10 0.04199 0.2346

56 1237.38 37.10 3.109E − 05 36.83

57 1008.12 30.22 3.723E − 07 151.6

58 1007.63 30.21 0.05437 0.03638

59 1006.34 30.17 1.318E − 05 266.7

60 1006.16 30.16 0.001838 0.02923

61 904.56 27.12 0.5049 0.3959

62 903.76 27.09 0.07327 0.4346

63 902.90 27.07 5.48E − 05 864.6

64 901.73 27.03 1.326E − 07 314

65 897.66 26.91 4.072E − 07 5.383

66 894.82 26.83 4.461E − 05 63.81

67 893.47 26.79 2.608E − 07 0.001199

68 893.20 26.78 0.6457 0.5079

69 372.15 11.16 6.641E − 08 50.86

70 371.15 11.13 5.304E − 06 1.388

71 370.64 11.11 0.0122 0.5956

72 369.74 11.08 7.854E − 08 0.4415

73 154.81 4.64 1.895E − 07 25.02

74 154.10 4.62 0.04454 0.004832

75 152.05 4.56 0.02324 0.4676

76 151.15 4.53 9.522E − 05 350.6

77 150.62 4.52 1.967E − 06 1.322

78 149.47 4.48 0.4623 0.4334

79 149.00 4.47 9.599E − 06 2.537

80 146.81 4.40 3.473E − 05 0.3659

81 146.17 4.38 0.0002059 758.5

82 134.92 4.04 0.333 0.1979

83 133.36 4.00 0.0004096 37.62

84 129.89 3.89 1.406E − 08 0.134

85 113.09 3.39 6.564E − 08 0.4895

86 112.85 3.38 4.748E − 06 6.478


10


87 112.77 3.38 0.02934 0.03387

88 111.98 3.36 6.697E − 05 11.47

89 111.11 3.33 4.768E − 07 4.233

90 110.18 3.30 2.467E − 07 9.509

91 104.35 3.13 9.389E − 09 11.27

92 98.05 2.94 1.916E − 06 166.5

93 96.46 2.89 1.886E − 09 7.869

94 96.21 2.88 6.495E − 09 5.675

95 94.62 2.84 3.379E − 05 21.5

96 94.47 2.83 0.0006471 0.7964

97 93.61 2.81 8.017E − 06 19.87

98 92.74 2.78 0.006481 0.07522

99 85.59 2.57 0.07697 0.01629

100 81.27 2.44 0.0181 0.002109

101 79.78 2.39 0.1715 0.01491

102 78.85 2.36 0.0009218 0.0121

103 76.82 2.30 4.425E − 08 0.003329

104 74.09 2.22 0.07271 0.5436

105 73.22 2.20 0.05239 1.861

106 73.15 2.19 0.000396 61.24

107 72.26 2.17 0.006724 3.181

108 71.11 2.13 0.6195 0.04409

109 70.34 2.11 4.596E − 06 0.003808

110 69.01 2.07 0.6704 0.003871

111 65.88 1.98 1.015E − 07 0.0005204

112 65.62 1.97 0.03266 0.2799

113 64.92 1.95 0.6579 0.02793

114 61.91 1.86 0.228 0.0007705

115 53.97 1.62 3.352E − 05 573.9

116 51.22 1.54 3.274E − 05 237.2

117 49.30 1.48 0.08059 0.05986

118 46.92 1.41 3.306E − 07 0.04197

119 44.54 1.34 0.03021 0.02288

120 39.80 1.19 8.881E − 07 38.97

121 37.78 1.13 1.091E − 07 2.288

122 37.76 1.13 0.001627 0.03287

123 37.00 1.11 4.024E − 06 188.1

124 35.62 1.07 0.005145 0.002035

125 34.29 1.03 1.192E − 06 1.682

126 33.79 1.01 1.375E − 07 0.005215

127 32.39 0.97 9.404E − 05 193.2

128 32.27 0.97 0.007264 0.5796

129 32.03 0.96 0.0788 0.1723


11


130 30.53 0.92 0.126 0.04693

131 28.63 0.86 2.402E − 07 0.007629

132 28.15 0.84 3.777E − 06 0.006572

133 27.22 0.82 0.0002582 10.12

134 24.66 0.74 0.03026 0.0006232

135 23.51 0.70 3.09E − 06 0.4463

136 22.49 0.67 1.649E − 06 0.01242

137 20.98 0.63 0.02341 0.1154

138 19.60 0.59 0.008824 0.06632

139 17.35 0.52 0.0004808 0.005515

140 16.76 0.50 1.051E − 07 0.00412

141 15.31 0.46 5.285E − 06 16.81

142 0.18 0.01 3.829E − 07 0

143 0.28 0.01 1.456E − 07 0

144 0.41 0.01 4.973E − 07 0

Table III: Phonons in the orthorhombic phase of MAPbI3.

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1 282.37 8.47 0.00 0.00

2 886.49 26.58 23.49 0.03

3 886.49 26.58 23.49 0.03

4 922.64 27.66 4.85 7.21

5 1239.34 37.15 3.08 0.54

6 1239.35 37.15 3.08 0.53

7 1418.43 42.52 1.26 0.56

8 1450.63 43.49 21.75 3.85

9 1450.63 43.49 21.75 3.85

10 1478.47 44.32 98.51 1.76

11 1621.59 48.61 38.06 4.07

12 1621.59 48.61 38.06 4.07

13 3017.84 90.47 0.57 131.61

14 3118.99 93.51 1.19 33.87

15 3118.99 93.51 1.19 33.89

16 3321.48 99.58 39.11 92.58

17 3395.47 101.79 111.20 24.61

18 3395.47 101.79 111.20 24.60

Table IV. Molecular vibration data from a Gaussian098 calculation on methylammonium at the

PBEPBE/AUG-cc-pVQZ level of theory.

∗ [email protected]

1 M. T. Weller, O. J. Weber, P. F. Henry, A. M. Di Pumpo, and T. C. Hansen, Chem. Commun.

51, 4180 (2015).

2 A. Fonari and S. Stauffer, “Vasp-raman,” https://github.com/raman-sc/VASP/ (2013).

3 G. Kresse and J. Furthmuller, Phys. Rev. B 54, 11169 (1996).

4 G. Kresse and J. Furthmuller, Comput. Mater. Sci. 6, 15 (1996).

5 A. Togo and I. Tanaka, Scr. Mater. 108, 1 (2015).

6 A. Togo, F. Oba, and I. Tanaka, Phys. rev. B 78, 134106 (2008).

7 WMD-Group, “Mapi phonon data,” https://github.com/WMD-Bath/Phonons/tree/master/

2015_MAPbI3 (2015).

8 M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman,

G. Scalmani, V. Barone, B. Mennucci, G. A. Petersson, H. Nakatsuji, M. Caricato, X. Li, H. P.

13

mailto:[email protected]

http://pubs.rsc.org/en/content/articlehtml/2015/cc/c4cc09944c

http://pubs.rsc.org/en/content/articlehtml/2015/cc/c4cc09944c

https://github.com/raman-sc/VASP/

https://github.com/WMD-Bath/Phonons/tree/master/2015_MAPbI3

https://github.com/WMD-Bath/Phonons/tree/master/2015_MAPbI3

Hratchian, A. F. Izmaylov, J. Bloino, G. Zheng, J. L. Sonnenberg, M. Hada, M. Ehara, K. Toyota,

R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T. Vreven,

J. A. Montgomery, Jr., J. E. Peralta, F. Ogliaro, M. Bearpark, J. J. Heyd, E. Brothers, K. N.

Kudin, V. N. Staroverov, R. Kobayashi, J. Normand, K. Raghavachari, A. Rendell, J. C. Burant,

S. S. Iyengar, J. Tomasi, M. Cossi, N. Rega, J. M. Millam, M. Klene, J. E. Knox, J. B. Cross,

V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, A. J. Austin,

R. Cammi, C. Pomelli, J. W. Ochterski, R. L. Martin, K. Morokuma, V. G. Zakrzewski, G. A.

Voth, P. Salvador, J. J. Dannenberg, S. Dapprich, A. D. Daniels, . Farkas, J. B. Foresman, J. V.

Ortiz, J. Cioslowski, and D. J. Fox, “Gaussian09 Revision A.01,” Gaussian Inc. Wallingford CT

2009.

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Lattice dynamics and vibrational spectra of the orthorhombic ......2015/09/25 · Lattice dynamics...

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