Lattice dynamics and vibrational spectra of the orthorhombic ......2015/09/25 · Lattice dynamics...
Transcript of 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)
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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.
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Phonon Mode Wavelength (cm−1) Frequency (THz) i.r. activity Raman intensity
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)
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Phonon Mode Wavelength (cm−1) Frequency (THz) i.r. activity Raman intensity
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
Table II: (Tetragonal phase, continued)
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Phonon Mode Wavelength (cm−1) Frequency (THz) i.r. activity Raman intensity
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
Table II: (Tetragonal phase, continued)
7
Phonon Mode Wavelength (cm−1) Frequency (THz) i.r. activity Raman intensity
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.
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Phonon Mode Wavelength (cm−1) Frequency (THz) i.r. activity Raman intensity
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
Phonon Mode Wavelength (cm−1) Frequency (THz) i.r. activity Raman intensity
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
Table III: (Orthorhombic phase, continued)
10
Phonon Mode Wavelength (cm−1) Frequency (THz) i.r. activity Raman intensity
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
Table III: (Orthorhombic phase, continued)
11
Phonon Mode Wavelength (cm−1) Frequency (THz) i.r. activity Raman intensity
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.
12
Phonon Mode Wavelength (cm−1) Frequency (THz) i.r. activity Raman intensity
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.
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