Supplementary Information
Ironvacancy formation energies and unit cell structures
We used several unit cells for pure and alloyed FeO containing one iron vacancy. These cells differed in the position of the alloying metal cations and in the location of the vacancy-generated holes(Table S1 and Table S2 specify the structure of each cell, specifically the fractional coordinates and lattice vectors, respectively). These models for FeO alloys involved ordered distributions of cations around the vacancy rather than random distributions, which is of course an approximation to the likely case in a real sample. However, calculations considering full randomness in the placement of both metal cations and the vacancy would require supercell sizes that would be prohibitively expensive to calculate. Hence, we considered a wide range of ordered alloys instead. The criteria for distributing the metal cations was to construct cells with different numbers of non-Fe cations placed close to the vacancy and placed on sites that in pure FeO occupy vacancy-generated holes.The location of the iron vacancy was chosen to be at the center of the unit cells. As can be seen in Figure S1, the formation energy depends strongly on the metal and hole ordering (Figure 2 in the main text includes the average and range of these formation energies).
Figure S1. PBE+U iron vacancy formation energy for pure and alloyed FeO under oxygen-rich conditions. The formation energy was calculated for seven cells that differ by alloying metal cation ordering and hole locations (the cell number is shown near each data point). For pure FeO, the formation energy was calculated for three different hole locations.
Table S1.Sample optimized unit cell fractional coordinates of cells with an iron vacancy. The primary location of two vacancy-generated holes is indicated by gray-shaded rows. These cell parameters are shown for Fe0.5Zn0.5Osince other alloys have the same hole locations, and consequently have similar deviations in bond distances compared to the host cells.
Cell number / Atom type / Atom number / Fractional coordinatesX / Y / Z
1 / O / 1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16 / 0.122 / 0.119 / 0.137
0.369 / 0.385 / 0.375
0.622 / 0.144 / 0.111
0.908 / 0.360 / 0.368
0.116 / 0.626 / 0.131
0.374 / 0.909 / 0.354
0.640 / 0.627 / 0.096
0.857 / 0.886 / 0.382
0.149 / 0.111 / 0.614
0.356 / 0.378 / 0.902
0.621 / 0.096 / 0.646
0.891 / 0.372 / 0.865
0.089 / 0.643 / 0.633
0.384 / 0.857 / 0.883
0.642 / 0.616 / 0.613
0.866 / 0.882 / 0.874
Fe (positive spin) / 17
18
19 / 0.503 / 0.501 / 0.998
0.502 / 0.000 / 0.498
0.002 / 0.499 / 0.497
Fe (negative spin) / 20
21
22
23 / 0.252 / 0.253 / 0.246
0.253 / 0.252 / 0.751
0.255 / 0.747 / 0.742
0.748 / 0.748 / 0.753
M (positive spin) / 24
25
26
27 / 0.998 / 0.998 / 0.004
0.498 / 1.000 / 0.003
1.000 / 0.499 / 1.000
0.002 / 0.997 / 0.502
M (negative spin) / 28
29
30
31 / 0.740 / 0.255 / 0.267
0.259 / 0.740 / 0.263
0.744 / 0.740 / 0.254
0.739 / 0.260 / 0.740
2 / O / 1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16 / 0.146 / 0.124 / 0.105
0.362 / 0.377 / 0.394
0.621 / 0.132 / 0.133
0.906 / 0.352 / 0.363
0.111 / 0.628 / 0.138
0.395 / 0.883 / 0.345
0.621 / 0.638 / 0.109
0.872 / 0.891 / 0.371
0.128 / 0.106 / 0.634
0.378 / 0.365 / 0.888
0.600 / 0.118 / 0.653
0.896 / 0.367 / 0.867
0.104 / 0.627 / 0.641
0.370 / 0.880 / 0.872
0.632 / 0.615 / 0.632
0.860 / 0.886 / 0.873
Fe (positive spin) / 17
18
19 / 0.503 / 0.997 / 0.003
0.006 / 0.994 / 0.497
0.994 / 0.501 / 0.009
Fe (negative spin) / 20
21
22
23 / 0.740 / 0.264 / 0.258
0.747 / 0.741 / 0.256
0.255 / 0.268 / 0.737
0.260 / 0.737 / 0.740
M (positive spin) / 24
25
26
27 / 0.501 / 0.997 / 0.500
0.996 / 0.002 / 0.000
0.495 / 0.504 / 0.998
0.998 / 0.497 / 0.503
M (negative spin) / 28
29
30
31 / 0.257 / 0.246 / 0.249
0.250 / 0.751 / 0.252
0.751 / 0.259 / 0.730
0.744 / 0.752 / 0.750
3 / O / 1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16 / 0.133 / 0.133 / 0.108
0.362 / 0.375 / 0.396
0.603 / 0.142 / 0.141
0.909 / 0.357 / 0.363
0.111 / 0.622 / 0.137
0.373 / 0.908 / 0.355
0.634 / 0.632 / 0.095
0.883 / 0.879 / 0.370
0.120 / 0.116 / 0.628
0.367 / 0.372 / 0.903
0.611 / 0.117 / 0.635
0.904 / 0.352 / 0.872
0.116 / 0.630 / 0.628
0.376 / 0.865 / 0.871
0.638 / 0.615 / 0.619
0.865 / 0.879 / 0.877
Fe (positive spin) / 17
18
19 / 0.500 / 0.996 / 0.504
0.503 / 0.500 / 1.000
0.999 / 0.496 / 0.503
Fe (negative spin) / 20
21
22
23 / 0.251 / 0.280 / 0.734
0.254 / 0.745 / 0.746
0.250 / 0.251 / 0.250
0.756 / 0.745 / 0.744
M (positive spin) / 24
25
26
27 / 0.502 / 0.003 / 0.994
0.006 / 0.991 / 0.503
0.998 / 0.994 / 0.008
0.986 / 0.505 / 0.008
M (negative spin) / 28
29
30
31 / 0.744 / 0.256 / 0.260
0.741 / 0.734 / 0.261
0.260 / 0.752 / 0.248
0.743 / 0.256 / 0.738
4 / O / 1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16 / 0.145 / 0.123 / 0.105
0.361 / 0.376 / 0.396
0.620 / 0.133 / 0.133
0.907 / 0.352 / 0.363
0.112 / 0.628 / 0.138
0.395 / 0.884 / 0.345
0.620 / 0.638 / 0.110
0.872 / 0.891 / 0.371
0.128 / 0.107 / 0.634
0.379 / 0.364 / 0.888
0.600 / 0.117 / 0.653
0.896 / 0.368 / 0.867
0.104 / 0.626 / 0.642
0.370 / 0.880 / 0.872
0.632 / 0.616 / 0.630
0.860 / 0.886 / 0.873
Fe (positive spin) / 17
18
19 / 0.502 / 0.998 / 0.003
0.994 / 0.500 / 0.010
0.007 / 0.994 / 0.498
Fe (negative spin) / 20
21
22
23 / 0.740 / 0.264 / 0.258
0.747 / 0.741 / 0.255
0.255 / 0.267 / 0.738
0.260 / 0.738 / 0.739
M (positive spin) / 24
25
26
27 / 0.996 / 0.003 / 1.000
0.496 / 0.505 / 0.997
0.999 / 0.498 / 0.502
0.501 / 0.998 / 0.500
M (negative spin) / 28
29
30
31 / 0.258 / 0.247 / 0.248
0.250 / 0.750 / 0.253
0.751 / 0.259 / 0.729
0.743 / 0.752 / 0.751
5 / O / 1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16 / 0.137 / 0.131 / 0.108
0.365 / 0.378 / 0.392
0.614 / 0.132 / 0.141
0.912 / 0.348 / 0.365
0.105 / 0.628 / 0.143
0.402 / 0.888 / 0.333
0.628 / 0.639 / 0.098
0.874 / 0.889 / 0.373
0.122 / 0.101 / 0.642
0.379 / 0.369 / 0.883
0.585 / 0.121 / 0.660
0.900 / 0.362 / 0.862
0.106 / 0.636 / 0.629
0.372 / 0.872 / 0.874
0.631 / 0.611 / 0.632
0.863 / 0.883 / 0.869
Fe (positive spin) / 17
18
19 / 0.504 / 0.019 / 0.980
0.498 / 0.997 / 0.506
0.498 / 0.499 / 0.005
Fe (negative spin) / 20
21
22
23 / 0.747 / 0.742 / 0.256
0.236 / 0.283 / 0.740
0.262 / 0.737 / 0.742
0.752 / 0.746 / 0.747
M (positive spin) / 24
25
26
27 / 0.041 / 0.976 / 0.491
0.994 / 0.998 / 0.007
0.998 / 0.493 / 0.505
0.978 / 0.503 / 0.021
M (negative spin) / 28
29
30
31 / 0.734 / 0.257 / 0.277
0.256 / 0.249 / 0.247
0.254 / 0.754 / 0.248
0.754 / 0.260 / 0.726
6 / O / 1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16 / 0.139 / 0.132 / 0.102
0.366 / 0.374 / 0.393
0.615 / 0.138 / 0.134
0.886 / 0.370 / 0.373
0.092 / 0.636 / 0.144
0.381 / 0.888 / 0.363
0.634 / 0.626 / 0.103
0.885 / 0.889 / 0.360
0.116 / 0.110 / 0.640
0.365 / 0.375 / 0.897
0.618 / 0.113 / 0.637
0.909 / 0.362 / 0.856
0.113 / 0.631 / 0.627
0.386 / 0.860 / 0.867
0.634 / 0.625 / 0.607
0.860 / 0.868 / 0.898
Fe (positive spin) / 17
18
19 / 0.500 / 0.999 / 0.500
0.501 / 0.499 / 0.000
0.000 / 0.500 / 0.500
Fe (negative spin) / 20
21
22
23 / 0.747 / 0.259 / 0.252
0.735 / 0.722 / 0.276
0.263 / 0.280 / 0.724
0.253 / 0.741 / 0.749
M (positive spin) / 24
25
26
27 / 0.500 / 0.002 / 0.998
0.001 / 1.000 / 0.499
0.001 / 0.999 / 0.000
1.000 / 0.500 / 0.000
M (negative spin) / 28
29
30
31 / 0.248 / 0.249 / 0.254
0.259 / 0.754 / 0.246
0.741 / 0.246 / 0.753
0.751 / 0.752 / 0.746
7 / O / 1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16 / 0.131 / 0.135 / 0.109
0.367 / 0.378 / 0.390
0.626 / 0.105 / 0.144
0.911 / 0.364 / 0.356
0.143 / 0.617 / 0.129
0.382 / 0.889 / 0.345
0.622 / 0.648 / 0.096
0.873 / 0.889 / 0.372
0.122 / 0.100 / 0.646
0.383 / 0.364 / 0.881
0.601 / 0.123 / 0.648
0.876 / 0.372 / 0.873
0.106 / 0.626 / 0.635
0.359 / 0.905 / 0.863
0.637 / 0.611 / 0.624
0.863 / 0.879 / 0.874
Fe (positive spin) / 17
18
19 / 0.499 / 0.010 / 0.995
0.499 / 0.995 / 0.504
0.505 / 0.499 / 0.000
Fe (negative spin) / 20
21
22
23 / 0.249 / 0.268 / 0.741
0.262 / 0.734 / 0.743
0.261 / 0.246 / 0.248
0.742 / 0.756 / 0.746
M (positive spin) / 24
25
26
27 / 0.012 / 0.991 / 0.499
0.996 / 0.995 / 0.008
0.002 / 0.492 / 0.501
0.990 / 0.504 / 0.007
M (negative spin) / 28
29
30
31 / 0.735 / 0.264 / 0.266
0.740 / 0.735 / 0.264
0.249 / 0.752 / 0.256
0.755 / 0.253 / 0.734
Table S2.Sample optimized lattice constants and angles of unit cells with an iron vacancy. These parameters are shown only for the Fe0.5Zn0.5O alloy as a representative case.
Cell number / Lattice constants (Å) / Lattice angles (o)1 / 10.607, 10.610, 10.657 / 33.67, 33.65, 33.60
2 / 10.575, 10.477, 10.587 / 33.79, 33.94, 33.66
3 / 10.591, 10.600, 10.624 / 33.73, 33.68, 33.61
4 / 10.576, 10.474, 10.598 / 33.79, 33.95, 33.67
5 / 10.632, 10.511, 10.585 / 33.73, 34.01, 33.59
6 / 10.581, 10.582, 10.635 / 33.71, 33.67, 33.51
7 / 10.603, 10.545, 10.588 / 33.61, 33.80, 33.59
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