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J. Semicond. > 2020, Volume 41 > Issue 5 > 052201

ARTICLES

Comprehensive first-principles studies on phase stability of copper-based halide perovskite derivatives AlCumXn (A = Rb and Cs; X = Cl, Br, and I)

Zhongti Sun1, 2, Xiwen Chen1, 2 and Wanjian Yin1, 2, 3,

+ Author Affiliations

 Corresponding author: Wanjian Yin, Email: wjyin@suda.edu.cn

DOI: 10.1088/1674-4926/41/5/052201

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Abstract: Recently, inorganic copper-based halide perovskites and their derivatives (CHPs) with chemical formulas AlCumXn (A = Rb and Cs; X = Cl, Br and I; l, m, and n are integers.), have received increasing attention in the photoluminescence field, due to their lead-free, cost-effective, earth-abundant and low electronic dimensionality. Ascribed to flexible valence charge of Cu (Cu1+ and Cu2+) and complex competing phases, the crystal structures and phase stabilities of CHPs are complicated and ambiguous, which limits their experimental applications. Via comprehensive first-principles calculations, we have investigated thermodynamic stabilities of possible crystal phases for AlCumXn by considering all the possible secondary phases existing in inorganic crystal structure database (ICSD). Our results are in agreement with existing experiments and further predicted the existence of 10 stable CHPs, i.e. Rb3Cu2Br5, Rb3Cu2I5, RbCu2Cl3, Rb2CuI3, Rb2CuBr4, RbCuBr3, Rb3Cu2Br7, Cs3Cu2Br7, Cs3Cu2Cl7 and Cs4Cu5Cl9, which have not yet been reported in experiments. This work provides a phase and compositional map that may guide experiments to synthesize more novel inorganic CHPs with diverse properties for potential functional applications.

Key words: first-principles calculationscopper-based halide perovskitestabilityphase diagram

Artificial lighting accounts for one-fifth of global electricity consumption, with a half of that amount consumed by inefficient incandescent and fluorescent emission sources[1, 2]. Recently, metal halide perovskites have gained much attention thanks to their outstanding optoelectronic characters including high photo-absorption efficiency, tunable emission across the entire visible spectrum, exceptional defect tolerance and low-cost synthesis processing[3-5]. Nevertheless, so far, the best-performing halides contain hazardous and bioaccumulative lead and have unsatisfactory stability against moisture and temperature, particularly for organic–inorganic hybrid lead halide perovskites[6-9]. Nowadays replacing the toxic Pb in the perovskite structures with alternative non-toxic, environment-friendly, earth-abundant and cost-effective elements such as transition metals is of critical importance for improving light-emitting capability[10-14].

Recently, Cu-based halide perovskites and their derivatives (CHPs) have been emerging and attracted increasing attention because of the replacement of Pb with abundant, economic and environment-friendly Cu element[10-14]. The rich chemistry of Cu with multiple valence states and low coordination number lead to their complex crystal structures, including 2D layer, 1D chain, 0D isolated units[15]. These low-dimensional crystal structures, resulting in low electronic dimensionality, may give rise to large exciton binding energy (Eb) and high photoluminescent quantum yield (PLQY) due to the quantum confinement effect (QCE)[14, 16]. For example, Eb of 0D Cs4PbBr6 with ~240 meV is much larger than 3D CsPbBr3 with ~18 meV[8, 9]. Recently, Hosono et al. reported in experiment that Cs3Cu2I5 (named as 325-type) films and single crystals owned high PLQY with ~60% and ~90%, respectively[14]. In crystal structure of Cs3Cu2I5 compounds, spatially isolated [Cu2I5]3– anion is surrounded by Cs+ cations and two Cu+ ions possess lower coordination with a tetrahedral and a trigonal types, respectively. Spatially isolated [Cu–I] polyhedron induces enormous Eb with ~490 meV, much higher than Pb-based halide perovskites[14]. Zhao et al. also discovered that another type of CHP Cs2CuX4 (X = Cl, Br, and Br/I, named as 214-type) quantum dots possessed high PLQY of ~50% for blue-green light emitting and excellent air and photo-stability, where spatially isolated [Cu–X] tetrahedron is also surrounded by Cs+ ions and Cu2+ ion possessing tetrahedral coordinations[17]. In the Cs2CuBr4 synthesis processing, the phenomenon about Cu2+ ion partially reducing to Cu+ was observed through X-ray diffraction and the X-ray photoelectron spectroscopy characteristics[17].

Apart from 325- and 214-type CHPs which have been reported in lighting application, other phases such as 123-, 113-, 213-, 327-, and 459-type, have also been reported in experiments[15, 18-21]. Diverse phases of CHPs with isolated [Cu–X] building blocks provide a treasure trove for potential applications in lighting. Nevertheless, the phase stability of AlCumXn (A = Rb and Cs; X = Cl, Br, and I) have not been clearly investigated as shown in Table 1. This has hampered further development of those materials for practical applications. Meanwhile, the ample crystal structures together with variable valence states of Cu, make it difficult to control the synthesis of CHPs. Therefore, it is necessary to provide a landscape of phase stability for CHPs and suggestions of chemical environments to synthesize particular compounds per request.

Table  1.  The Space group of existing CHPs with various types encompassing 325-, 123-, 213-, 459-, 214-, 113-, and 327-type from inorganic crystal structure database (ICSD). ‘√’ and blank grid symbol indicates the existing and non-existing phase in experiment, respectively.
TypeSpace group (No.)Rb Cs
ClBrI ClBrI
325Pnma (62)
123Cmcm (63)
213Pnma (62)
459Pc (7)
214Pnma (62)
Cmca (64)
113P6122 (178)
C2221 (20)
Pbcn (60)
327Ccca (68)
DownLoad: CSV  | Show Table

In this paper, first-principles calculations are performed to comprehensively investigate the thermodynamic stability of CHPs (AlCumXn, A = Rb and Cs; X = Cl, Br, and I) based on thermodynamic equilibrium growth condition. In total, there are 42 CHPs compounds with seven kinds of stoichiometric ratio including A3Cu2X5, ACu2X3, A2CuX3, A4Cu5X9, A2CuX4, ACuX3, and A3Cu2X7, as shown in Table 1. For chemical environments and stability calculations, all possible competing phases including compositional elements Rb, Cs, Cu, Cl, Br, I, binary compounds and ternary compounds from inorganic crystal structure database (ICSD) have been considered. We have found that most of existing AlCumXn phases in experiments have a stable growth region and positive decomposition energy in our calculations, which confirms the reliability of our calculations. Moreover, we also acquire ten new and stable phases encompassing Rb3Cu2I5, Rb3Cu2Br5, RbCu2Cl3, Rb2CuI3, Rb2CuBr4, RbCuBr3, Rb3Cu2Br7, Cs3Cu2Br7, Cs3Cu2Cl7, and Cs4Cu5Cl9, which are not yet reported experimentally. Therefore, our work provides prospective guidance for experiment to synthesize the above phases, amplifying the scope of phases of CHPs.

All of the calculations were executed with spin-unrestricted density functional theory method, as implemented in the Vienna ab-initio simulation package (VASP)[22] by using the projector augmented wave (PAW) pseudopotential[23]. We employ the generalized gradient approximation (GGA) parametrized by Perdew, Burker, and Ernzerhof (PBE)[24] as electronic exchange-correlation functional. The kinetic energy cutoff with plane wave basis set is 400 eV and the k-point meshes with grid spacing of 2π × 0.025 Å–1. All of the structures were fully relaxed until the total energy and force per atom were less than 10–4 eV and –0.01 eV/Å, respectively.

To evaluate the thermodynamic stability of CHPs AlCumXn (A = Rb and Cs; X = Cl, Br, and I) with different types, we first calculate the chemical potential range for equilibrium growth of compound to identify the proper chemical potentials for synthesizing particular compounds in experiments[25, 26]. Second, we quantitatively calculated the thermodynamic stability via considering the optimal decomposition pathways to their competing phases through linear programming. For calculation of chemical potential range, the chemical potential μα (α is the element that constituted to the CHPs) is constrained by the values that keep a stable host compound, and avoid the formation of other competing phases, including elemental solids. The thermodynamic equilibrium growth conditions need to satisfy the following three relations.

lμA+mμCu+nμX=ΔH(AlCumXn),l,m,n=1,2,,N, (1)
μα (2)
{h_i}{\mu _{\rm{A}}} + {k_i}{\mu _{{\rm{Cu}}}} + {l_i}{\mu _{\rm{X}}} \leqslant \Delta H\left( {{{\rm{A}}_{{h_i}}}{\rm{C}}{{\rm{u}}_{{k_i}}}{{\rm{X}}_{{l_i}}}} \right),\;\;i = 1,2, \ldots ,N, (3)

where μα is the chemical potential of constituent element α referring to the stable solid/gas in the growth conditions. ΔH is the formation enthalpy, AlCumXn and { {{\rm{A}}_{{h_i}}}{\rm{C}}{{\rm{u}}_{{k_i}}}{{\rm{X}}_{{l_i}}}} represent the thermodynamic equilibrium phase and all the existing competing phases, respectively. Eq. (1) is for the thermodynamic equilibrium growth condition, Eq. (2) is to avoid the atomic species that depositing to elemental phases, Eq. (3) is to hamper all the existing competing phase.

Then, the thermodynamic stability of CHPs AlCumXn was furtherly confirmed through decomposition energy calculation based on optimal decomposition pathway (ODP) using linear programming method. Specific details are as follows:

{{\rm{A}}_l}{\rm{C}}{{\rm{u}}_m}{{\rm{X}}_n} \to \mathop \sum \limits_{i = 1}^i {x_i}{}{{\rm{A}}_{{h_i}}}{\rm{C}}{{\rm{u}}_{{k_i}}}{{\rm{X}}_{{l_i}}}, (4)
\Delta {H_d} = \mathop \sum \limits_{i = 1}^i {x_i}E\left( {{{\rm{A}}_{{h_i}}}{\rm{C}}{{\rm{u}}_{{k_i}}}{{\rm{X}}_{{l_i}}}} \right) - E\left( {{{\rm{A}}_l}{\rm{C}}{{\rm{u}}_m}{{\rm{X}}_n}} \right), (5)
\mathop \sum \limits_{i = 1}^i {x_i}{h_i} = l,\quad\mathop \sum \limits_{i = 1}^i {x_i}{k_i} = m,\quad\mathop \sum \limits_{i = 1}^i {x_i}{l_i} = n, (6)
0 \leqslant {x_i} \leqslant {\rm{min}}\left( {\frac{l}{{{h_i}}},\frac{m}{{{k_i}}},\frac{n}{{{l_i}}}} \right), (7)

where the xi is the molar fraction of possible competing phases, unknown variables. Eq. (4) is the decomposition pathway of host compounds, Eq. (5) is the decomposition energy between existing competing phases and host phase, Eq. (6) is the mass-conservation constraints for all atomic species, Eq. (7) is the minimum value of xi. The linear programming approach ensures that the calculated decomposition energy is based on the optimal decomposition pathway. If the value of ΔHd is a positive number, then this decomposition reaction is an endothermic reaction, indicating that this compound is thermodynamically stable.

A3Cu2X5 phase exhibits orthorhombic crystal structure with space group of Pnma (No. 62) as shown in Fig. 1(a). It has two types of Cu+ ion sites, a tetrahedral site and a trigonal site, each of which constitutes spatially isolated [Cu2X5]3 (X = Cl, Br, I), encircled by A+ (A = Rb, Cs) ions. Thermodynamic stability of six kinds of 325-type CHPs are evaluated based on thermodynamic equilibrium growth conditions and decomposition energy with ODP as shown in Fig. 1(b) and Table 2, respectively. Except for Rb3Cu2Cl5, all five compounds possess stability region in cyan polygon. In consistent with experiments, Cs3Cu2X5 (X = Cl, Br, I) have been synthesized in experiments and Cs3Cu2I5 has been applied to the luminescent equipment with high PLQY[14]. Our results show that Rb3Cu2I5 and Rb3Cu2Br5 can also be stable but Rb3Cu2Cl5 is unstable. The minimum decomposition energies together with corresponding decomposition pathways calculated by linear programing method have been shown in Table 2. Interestingly, the ODP of Cs3Cu2Cl5 perovskite are different for Cs3Cu2Br5 and Cs3Cu2I5, i.e. Cs3Cu2X5 → 2CsX + CsCu2X3, X = Br and I, their ΔHd are 25 and 29 meV/atom for the X site of Br and I, respectively. These decomposition reactions are non-redox processes. In contrast to these two compounds, the ODP of Cs3Cu2Cl5 perovskite is a disproportionation reaction with ΔHd of 33 meV/atom, namely Cs3Cu2Cl5 → Cu + CsCl + Cs2CuCl4, the competing phase has CsCl secondary phase, it is also consistent with experiment that CsCl additional phase observed as minor impurity[15]. So it should be carefully controlled in the synthesis process. If the decomposition pathway of Cs3Cu2Cl5 perovskite is same as the ODP of Cs3Cu2X5 (X = Br and I), then its decomposition energy is 39 meV/atom, which is a little larger than the ODP by 6 meV/atom. For Rb3Cu2X5 (X = Cl, Br, and I), their ODPs are all non-redox reactions, Rb3Cu2I5 phase owns the similar ODP with the Cs3Cu2I5 phase by ΔHd of 12 meV/atom, but different from the ODP of Rb3Cu2Br5 phase with ΔHd of 5 meV/atom, i.e., Rb3Cu2Br5 → 4/3Rb2CuBr3 + 1/3RbCu2Br3. For Rb3Cu2Cl5, because of more complex competing phases, the ODP with ΔHd of –2 meV/atom is Rb3Cu2Cl5 → 7/5RbCl + 2/5Rb4Cu5Cl9, suggesting its poorer stability than its bromide and iodide counterparts.

Figure  1.  (Color online) (a) The optimized structure of CHPs with 325-type, they own the isostructural model with space group of Pnma, isolated [Cu2X5]3– anion unit is composed of two types of Cu+ sites, a trigonal site and a tetragonal site. (b) Calculated phase stability regions versus μCu and μX (referring to the chemical potential of Cu and X from that of their elementary substance) from left to right for the X site of I, Br, and Cl element and up to down for Cs and Rb element on A site, respectively. The cyan polygon region represents thermodynamic stability growth region, which is encircled by possible competing phases using colored line (red, blue, violet, and pink). A, Cu, and X atoms are in purple, coral and brown, respectively.
Table  2.  Calculated decomposition energies together with ODP in the CHPs AlCumXn (A = Rb and Cs; X = Cl, Br, and I; l, m, and n are integers).
CompoundΔHd (meV/atom)Optimal decomposition pathway
325-typeCs3Cu2I525Cs3Cu2I5 → 2CsI + CsCu2I3
Cs3Cu2Br529Cs3Cu2Br5 → 2CsBr + CsCu2Br3
Cs3Cu2Cl533Cs3Cu2Cl5 → Cu + CsCl + Cs2CuCl4
Rb3Cu2I513Rb3Cu2I5 → 2RbI + RbCu2I3
Rb3Cu2Br55Rb3Cu2Br5 → 4/3Rb2CuBr3 + 1/3RbCu2Br3
Rb3Cu2Cl5–2Rb3Cu2Cl5 → 7/5RbCl + 2/5Rb4Cu5Cl9
123-typeCsCu2I30CsCu2I3 → 4/3CuI + 1/3Cs3Cu2I5
CsCu2Br322CsCu2Br3 → 4/3CuBr + 1/3Cs3Cu2Br5
CsCu2Cl324CsCu2Cl3 → 4/3CuCl + 1/3Cu3Cu2Cl5
RbCu2I323RbCu2I3 → RbI + 2CuI
RbCu2Br328RbCu2Br3 → 3/2CuBr + 1/2Rb2CuBr3
RbCu2Cl36RbCu2Cl3 → 3/4CuCl + 1/4Rb4Cu5Cl9
213-typeCs2CuI3–22Cs2CuI3 → 1/2CsI + 1/2Cs3Cu2I5
Cs2CuBr3–16Cs2CuBr3 → 1/2CsBr + 1/2Cs3Cu2Br5
Cs2CuCl3–19Cs2CuCl3 → 1/2CsCl + 1/2Cs3Cu2Cl5
Rb2CuI36Rb2CuI3 → 3/2RbI + 1/2RbCu2I3
Rb2CuBr36Rb2CuBr3 → 3/2RbBr + 1/2RbCu2Br3
Rb2CuCl38Rb2CuCl3 → 1/2Cu + RbCl + 1/2Rb2CuCl4
459-typeCs4Cu5I9–20Cs4Cu5I9 → 3/4Cs3Cu2I5 + 7/4CsCu2I3
Cs4Cu5Br9–9Cs4Cu5Br9 → 3/4Cs3Cu2Br5 + 7/4CsCu2Br3
Cs4Cu5Cl98Cs4Cu5Cl9 → 3/4Cs3Cu2Cl5 + 7/4CsCu2Cl3
Rb4Cu5I9–17Rb4Cu5I9 → 3/2RbI + 5/2RbCu2I3
Rb4Cu5Br9–4Rb4Cu5Br9 → Rb2CuBr3 + 2RbCu2Br3
Rb4Cu5Cl922Rb4Cu5Cl9 → 12/5Cu + 1/5Rb2CuCl3 + 6/5Rb3Cu2Cl7
214-typeCs2CuI4–17Cs2CuI4 → 1/2CsI3 + 1/2Cs3Cu2I5
Cs2CuBr414Cs2CuBr4 → 1/2CsBr + 1/4CsBr3 + 1/2CsCuBr3 + 1/4Cs3Cu2Br5
Cs2CuCl434Cs2CuCl4 → CsCl + CsCuCl3
Rb2CuI4–2Rb2CuI4 → RbI + 1/2RbI3 + 1/2RbCu2I3
Rb2CuBr410Rb2CuBr4 → 2RbBr + CuBr2
Rb2CuCl4–9Rb2CuCl4 → 1/2RbCl + 1/2Rb3Cu2Cl7
113-typeCsCuI3–34CsCuI3 → 1/2CsI3 + 1/2CsCu2I3
CsCuBr319CsCuBr3 → 1/2CuBr2 + 1/2Cs2CuBr4
CsCuCl35CsCuCl3 → 1/2CuCl2 + 1/2Cs2CuCl4
RbCuI3–42RbCuI3 → 1/2RbI3 + 1/2RbCu2I3
RbCuBr321RbCuBr3 → RbBr + CuBr2
RbCuCl3–10RbCuCl3 → 1/3CuCl2 + 1/3Rb3Cu2Cl7
327-typeCs3Cu2I7–31Cs3Cu2I7 → CsI3 + 1/2Cs3Cu2I5 + 1/2CsCu2I3
Cs3Cu2Br79Cs3Cu2Br7 → Cs2CuBr4 + CsCuBr3
Cs3Cu2Cl79Cs3Cu2Cl7 → CsCuCl3 + Cs2CuCl4
Rb3Cu2I7–31Rb3Cu2I7 → RbI + RbI3 + RbCu2I3
Rb3Cu2Br723Rb3Cu2Br7 → 3RbBr + 2CuBr2
Rb3Cu2Cl715Rb3Cu2Cl7 → Rb2CuCl4 + RbCuCl3
DownLoad: CSV  | Show Table

ACu2X3 phase exhibits orthorhombic space group of Cmcm (No. 63), the 1D chain with two [Cu–X] tetrahedra through edge-sharing in a row, isolated by A+ ion, as shown in Fig. 2(a). Fig. 2(b) shows the stability region of ACu2X3 phase in chemical potential map. The results show that all the ACu2X3 (A = Rb and Cs; X = Cl, Br, and I) compounds have thermodynamic stability region with cyan polyhedron, surrounded by the boundary composed of competing phases, which is in agreement with existing experiments that five of them have been synthesized successfully in experiments[15], except for RbCu2Cl3. The minimum decomposition energies together with corresponding decomposition pathways have been shown in Table 2, well matching the thermodynamic stability region calculations. CsCu2X3 possess the same ODP, i.e., CsCu2X3 → 4/3CuX + 1/3Cs3Cu2X5 (X = Cl, Br, and I). Their corresponding ΔHd are 0, 22, and 24 meV/atom for CsCu2I3, CsCu2Br3, CsCu2Cl3, respectively. The ODPs of RbCu2I3, RbCu2Br3, and RbCu2Cl3 are all different, i.e., RbCu2I3 → RbI + 2CuI, RbCu2Br3 → 3/2CuBr + 1/2Rb2CuBr3, RbCu2Cl3 → 3/4CuCl + 1/4Rb4Cu5Cl9. Their decomposition energies are 23, 27, and 6 meV/atom for RbCu2I3, RbCu2Br3, and RbCu2Cl3, respectively. Considering that CsCu2I3 has a small stability region and tiny ΔHd, experimental synthesis of its Rb counterpart may be easier since RbCu2Cl3, has much larger stable region and corresponding larger decomposition energies, which may be more useful in photoluminescence fields than CsCu2X3.

Figure  2.  (Color online) (a) The structure model of CHPs with 123-type, they all own octahedral structure with the space group of Cmcm (No. 63), composed of edge-sharing [CuX4] tetrahedron 1D chain. (b) Calculated thermodynamic stability regions of ACu2X3 (A = Rb and Cs; X = Cl, Br, and I) CHPs versus μCu and μX (deviation of actual chemical potential of Cu and X from that of their elementary substance). The above from left to right is the CHP for the X site of I, Br, and Cl element, and up to down is for Cs and Rb element on A site, respectively. The cyan polygon region represents thermodynamic stable interval, which is surrounded by competing phases using colored line (red, blue, orange, violet, and pink). A, Cu, and X atoms are in purple, coral and brown, respectively.

In contrast from the ACu2X3 phase with wider 1D chain by two Cu+ ions in one row, the A2CuX3 phase with the symmetry of Pnma (No. 62) also owns a 1D chain with only one Cu+ ion via vertex-sharing one line in Fig. 3(a). Their phase stability regions versus the chemical potential of Cu and X element are shown in Fig. 3(b). Only Rb2CuI3 and Rb2CuBr3 possess slim stability region with cyan polyhedron. Meanwhile, Rb2CuBr3 phase has been synthesized successfully in experiments[15]. Even though Rb2CuCl3 perovskite has no stability region from simulation, the decomposition energy calculations confirmed that its ΔHd with ODP is a positive number with 8 meV/atom, namely Rb2CuCl3 → 1/2Cu + RbCl + 1/2Rb2CuCl4, as shown in Table 2. Indeed, Rb2CuCl3 exists in experiments and the additional competing phase RbCl was also observed, consistent with our predictions in the ODP[15]. In addition, Rb2CuI(Br)3 phases own the same ODP with positive ΔHd, i.e. Rb2CuX3 → 3/2RbX + 1/2RbCu2X3, X = Br, I. While the 213-type CHP with the A site of Cs element also possess the same ODP, namely Cs2CuX3 → 1/2CsX + 1/2Cs3Cu2X5, X = Cl, Br, and I, their ΔHd are all negative indicating their instability.

Figure  3.  (Color online) (a) The structure model of CHPs with 213-type, they possess isostructural model with Pnma symmetry, which is composed of 1D [Cu–X] tetrahedron chain with isolated alkali metal cation (Rb+ , Cs+ ). (b) Calculated phase stability regions in cyan polygon of A2CuX3 (A = Cs and Rb; X = I, Br, and Cl) CHPs versus μCu and μX (deviation of actual chemical potential of Cu and X from that of their elementary substance). The cyan polygon region indicates thermodynamic phase stability growth interval, which is encompassed by competing phases with colored line (red, blue, and pink). A, Cu, and X atoms are in purple, coral and brown, respectively.

A4Cu5X9 compound is also a class of complex Cu-based compounds in Fig. 4(a). The crystal structure with the space group of Pc (No. 7) owns three types of Cu+ site, a tetragonal site, a trigonal site, and a 2-fold coordination site, which forms 0D isolated [Cu5X9]4– anion, isolated by A+ ions. Their phase stability regions versus the chemical potential of Cu and X element are shown in Fig. 4(b). Only two compounds, Rb4Cu5Cl9 and Cs4Cu5Cl9 own slim stability region with cyan polygon, surrounded by competing phases. The decomposition energies are 21 and 8 meV/atom for Rb4Cu5Cl9 and Cs4Cu5Cl9, respectively, in Table 2. Other 459-type CHP have negative ΔHd with the ODP. It is observed that the ODP for Rb4Cu5Cl9 phase is a disproportionation reaction, i.e., Rb4Cu5Cl9 → 12/5Cu + 1/5Rb2CuCl3 + 6/5Rb3Cu2Cl7, while for the Cs4Cu5Cl9, it is a non-redox reaction, i.e., Cs4Cu5Cl9 → 3/4Cs3Cu2Cl5 + 7/4CsCu2Cl3. Experimentally, Rb4Cu5Cl9 perovskite had been able to synthesize successfully, matches well with our predictions[15].

Figure  4.  (Color online) (a) The structure model of 459-type CHPs with space group of Pc, they own isolated [Cu5X9]4– anion with three types of Cu+ ions, a tetrahedral site, a trigonal site and a 2-fold coordination site. (b) Calculated thermodynamic stability regions of 459-type CHPs against μCu and μX (deviation of actual chemical potential of Cu and X from that of their elementary substance). The cyan polygon region reveals thermodynamic stable growth interval and each colored line corresponds to one most probable competing phase. A, Cu, and X atoms are in purple, coral and brown, respectively.

Since all the above CHPs own monovalent Cu+ ion on B site, their maximum coordination number is four, induced by higher 3d10 energy level and smaller ion radius of Cu, in consistent with the report by Xiao et al.[16]. The CHPs with divalent Cu2+ ion on B site also possess abundant phases, such as 214-, 113-, and 327-type, most of which are constituted with elongated [Cu–X] octahedra, induced by Jahn-Teller distortion, except for 214-type with space group of Pnma (No. 62), which is composed of 0D [Cu–X] tetrahedra, isolated by A+ ions, as shown in Fig. 5(a). In addition to Pnma crystal structure, Rb2CuCl4 compounds can exist in Cmca (No. 64) structure with 2D layers of corner-sharing [CuCl4]2– octahedra[17-19]. The comparisons of total energy for non-existing compounds with two crystal structures are calculated in Table 3. The equilibrium growth region of A2CuX4 compounds with stable crystal phases are assessed in Fig. 5(b). Cs2CuCl4 undergoes non-redox ODP with ΔHd of 34 meV/atom: Cs2CuCl4 → CsCl + CsCuCl3, while Cs2CuBr4 goes through a redox ODP with ΔHd of 14 meV/atom, i.e., Cs2CuBr4 → 1/2CsBr + 1/4CsBr3 + 1/2CsCuBr3 + 1/4Cs3Cu2Br5, due to more competing phases. Experimentally, the Cu2+ ions of Cs2CuBr4 perovskite can be partially reduced to Cu+ ions. Our calculations reveal that the Cu+ may exist in the occurrence of Cs3Cu2Br5 compound[17]. Although Rb2CuCl4 has been reported in experiments, we haven’t found its stability region and its ΔHd is also negative (–9 meV/atom) with ODP, Rb2CuCl4 → 1/2RbCl + 1/2Rb3Cu2Cl7. The discrepancies may be ascribed to the computational errors. Meanwhile, we suggested to double check the experimental results for Rb2CuCl4, in particular to possible existence of secondary phases including RbCl and Rb3Cu2Cl7. For A2CuX4 compounds, we discover a novel and stable 214-type CHPs Rb2CuBr4 via phase stability region in cyan polygon and decomposition energy with ODP by ΔHd of 10 meV/atom, i.e. Rb2CuBr4 → 2RbBr + CuBr2.

Table  3.  The relative energy per formula unit (eV/f.u.) of 214-type CHPs including Cs2CuI4, Rb2CuI4, and Rb2CuBr4 in the different space group encompassing Pnma and Cmca, which are all non-existing phase in the ICSD.
Space groupCs2CuI4Rb2CuI4Rb2CuBr4
Pnma0.000.000.00
Cmca0.290.330.04
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Figure  5.  (Color online) (a) The structure model of 214-type CHPs, most of them possess octahedral space group Pnma with isolated [Cu–X] tetrahedron. But for Rb2CuCl4, it owns Cmca symmetry with 2D [Cu2Cl4]2– layers, induced by [Cu-Cl] octahedron Jahn-Teller distortion. (b) Calculated thermodynamic stability regions of A2CuX4 (A = Rb and Cs; X = Cl, Br, and I) halide perovskites versus μCu and μX (deviation of actual chemical potential of Cu and X from that of their elementary substance). The horizontal and vertical axis is from I to Cl element and from Cs to Rb element, respectively. The cyan polygon region shows thermodynamic stability growth interval, which is encircled by most probable competing phases with colored lines (red, blue, violet, and pink). A, Cu, and X atoms are in purple, coral and brown, respectively.

Due to the divalent Cu2+ ions, the crystal structure of ACuX3 compounds also own elongated [Cu–X] octahedra via corner- and face-sharing connection, forming spatially isolated 1D coplanar chain and 3D network through vertex-sharing, surrounded by A+ ion in Fig. 6(a). Experimentally, CsCuBr3, CsCuCl3, and RbCuCl3 compounds have been synthesized successfully, where CsCuBr3 phase with space group of C2221 symmetry (No. 20) owns 3D network via vertex-sharing connection by coplanar double [CuX6] octahedron unit, while CsCuCl3 and RbCuCl3 phases possess 1D chain through face-sharing [CuX6] octahedron, they have different space group P6122 (No. 178) and Pbcn (No. 60), respectively[20, 21]. The stable structures of other non-existing 113-type compounds in experiment are calculated according to the above existing crystal structures, as summed in Table 4. These stable structures with the lowest energy all own C2221 symmetry, same as CsCuBr3 phase. Then the phase stability regions of the above six 113-type CHP are evaluated via thermodynamic equilibrium growth conditions, as shown in Fig. 6(b). In consistent with the experiment, CsCuBr(Cl)3 compounds all possess slim stability region. Theoretical calculations did not find stability region for experiment existing RbCuCl3, which may due to the computational errors or experimental ignorance of secondary phases, similar to the case of Rb2CuCl4. Meanwhile, we discover a new stable RbCuBr3, with long and narrow stability region and positive decomposition energies of 20 meV/atom, i.e., RbCuBr3 → RbBr + CuBr2, as shown in Table 2. This means that RbCuBr3 compound is not prone to disintegrating their competing phases RbBr and CuBr2. Based on the above research, we also find a new 113-type CHPs with C2221 symmetry RbCuBr3 to be stable.

Table  4.  The relative energy per formula unit (eV/f.u.) of 113-type CHP including CsCuI3, RbCuI3, and RbCuBr3 in the different space group containing C2221, P6122, Pbcn, which are non-existing phase in the ICSD.
Space groupCsCuI3RbCuI3RbCuBr3
C22210.000.000.00
P61220.030.020.10
Pbcn0.150.090.11
DownLoad: CSV  | Show Table
Figure  6.  (Color online) (a) The structure model of 113-type CHPs, even though they possess different structures, they all have the same [CuX6] octahedron unit via face- and corner-sharing. (b) Calculated thermodynamic stability regions of ACuX3 (A = Rb and Cs; X = Cl, Br, and I) versus μCu and μX (deviation of actual chemical potential of Cu and X from that of their elementary substance). The horizontal and vertical axis is from I to Cl element and from Cs to Rb element, respectively. The cyan polygon region represents thermodynamic stable growth interval, which is surrounded by most probable competing phases using colored line (red, blue, orange, violet, and pink). A, Cu, and X atoms are in purple, coral and brown, respectively.

Last but not least, A3Cu2X7 phase with Cu2+ ion on B site owns spatially isolated 2D [Cu2Cl7]3– anion layer with double [Cu–X] octahedron layer by A+ ions, disparity with Rb2CuCl4 by single [Cu–Cl] octahedron layer, as illustrated in Fig. 7(a). Their stability growth regions in cyan polygon are also assessed against μCu and μX in Fig. 7(b). Except for Cs(Rb)3Cu2I7 compounds, others possess stability region with cyan polygon, consistent with the predictions of decomposition energy in Table 2. Experimentally, Rb3Cu2Cl7 compound has been synthesized successfully, our prediction signifies the experimental discovery[15]. In the 327-type CHP, we additionally discover three stable compounds, named as Cs3Cu2Br(Cl)7 and Rb3Cu2Br7. Their ODPs are all non-redox reaction, where Cs3Cu2Br(Cl)7 compounds own similar ODP with ΔHd of 9 and 9 meV/Å for the X site of Br and Cl element, respectively, i.e. Cs3Cu2X7 → Cs2CuX4 + CsCuX3, X = Br, Cl. For Rb3Cu2Br7 phase, the ODP with ΔHd of 23 meV/Å is Rb3Cu2Br7 → 3RbBr + 2CuBr 2. Therefore, three new compounds in the 327-type CHPs, namely Cs3Cu2Br(Cl)7 and Rb3Cu2Br7 are predicted to be stable.

Figure  7.  (Color online) (a) The structure model of 327-type CHPs, they all own tetragonal space group Ccca with isolated [Cu2X7]3– anion composing of elongated [Cu–X] octahedron unit. (b) Calculated thermodynamic stability regions of 327-type CHPs versus μCu and μX (deviation of actual chemical potential of Cu and X from that of their elementary substance). The cyan polygon region represents phase stability growth condition, which is encircled by competing phases using colored line (red, blue, violet, and pink). A, Cu, and X atoms are in purple, coral and brown, respectively.

Table 5 summarizes the phase stability cases encompassing phase stability region and decomposition energy of ODP, whether or not they exist at room temperature. Most of existing phases are stable according to our predictions, except for Rb2CuCl4 and RbCuCl3 perovskites because they have more binary and ternary secondary phases and computational errors. Surprisingly, we also discover 10 novel CHPs with specific stability region and positive decomposition energy with ODP (i.e., Rb3Cu2I(Br)5, RbCu2Cl3, Rb2CuI3, Rb2CuBr4, RbCuBr3, Rb3Cu2Br7, Cs3Cu2Br(Cl)7 and Cs4Cu5Cl9) which have not yet been reported in experiment. Our results offer importance guidance to synthesize these phases, consequently broadening the range of existing CHPs.

Table  5.  Summary for the stability region and decomposition energy of ODP in the different type CHPs AlBmXn (A = Rb and Cs; B = Cu; X = Cl, Br, and I; l, m, and n are integers; named as lmn-type). For each type CHP, number 1 and 2 represent decomposition energy and stability region, respectively. ‘√’ and ‘×’ symbols indicate ‘stable’ and ‘non-stable’ phase, respectively. Yellow square shows that this type is existing phase from inorganic Crystal Structure Database (ICSD).
ABX325123213459214113327
CsCuI××××××××××
Br××××
Cl××
RbI××××××××
Br××
Cl×××××××
Note: 1: Decomposition energy.
2: Stability region. √: stable. × : Non-stable. : Exist.
DownLoad: CSV  | Show Table

In summary, we have systematically studied the stability of all ternary CHPs considering thermodynamic equilibrium growth conditions and decomposition energies. They all own lower electronic dimensionality including 2D layered, 1D chained and 0D isolated unit, surrounded by A+ ions. The coordination number of monovalent Cu (Cu+) in the CHP is less than 4, namely, 2-fold, trigonal, tetragonal site. The vast majority of CHPs with Cu2+ ion possess elongated octahedron induced by Jahn-Teller distortion. Most of existing CHPs are predicted to be stable, which is in consistent with the experiment. Furthermore, we discovered ten novel phases with specific stability region and positive decomposition energy with ODP via element exchange method, i.e. Rb3Cu2I(Br)5, RbCu2Cl3, Rb2CuI3, Rb2CuBr4, RbCuBr3, Rb3Cu2Br7, Cs3Cu2Br(Cl)7 and Cs4Cu5Cl9, which are not yet reported in experiment. Our predictions may provide insights for experimentalists to synthesize more novel inorganic CHPs, and will therefore tremendously expand the scope of existing CHP with promising applications.

The authors acknowledge funding support from National Natural Science Foundation of China (grant No. 11674237 and 51602211); National Key Research and Development Program of China (grant No. 2016YFB0700700); Natural Science Foundation of Jiangsu Province of China (grant No. BK20160299); the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD); and China Post-doctoral Foundation (grant No. 7131705619). The theoretical work was carried out at National Supercomputer Center in Tianjin and the calculations were performed on TianHe-1(A).



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Fig. 1.  (Color online) (a) The optimized structure of CHPs with 325-type, they own the isostructural model with space group of Pnma, isolated [Cu2X5]3– anion unit is composed of two types of Cu+ sites, a trigonal site and a tetragonal site. (b) Calculated phase stability regions versus μCu and μX (referring to the chemical potential of Cu and X from that of their elementary substance) from left to right for the X site of I, Br, and Cl element and up to down for Cs and Rb element on A site, respectively. The cyan polygon region represents thermodynamic stability growth region, which is encircled by possible competing phases using colored line (red, blue, violet, and pink). A, Cu, and X atoms are in purple, coral and brown, respectively.

Fig. 2.  (Color online) (a) The structure model of CHPs with 123-type, they all own octahedral structure with the space group of Cmcm (No. 63), composed of edge-sharing [CuX4] tetrahedron 1D chain. (b) Calculated thermodynamic stability regions of ACu2X3 (A = Rb and Cs; X = Cl, Br, and I) CHPs versus μCu and μX (deviation of actual chemical potential of Cu and X from that of their elementary substance). The above from left to right is the CHP for the X site of I, Br, and Cl element, and up to down is for Cs and Rb element on A site, respectively. The cyan polygon region represents thermodynamic stable interval, which is surrounded by competing phases using colored line (red, blue, orange, violet, and pink). A, Cu, and X atoms are in purple, coral and brown, respectively.

Fig. 3.  (Color online) (a) The structure model of CHPs with 213-type, they possess isostructural model with Pnma symmetry, which is composed of 1D [Cu–X] tetrahedron chain with isolated alkali metal cation (Rb+ , Cs+ ). (b) Calculated phase stability regions in cyan polygon of A2CuX3 (A = Cs and Rb; X = I, Br, and Cl) CHPs versus μCu and μX (deviation of actual chemical potential of Cu and X from that of their elementary substance). The cyan polygon region indicates thermodynamic phase stability growth interval, which is encompassed by competing phases with colored line (red, blue, and pink). A, Cu, and X atoms are in purple, coral and brown, respectively.

Fig. 4.  (Color online) (a) The structure model of 459-type CHPs with space group of Pc, they own isolated [Cu5X9]4– anion with three types of Cu+ ions, a tetrahedral site, a trigonal site and a 2-fold coordination site. (b) Calculated thermodynamic stability regions of 459-type CHPs against μCu and μX (deviation of actual chemical potential of Cu and X from that of their elementary substance). The cyan polygon region reveals thermodynamic stable growth interval and each colored line corresponds to one most probable competing phase. A, Cu, and X atoms are in purple, coral and brown, respectively.

Fig. 5.  (Color online) (a) The structure model of 214-type CHPs, most of them possess octahedral space group Pnma with isolated [Cu–X] tetrahedron. But for Rb2CuCl4, it owns Cmca symmetry with 2D [Cu2Cl4]2– layers, induced by [Cu-Cl] octahedron Jahn-Teller distortion. (b) Calculated thermodynamic stability regions of A2CuX4 (A = Rb and Cs; X = Cl, Br, and I) halide perovskites versus μCu and μX (deviation of actual chemical potential of Cu and X from that of their elementary substance). The horizontal and vertical axis is from I to Cl element and from Cs to Rb element, respectively. The cyan polygon region shows thermodynamic stability growth interval, which is encircled by most probable competing phases with colored lines (red, blue, violet, and pink). A, Cu, and X atoms are in purple, coral and brown, respectively.

Fig. 6.  (Color online) (a) The structure model of 113-type CHPs, even though they possess different structures, they all have the same [CuX6] octahedron unit via face- and corner-sharing. (b) Calculated thermodynamic stability regions of ACuX3 (A = Rb and Cs; X = Cl, Br, and I) versus μCu and μX (deviation of actual chemical potential of Cu and X from that of their elementary substance). The horizontal and vertical axis is from I to Cl element and from Cs to Rb element, respectively. The cyan polygon region represents thermodynamic stable growth interval, which is surrounded by most probable competing phases using colored line (red, blue, orange, violet, and pink). A, Cu, and X atoms are in purple, coral and brown, respectively.

Fig. 7.  (Color online) (a) The structure model of 327-type CHPs, they all own tetragonal space group Ccca with isolated [Cu2X7]3– anion composing of elongated [Cu–X] octahedron unit. (b) Calculated thermodynamic stability regions of 327-type CHPs versus μCu and μX (deviation of actual chemical potential of Cu and X from that of their elementary substance). The cyan polygon region represents phase stability growth condition, which is encircled by competing phases using colored line (red, blue, violet, and pink). A, Cu, and X atoms are in purple, coral and brown, respectively.

Table 1.   The Space group of existing CHPs with various types encompassing 325-, 123-, 213-, 459-, 214-, 113-, and 327-type from inorganic crystal structure database (ICSD). ‘√’ and blank grid symbol indicates the existing and non-existing phase in experiment, respectively.

TypeSpace group (No.)Rb Cs
ClBrI ClBrI
325Pnma (62)
123Cmcm (63)
213Pnma (62)
459Pc (7)
214Pnma (62)
Cmca (64)
113P6122 (178)
C2221 (20)
Pbcn (60)
327Ccca (68)
DownLoad: CSV

Table 2.   Calculated decomposition energies together with ODP in the CHPs AlCumXn (A = Rb and Cs; X = Cl, Br, and I; l, m, and n are integers).

CompoundΔHd (meV/atom)Optimal decomposition pathway
325-typeCs3Cu2I525Cs3Cu2I5 → 2CsI + CsCu2I3
Cs3Cu2Br529Cs3Cu2Br5 → 2CsBr + CsCu2Br3
Cs3Cu2Cl533Cs3Cu2Cl5 → Cu + CsCl + Cs2CuCl4
Rb3Cu2I513Rb3Cu2I5 → 2RbI + RbCu2I3
Rb3Cu2Br55Rb3Cu2Br5 → 4/3Rb2CuBr3 + 1/3RbCu2Br3
Rb3Cu2Cl5–2Rb3Cu2Cl5 → 7/5RbCl + 2/5Rb4Cu5Cl9
123-typeCsCu2I30CsCu2I3 → 4/3CuI + 1/3Cs3Cu2I5
CsCu2Br322CsCu2Br3 → 4/3CuBr + 1/3Cs3Cu2Br5
CsCu2Cl324CsCu2Cl3 → 4/3CuCl + 1/3Cu3Cu2Cl5
RbCu2I323RbCu2I3 → RbI + 2CuI
RbCu2Br328RbCu2Br3 → 3/2CuBr + 1/2Rb2CuBr3
RbCu2Cl36RbCu2Cl3 → 3/4CuCl + 1/4Rb4Cu5Cl9
213-typeCs2CuI3–22Cs2CuI3 → 1/2CsI + 1/2Cs3Cu2I5
Cs2CuBr3–16Cs2CuBr3 → 1/2CsBr + 1/2Cs3Cu2Br5
Cs2CuCl3–19Cs2CuCl3 → 1/2CsCl + 1/2Cs3Cu2Cl5
Rb2CuI36Rb2CuI3 → 3/2RbI + 1/2RbCu2I3
Rb2CuBr36Rb2CuBr3 → 3/2RbBr + 1/2RbCu2Br3
Rb2CuCl38Rb2CuCl3 → 1/2Cu + RbCl + 1/2Rb2CuCl4
459-typeCs4Cu5I9–20Cs4Cu5I9 → 3/4Cs3Cu2I5 + 7/4CsCu2I3
Cs4Cu5Br9–9Cs4Cu5Br9 → 3/4Cs3Cu2Br5 + 7/4CsCu2Br3
Cs4Cu5Cl98Cs4Cu5Cl9 → 3/4Cs3Cu2Cl5 + 7/4CsCu2Cl3
Rb4Cu5I9–17Rb4Cu5I9 → 3/2RbI + 5/2RbCu2I3
Rb4Cu5Br9–4Rb4Cu5Br9 → Rb2CuBr3 + 2RbCu2Br3
Rb4Cu5Cl922Rb4Cu5Cl9 → 12/5Cu + 1/5Rb2CuCl3 + 6/5Rb3Cu2Cl7
214-typeCs2CuI4–17Cs2CuI4 → 1/2CsI3 + 1/2Cs3Cu2I5
Cs2CuBr414Cs2CuBr4 → 1/2CsBr + 1/4CsBr3 + 1/2CsCuBr3 + 1/4Cs3Cu2Br5
Cs2CuCl434Cs2CuCl4 → CsCl + CsCuCl3
Rb2CuI4–2Rb2CuI4 → RbI + 1/2RbI3 + 1/2RbCu2I3
Rb2CuBr410Rb2CuBr4 → 2RbBr + CuBr2
Rb2CuCl4–9Rb2CuCl4 → 1/2RbCl + 1/2Rb3Cu2Cl7
113-typeCsCuI3–34CsCuI3 → 1/2CsI3 + 1/2CsCu2I3
CsCuBr319CsCuBr3 → 1/2CuBr2 + 1/2Cs2CuBr4
CsCuCl35CsCuCl3 → 1/2CuCl2 + 1/2Cs2CuCl4
RbCuI3–42RbCuI3 → 1/2RbI3 + 1/2RbCu2I3
RbCuBr321RbCuBr3 → RbBr + CuBr2
RbCuCl3–10RbCuCl3 → 1/3CuCl2 + 1/3Rb3Cu2Cl7
327-typeCs3Cu2I7–31Cs3Cu2I7 → CsI3 + 1/2Cs3Cu2I5 + 1/2CsCu2I3
Cs3Cu2Br79Cs3Cu2Br7 → Cs2CuBr4 + CsCuBr3
Cs3Cu2Cl79Cs3Cu2Cl7 → CsCuCl3 + Cs2CuCl4
Rb3Cu2I7–31Rb3Cu2I7 → RbI + RbI3 + RbCu2I3
Rb3Cu2Br723Rb3Cu2Br7 → 3RbBr + 2CuBr2
Rb3Cu2Cl715Rb3Cu2Cl7 → Rb2CuCl4 + RbCuCl3
DownLoad: CSV

Table 3.   The relative energy per formula unit (eV/f.u.) of 214-type CHPs including Cs2CuI4, Rb2CuI4, and Rb2CuBr4 in the different space group encompassing Pnma and Cmca, which are all non-existing phase in the ICSD.

Space groupCs2CuI4Rb2CuI4Rb2CuBr4
Pnma0.000.000.00
Cmca0.290.330.04
DownLoad: CSV

Table 4.   The relative energy per formula unit (eV/f.u.) of 113-type CHP including CsCuI3, RbCuI3, and RbCuBr3 in the different space group containing C2221, P6122, Pbcn, which are non-existing phase in the ICSD.

Space groupCsCuI3RbCuI3RbCuBr3
C22210.000.000.00
P61220.030.020.10
Pbcn0.150.090.11
DownLoad: CSV

Table 5.   Summary for the stability region and decomposition energy of ODP in the different type CHPs AlBmXn (A = Rb and Cs; B = Cu; X = Cl, Br, and I; l, m, and n are integers; named as lmn-type). For each type CHP, number 1 and 2 represent decomposition energy and stability region, respectively. ‘√’ and ‘×’ symbols indicate ‘stable’ and ‘non-stable’ phase, respectively. Yellow square shows that this type is existing phase from inorganic Crystal Structure Database (ICSD).

ABX325123213459214113327
CsCuI××××××××××
Br××××
Cl××
RbI××××××××
Br××
Cl×××××××
Note: 1: Decomposition energy.
2: Stability region. √: stable. × : Non-stable. : Exist.
DownLoad: CSV
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    Zhongti Sun, Xiwen Chen, Wanjian Yin. Comprehensive first-principles studies on phase stability of copper-based halide perovskite derivatives AlCumXn (A = Rb and Cs; X = Cl, Br, and I)[J]. Journal of Semiconductors, 2020, 41(5): 052201. doi: 10.1088/1674-4926/41/5/052201
    Z T Sun, X W Chen, W J Yin, Comprehensive first-principles studies on phase stability of copper-based halide perovskite derivatives AlCumXn (A = Rb and Cs; X = Cl, Br, and I)[J]. J. Semicond., 2020, 41(5): 052201. doi: 10.1088/1674-4926/41/5/052201.
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    Received: 21 February 2020 Revised: 03 March 2020 Online: Accepted Manuscript: 21 April 2020Uncorrected proof: 23 April 2020Published: 13 May 2020

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      Zhongti Sun, Xiwen Chen, Wanjian Yin. Comprehensive first-principles studies on phase stability of copper-based halide perovskite derivatives AlCumXn (A = Rb and Cs; X = Cl, Br, and I)[J]. Journal of Semiconductors, 2020, 41(5): 052201. doi: 10.1088/1674-4926/41/5/052201 ****Z T Sun, X W Chen, W J Yin, Comprehensive first-principles studies on phase stability of copper-based halide perovskite derivatives AlCumXn (A = Rb and Cs; X = Cl, Br, and I)[J]. J. Semicond., 2020, 41(5): 052201. doi: 10.1088/1674-4926/41/5/052201.
      Citation:
      Zhongti Sun, Xiwen Chen, Wanjian Yin. Comprehensive first-principles studies on phase stability of copper-based halide perovskite derivatives AlCumXn (A = Rb and Cs; X = Cl, Br, and I)[J]. Journal of Semiconductors, 2020, 41(5): 052201. doi: 10.1088/1674-4926/41/5/052201 ****
      Z T Sun, X W Chen, W J Yin, Comprehensive first-principles studies on phase stability of copper-based halide perovskite derivatives AlCumXn (A = Rb and Cs; X = Cl, Br, and I)[J]. J. Semicond., 2020, 41(5): 052201. doi: 10.1088/1674-4926/41/5/052201.

      Comprehensive first-principles studies on phase stability of copper-based halide perovskite derivatives AlCumXn (A = Rb and Cs; X = Cl, Br, and I)

      DOI: 10.1088/1674-4926/41/5/052201
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      • Corresponding author: Email: wjyin@suda.edu.cn
      • Received Date: 2020-02-21
      • Revised Date: 2020-03-03
      • Published Date: 2020-05-01

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