# Halide Pb-Free Double–Perovskites: Ternary vs. Quaternary Stoichiometry

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## Abstract

**:**

## 1. Introduction

## 2. Ternary Perovskites

#### 2.1. Sn Halide Perovskites

#### 2.2. Ge Halide Perovskites

#### 2.3. Bi and Other Halide Perovskites

#### 2.4. Ternary Halide Double-Perovskites

## 3. Quaternary Double-Perovskites

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**2D perovskite (PEA)${}_{2}$(MA)${}_{2}$[Pb${}_{3}$I${}_{10}$] (1). The inorganic layers in 1 can be structurally derived from MAPbI${}_{3}$ by slicing along specific crystallographic planes. Inset: a PEA cation in the organic layers. Atom colors: Pb = turquoise; I = purple; N = blue; C = gray. Disordered atoms and hydrogens omitted for clarity. (Reprinted with permission from [39]. Copyright 2014 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim).

**Figure 2.**Illustration of phase change details of four CsSnI${}_{3}$ polymorphs and their crystal structures. How phase transitions of CsSnI${}_{3}$ polymorphs proceed is displayed with synthesis conditions and conversion temperatures obtained by in situ, temperature-dependent synchrotron powder XRD studies. Crystal structures of the respective polymorphs are shown: (

**a**) black cubic (B-$\alpha $) at 500 K; (

**b**) tetragonal (B-$\beta $) at 380 K; (

**c**) orthorhombic (B-$\gamma $) at 300 K; (

**d**) yellow (Y) phase at 300 K. Disordered atoms in (

**c**) are omitted for clarity. Cs atoms, blue; Sn atoms, yellow; I atoms, violet. Green dashed lines represent a unit cell. (Reproduced with permission from [60]. Copyright (2012) American Chemical Society.)

**Figure 3.**Lateral view of the $C{s}_{2}$Au${}_{2}$I${}_{6}$ (mauve: I atoms, blue: Au atoms, cyan: Cs atoms). (Reproduced from [53] with permission from The Royal Society of Chemistry).

**Figure 4.**Lateral view of the wavefunction square modulus of (

**a**) the first optically inactive (dark) and (

**b**) the first bright exciton (mauve: I atoms, blue: Au atoms, cyan: Cs atoms; the orange isosurface represents the probability of finding the electron when the hole position (yellow spot) is fixed near a given atomic site). (Reproduced from [53] with permission from The Royal Society of Chemistry).

**Figure 5.**Experimental synthesis and characterization of Cs${}_{2}$BiAgCl${}_{6}$. (

**a**) UV–Vis optical absorption spectrum of Cs${}_{2}$BiAgCl${}_{6}$. The inset shows the Tauc plot, corresponding to an indirect allowed transition (assuming the expression: ($\alpha $h$\nu $)1/2 = C(h$\nu $ – E${}_{g}$), where $\alpha $ is the absorption coefficient, h$\nu $ is the energy of the incoming photon, E${}_{g}$ is the optical band gap, and C is a constant). The straight lines are fitted to the linear regions of the absorption spectrum and Tauc plot, and the intercepts at 2.32 eV and 2.54 eV marked on the plot are calculated from the fit. (

**b**) Steady-state photoluminescence (PL) spectrum of Cs${}_{2}$BiAgCl${}_{6}$, deposited on glass. (

**c**) Time-resolved photoluminescence decay of Cs${}_{2}$BiAgCl${}_{6}$, deposited on glass. The data were fitted using a biexponential decay function. The decay lifetimes of 15 (fast) and 100 ns (slow) were estimated from the fit. (Adapted with permission from [132]. Copyright (2016) American Chemical Society.)

**Figure 6.**(

**A**) X-ray structure of the ordered double perovskite Cs${}_{2}$AgBiBr${}_{6}$ (1). Orange, gray, turquoise, and brown spheres represent Bi, Ag, Cs, and Br atoms, respectively. (

**B**) Photograph of a single crystal of 1. (

**C**) The Bi${}^{3+}$ face-centered-cubic sublattice in 1, consisting of edge-sharing tetrahedra. (Reprinted with permission from [138]. Copyright (2016) American Chemical Society).

**Figure 7.**Schematic of the synthesis route for Cs${}_{2}$AgBiBr${}_{6}$ thin films. The film formation (3.) occurs already while the substrate is spinning. (Reproduced from [149] with permission from The Royal Society of Chemistry).

**Figure 8.**(

**Left**) (A,B) Absorption (blue) and emission (red) spectra of 8 nm Cs${}_{2}$AgBiCl${}_{6}$ (A) and Cs${}_{2}$AgBiBr${}_{6}$ (B) nanocrystals. Absorption spectra were collected from hexane solutions at room temperature and emission spectra were collected on thin films at 20 K using 405 nm (for Cs${}_{2}$AgBiBr${}_{6}$) or 365 nm (for Cs${}_{2}$AgBiCl${}_{6}$) excitation. (

**Right**): Tauc analysis of indirect bandgaps in Cs${}_{2}$AgBiX${}_{6}$. (X = Cl, Br, I). (Adapted with permission from [144]. Copyright (2018) American Chemical Society).

**Figure 9.**Quasiparticle (QP) electronic band structures obtained within the GW perturbative approach; red (blue) indicates occupied (unoccupied) bands. The top of the valence band has been shifted to zero energy for all cases. (Reprinted with permission from [54]. Copyright (2020) American Chemical Society).

**Figure 10.**(

**Left**) Imaginary part of the dielectric function for the three double perovskites, obtained taking into account the QP corrections calculated at the GW level of approximation and also including the excitonic and local-field effects through the solution of the BSE. The up-oriented (down) arrows (and relative numbers) indicate the energetic positions of the indirect (direct) minimum QP gap. (

**Right**) Theoretical absorption coefficient with (orange solid curve) and without (orange dashed curve) the local field and excitonic effects, compared with the experimental curve (black curve) from [138]. The red (dashed and solid) curves are the EELS spectra calculated with e–h effects included for finite transferred momentum Q corresponding to the lowest indirect transition L–X and $\Gamma $–X, respectively. The energetic region where the PL is observed is indicated schematically by the shaded yellow area. (Reprinted with permission from [54]. Copyright (2020) American Chemical Society).

**Table 1.**Main structural, electronic, optical, and PV properties of the 3D ternary single and double-perovskites discussed in the text. In the first column, the species and the crystal symmetry is reported (for CsGeI${}_{3}$, L and H are low and high-temperature polymorphs, respectively) In the second, both theoretical (in parenthesis the level of theory) and experimental values of the lattice parameters are reported. The third column contains the bandgap, theoretical (still in parenthesis the level of calculation) and experimental (in parenthesis the experimental methodology Absorption/Reflectivity and Photoluminescence). The direct (d) and the indirect (i) nature of the gap is similarly reported. The fourth column contains available PV parameters, i.e., the short-circuit current (J${}_{sc}$), the open-circuit voltage (V${}_{oc}$), the fill factor (FF), and the Photoconversion Efficiency ($\eta $)

Lattice | E${}_{\mathit{gap}}$ | J${}_{\mathit{sc}}$(mA cm${}^{-2}$); V${}_{\mathit{oc}}$ (V); | |
---|---|---|---|

Parameters (Å) | (eV) | FF (%); $\mathit{\eta}$ (%) | |

single-perovskite | |||

$\alpha $-CsSnBr${}_{3}$ (P${}_{m3m}$) | a = 5.804 ${}^{a}$; 5.797 ${}^{b}$ | 1.8 (Abs) ${}^{c}$; 1.75 (Abs) ${}^{b}$; 0.351 (LDA, FP-LMTO), 1.690 (QSGW), 1.382 (QSGW+ SOC) ${}^{d}$, 0.58 (LMTO-ASA) ^{e} | 1.57; 0.19; 0.34; 0.10 ${}^{b}$ with SnF${}_{2}$: 3.99; 0.41; 0.58; 0.95 ${}^{b}$; 0.4; 0.1; 33; 0.01 ${}^{f}$ w SnF${}_{2}$: 9.1; 0.42; 57; 2.17 (rev) ${}^{f}$ |

CsSnIBr${}_{2}$ | a = b = c = 5.916 ${}^{b}$ | 1.65 (Abs) ${}^{b}$ | w SnF${}_{2}$ 11.57; 0.311; 0.43; 1.56 ${}^{b}$ |

CsSnI${}_{2}$Br | a = 8.610, b = 8.580, c = 12.393 ${}^{b}$ | 1.37 (Abs) ${}^{b}$ | w SnF${}_{2}$ 15.06; 0.289; 0.38; 1.67 ${}^{b}$ |

$\gamma $-CsSnI${}_{3}$ (Pnam/Pnma) | a = 8.6885, b = 12.3775, c = 8.6384 (Pnam) ${}^{g}$; a = 8.688, b = 8.643, c = 12.378 (Pnma) ${}^{h}$; a = 8.711, b = 8.640, c = 12.398 (Pnma) ${}^{b}$ | 1.27 (Abs) ${}^{b}$; 1.3 (Abs) ${}^{g}$, 0.503 (LDA, FP- LMTO) ${}^{d}$, 0.561 (GGA) ${}^{i}$ | 0.22; 0.0023; 0.57; 3.0×10${}^{-4}$ ${}^{b}$; w SnF${}_{2}$: 27.67; 0.201; 0.29; 1.66 ${}^{b}$ |

L-CsGeI${}_{3}$ (R${}_{3m}$) | a = 5.983, $\alpha $ = 88.61${}^{\xb0}$ ${}^{j}$; a = 5.98, $\alpha $ = 88.6${}^{\xb0}$ ${}^{k}$ | 1.63 (Abs) ${}^{k}$ | 5.7; 0.074; 0.27; 0.11 ${}^{k}$ |

H-CsGeI${}_{3}$ (P${}_{m3m}$) | a = 6.05 ${}^{j}$; a = 5.99 ${}^{k}$ | 0.62 (GGA) ${}^{k}$, 1.93($\Delta $${}^{sol}$ ${}^{l}$) ${}^{k}$ | |

double-perovskite | |||

Cs${}_{2}$In${}_{2}$F${}_{6}$ (F${}_{m}$${}_{\overline{3}}$${}_{m}$) | a = 9.461 (PBE) ${}^{m}$ | 5.50 (d)(BSE + SOC) ${}^{m}$ | SLME: 0.1 (BSE + SOC) ${}^{m}$ |

Cs${}_{2}$In${}_{2}$Br${}_{6}$ (F${}_{m}$${}_{\overline{3}}$${}_{m}$) | a = 11.4771 (PBE) ${}^{m}$ | 2.15 (d) (BSE + SOC) ${}^{m}$ | SLME:11.5 (BSE + SOC) ${}^{m}$; SLME: 11.2 (HSE06 + SOC) ${}^{n}$ |

Cs${}_{2}$Au${}_{2}$Cl${}_{6}$ (I${}_{4/mmm}$) | a = 7.495, c = 10.880 ^{o} | 2.04 (Reflec) ${}^{p}$; 2.08 (HSE06 + GW) ${}^{q}$ | 12.20; 1.72; 0.92; SLME: 19.40 (HSE06 + GW) ${}^{q}$ |

Cs${}_{2}$Au${}_{2}$Br${}_{6}$ (I${}_{4/mmm}$) | a = 7.7592, c = 11.3079 ${}^{r}$; a = 7.759, c = 11.308 ^{o} | 1.60 (Reflec) ${}^{p}$; 1.61 (HSE06 + GW) ${}^{q}$ | 22.90; 1.31; 0.91; SLME: 27.19 (HSE06 + GW) ${}^{q}$ |

Cs${}_{2}$Au${}_{2}$I${}_{6}$ (I${}_{4/mmm}$) | a = 8.284, c = 12.092 ${}^{s}$; a = 8.284, c = 12.092 ^{o} | 1.3 (Reflec) ${}^{p}$; 0.79 (PBE) ${}^{t}$; 1.21 (HSE06) ${}^{t}$; 1.35 (BSE + SOC) ${}^{u}$ 1.45 (HSE06 + GW) ${}^{q}$; 1.34 ${}^{w}$(GLLB-SC ${}^{v}$) | 33.02; 1.04; 0.89; SLME: 30.41 (HSE06 + GW) ${}^{q}$; SLME: 30 (BSE + SOC) ${}^{m}$ |

^{e}Ref. [116]; ${}^{f}$ Ref. [117]; ${}^{g}$ Ref. [60]; ${}^{h}$ Ref. [118]; ${}^{i}$ Ref. [119]; ${}^{j}$ Ref. [120]; ${}^{k}$ Ref. [71]; ${}^{l}$ Ref. [121]; ${}^{m}$ Ref. [54]; ${}^{n}$ Ref. [122];

^{o}Ref. [123]; ${}^{p}$ Ref. [101]; ${}^{q}$ Ref. [124]; ${}^{r}$ Ref. [125]; ${}^{s}$ Ref. [99]; ${}^{t}$ Ref. [100]; ${}^{u}$ Ref. [53]; ${}^{v}$ Ref. [126]; ${}^{w}$ Ref. [127].

**Table 2.**Main structural, electronic, optical, and PV properties of the 3D quaternary double-perovskites discussed in the text. In the first column, the species and the symmetry is reported. In the second, both theoretical (in parentheses, the level of theory) and experimental values of the lattice parameters are reported. The third column contains the bandgap, theoretical (still in parentheses, the level of calculation), and experimental (in parentheses, the experimental methodology, and absorption and photoluminescence values) values. The direct (d) and the indirect (i) nature of the gap is similarly reported. The fourth column contains the available data for the Photoconversion Efficiency ($\eta $).

Lattice Parameter (Å) | E${}_{\mathit{gap}}$ (eV) | $\mathit{\eta}$ (%) | |
---|---|---|---|

Cs${}_{2}$AgBiCl${}_{6}$ (F${}_{m}$${}_{\overline{3}}$${}_{m}$) | a = 10.785 ${}^{a}$; a = 10.777 ${}^{b}$; a = 10.7774 ${}^{c}$; a = 10.6959 (PBESol) ${}^{d}$ | 2.84 (Abs) ${}^{a}$; 2.2 (PL) ${}^{b}$; 2.15 (PL) ^{e}; 2.77 (Abs) ${}^{c}$; 2.89 (Abs,i) ${}^{f}$; 2.62 (HSE06 + SOC) ${}^{g}$; 2.35(i)–2.87(d) (HSE06 + SOC) ${}^{d}$ | 3.90 (HSE06 + SOC) ${}^{d}$ |

Cs${}_{2}$AgBiBr${}_{6}$ (F${}_{m}$${}_{\overline{3}}$${}_{m}$) | a = 11.25 ${}^{h}$; a = 11.2711 ${}^{c}$; a = 11.2011 (PBESol) ${}^{d}$ | 1.95 (i), 2.21 (d) (Abs) ${}^{h}$; 2.19 (Abs) ${}^{c}$; 2.33 (Abs,i) ${}^{f}$; 1.87–2.01 (PBE-G${}_{0}$W${}_{0}$) ${}^{i}$; 1.79(i)–2.45(d) (HSE06 + SOC)${}^{d}$; 1.8(i)–2.36 (d) (BSE + SOC) ${}^{j}$ | 7.25 (simul.) ${}^{k}$; 1.44 ${}^{l}$; 2.23 ${}^{m}$; 2.43 ${}^{n}$; 2.84 (+N719 interlayer) ^{o}; 7.92 (HSE06 + SOC) ${}^{d}$; 10.5 (BSE + SOC) ${}^{j}$ |

Cs${}_{2}$AgBiI${}_{6}$ (F${}_{m}$${}_{\overline{3}}$${}_{m}$) | a = 11.931 (PBESol) ${}^{d}$ | 1.89 (Abs,i) ${}^{f}$; 1.08(i)–1.79(d) (HSE06 + SOC) ${}^{d}$ | 12.37 (HSE06 + SOC) ${}^{d}$ |

Cs${}_{2}$AgInCl${}_{6}$ (F${}_{m}$${}_{\overline{3}}$${}_{m}$) | 10.48059 ${}^{p}$; a = 10.467, a = 10.20 (LDA) ${}^{q}$; 10.60 (HSE06) ${}^{r}$ | 3.23 (PL) ${}^{p}$; 3.3 (Abs), 2.1–2.6 (HSE06), 2.9–3.3 (PBE0) ${}^{q}$ | |

Cs${}_{2}$AgInBr${}_{6}$ (F${}_{m}$${}_{\overline{3}}$${}_{m}$) | a = 10.74 (LDA) ${}^{q}$ | 1.49 (HSE06 + SOC) ${}^{r}$ | 22.5 (HSE06 + SOC) ${}^{r}$ |

Cs${}_{2}$InBiCl${}_{6}$ (F${}_{m}$${}_{\overline{3}}$${}_{m}$) | a = 11.48(PBE). 11.42 (HSE06) ${}^{r}$ | 0.28 (HSE06 + SOC) ${}^{d}$; 0.88 (HSE06 + SOC) ${}^{s}$ | 10.25 (HSE06 + SOC) ${}^{d}$; 30 (HSE06 + SOC) ${}^{g}$; 24.9 (HSE06 + SOC) ${}^{r}$ |

Cs${}_{2}$InBiBr${}_{6}$ (F${}_{m}$${}_{\overline{3}}$${}_{m}$) | a = 11.95 (GGA) ${}^{t}$; a = 11.93 (PBE) ${}^{g}$ | 0.36 (HSE06 + SOC) ${}^{d}$; 0.33 (HSE06 + SOC) ${}^{s}$; 0.29 (HSE06 + SOC) ${}^{r}$ | 10.43 (HSE06 + SOC) ${}^{d}$; 31.9 (HSE06 + SOC) ${}^{r}$ |

Cs${}_{2}$InBiI${}_{6}$ (F${}_{m}$${}_{\overline{3}}$${}_{m}$) | 12.69 (PBE) ${}^{g}$ | 0.0 (HSE06 + SOC) ${}^{g}$; 0.21 (HSE06 + SOC) ${}^{s}$ | |

Cs${}_{2}$AgSbCl${}_{6}$ (F${}_{m}$${}_{\overline{3}}$${}_{m}$) | 10.664 ${}^{u}$; 10.84 (PBE) ${}^{g}$ | 2.54 (Abs) ${}^{u}$; 2.40 (HSE06 + SOC) ${}^{g}$ | |

Cs${}_{2}$AgSbBr${}_{6}$ (F${}_{m}$${}_{\overline{3}}$${}_{m}$) | a = 11.1583 ${}^{v}$, 11.1602 (optB86b-vdW) ${}^{v}$ | 1.89 (Abs, i), 1.64 (Reflec)${}^{v}$; 1.46 (HSE06 + SOC) ${}^{v}$ | 0.1 ${}^{v}$ |

^{e}Ref. [143]; ${}^{f}$ Ref. [144]; ${}^{g}$ Ref. [52]; ${}^{h}$ Ref. [138]; ${}^{i}$ Ref. [145]; ${}^{j}$ Ref. [54]; ${}^{k}$ Ref. [146]; ${}^{l}$ Ref. [147]; ${}^{m}$ Ref. [148]; ${}^{n}$ Ref. [149];

^{o}Ref. [150]; ${}^{p}$ Ref. [134]; ${}^{q}$ Ref. [133]; ${}^{r}$ Ref. [122]; ${}^{s}$ Ref. [151]; ${}^{t}$ Ref. [152]; ${}^{u}$ Ref. [153]; ${}^{v}$ Ref. [137].

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Palummo, M.; Varsano, D.; Berríos, E.; Yamashita, K.; Giorgi, G.
Halide Pb-Free Double–Perovskites: Ternary vs. Quaternary Stoichiometry. *Energies* **2020**, *13*, 3516.
https://doi.org/10.3390/en13143516

**AMA Style**

Palummo M, Varsano D, Berríos E, Yamashita K, Giorgi G.
Halide Pb-Free Double–Perovskites: Ternary vs. Quaternary Stoichiometry. *Energies*. 2020; 13(14):3516.
https://doi.org/10.3390/en13143516

**Chicago/Turabian Style**

Palummo, Maurizia, Daniele Varsano, Eduardo Berríos, Koichi Yamashita, and Giacomo Giorgi.
2020. "Halide Pb-Free Double–Perovskites: Ternary vs. Quaternary Stoichiometry" *Energies* 13, no. 14: 3516.
https://doi.org/10.3390/en13143516