Tolerance Factors Revisited: Geometrically Designing the Ideal

Subscriber access provided by Vanderbilt Libraries

Article

Tolerance Factors Revisited: Geometrically Designing the Ideal Environment for Perovskite Dopants Ka Yi Tsui, Nicole Onishi, and Robert F. Berger J. Phys. Chem. C, Just Accepted Manuscript • Publication Date (Web): 22 Sep 2016 Downloaded from http://pubs.acs.org on September 22, 2016

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

The Journal of Physical Chemistry C is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 24

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry

Tolerance Factors Revisited: Geometrically Designing the Ideal Environment for Perovskite Dopants Ka Yi Tsui, Nicole Onishi, and Robert F. Berger* Western Washington University, 516 High Street, Bellingham, WA 98225, USA

ABSTRACT. Focusing on case studies relevant to solar energy conversion, the replacement of lead with a layer of germanium or isolated germanium atoms in CsPbCl3 and CsPbBr3, we develop a novel geometric approach to design optimal environments for perovskite dopants. In doing so, we extend the sphere-packing arguments that motivate Goldschmidt tolerance factors beyond bulk ABX3 perovskite compounds, to doped and substituted perovskite superstructures. To assess the stability of our proposed superstructures relative to competing phases and structural distortions, we compute total energies and phonon frequencies using density functional theory (DFT)-based methods. We extend these ideas toward the formulation of a generalized tolerance factor that applies to perovskite dopant environments, and identify superstructures in which the stability of these dopants is significantly improved relative to the bulk parent compounds. This approach holds promise in uncovering general design rules for stable doped perovskites.

ACS Paragon Plus Environment

1


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 2 of 24

INTRODUCTION. Compounds crystallizing in the perovskite structure (ABX3, Fig. 1a) incorporate a wide range of elements at the A, B, and X sites, and are used in a variety of applications. A simple but long-used framework for predicting the structural stability of a perovskite compound is the Goldschmidt tolerance factor.1 Assuming the ions in a perovskite are hard spheres, the tolerance factor (defined as

A

√

X B

X

) is essentially a measure of how well

the spheres pack. Empirically, a tolerance factor close to 1 suggests that a combination of elements is likely to exist as an undistorted perovskite. Elements with tolerance factors slightly below or above 1 typically undergo rotations of their B–X octahedra or ferroelectric distortions, respectively. Elements whose tolerance factors are far from 1 rarely take up the perovskite structure.2,3 This reasoning is quite powerful for compounds of the stoichiometry ABX3, including compounds related to the ones we explore in this work.4–7 Yet, these hard-sphere-based arguments are not typically extended to assess the stability of superstructures in which additional elements are doped or substituted. This is a missed opportunity, as such doping and elemental substitution are often instrumental in tuning perovskites for applications of interest. Consider CsPbCl3 (t = 0.87) and CsPbBr3 (t = 0.86), two of a class of lead-halide compounds of interest in perovskite solar cells.8–10 Both compounds are undistorted cubic perovskites at or near room temperature.11,12 The continued development of this class of materials for photovoltaic applications requires novel routes to controllably tune their electronic structure and band gap, often via doping or elemental substitution. In past experimental work, substitution at the A, B, and X sites have demonstrated ways to tune band gaps throughout the visible spectrum.13–16 Relevant to this paper, the B-site replacement of lead with germanium is desirable in the push toward lead-free perovskite light absorbers.17 While there exist a number of distorted germanium-halide perovskites,18–21 the inclusion of germanium in perovskite


2

Page 3 of 24

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


photovoltaics remains underexplored.

Figure 1. a) Cubic unit cell of a perovskite ABX3, with bonds shown to highlight the connectivity of B–X octahedra. The superstructures computed in this paper introduce b) a layer of B-site germanium into CsPbX3 (X = Cl−, Br−), and c) an isolated B-site germanium atom into CsPbX3 (X = Cl−, Br−).

In this paper, we extend the concept of tolerance factors to develop and test a novel geometric approach to stabilize target dopants in perovskite compounds. Using layers of germanium atoms and isolated germanium atoms in CsPbCl3 and CsPbBr3 as case studies, we design optimal chemical environments for stabilizing these perovskite dopants, and use density functional theory (DFT)-based calculations to assess their energetic stability and resistance to distortion. We identify superstructures and chemical environments in which the stability of these dopants is significantly improved relative to the parent compounds, and highlight the promise of our approach. The power of our reasoning is not limited to these particular compounds or to solar energy conversion applications. These ideas can be extended toward the formulation of general design rules for the stabilization of perovskite dopants.


3


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 4 of 24

COMPUTATIONAL METHODS. Crystal structures in this work are optimized and their energies computed using DFT within the Perdew-Burke-Ernzerhof (PBE) functional,22 using the VASP package23,24 and PAW potentials. The reliability of this methodology in capturing structural energetics has been tested extensively in the past.25,26 A plane-wave cutoff of 500 eV is used throughout. Unit cells containing a single perovskite formula unit are treated with a Γcentered 6

6

6 k-point mesh. For calculations requiring larger unit cells, proportionally

fewer k-points are used. We treat structures into which a dopant layer is introduced with unit cells two perovskite units tall (as in Fig. 1b), with in-plane lattice parameters constrained to the PBE-optimized values of the respective cubic parent compounds (CsPbCl3 and CsPbBr3). The perpendicular lattice parameter (the c-axis in Fig. 1b) and atomic positions are allowed to relax. We treat superstructures into which an isolated dopant atom is introduced with unit cells 2

2

2 perovskite units in size (as in Fig. 1c), with all lattice parameters constrained to the

PBE-optimized values of the respective cubic parent compounds. Symmetries are constrained to prevent ferroelectric distortions and B–X octahedral rotations. Zone-center phonon modes and frequencies are computed using density functional perturbation theory, in order to assess the stability of the high-symmetry structures with respect to these distortions. For structures into which a dopant layer is introduced, unit cells for phonon calculations are enlarged to √2

√2

2 perovskite units in order to consider the possibility of octahedral rotations. While tolerance factors can in principle use any definition of ionic radius, our analysis uses perhaps the most common, the Shannon crystal radius.27 Shannon crystal radii of the ions relevant to this work are given in the Supporting Information (SI).


4

Page 5 of 24

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


RESULTS AND DISCUSSION. We first consider the challenge of replacing a layer of lead in CsPbCl3 with germanium (Fig. 1b). This is synthetically difficult in large part because Ge2+ (0.87 Å) has a much smaller crystal radius than Pb2+ (1.33 Å). To better accommodate the size of germanium, we invoke Goldschmidt’s hard-sphere reasoning to hypothesize that introducing germanium within a layer of larger Xʹ anions will lead to greater structural stability of the dopant layer. By the argument illustrated in Fig. 2a, these spheres pack best in this plane when the sum of the lead and chloride radii is equal to the sum of the germanium and Xʹ radii. Thus, the optimal radius of Xʹ is 2.13 Å, close to the radius of I− (2.06 Å).

Figure 2. Schematic illustration of an optimal environment for a layer of germanium in CsPbCl3. a) Because germanium is smaller than lead, we pair it with an Xʹ anion larger than chloride. In the layers above and below the germanium dopant, we consider replacing cesium with an Aʹ cation b) whose inplane (equatorial) radius is similar to cesium, but c) whose perpendicular (axial) radius is shorter.

We use DFT calculations to test our hypothesis in two ways, by assessing the energetic stability of modified superstructures relative to both competing phases and structural distortions. First, we compute a parameter that we call “dopant stabilization energy” (DSE). We define DSE as the per-atom energetic preference for a dopant to be substituted into a modified environment, rather than the parent compound. For example, the DSE for doping germanium into an iodide


5


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 6 of 24

layer within CsPbCl3 is defined as: DSE

Cs PbGeCl I

Cs Pb Cl

Cs PbGeCl

Cs Pb Cl I

A negative DSE indicates that a modified environment is more conducive than the parent compound to the introduction of a dopant. In this case, an iodide layer in CsPbCl3 has a DSE of −1.17 eV toward germanium doping, while a bromide layer has a DSE of −0.38 eV. This is consistent with our expectations based on crystal radius, and promising toward the possibility of stabilizing germanium within CsPbCl3. However, relative energetic stability alone does not indicate that a phase is likely to be even metastable. Goldschmidt tolerance factors have proven predictive in part because a compound’s proximity to t = 1 is a proxy for its resistance to structural distortion. To test whether our geometry-based superstructure design accomplishes this same goal, we compute zone-center phonon frequencies to probe these structures’ resistance to distortion. The lack of significantly imaginary phonon frequencies suggests that a phase is metastable. In this case, the most imaginary phonon frequency of the parent compound CsPbCl3, which is known to remain undistorted above 320 K,14 is 43i cm−1 and corresponds to Pb–Cl octahedral rotations. When a layer of lead is replaced by germanium, the most imaginary frequency is raised to 170i cm−1, corresponding to polar distortions in the germanium layer (due to its smaller radius). When the germanium layer is accompanied by iodide, the most imaginary frequency is reduced somewhat to 76i cm−1, meaning the metastability of a germanium layer within CsPbCl3 is improved when accompanied by iodide. By looking to more distant neighbors of the germanium layer, we consider whether its geometric environment in CsPbCl3 can be optimized even further. While the radii of germanium and iodide result in favorable in-plane bond distances, they leave each germanium cation far


6

Page 7 of 24

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


from the chloride anions above and below it in the perpendicular direction. To remedy this, we propose using an Aʹ cation to replace cesium in the layers above and below germanium. To ensure that the superstructure is isoelectronic with CsPbCl3, this Aʹ cation must have the same +1 charge as cesium. As illustrated in Fig. 2b, the packing of ions is optimized when the in-plane size of Aʹ (its equatorial radius) matches that of cesium (2.02 Å). Fig. 2c shows how we might improve the packing of ions in the direction perpendicular to the dopant plane. If the Aʹ cation is disc-shaped, rather than spherical, all ions can regain their preferred proximity. Using the reasoning illustrated in Fig. 2c, the optimal perpendicular (axial) radius of Aʹ is 1.17 Å when Xʹ is iodide. While no cation has exactly these optimal dimensions, there exist reasonable approximations. Given the demonstrated incorporation of a flexible library of monovalent organic and inorganic A-site cations of various sizes and shapes into lead-halide perovskites,14,28 we compute the planar aromatic cyclopropenyl cation ([C3H3]+). When both iodide and cyclopropenyl cation accompany germanium in this superstructure, both the DSE (−1.11 eV) and the most imaginary phonon frequency (78i cm−1) are similarly favorable to the case with only iodide. This suggests that the size effects of more distant Aʹ neighbors on the stability of a germanium dopant layer are not nearly as strong as the effects of the Xʹ nearest neighbors. In the left side of Fig. 3, DSEs and the most imaginary phonon frequencies are shown for the replacement of a layer of lead in CsPbCl3 with germanium in a variety of environments (Cl−, Br−, and I− at the Xʹ site; K+, Rb+, Cs+, and [C3H3]+ at the Aʹ site). In Fig. 3a, it is clear that DSEs are dictated primarily by the radius of Xʹ, with iodide leading to the most energetic stabilization. The most imaginary phonon frequencies of the germanium-containing superlattices are plotted separately in terms of polar distortive modes along in-plane (Fig. 3b) and perpendicular (Fig. 3c)


7


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 8 of 24

directions. For nearly all of these compounds, the most unstable phonon modes overall are among the polar modes plotted in Fig. 3b,c. A stated above, a large radius of Xʹ (e.g., iodide) reduces the tendency toward in-plane distortions, while changes in the axial radius of Aʹ do not have a noticeable effect on the tendency toward perpendicular distortions. In sum, our findings suggest that an optimally stable structural environment for a layer of germanium in CsPbCl3 can be designed by considering its surrounding nearest-neighbor distances and engineering the dimensions of these neighboring ions. The parent compound on which we have focused so far, CsPbCl3, is not used in photovoltaic technologies as often as its bromide and iodide analogs. We have chosen it because it allows for the most flexibility in picking a larger Xʹ anion. However, the observed trends are quite general. The right half of Fig. 3 shows the analogous calculations of DSEs and phonon frequencies for the introduction of a germanium layer into the more technologically relevant CsPbBr3. When a layer of lead in CsPbBr3 is replaced by germanium, the most imaginary frequency is 130i cm−1, corresponding to in-plane polar distortions in the germanium layer. When the germanium layer is accompanied by iodide, the most imaginary frequency is reduced to 75i cm−1 and the DSE is −0.55 eV. Thus, the stability of a germanium layer within CsPbBr3 is significantly improved when accompanied by iodide, just as it was in CsPbCl3.


8

Page 9 of 24

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 3. a) Dopant stabilization energies (DSE, defined in the text) of a variety of environments (Cl−, Br−, and I− at the Xʹ site; K+, Rb+, Cs+, and [C3H3]+ at the Aʹ site) toward the introduction of a layer of germanium into CsPbX3. The most imaginary phonon frequencies are plotted for polar distortive modes along b) in-plane and c) perpendicular directions for structures containing germanium. Panel c uses a recently-reported atomic radius of carbon29 as the axial radius of cyclopropenyl cation. The left side of the figure considers CsPbCl3 as the parent compound, while the right side considers CsPbBr3.


9


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 10 of 24

While the results shown in Fig. 3 are promising in their suggestion that doped and substituted perovskites are amenable to sphere-packing arguments, our approach up to this point has been more suited for use on a case-by-case basis than toward the efficient screening of novel compounds. The power of the Goldschmidt tolerance factor lies in the fact that it is a single number, based entirely on ionic radii, that indicates the approximate stability of any combination of elements in the ABX3 perovskite structure. Without any experiment or electronic structure calculation, a tolerance factor facilitates the rough prediction of whether three elements are likely to exist as a bulk perovskite, and if so, qualitatively how its structure is prone to distort. In contrast, there is no such general predictive framework for doped, co-doped, and substituted perovskite variants. For the remainder of this paper, we begin to design a simple quantitative metric, akin to a tolerance factor, that assesses the stability of the environment of a general perovskite dopant atom. To do this, we again focus on the challenge of introducing B-site germanium into the lattices of CsPbCl3 and CsPbBr3. This time, rather than considering a germanium layer (Fig. 1b), we consider an isolated germanium dopant atom (Fig. 1c). When a germanium atom replaces lead in CsPbCl3, it is too small for its immediate surroundings, likely creating structural instability and perhaps severe distortion. However, if we allow some or all of its six nearestneighboring chloride anions to also be replaced, there is a possibility to improve the packing. In CsPbCl3, we focus on a seven-atom octahedral PbCl6 motif, which consists of three-atom Cl−Pb−Cl chains along the x, y, and z axes (Fig. 4a, left). The parent compound, a stable perovskite CsPbCl3, has an appropriate amount of space to accommodate these chains. When some of these atoms are replaced by germanium and perhaps X′, these chains become longer or shorter (Fig. 4a, right). We define a geometry-based metric tdop as the sum of squares of the


10

Page 11 of 24

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


percent change in each of these three chain lengths upon doping: ,dop dop

,par ,par

,dop

,par ,par

,dop

,par ,par

The lengths dpar and ddop, three-atom chain lengths in the parent and doped compounds, are defined in Fig. 4a. The deviations in length are squared in this formula from the simple viewpoint that potential energy surfaces generally behave as parabolas around a minimum energy for small changes in geometry. By this definition, tdop is non-negative, and is zero only when the combined sizes of dopant atoms perfectly match those in the parent compound. Based solely on geometry, we would expect dopant environments to be most stable when tdop is close to zero.

Figure 4. Demonstration of how a simple geometry-based metric tdop captures the structural stability of a general doped perovskite compound. a) The immediate environment of a B-site atom can be thought of as three-atom chains along the x, y, and z axes in the parent (left) and doped (right) compounds. There is close correlation between tdop and DFT-computed dopant stabilization energy (both defined in the text) for the doping of a germanium atom into b) CsPbCl3 and c) CsPbBr3, surrounded by all geometrically distinct placements of iodide co-dopant anions.


11


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 12 of 24

To test this hypothesis, we have computed the dopant stabilization energies of a germanium atom doped into CsPbCl3 and surrounded by each geometrically distinct arrangement of six chloride and/or iodide anions (Fig. 4b). Similarly to the case of layered superstructures, DSE is here defined as the per-dopant energetic preference for a given motif compared to the introduction of all the same atoms separately within the parent compound. For example, the DSE for introducing a GeCl6-nIn motif into CsPbCl3 is defined as: DSE

Cs Pb GeCl

I

Cs Pb Cl

Cs Pb GeCl

Cs Pb Cl

I

As expected, greater energetic stability correlates strongly with small values of tdop. The most stable environment, with tdop very close to zero, somewhat unexpectedly has a GeCl3I3 motif with one iodide anion along each axis. This is because the placement of two iodide anions along a given axis overcompensates for the decrease in B-site size, causing tdop to increase and destabilizing the DSE. Perhaps the most notable feature of Fig. 4b is its striking linearity, which provides compelling evidence that such a metric could possess significant predictive power. In other words, if such a simple geometry-based quantity correlates precisely with more timeconsuming DFT calculations of the structural energies of doped perovskites, then this quantity can serve as an extremely efficient predictor of stability. Fig. 4c shows a qualitatively similar result for the doping of an isolated germanium atom into CsPbBr3. Replacing the nearest neighbors of germanium by iodide anions reduces the value of tdop and stabilizes the dopant. Unlike the case of CsPbCl3, germanium in CsPbBr3 has the smallest value of tdop and is most effectively stabilized when surrounded by six iodide anions. Once again, it is important to note that DSE correlates strongly with the geometric parameter tdop, indicating that the stability of a perovskite dopant environment is amenable to similar hardsphere-based arguments as bulk perovskites.


12

Page 13 of 24

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


CONCLUSIONS. We have considered dopants of interest in perovskite photovoltaic applications (a germanium layer and an isolated germanium atom in CsPbCl3 and CsPbBr3), and have devised a geometry-based approach to efficiently predict stable chemical environments for perovskite dopants. Given the demonstrated synthesis of perovskites with an expanding library of organic and inorganic components of varying sizes and shapes, the type of bottom-up design suggested by this work is increasingly feasible. And while the field of computational materials design has surely advanced in recent years in the development of ab initio predictors of structural stability, we have demonstrated here that classic geometric arguments can still lead to novel predictions. Our approach can in principle be extended to other compounds and crystallographic sites (e.g., doping at the A, B, and X sites of prototypical water-splitting photocatalyst SrTiO33034

), and even to ionic crystals other than perovskites. We reserve further exploration of the

quantitative details of a fully generalized tolerance factor for future work.


13


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 14 of 24

ASSOCIATED CONTENT Supporting Information Shannon crystal radii, phonon frequencies, and dopant stabilization energies. This material is available free of charge via the Internet at http://pubs.acs.org. AUTHOR INFORMATION Corresponding Author *Robert F. Berger. E-mail: [email protected]. Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Acknowledgment We gratefully acknowledge Western Washington University and the Research Corporation for Scientific Advancement for financial support, the latter through a Cottrell College Science Award.


14

Page 15 of 24

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


REFERENCES [1] Goldschmidt, V. M. Die Gesetze der Krystallochemie. Naturwissenschaften 1926, 14, 477485. [2] Megaw, H. D. Crystal Structure of Double Oxides of the Perovskite Type. Proc. Phys. Soc. 1946, 58, 133-152. [3] Woodward, P. M. Octahedral Tilting in Perovskites II: Structure Stabilizing Forces. Acta Crystallogr. 1997, B53, 44-66. [4] Filip, M. R.; Eperon, G. E.; Snaith, H. J.; Giustino, F. Steric Engineering of Metal-Halide Perovskites with Tunable Optical Band Gaps. Nat. Commun. 2014, 5, 5757. [5] Kieslich, G.; Sun, S.; Cheetham, A. K. An Extended Tolerance Factor Approach for OrganicInorganic Perovskites. Chem. Sci. 2015, 6, 3430-3433. [6] Navas, J.; Sánchez-Coronilla, A.; Gallardo, J. J.; Martín, E. I.; Hernández, N. C.; Alcántara, R.; Fernández-Lorenzo, C.; Martín-Calleja. Revealing the Role of Pb2+ in the Stability of Organic-Inorganic Hybrid Perovskite CH3NH3Pb1−xCdxI3: An Experimental and Theoretical Study. J. Phys. Chem. Chem. Phys. 2015, 17, 23886-23896. [7] Jacobsson, T. J.; Pazoki, M.; Hagfeldt, A.; Edvinsson, T. Goldschmidt’s Rules and Strontium Replacement in Lead Halogen Perovskite Solar Cells: Theory and Preliminary Experiments on CH3NH3SrI3. J. Phys. Chem. C 2015, 119, 25673-25683. [8] Snaith, H. J. Perovskites: The Emergence of a New Era for Low-Cost, High-Efficiency Solar Cells. J. Phys. Chem. Lett. 2013, 4, 3623-3630. [9] Gao, P.; Grätzel, M.; Nazeeruddin, M. K. Organohalide Lead Perovskites for Photovoltaic Applications. Energy Environ. Sci. 2014, 7, 2448-2463.


15


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 16 of 24

[10] Green, M. A.; Ho-Baillie, A.; Snaith, H. J. The Emergence of Perovskite Solar Cells. Nat. Photonics 2014, 8, 506-514. [11] Møller, C. K. A Phase Transition in Caesium Plumbochloride. Nature 1957, 180, 981-982. [12] Hirotsu, S.; Harada, J.; Iizumi, M.; Gesi, K. Structural Phase Transitions in CsPbBr3. J. Phys. Soc. Jpn. 1974, 37, 1393-1398. [13] Kojima, A.; Teshima, K.; Shirai, Y.; Miyasaka, T. Organometal Halide Perovskites as Visible-Light Sensitizers for Photovoltaic Cells. J. Am. Chem. Soc. 2009, 131, 6050-6151. [14] Stoumpos, C. C.; Malliakas, C. D.; Kanatzidis, M. G. Semiconducting Tin and Lead Iodide Perovskites with Organic Cations: Phase Transitions, High Mobilities, and Near-Infrared Photoluminescent Properties. Inorg. Chem. 2013, 52, 9019-9038. [15] Noh, J. H.; Im, S. H.; Heo, J. H.; Mandal, T. N.; Seok, S. I. Chemical Management for Colorful, Efficient, and Stable Inorganic-Organic Hybrid Nanostructured Solar Cells. Nano Lett. 2013, 13, 1764-1769. [16] Hao, F.; Stoumpos, C. C.; Chang, R. P. H.; Kanatzidis, M. G. Anomalous Band Gap Behavior in Mixed Sn and Pb Perovskites Enables Broadening of Absorption Spectrum in Solar Cells. J. Am. Chem. Soc. 2014, 136, 8094-8099. [17] Boix, P. P.; Agarwala, S.; Koh, T. M.; Mathews, N.; Mhaisalkar, S. G. Perovskite Solar Cells: Beyond Methylammonium Lead Iodide. J. Phys. Chem. Lett. 2015, 6, 898-907. [18] Thiele, G.; Rotter, H. W.; Schmidt, K. D. Kristallstrukturen und Phasentransformationen von Caesiumtrihalogenogermenaten(II) CsGeX3 (X = Cl, Br, I). Z. Anorg. Allg. Chem. 1987, 545, 148-156. [19]

Thiele,

G.;

Rotter,

H.

W.;

Schmidt,

K.

D.

Die

Kristallstrukturen

und

Phasentransformationen von RbGeBr3. Z. Anorg. Allg. Chem. 1988, 569, 7-16.


16

Page 17 of 24

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


[20] Serr, B. R.; Heckert, G.; Rotter, H. W.; Thiele, G.; Ebling, D. Structural and Spectroscopic Studies on Trimorphous MeNH3GeCl3. J. Mol. Struct. 1995, 348, 95-98. [21] Stoumpos, C. C.; Frazer, L.; Clark, D. J.; Kim, Y. S.; Rhim, S. H.; Freeman, A. J.; Ketterson, J. B.; Jang, J. I.; Kanatzidis, M. G. Hybrid Germanium Iodide Perovskite Semiconductors: Active Lone Pairs, Structural Distortions, Direct and Indirect Energy Gaps, and Strong Nonlinear Optical Properties. J. Am. Chem. Soc. 2015, 137, 6804-6819. [22] Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865-3868. [23] Kresse, G.; Furthmüller. Efficient Iterative Schemes for Ab Initio Total-Energy Calculations Using a Plane-Wave Basis Set. J. Phys. Rev. B 1996, 54, 11169-11186. [24] Kresse, G.; Joubert, D. From Ultrasoft Pseudopotentials to the Projector Augmented-Wave Method. Phys. Rev. B 1999, 59, 1758-1775. [25] Paier, J.; Hirschl, R.; Marsman, M.; Kresse, G. The Perdew-Burke-Ernzerhof ExchangeCorrelation Functional Applied to the G2-1 Test Set Using a Plane-Wave Basis Set. J. Chem. Phys. 2005, 122, 234102. [26] Hafner, J. Ab-Initio Simulations of Materials Using VASP: Density-Functional Theory and Beyond. J. Comput. Chem. 2008, 29, 2044-2078. [27] Shannon, R. D. Revised Effective Ionic Radii and Systematic Studies of Interatomic Distances in Halides and Chalcogenides. Acta Crystallogr. 1976, A32, 751-767. [28] Borriello, I.; Cantele, G.; Ninno, D. Ab Initio Investigation of Hybrid Organic-Inorganic Perovskites Based on Tin Halides. Phys. Rev. B 2008, 77, 235214. [29] Pyykkö, P.; Atsumi, M. Molecular Single-Bond Covalent Radii for Elements 1-118. Chem. Eur. J. 2008, 15, 186-197.


17


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 18 of 24

[30] Kato, H.; Kudo, A. Visible-Light-Response and Photocatalytic Activities of TiO2 and SrTiO3 Photocatalysts Codoped with Antimony and Chromium. J. Phys. Chem. B 2002, 106, 5029-5034. [31] Konta, R.; Ishii, T.; Kato, H.; Kudo, A. Photocatalytic Activities of Noble Metal Ion Doped SrTiO3 under Visible Light Radiation. J. Phys. Chem. B 2004, 108, 8992-8995. [32] Miyauchi, M.; Takashio, M.; Tobimatsu, H. Photocatalytic Activity of SrTiO3 Codoped with Nitrogen and Lanthanum under Visible Light Illumination. Langmuir 2004, 20, 232236. [33] Irie, H.; Maruyama, Y.; Hashimoto, K. Ag+- and Pb2+-Doped SrTiO3 Photocatalysts: A Correlation Between Band Structure and Photocatalytic Activity. J. Phys. Chem. C 2007, 111, 1847-1852. [34] Iwashina, K.; Kudo, A. Rh-Doped SrTiO3 Photocatalyst Electrode Showing Cathodic Photocurrent for Water Splitting under Visible-Light Irradiation. J. Am. Chem. Soc. 2011, 133, 13272-13275.


18

Page 19 of 24

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


TABLE OF CONTENTS IMAGE


19

The Journal of Physical Chemistry Page 20 of 24

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16


Page 21 The of Journal 24 of Physical Chemistry

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37


Page 23 The of Journal 24 of Physical Chemistry

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18



1 2 3 4 5 6 7


Tolerance Factors Revisited: Geometrically Designing the Ideal

Recommend Documents