Matematisk-fysiske Meddelelser
udgivet a f
Det Kongelige Danske Videnskabernes Selska b
Bind 35, nr. 5
Mat . Fys . Medd . Dan . Vid . Selsk . 35, no . 5 (1966 )
1.
THE STRUCTUR E
OF WHITE CESIUM LEAD(II )
BROMIDE, CsPbBr3
BY
ASTRID MARSTRANDER AN D
CHRISTIAN KNAKKERGÅRD MØLLE R
København 196 6
Kommissionær : Munksgaard
Synopsi s
Crystals of the white modification of CsPbBr 3 -contaminated with orang e
crystals of the same composition-can be obtained from aqueous solutions o f
CsBr and PhBr 2 . The white crystals appear to be only slightly less stable than th e
orange ones . They are needle-shaped with y' parallel with the needle axis an d
they undergo a phase transition to the orange modification at 130°G . The X-ray
analysis shows that the white crystals are orthorhombic belonging to space grou p
no . 62 Pmnb, and a = 4 .597 A, b = 9 .72 Å, c = 16 .81 A . The structure is quit e
analogous to that of the yellow CsPbI3 . Distorted PbBra-octahedra sharin g
Br-atoms form chain-like, polynuclear ions (PbBrDn running parallel with the a axis . The Pb-Br-distances vary from 2 .82 A to 3 .29 Å .
PRINTED IN DENMAR K
BIANCO LUNGS BOGTRYKKERI AIS
Introduction
It has been shown previously that CsPbI 3 exists in two modifications, a
black metastable form with perovskite structure and a yellow orthorhombi c
form which is stable under ordinary conditions' . CsPbBr 3 apparently als o
exists in two forms, an orange-coloured form with perovskite structure, whic h
already has been investigated 2 , and the supposed analogue of the yellow
orthorhombic CsPbI 3 , which has been prepared by WELLS and co-workers 3 .
Although a fairly complete X-ray analysis has been done on the orthorhombic CsPb I 3 , it seemed worth while to make an independent investigatio n
of the white CsPbBr3 in order to check the irregular octahedral coordinatio n
of the halogen atoms around the lead atoms which was found in the forme r
compound . Also, in the previous investigation no distinction could be mad e
between the halogen atoms and the cesium atoms because of their equa l
scattering powers . And finally, it might be interesting to see if the atomi c
parameters would be the same as in CsPbI 3 in spite of differences in ab sorption and dispersion effects .
Preparation and properties of the white CsPbBr 3 -crystal s
We have obtained the white modification of CsPbB r3 in the following way .
First CsBr was prepared from Cs2 CO 3 and an aqueous solution of HBr .
PbBr2 was precipitated from aqueous solutions of Pb(NO 3 ) 2 and HBr ,
recrystallized a few times in hot water . All the chemicals were Riedel de Haën pro analysi .
Aqueous solutions with well-defined concentrations of CsBr were nex t
prepared and saturated with PbBr2 by boiling . Undissolved PbBr2 wa s
separated from the still hot solutions . On addition of an amount of hot o r
cold water to each solution so that the CsBr-concentrations as well as th e
i
C . K . MOLLER, The Structure of CsPbI 3 . Mat. Fys . Medd . Dan . Yid . Selsk . 32 No . 1 (1959) .
3 C . K . MØLLER, The Structure of Perovskite-like Cæsium Plumbo Trihalides . Mat . Fys .
Medd . Dan . Vid . Selsk . 32 No . 2 (1959) .
FI . L . WELLS, Z . anorg. Chem . 3, 195 (1893) .
1*
4
Nr . 5
temperatures were kept within a certain range a precipitation of crystal s
usually resulted .
White needle-shaped crystals were obtained when the final concentratio n
of CsBr was in the range 23 .5-27 .5 g CsBr/100 g H2 O, and the temperatur e
at which they appeared was usually 23-25°C ; but they were always contaminated with orange crystals, and sometimes also with thin flaky crystal s
(of CsPb 2 Br 5 ?), the latter ones, however, disappearing after some time .
To avoid the formation of basic salts the solutions were mostly kept aci d
with pH - 1-3 . Higher pH-values seemed to change the conditions for precipitation of the white crystals of CsPbBr 3 in the direction of higher CsBrconcentrations . Supersaturated solutions easily resulted so that seeding ofte n
was necessary .
Sometimes very thin needles of white crystals å - I. cm long were obtained .
Apparently they grew very quickly under special conditions .
Only by hand-sorting under a microscope was it possible to obtain a
pure product of white crystals-free from orange-coloured contaminations .
Under the polarizing microscope these crystals showed extinction parallel
with and perpendicular to the needle-axis . When heated under the micro scope on a hot stage the white crystals changed irreversibly into the orang e
modification at 130°C-this temperature being about 10°C lower than tha t
mentioned by WELLS' .
The X-ray work to be mentioned shows that the crystals have the stoichiometric. composition CsPbBr3 as found by WELLS et al l .
Stability of the white CsPbBr 3 -crystal s
From the observation that the white needle-shaped crystals and th e
orange crystals could co-exist at room temperature (18-20°C) for month s
in aqueous solutions of CsBr with concentrations as mentioned above, it
would appear that there can be only a small difference in free energy betwee n
the two forms . The white crystals eventually slowly disappeared and onl y
orange-coloured crystals were left . With crystals of the same compositio n
the CsBr-concentration of the solution would not be expected to influenc e
the relative stability of the two forms, and hence it is concluded that th e
orange crystals are slightly more stable than the white ones . When dry, th e
white crystals can be kept at room temperature indefinitely .
An attempt was made to measure the difference in free energy betwee n
the two modifications . Electrochemical cells of the following type wer e
constructed :
\T r . 5
5
Pt I Pb(Hg) I CsPbBr3 (orange) I solution 27g CsBr/100g H 2 O I CsPbBr 3(white )
Pb(Hg) I Pt .
They were kept at temperatures 19 .5°C or 22 .5°C . However, it wa s
difficult to obtain reliable values for the emf .'s of the cells . Shortly afte r
assemblage the cell had an emf. of 2-3 mv, but then drifted slowly toward s
lower values . Only on one occasion did the emf. stay within the interval 2 .53 .0 mv the first 24 hours after construction of the cell .
The electrode with the white CsPbB r 3 -crystals was the positive electrode ,
suggesting the electrode processes :
2 e- + CsPbBr3 (white) - Cs + + 3 Br- + P b
Cs + + 3 Br- + Pb -> CsPbBr3 (orange) + 2 e Hence the white crystals are less stable than the orange ones . If a valu e
of c . 3 mv for the emf . is accepted as being significant, the corresponding
difference in free energy is J G = 3 . 10 - 3 . 9600 0 . 2 -600 Joule or 140 cal/mole ,
which is quite small .
X-ray investigation
Oscillation and Weissenberg diagrams of single crystals of the whit e
CsPbBr 3-compound showed that they had orthorhombic symmetry, an d
preliminary values for the crystal axes were determined from these photo graphs . Refined values were obtained from powder photographs in a Guinie r
type focusing camera as previously described 1 , and Table 1 shows a comparison of the observed sin 2 0-values with those calculated from the finall y
accepted unit cell axes :
a - 4 .597±- 0 .005Å, b = 9 .721O .01Å, c = 16 .81l0 .02Å .
From the similarity of the powder patterns of the yellow CsPbI 3 and of the
white CsPbB r3 it is concluded that the two compounds are isomorphous wit h
the same number of molecules in the unit cell, i . e . 4 . On this basis and with
the . unit cell axes given above the molar volume for white CsPbB r3 is 113 .7 cc .
This may be compared with the molar volume 120 .5 cc for the orange
modification and a value of 103 .0 calculated from the molar volumes o f
CsBr and PhBr2 . We thus find the same trend as for the analogous iodides 4 .
4
G . K . MOLLER, The Structure of Cæsium Hexahalogeno-Plumbates(II) . Mat. Fys . Medd .
Dan . Vid . Selsk . 32 No. 3, p . 6 (1960) .
6
Nr . 5
TABLE 1 . Observed and calculated sin 2 O-values for white CsPbBr 3 ,
CuKa-radiation .
Estimate d
intensity
Indices
011
002
012
020
013
f
J}
031
122
0252
l
~
m-w
0401
0426
w
0441
m
-w,
m
w
s
008 4
l
008 4
014 7
J
0252
1
0555
055 4
058 9
0589
058 8
0616
058 8
0617
10 4 x
sin'O eUs
104 x
sin-Øoal c
032
123
vw
vw
0653
0721
105
in
vw
0809
065 1
072 2
080 7
0820
082 0
087 0
vw
0869
086 9
086 9
w
m-w
0932
093 2
112 5
131
132
039 9
042 8
044 1
053 3
Estimate d
intensity
124
0365
0532
Indices
016
115
0252
0273
0272
0364
s
m
023
015
024
0148
w
104 x
sinz0 calc
(
S
0083
m-w
014
112
121
m -w
w
1
021
111
120
113
104 x
sin 2 0eus
200
134
w
vw
212
1125
1187
1270
118 4
127 2
126
117
w
1294
129 0
213
220
s
1377
137 5
137 7
vw
1716
224
215
~
TABLE 2 . Atomic parameters in white CsPbBr3 .
All the atoms are in the special positions :
1
3
3 1
4 yz'
4 yz'
42
1
y2-+z,
11
42
1
+y 2
and for
Cs
x
1
4
y = 0 .089
z = 0 .329
y = 0 .163
_=0 .06 3
3
Pb
4
Br
x
1
4
y = 0.335
z = 0 .00 0
Br "
3
x= 4
y=0 .028
z=0 .11 6
Br,,
x_
y=0 .302
z=0 .21 1
3
4
137 7
171 3
171 4
Nr . 5
7
C_
2
Pb-P b
b
2
o
1 A
Pb-P b
Fig . 1 . Patterson projection of the white CsPhBr 3 on (100) . Contours are drawn at the relativ e
densities 0 (dashed), 25, 50, 75, 100, 150 and 200 .
In order to see if there should be any relation between lattice planes i n
the orange and the white modifications of CsPbBr 3 , oscillation diagrams
were taken of a single crystal of white CsPbBr 3 . Then the crystal was heate d
in a controlled flow of hot N 2 -gas and thus partly converted to the orang e
modification while another oscillation diagram was taken . The latter show s
a powder pattern superimposed on an oscillation diagram of while CsPbBr 3 ,
but apparently there is no simple connection between "old" and "new "
X-ray reflections, and it appears that the crystal is converted into a disordere d
powder of orange CsPbBr 3 within the boundary of the original crystal .
With CuK,,-radiation intensities were obtained from Weissenberg expo sures by a multiple film technique as previously described r . The crystal wa s
rotated about the a-axis-which is also the needle axis . Its length was 0 .42 m m
and the cross section of the crystal 0 .035 x 0 .010 mm 2 .
Reflections of the type hOI were absent for h +1 odd and hkO were absen t
for k odd . No other systematic absences were observed, but I(Okl) an d
I(2k1) appeared to be equal for all values of k and 1 . As these rules are exactl y
the same as for yellow CsPbI 3i it is inferred that the space group is also the
the same, no . 62 Pmnb .
The procedure and the arguments for determining the atomic arrangemen t
from the observed intensities were from now exactly the same as described
8
Nr . 5
Fig . 2 . Electron projection of the white CsPbBr 3 on (100) . Contours are drawn at the relativ e
densities 0 (dashed), 100, 200, 300, 400, 600 and 800 .
for CsPbI3 1 and no detailed account of it will be given . Suffice it to say tha t
the structure of white CsPbBr3 was solved independently of that of th e
analogous iodide and hence both Patterson and electron projections as wel l
as difference maps were evaluated (figs . 1 and 2) . The Fourier synthese s
and the structure factors were calculated on a GIER electronic compute r
using programmes which had originally been worked out by J . DANIELSEN 5 ,
and atomic scattering factors from FORSYTH and WELLS' paper s .
5
J . DANIELSEN, Acta Cryst . 16 Suppl . A 171 (1963) .
s J . B . FOESYTx and M . NELLS, Acta Cryst . 12, 412 (1959) .
Nrr .. 5
9
3 . Comparison of calculated and observed structure factor s
for white CsPbBr3 (brought on the same relative scale) .
TABLE
hkl
Fobs ~
Fcalc
0 02
105
0 0 4
27
+
-
0 0 6
0 08
41
144
0 010
0 012
0 014
22
45
0 016
0 018
~
I F obs
F c.alc
hk
I
Fobs
F cal c
0 2 15
0 2 19
46
+
47
0 5 1
79
+ 83
10
65
-
+ 31
- 129
0 2 20
0 2 21
23
10
76
32
139
74
12
0 5 2
0 5 3
0 5 4
+ 16 4
- 74
+ 10 2
+
10
0 3 1
22
+ 46
+ 65
0 3 2
0 3 3
121
84
19
+ 147
- 79
0 5 5
0 5 6
0 5 7
77
58
85
99
+ 102
0 3 4
128
130
122
67
16
-
133
149
0 5 9
0 5 10
0 020
0 3 5
0 3 7
- 137
- 138
+ 166
0 5 11
31
0 11
0 1 2
0 1 3
49
85
+
-
65
+ 27
96
225
0 5 15
0 14
0 1 5
0 16
166
201
+
- 155
31
199
0 5 12
0 5 14
0 3 10
40
0 3 11
0 1 7
0 1 8
118
108
94
0 3 12
0 3 13
70
40
- 36
+ 62
170
- 227
- 164
+ 92
0 3 15
0 19
25
+
0 3 16
0 1 10
0 1 11
24
94
+
-
21
17
0 1 12
0 1 13
0 1 14
115
0 1 15
0 116
57
51
-I-
0 1 17
0 1 20
0 20
14
43
59
+
-
0 2 1
0 22
0 23
79
42
79
87
63
130
0 2 4
0 25
0 26
138
72
0 27
0 28
149
93
63
0 29
0 2 10
73
12
0 2 11
0 2 14
162
104
+
-
85
hkl
23
54
85
77
94
+ 119
- 40
+
0 3 8
0 3 9
0 3 17
0 3 19
-
-I-
+
38
0 5 17
0 5 18
0 6 0
4.3
-
39
0 6 1
42
41
-
39
48
0 6 2
0 6 4
28
-
25
0 6 6
18
21
72
0 6 13
58
17
0 4 3
161
47
+ 204
- 42
0 6 14
130
+ 133
52
68
42
67
- 59
- 104
-
0 4 8
66
- 155
- 156
0 4 10
115
67
56
-
+ 108
+ 55
75
+
76
+
51
117
97
+ 13 3
+ 93
137
+ 16 5
+ 60
68
120
41
84
0 7 1
33
82
0 7 2
0 7 3
75
82
122
- 11 8
- 21
+ 36
- 35
-
25
+ 11 4
+ 83
+ 30
+ 83
- 77
- 77
-
53
0 7 6
0 7 7
90
76
-
90
0 7 9
89
77
-
0 7 10
0 7 12
96
71 .
+
39
78
34
47
50
-
42
44
0 7 17
30
0 8 0
0 8 1
92
35
0 8 3
0 8 4
48
33
30
- 87
+ 25
- 45
54
0 4 11
0 4 12
+ 54
- 148
0 4 13
0 4 14
+ 76
+ 58
+
1
+ 181
0 4 15
0 4 16
0 4 17
0 4 18
42
33
+
-
51
37
- 117
0 4 19
23
+
26
-
0 6 16
0 6 18
58
48
26
104
54
77
- 128
- 66
+ 26
50
40
-
1.14
69
-
35
33
0 4 1
0 4 2
-
+ 50
+ 13
53
39
0 6 9
0 6 11
0 6 12
77
62
0 4 4
0 4 5
0 4 6
0 4 7
12
29
+ 31
- 128
- 57
+
0 3 20
0 4 0
51
108
- 11 5
- 82
- 76
+
+
-
95
63
29
10
Nr . ~
TABLE 3
h Ic 1
F
obs !
Fcalo
hkI
- 141
(continued)
1 Fobs 1
1 38
139
28
90
-
-33
+ 122
1 3 10
1 3 11
91
- 230
1 3 12
1 3 14
61
73
+ 94
+ 61
+ 80
68
50
+
-
70
60
38
+
38
55
77
+
-
74
88
F catc
1 1 2
77
+
11 3
11 5
153
43
1.33
213
085
087
131
24
0 88
0 89
0 8 11
43
7
+ 37
39
57
+ 34
+ 43
0 8 13
0 8 14
98
33
+
-
97
35
1 1 6
1 1 7
11 8
1 1 9-
0 8 15
09 1
24
-
28
1 1 10
- 53
+ 22
-
63
64
44
97
+
44
76
31
-
095
097
1 1 11
1 1 12
1 1 14
77
093
63
20
+ 92
- 65
1 . 1 15
1 1 16
38
19
+
90
82
1 1 17
1 1 18
40
0 98
099
0 9 10
0 9 14
010 1
010 2
010 3
010 6
010 10
011 1
011 2
011 3
011 4
011 5
011 7
011 10
012 0
012 2
64
93
80
32
-I-
31
1 1 19
59
96
+ 60
- 90
1 1 20
1 1 21
74
57
+ 66
+ 48
120
1 21
20
+ 19
- 21
+ 46
1 22
+ 47
1 25
35
.25
+
-
79
39
1 26
127
25
-
27
25
67
43
+
1 29
1 2 10
1 2 13
23
58
52
80
1 0 1
21
1 03
10 5
1 07
103
291
46
10 9
1 0 11
99
76
1 0 13
1 0 15
1 0 17
1 0 21
171
1 1 1
-I-
74
45
-
18
+ 67
+ 332
+
-
24
89
+
123
1 2 4
123
160
164
41
26
76
-144
+ 105
-160
- 183
+ 30
+ 39
- 27
+ 38
1 3 15
1 3 16
1 3 17
1 3 18
1 3 20
Peale
21
94
1 4 0
44
133
- 58
- 17 6
14 2
14 3
130
129
- 15 4
- 14 6
- 23
+
44
18
144
14 5
33
1.03
+
19
14 6
58
80
+ 106
- 204
14 7
1 48
74
114
1 4 10
92
91
+ 304
- 91
1 4 12
1 4 13
118
77
63
31
+
-
56
20
1 4 14
1 4 15
35
- 14 6
+ 80
- 31
- 155
1 4 16
30
79
+ 30
- 92
-
23
52
1 4 17
1 4 18
34
53
-
1 4 19
1 5 1
21 .
34
-
65
25
26
1 52
100
-
99
1 53
1 5 4
57
150
16
41
87
132
200
158
31
59
41
+
-
+
-
52
30
+ 46
1 2 14
1 2 15
97
31
+ 117
+ 33
1 2 16
1 2 18
102
+ 125
27
54
+ 29
- 71
26
80
1 2 19
1 2 20
1 31
1
h RI
obs
~ F
- 10 3
- 52
-I- 6 7
+ 12 5
+ 90
35
155
77
- 55
+ 17 8
+ 81
+ 40
1 57
159
152
128
+ 17 9
+ 13 9
132
141
+ 86
- 175
1 5 11
1 5 12
76
66
+ 77
- 68
65
133
1 3 4
105
176
- 111
- 222
1 5 13
1 5 14
38
36
-
135
1 36
18
14
-
2
1 5 15
64
-
29
60
43
+ 58
+ 73
1 37
66
+
1 5 16
1 6 1
32
111
42
+ 154
7
64
+
98
55
55
69
- 210
30
+ 131
Nr . ~
11
TABLE 3 (continued )
hk1
F obs
Fmk;
hk1
62
27
79
+ 21
+ 80
1
1 63
1 6 4
1 65
80
-
1
1
1
67
68
1 69
1. 6 11
1
74
123
1 6 14
1 7 1
i 7
1
1
1.
1
1
1
1
1
4
57
+
90
1
1
1
1
77
78
121
61
- 132
- 58
8
12
13
14
9 2
9 3
9 4
9 5
19 6
86
-
67
-
90
73
1 9 9
1 9 10
33
-
30
1
44
-
49
19
TABLE 4 .
Pb'-Br 4
Pb l-Br 2
Pb l-Br'
Ph i-BO
Pb l-Pb 2
Ph-Cs
Cs 4-Br°
Cs 4 -Bra
Cs i -Br s
Cs I -Br'
Cs i -Br 4
Cs 4 -Br'
Br l -Br l
Br l -Br 2
Br l -Br 3
Br 4 -Br'
8 5
8 8
62
94
- 133
+ 79
Distance
60
18
1 8
76
85
7
7
8 2
62
62
-
- 109
11
12
13
14
8 0
8 1
46
10
208
43
29
48
103
7
59
-
+
75
76
7
15
7
36
66
119
+ 66
+ 132
~obs
1 7 16
1 7 17
1
1
1
1
1
1
54
72
6 13
75
I
9
11
12
72
35
l
It k l
Foalc
+
64
+ 53
6
+
+ 258
-
35
53
+
-
50
-
68
39
48
+
+
29
49
+ 28
- 50
62
98
+ 62
95
98
-
101
59
38
-
58
35
33
-I- 34
24
66
-
53
+
33
68
+
19
1
9
I
13
14
1
1 1.0
1 10 2
1 10 3
1 10 4
1 10 6
1 10 7
1 10 8
1 10 9
1 10 10
1 10 11
1 11 2
1 11 3
1 11 5
1 11 7
1 11 8
1 11 9
1 12 0
1 12 3
F obs l
~ c alc
21
- 24
38
+ 44
24
- 24
80
63
-
62
-
37
52
+ 38
- 51
38
23
+
27
+
19
74
+
+
82
41
+
44
56
+ 61
+ 33
56
61
60
38
-I- 1 4
30
29
69
81
55
23
+
-
10 7
37
56
+
74
30
Interatomic distances in white CsPbBr3 .
From this
investigation
3 .04 Å
From
Pauling' s
radii
ionic
3 .16 Å
From Goldschmidt' s
radii
3 .28 Å
3 .29 3 .08 2 .82 -
4 .46 5 .08 3 .76 3 .79 3 .75 -
3 .84 3 .67 3 .67 4 .60 4 .24 4 .03 -
4 .24 -
3 .64 -
3 .63 -
12
Nr . 5
Structure factors which have been calculated from the atomic parameter s
in Table 2 are compared with the observed values in Table 3 after they hav e
been brought on the same relative scale . Interatomic distances obtained wit h
these parameters are given in Table 4 .
Conclusion
The structure of the white CsPbBr3 as determined from the present wor k
is in complete analogy with that of the yellow CsPbI 3 and exhibits the sam e
kind of irregular octahedral coordination of the halogen atoms around th e
lead atoms . In both structures catena-ions (PbX3)n are parallel to the a-axi s
and the Cs-ions are held between these chain-like ions . One of the leadhalogen distances is considerably shorter than the others and also shorte r
than the sum of the corresponding ionic radii or Slater atomic radii :
2 .82Å against 3 .16Å or 2 .95Å, respectively . This might indicate a stronge r
bonding between lead and this particular halogen atom .
The variations of the interatomic distances in the two analogous crystal s
are also quite similar although the dispersion effects have not been considere d
in case of the bromide . One might, therefore, be tempted to conclude tha t
if an uncertainty of O .05Å on the interatomic distances can be tolerated ,
the influence of dispersion may be neglected .
Acknowledgement s
One of us (A .M .) is much indebted to the Carlsberg Foundation for
financial support during this investigation . We are very grateful to cand . mag .
E . BANG and cand . mag . B . SVEJGÅRD, lecturer in mathematics at the University of Copenhagen, for their continual help and guidance in computational matters in connection with this work .
J . C . SLATER, J.
Chem . Phys . 41, 3199 (1964) .
Chemistry Department I, Inorganic Chemistry ,
The H. C . Ørsted Institute ,
University of Copenhagen, Denmark