Orientation of organic cations in hybrid inorganic-organic perovskite CH3NH3PbI3 from subatomic resolution single crystal neutron diffraction structural studies

Article abstract of DOI:10.1021/acs.cgd.6b00297

We report the crystal growth of well-faceted single crystals of methylammonium lead iodide, CH₃NH₃PbI₃, and detailed single crystal neutron diffraction structural studies aimed at elucidating the orientation of the methylammonium (CH₃NH₃⁺) cation in the tetragonal and cubic phases of the hybrid inorganic-organic perovskite. Room temperature experiments reveal a tetragonal structure where the protonated amine substituent (-NH₃⁺) of the cation is disordered in four positions, each preferentially located near the neighboring iodine of the [PbI₆] octahedra, while the methyl substituent (-CH₃) is disordered in eight positions located near the body position of the unit cell. High temperature experiments show a cubic structure where the cation aligns along the [011] (edge), the [111] (diagonal), and the [100] (face) directions of the unit cell. The resulting site occupancy ratio suggests the CH₃NH₃⁺ cation resides primarily along the [011] direction, in agreement with reported DFT calculations. One important feature that was observed for both tetragonal and cubic structures measured at 295 and 350 K, respectively, is the middle point of the C-N bond being located off-center from the high symmetry sites in the crystal structure, induced by the formation of hydrogen bond-like interactions between the -NH₃⁺ substituent of the organic cation and the iodine atoms of [PbI₆] octahedra.

Full text of DOI:10.1021/acs.cgd.6b00297

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Article
Orientation of Organic Cations in Hybrid Inorganic-Organic
Perovskite CH3NH3PbI3 from Sub-atomic Resolution
Single Crystal Neutron Diffraction Structural Studies
Yixin Ren, Iain W.H. Oswald, Xiaoping Wang, Gregory T. McCandless, and Julia Y Chan
Cryst. Growth Des., Just Accepted Manuscript • DOI: 10.1021/acs.cgd.6b00297 • Publication Date (Web): 30 Mar 2016
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Orientation of Organic Cations in Hybrid InorganicꢀOrganic Perovskite CH3NH3PbI3 from
Subꢀatomic Resolution Single Crystal Neutron Diffraction Structural Studies
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Yixin Ren,† Iain W. H. Oswald,† Xiaoping Wang,‡,* Gregory T. McCandless,† Julia Y. Chan†,*
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†Department of Chemistry and Biochemistry, The University of Texas at Dallas, Richardson,
Texas 75080, United States
‡Chemical and Engineering Materials Division, Neutron Sciences Directorate, Oak Ridge
National Laboratory, Tennessee 39831, United States
Abstract
We report the crystal growth of wellꢀfaceted single crystals of methylammonium lead
iodide, CH3NH3PbI3, and detailed single crystal neutron diffraction structural studies aimed at
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elucidating the orientation of the methylammonium (CH3NH3 ) cation in the tetragonal and cubic
phases of the hybrid inorganicꢀorganic perovskite. Room temperature experiments reveal a
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tetragonal structure where the protonated amine substituent (–NH3 ) of the cation is disordered in
four positions, each preferentially located near the neighboring iodine of the [PbI6] octahedra,
while the methyl substituent (–CH3) is disordered in eight positions located near the body
position of the unit cell. High temperature experiments show a cubic structure where the cation
aligns along the [011] (edge), the [111] (diagonal), and the [100] (face) directions of the unit cell.
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The resulting site occupancy ratio suggests the CH3NH3 cation resides primarily along the [011]
direction, in agreement with reported DFT calculations. One important feature that was observed
for both tetragonal and cubic structures measured at 295 K and 350 K, respectively, is the middle
point of the C–N bond being located offꢀcenter from the high symmetry sites in the crystal
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structure, induced by the formation of hydrogen bondꢀlike interactions between the –NH3
substituent of the organic cation and the iodine atoms of [PbI6] octahedra.
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Introduction
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The hybrid inorganicꢀorganic CH3NH3PbI3 perovskite is a promising material for
photovoltaics, with conversion efficiencies exceeding 20%.1ꢀ3 The positioning, orientation and
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rotational dynamics4,5 of CH3NH3 cations have a direct impact on the electronic properties of
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the material and, therefore, a strong influence on photovoltaic performance.2,3 Theoretical studies
based on density functional theory (DFT) calculations have suggested that molecular rotations
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and orientation of the CH3NH3 cation can lead to a dynamic change of the band structure,
possibly explaining the slow carrier recombination and the superior solar energy conversion
efficiency of CH3NH3PbI3.6,7 For instance, in the cubic phase, calculations show when CH3NH3
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cations orient along the [011] direction, an indirect band gap is present with an energy of 1.629
eV, while ordering along the [111] direction results in a direct gap of 1.611 eV.6,8 Thus,
determining the exact location of C, N, and H atoms in CH3NH3PbI3 single crystals will allow
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one to resolve the details of the orientation of CH3NH3 cation in the crystal structure.
In previous structural studies using Xꢀray diffraction techniques, the best space group to
model the structure has proven controversial for the tetragonal phase, adopted between 165 K
and 330 K. Numerous structures have been reported using various space groups including I4cm,9
I4/m,1 and I4/mcm.4,10 Some reported models omit the CH3NH3 cation altogether, highlighting
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the difficulty in accurately modeling the structure of this material. The controversial results
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surrounding the orientation of the CH3NH3 cation calls for accurate and inꢀdepth structural
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studies of the CH3NH3 cation in single crystalline CH3NH3PbI3. In this work, we report the high
resolution structures of CH3NH3PbI3 measured at 295 K and 350 K using the TOPAZ single
crystal neutron diffractometer at the ORNL Spallation Neutron Source. Neutron diffraction is an
excellent technique for investigating materials with similar atomic numbers such as carbon and
nitrogen; additionally, hydrogen atoms can be identified definitively due to their negative
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scattering length. The TOPAZ instrument uses the neutron wavelengthꢀresolved Laue technique
for threeꢀdimensional reciprocal space mapping, capable of measuring a structure at subꢀatomic
resolution. Our results reported herein based on data collected at 295 K (dmin = 0.59 Å) reveal
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that the protonated amine substituent of the CH3NH3 cation is disordered in four positions,
while the methyl substituent is disordered in eight positions. Additionally, our results confirm a
recent report using neutron powder diffraction that the best space group to model the tetragonal
room temperature structure is I4/mcm.11 Experiments on the high temperature cubic phase
collected at 350 K (dmin = 0.58 Å) reveal that there still remains an orientational preference for
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the CH3NH3 cation, primarily aligned along the [011] direction.
An important feature revealed by our experiments for both tetragonal and cubic structures
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is the location of CH3NH3 cations being slightly off the bodyꢀcenter position, which is different
from what has been reported in powder neutron diffraction data.11 We believe the driving force
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for the CH3NH3 cation to move away from the ideal Aꢀsite is due to the formation of hydrogen
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bonds between the protonated amine (–NH3 ) of the organic cation and the iodine atom of [PbI6]
octahedra. This concept can be supported with static DFT calculations by the analysis of
structural parameters such as the NH3 ꢁꢁꢁI interatomic distances.12
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Experimental Section
Synthesis.
Small crystals (< 1mm3) of CH3NH3PbI3 were prepared by following a similar method
described by Poglitsch and Weber with a few modifications.4 The following reagents: lead(II)
acetate trihydrate (Pb(CH3COOH)2ꢁ3H2O, 99%), hydriodic acid (HI, 57% w/w aq. soln.,
stabilized with 1.5% hypophosphorous acid), and methylamine (CH3NH2, 40% w/w aq. soln.)
were used as received without further purification. Pb(CH3COOH)2ꢁ3H2O (9.7664 g, 0.02574
mol) was dissolved in 30.0 mL HI in a 50 mL round bottom flask. The reaction mixture was
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stirred for 15 min at 100 °C until all the solid was dissolved in the solution. To this solution, a
mixture of 7.0 mL of HI and 2.5 mL (0.06407 mol) of CH3NH2 was added. The temperature was
decreased to 75 °C to induce the saturation of the solute and allow the formation of small
CH3NH3PbI3 single crystals. Small, black, shiny crystals of CH3NH3PbI3 were successfully
grown in the bottom of the flask after one day.
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For large CH3NH3PbI3 single crystal growth, we have found a simplified synthetic
method produces large crystals up to 5 mm in size synchronously in high synthetic yield (shown
in Figure 1). A 15 mL aliquot of the mixed hot solution was transferred to a 20 mL vial, where
the temperature of the solution was allowed to cool to 25 °C, and after 3ꢀ4 days multiple shiny
single crystals with average dimensions of 3 x 4 x 4 mm3 were grown. The reaction scheme is
shown in Figure 2.
5 mm
Figure 1. As grown wellꢀfaceted single crystals from a supersaturated solution at room temperature.
Figure 2. Schematic diagram of the crystallization process. PbAc = lead(II) acetate trihydrate,
MA = methylamine.
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Single Crystal Neutron Diffraction
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Single crystal neutron diffraction was used to study the orientation and disorder of the
methylammonium cation located between [PbI6] octahedra in CH3NH3PbI3 at the Spallation
Neutron Source (SNS).13 A single crystal with dimensions of 1.5 x 1.8 x 2.1 mm3 was mounted
onto a MiTeGen pin with superglue and positioned onto the goniometer. High resolution singleꢀ
crystal neutron diffraction experiments were performed using the TOPAZ neutron timeꢀofꢀflight
single crystal Laue diffractometer. Data collections were conducted at 295 K and 350 K for the
same single crystal sample using neutrons with wavelengths in the range of 0.4 to 3.3 Å. Sample
orientations were optimized with CRYSTALPLAN.14 Data were collected with 21 detectors and
used 12 and 5 crystal orientations, respectively to ensure a good (> 98%) coverage and
redundancy for each data collection, with collection times of approximately 2 h per sample
orientation. The integrated raw Bragg intensities were obtained using the 3ꢀD ellipsoidal Qꢀspace
integration method.15 Data reduction including Lorentz, absorption, timeꢀofꢀflight spectrum and
detector efficiency corrections were carried with ANVRED3 program.16 The reduced data were
merged and saved in SHELX HKLF 2 format. Initial models were based on the single crystal Xꢀ
ray diffraction refinement results, and the neutron modes were refined using SHELX2014.17,18
Hydrogen atoms on methlyammonium were placed with the riding constraint HFIX 137 that
allows for free rotation of the –CH3 / ꢀNH3 groups along the C─N bond, but keeps the C─H/N─
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H bond distances and “idealized” tetrahedral angles fixed at default values. HFIX 137 instruction
itself will not produce error estimates. Standard deviations of hydrogen bonding distances were
estimated from an unconstrained refinement by combining HTAB with L.S. 1 DAMP 0 0 and
MORE 3 instructions.18,19 VESTA was used for 3D visualization of the difference Fourier maps
to allow identification of structural disorder and regions of excess nuclear density.19
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Tetragonal phase at 295 K structural refinement.
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The structural model was initially refined with the Pb and I atom positions derived from
our preliminary single crystal Xꢀray diffraction data. Initial refinements included the atomic
positions and atomic displacement parameters (ADPs) for Pb and I. Due to the disorder observed
at the position of C and N atoms, the SUMP command was applied, which restrains the atomic
positions of the disorder sites. Additionally, a soft restraint (DFIX command) of the C─N bond
length was applied to ensure the C─N bond is within the sum of their atomic radii. The
tetragonal crystal forms twin domains, related by a 2ꢀfold rotation about (1 ꢀ1 ꢀ2) reciprocal
lattice direction of the tetragonal cell. The 2ꢀfold symmetry corresponds to the (0 ꢀ1 ꢀ1)
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ꢀ
reciprocal lattice direction of the aristotype Pm3m cubic cell. Since the point group symmetry of
the twin lattice differs from that of the tetragonal cell, the twin law can be classified as reticular
pseudoꢀmerohedric twin, with obliquity angle of 0.31° degrees calculated using the TwinRotMat
program in Platon.20 The corresponding TWIN command with the matrix transformation (ꢀ0.497
ꢀ0.503 ꢀ0.497, ꢀ0.503 ꢀ0.497 0.497, ꢀ1.005 1.005 ꢀ0.005) was applied in refinement of the
neutron structure. The corresponding BASF parameter was refined to 0.20, indicating a second
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domain of 20% overall. The disordered CH3NH3 cation was assigned to a negative part number
(part ꢀ1) to prevent bonds to symmetry generated atoms. In SHELX refinement, if the part
number n is negative, special position constraints will be suppressed and all atoms are treated as
if they were in general positions which [symmetry order] parameter = 1. Furthermore, the
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CH3NH3 cation resides near the 4b site with a D2d symmetry [order 32/4 = 8]. The site
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symmetry is higher than that of the C3v symmetry of methylammonium (CH3NH3 ), resulting in
the disorder of the cation in four locations. The N1 atom located at the 16l Wyckoff site is
supposed to have an order of 2 (32/16), but it was set to 1 in the crystallographic information file
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(CIF), with the same being done for C atom C2 at 32m site. Therefore, the occupancies of C, N
and H atoms in the crystal structure were fixed to 0.125 to match the unit cell contents of Pb
atoms located at the 4c site with a symmetry order 8, consisting with the formula CH3NH3Pb1I3
with Z =4. Final cycles of the I4/mcm refinement statistics indicate a good fit to the observed
data (R1 = 6.0%, wR2 = 15.0%, GOF = 1.04). The structural refinement data and atomic
coordinates with ADPs are summarized in Table 1 and 2. The selected bond lengths and angles
of the final structural refinement are summarized in Table 3.
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Cubic phase at 350 K structural refinement. The highest temperature phase T > 327 K
was confirmed to be cubic, consistent with previous reports. The refinement of the cubic
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structure used the model in space group Pm3m with Pb and I atoms located at (0,0,0) and
(0,0,1/2), as that previously described from powder Xꢀray diffraction data.1 The site occupancies
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of the disordered CH3NH3 moieties were refined using a model with the cation aligned along
the [111], [100], and the [011] directions of the unit cell. Final cycles of refinement converged to
R1 = 4.9%, wR2 = 7.5%, GOF = 1.28, with the resulting site occupancy ratio 0.143:0.187:0.670,
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indicating that the CH3NH3 cation resides primarily along the [011] direction. Full
crystallographic details regarding the structural refinement are shown in Table 1. The atomic
coordinates with anisotropic displacement parameters and selected bond lengths are summarized
in Table 4 and 5.
CCDC 1470054ꢀ1470055 contain the supplementary crystallographic data for
CH3NH3PbI3 measured at 295 K and 350 K. These data can be obtained free of charge from The
Cambridge Crystallographic Data Centre via www.ccdc.cam.ac.uk/data_request/cif.
Results and Discussion
Numerous single crystal Xꢀray diffraction experiments have been unable to determine the
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location of the CH3NH3 cation. Additionally, when the location and orientation were reported,
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these results have not been consistent with other studies. Our results using single crystal neutron
diffraction data measured at 295 K and 350 K have led to a structural model with detailed
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structural information for the CH3NH3 cation in the tetragonal and cubic phases. Tables 1ꢀ5
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include details regarding the structural model, atomic positions, pertinent atomic distances, and
angles. The relatively large differences between neutron scattering lengths of C and N (6.646 fm
and 9.360 fm, respectively), overcome the problems experienced when modeling the C/N
disorder via Xꢀray diffraction.21 Furthermore, single crystals provide high resolution data
necessary for observing the fine structural details related to the methylammonium cation.
Structural refinements of the tetragonal phase using various space groups including
previously reported I4cm, I4/m and I4/mcm were performed.1,22,9 All three space groups gave
reasonable statistics of R = 6%, 8.5%, 15% for I4/mcm, I4cm, and I4/m, respectively.
Structurally, the three models were very similar in regard to the [PbI6] octahedra structure. The
distorted bond angles between I2─Pb1─I2 were observed in all three cases. It was also found
necessary to restrain the CꢀN bond distance to a realistic value of 1.469 Å to prevent the model
from diverging, while still allowing this value to refine. However, doing so in space groups I4cm
and I4/m resulted in the presence of nonꢀpositive definites (NPDs) with this restraint. On the
other hand, no NPDs were observed for using space group I4/mcm, yielding a refined C–N bond
length of ꢀ1.467(3) Å, same to the bond length reported for methylammonium in
CH3NH3I⋅H2O.23 Therefore, we believe that I4/mcm is indeed the best space group to represent
the structure of CH3NH3PbI3, consistent with the reported neutron powder diffraction data.11
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Table 1. Crystal Data and Structure Refinement for CH3NH3PbI3 Obtained from Neutron
Diffraction
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295 K
350 K
Cubic
0.6ꢀ3.3
Crystal system
Tetragonal
0.6ꢀ3.3
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Wavelength (Å)
Space group
ꢀ
I4/mcm
Pm3m
Unit cell dimensions (Å)
a = 8.8796(6)
c = 12.6266(18)
995.6(2)
a = 6.315(3)
Volume (Å3)
251.8(4)
Z
4
1
Density (calculated) (g cmꢀ1)
Absorption coefficient (mmꢀ1)
F(000)
4.136
4.088
0.0654 + 0.05078 λ
1040
260
Crystal size (mm3)
1.5 x 1.8 x 2.1
1.5 x 1.8 x 2.1
7.9 to 78.1
ꢀ9 < h < 8
ꢀ10 < k < 10
ꢀ10 < l < 10
968
Theta range for data collection (°) 7.4 to 78.5
Index ranges
ꢀ13 < h < 14
ꢀ12 < k < 14
ꢀ16 < l < 20
Reflections collected
Independent reflections
Rint
3825
414
139
0.142
0.164
2
Refinement method
Data / restraints / parameters
Goodnessꢀofꢀfit on F2
R1[F2 > 2σ(F2)]a
Fullꢀmatrix leastꢀsquares on F
414 / 71 / 67
1.04
139 / 10 / 33
1.28
0.060
0.049
wR2(F2)b
0.150
0.075
Extinction coefficient
0.11(3)
1.3(3)
Largest diff. peak and hole (fm. Åꢀ3) 0.72 and ꢀ0.42
0.28 and ꢀ0.51
aR1(F) = Σ||Fo| − |Fc||/Σ|Fo|. bwR2(F2) = [Σ[w(Fo − Fc ) ]/Σ[w(Fo ) ]]1/2
2
2 2
2 2
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Table 2. Atomic Coordinates and Equivalent Isotropic Displacement Parameters for I4/mcm
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atom
Wyckoff Site
x
y
z
Occ
Ueq (Å2)a
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Pb1
I1
4c
1/2
1/2
1/2
3/4
1/2
1
1
1
0.0262(4)
0.069(2)
0.0686(15)
0.085(3)
0.103(7)
0.097(7)
0.092(7)
0.090(4)
0.104(8)
0.096(7)
0.109(8)
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4a
1/2
1/2
I2
8h
0.7868(4)
0.0696(8)
0.1649
0.0952
0.0294
ꢀ0.047(2)
ꢀ0.0757
ꢀ0.1433
ꢀ0.0049
0.2868(4)
0.4304(8)
0.4934
0.3444
0.3866
0.527(2)
0.6133
0.4610
0.5750
N1
32m
32m
32m
32m
32m
32m
32m
32m
0.2858(10) 1/8
H1A
H1B
H1C
C2
0.3002
0.2342
0.3556
1/8
1/8
1/8
0.2385(15) 1/8
H2A
H2B
H2C
0.2925
0.2213
0.1676
1/8
1/8
1/8
aUeq is defined as oneꢀthird of the trace of the orthogonalized Uij tensor.
Table 3. Selected Bond Lengths and Angles for CH3NH3PbI3 in the Tetragonal Phase, I4/mcm
at 295 K
Bond
Pb–I1 x 2
Bond length (esd) (Å)
3.1567(5)
Angle
Pb–I1–Pb
(°)
180.0
Pb–I2 x 4
C–N
3.1732(8)
1.467(3)
3.04(7)
Pb–I2–Pb
163.3(2)
N–H(1A)ꢁꢁꢁI1
N–H(1C)ꢁꢁꢁI2
C–H(2C)ꢁꢁꢁI2
2.96(5)
3.07(6)
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Table 4. Atomic Coordinates and Equivalent Isotropic Displacement Parameters for Pm3m at
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atom
Wyckoff Site
x
y
z
Occ
Ueq (Å2)a
8
9
Pb1
I1
1b
1/2
1/2
1/2
1/2
1
1
0.0301(3)
0.1219(1)
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3d
0
0
N1
8g
05890(13)
0.7171
0.5027
0.6414
0.4544(13)
0.3808
0.5488
0.3367
0.653(2)
0.7069
0.7069
0.7069
0.420(2)
0.3636
0.3636
0.3636
1/2
0.5890(13)
0.5027
0.6414
0.7171
0.4544(13)
0.3367
0.3808
0.5488
1/2
0.5890(13) 0.00297(1) 0.099(5)
H1A
H1B
H1C
C1
48n
48n
48n
8g
0.6414
0.7171
0.5027
0.00297(1) 0.092(5)
0.00297(1) 0.092(5)
0.00297(1) 0.092(5)
0.4544(13) 0.00297(1) 0.076(5)
H1D
H1E
H1F
N2
48n
48n
48n
6f
0.5488
0.3367
0.3808
1/2
0.00297(1) 0.092(5)
0.00297(1) 0.092(5)
0.00297(1) 0.092(5)
0.00038(8) 0.092(5)
0.00038(8) 0.092(5)
0.00038(8) 0.092(5)
0.00038(8) 0.092(5)
0.00038(8) 0.076(5)
0.00038(8) 0.092(5)
0.00038(8) 0.092(5)
0.00038(8) 0.092(5)
0.01397(1) 0.099(5)
0.01397(1) 0.092(5)
0.01397(1) 0.092(5)
0.01397(1) 0.092(5)
0.01397(1) 0.076(5)
0.01397(1) 0.092(5)
0.01397(1) 0.092(5)
0.01397(1) 0.092(5)
H2A
H2B
H2C
C2
48n
48n
48n
6f
0.4187
0.6537
0.4277
1/2
0.6305
0.5052
0.3643
1/2
H2D
H2E
H2F
N3
48n
48n
48n
12j
48n
48n
48n
12j
48n
48n
48n
0.5759
0.3418
0.5823
0.6054(9)
0.7506
0.6081
0.5727
0.4402(9)
0.4854
0.4214
0.2950
0.6389
0.4963
0.3648
0.6054(9)
0.5370
0.6795
0.7419
0.4402(9)
0.3158
0.3798
0.5062
H3A
H3B
H3C
C3
0.4712
0.6452
0.3836
1/2
H3D
H3E
H3F
0.6032
0.3445
0.5523
aUeq is defined as oneꢀthird of the trace of the orthogonalized Uij tensor.
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Table 5. Selected Bond Lengths for CH3NH3PbI3 in the Cubic Phase, Pm3m at 350 K
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Bond
Bond length (esd) (Å)
3.1575(15)
1.472(8)
1.471(9)
1.475(7)
Pb─I x 6
C1─N1
C2─N2
C3─N3
N–H1ꢁꢁꢁI1
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3.05(7), 3.10(5)
Figure 3a shows the regions of positive nuclear density in yellow arising from the carbon
and nitrogen atoms. The irregular shape of the density is elongated in four directions extending
+
from the interior indicating that either the methyl (–CH3) or protonated amine (–NH3 )
substituent are orientated toward the [PbI6] octahedra. The positive nuclear density is surrounded
by a sphere of negative nuclear density due to the presence of protons, which are represented in
blue as shown in Figure 3b. Closer inspection of the positive nuclear density reveals a larger
density at the four exterior termini nearest the [PbI6] octahedra. This signifies the protonated
amine substituent, which has a larger scattering factor due to the presence of nitrogen (versus
carbon), occupies these four positions. This is most likely due to the N–H bonds being more
polar than the C–H bonds, where the majority of the electronegativity is localized on the nitrogen
+
atom, favoring weak hydrogen bonding between the protonated amine (–NH3 ) substituent and
the electronegative iodine atoms of the neighboring [PbI6] octahedra. This interaction prevents
+
the orientation of the CH3NH3 cation from being completely random, essentially locking the
location of the protonated amine substituent. The difference Fourier map reveals the remaining
positive nuclear density surrounding the 4b Wyckoff sites is due to the carbon atoms of the
methyl substituent. We initially attempted to refine the model with the carbon atom constrained
to the 16l Wyckoff site where the N and C positions were assigned to (x, 1/2+x, z) with z equal
to 0.2855 for N and 0.2384 for C. This was based on the results of the previously reported
neutron powder diffraction studies of CH3NH3PbI3 perovskite;11 however, this resulted in
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anomalously large ADPs, as well as significantly poorer refinement statistics. Therefore, the
position of the carbon atom was allowed to freely refine, revealing the actual location to be
slightly off the ideal 16l Wyckoff site. This slight change in position generates two possible
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+
carbon positions through a mirror plane, resulting in the C termini in CH3NH3 to be disordered
in eight positions instead of 4 (Figure 4). This result is different from that of the reported neutron
powder diffraction studies where the carbon atom was located exactly at the 16l Wyckoff site;
however, structural details of the tetragonal phase were reported at 180 K, well below the
temperature of our experiment conducted at 295 K. This could support the hypothesis that the
splitting observed in our model is due to thermal disorder, as in the case of the neutron powder
diffraction experiments collected at 180 K, the thermal energy is minimized, resulting in the
carbon atom to be located at the ideal 16l Wyckoff site.
(a)
(b)
c
c
b
b
Figure 3. 3D difference Fourier maps from single crystal neutron diffraction data for
CH3NH3PbI3, (a) showing the region of positive (yellow) nuclear density indicates the disorder
of the CH3NH3 cation, (b) Showing the region of negative (blue) nuclear indicates a highly
+
disordered arrangement of the hydrogen atoms.
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Figure 4. The positive nuclear scattering has a larger value at the four exterior lobes indicating
the presence of nitrogen (shown in silver). The central disordered area has a lower scattering
factor due to the presence of carbon (shown in brown) that is disordered to generate a total of
eight positions.
As mentioned previously, large, spherical, negative nuclear scattering density was
observed surrounding the interior positive nuclear scattering density. This density is associated
with the presence of hydrogen atoms, having a negative scattering factor of ꢀ3.739 fm. The
hydrogen atoms are highly disordered and can be visualized explicitly in the difference Fourier
+
maps in Figure 3b. Each of the four possible –NH3 positions (Figure 5a) generate two N–H···I
contacts by symmetry with a distance of 2.96(5) Å. This distance is shorter than all other H···I
contacts, including contacts with the –CH3 substituent where the shortest C–H···I distance is
+
3.07(6) Å. Figure 5b shows one of the four possible orientations of the CH3NH3 cation with a
dashed line indicating the shortest N–H···I contact. This is shorter than the distance reported
using neutron powder diffraction at 180 K, which was 3.184(12) Å. It should also be noted that
the C–N–H angles (109.5 °) in our model are larger than those reported in the neutron powder
diffraction study (~ 84.14 °).11 Further, the bond distances and angles closely resembles that of
ammonium iodide (NH4I),24 where hydrogenꢀbonding plays an important role for the structural
stabilization. The detailed hydrogen bond lengths and angles of the neutron diffraction data are
given in Table 6.
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Figure 5. Left: The disordered methylammonium cation is shown with each N–HꢁꢁꢁI contact.
Right: A single CH3NH3 cation is shown with the disordered hydrogen atoms surrounding both
N and disordered C atom. Pbꢀgrey, Iꢀblack, Nꢀgrey, Cꢀbrown, Hꢀpink. The shortest IꢁꢁꢁH contact
is shown (dotted line).
+
Table 6. Hydrogen Bonds for I4/mcm (Å and °)
D–HꢁꢁꢁA
d(D–H)
1.03(6)
1.03(6)
d(HꢁꢁꢁA)
3.04(7)
2.96(5)
d(DꢁꢁꢁA)
3.898(7)
3.90 5(11)
bond angle (DHA)
141.1
N–H(1A)ꢁꢁꢁI(1)
N–H(1C)ꢁꢁꢁI(2)
152.8
“D” represents donor and “A” represents acceptor.
The [PbI6] octahedral framework is found to be distorted and tilted in the tetragonal phase
of CH3NH3PbI3 that can be represented using Glazer notation a0a0cꢀ.25 The notation “+” or “ꢀ”
represents inꢀphase or outꢀof phase, respectively, and are applied when describing the tilt or
rotations about the three I–Pb–I axes along the crystallographic a, b, c axes. The tilting angle of
16.75° results in an outꢀofꢀphase rotation of the [PbI6] octahedra along the cꢀaxis, adopting the
tetragonal I4/mcm space group.
With increasing temperature, CH3NH3PbI3 undergoes a phase transition from the
+
tetragonal to cubic phase at 327 K, with a concomitant increase in CH3NH3 cation disorder. Our
ꢀ
experiment at 350 K was successfully modeled using space group Pm3m with good statistical
values (R1 = 0.049, wR2 = 0.075). Through careful analysis of the 3D nuclear difference Fourier
+
maps for CH3NH3 at 350 K (Figure 6), we have found that the middle point of C–N bond is
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located offꢀcenter from the ideal Aꢀsite of the perovskite structure in the crystal structure. This is
evident in Figure 6a and b, where the positive nuclear density in yellow represents the center of
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+
the CH3NH3 cation. The surrounding hydrogen atoms are highly disordered, as shown in
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+
nuclear difference Fourier maps for CH3NH3 in Figure 6c, where blue region indicate the
+
negative nuclear density due to the hydrogen atoms. The final model resulted in the CH3NH3
cation being directed toward the face of the unit cell, disordered over six positions with weak N–
HꢁꢁꢁI interaction having hydrogen bond distances of 3.05 (7) Å and 3.10(5 Å (Figure 6d). All Pb–
I–Pb angles are linear resulting in a perfect octahedron, further indicating the weaker N–HꢁꢁꢁI
interaction, as compare to the tetragonal phase, where the stronger N–HꢁꢁꢁI interaction resulted in
the distortion and tilt of the [PbI6] octahedra.
Although a greater amount of disorder is present in the cubic phase than that in the
+
tetragonal phase, our data reveal that the disordered CH3NH3 cation preferentially aligns along
the [111], [100] and [011] directions. Furthermore, these orientations have site occupancy ratios
+
of 0.143 : 0.187 : 0.670 respectively, suggesting that the CH3NH3 cation resides primarily along
the [011] direction at high temperature. These results are in accordance with previous DFT
+
calculations that suggest the structure with the CH3NH3 cation oriented along the [011]
direction lies at an energetic minimum, albeit by only about 20 meV.6,8 The shallow energetic
minima corresponding to the various orientations could explain why our model has three primary
orientations, with a slight preference to align along the [011] direction. Additionally, the
calculations also predict a slight distortion of the surrounding [PbI6] octahedra when oriented
along the [011] direction, breaking the perfect 180° I–Pb–I angle. In our model, we observe large,
pancakeꢀshaped thermal ellipsoids for iodine (Figure 6d), indicating the actual location of the
iodine atoms may in fact be off the ideal 3d Wyckoff position. For the purpose of comparing our
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results with the DFT calculations, we intentionally moved I atom slightly off the 3d Wyckoff
position to allow it to freely refine (Details of the structure including hydrogen bond distances
with I moved off the axial position can be found in supporting information). Indeed, the refined
location of the I atom is slightly off of the edge of the unit cell with no significant statistical
change to the model (R1 = 0.048 and wR2 = 0.0721), in good agreement with those predicted by
calculations.
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(a)
(b)
(c)
(d)
+
Figure 6. 3D Nuclear difference Fourier maps for CH3NH3 at 350 K. (a) The region of positive
+
(yellow) nuclear density indicates disorder of C and N atoms in CH3NH3 , (b) Location of
disordered CN groups (N blue, C brown) and H atoms from refinement of the neutron structure
(c) View of the structure of CH3NH3PbI3 showing the region of negative (blue) nuclear and a
+
highly disordered arrangement of the hydrogen atoms. (d) Location of CH3NH3 with the CN
bond aligned along [011] direction.
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Conclusions
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We report a detailed description of the crystal structure of CH3NH3PbI3, including the
orientation, location and disorder of the methylammonium cation within the [PbI6] octahedra of
by using single crystal neutron diffraction. The tetragonal phase at 295 K was confirmed to be
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+
best modelled in I4/mcm. The CH3NH3 cations are disordered such that there are four possible
+
orientations of the –NH3 substituent being on the extremity nearest the neighboring I atom.
Conversely, the methyl substituent was found to have eight possible positions as opposed to the
four of the protonated amine substituent due to a greater ability to move as there are no means of
stabilizing its location. The high temperature (350 K) cubic phase was successfully modelled
+
ꢀ
using space group Pm3m. We have sucessfully located the CH3NH3 cation and discerned the C
+
and N atoms. More importantly, our data reveal a key feature of the orientation of the CH3NH3
+
cation where the CH3NH3 cation resides mainly along [011] direction, which is in good
agreement with reported DFT calculations. These findings provide important structural
information for both the tetragonal and cubic phases, and will help in understanding the origin of
the excellent photovoltaic performance of this material.
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Supporting Information
Crystallographic information files (CIF) of CH3NH3PbI3 at 295 K and 350 K. Additional 3D
difference Fourier maps for the refined structure of CH3NH3PbI3 at 295 K presented in Figures
S1ꢀS3. This material is available free of charge via the Internet at http://pubs.acs.org.
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Author Information
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Corresponding Author
*Eꢀmail: Julia.Chan@utdallas.edu. Tel: (972)883ꢀ3595.
*Eꢀmail: wangx@ornl.gov. Tel: (865)200ꢀ2500.
Notes
The authors declare no competing financial interest.
All authors contributed equally to this work.
Acknowledgements
JYC acknowledges NSFꢀDMRꢀ1360863 for partial funding of this work. Neutron single crystal
diffraction measurements were performed at the Spallation Neutron Source, which is sponsored
by the Division of Scientific User Facilities, Office of Basic Energy Sciences, US Department of
Energy, under Contract No. DE.ꢀAC05ꢀ00OR22725 with UTꢀBattelle, LLC.
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Schultz, A. J.; Jorgensen, M. R. V.; Wang, X.; Mikkelson, R. L.; Mikkelson, D. J.; Lynch, V. E.;
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Orientation of Organic Cations in Hybrid InorganicꢀOrganic Perovskite CH3NH3PbI3 from
Subꢀatomic Resolution Single Crystal Neutron Diffraction Structural Studies
Yixin Ren, Iain W. H. Oswald, Xiaoping Wang, Gregory T. McCandless, Julia Y. Chan
Synopsis:
Subꢀatomic resolution single crystal neutron diffraction revealed offꢀcenter placement and
orientation of the disordered methylammonium cation in the hybrid organicꢀinorganic perovskite
CH3NH3PbI3 in the room temperature (295 K) tetragonal phase and the high temperature (350 K)
cubic phase.
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