Perovskite materials and methods of making the same

Abstract

The present disclosure relates to a perovskite sheet that includes two outer layers, each including A′X′; and a first layer that includes BX.sub.2, where B is a first cation, A′ is a second cation, X is a first anion, X′ is a second anion, and the first BX.sub.2 layer is positioned between the two outer layers.

Claims

1. A perovskite sheet comprising, in order: a first layer comprising A′X′; a second layer comprising BX.sub.2; a third layer comprising AX; a fourth layer comprising BX.sub.2; and a fifth layer comprising A′X′, wherein: B is a first cation comprising lead, A′ is a second cation comprising at least one of hydrogen, methylammonium (MA), formamidinium (FA), or cesium, A is a third cation comprising at least one of MA, FA, or cesium, X is a first anion comprising bromide, X′ is a second anion comprising at least one of bromide or acetate (AC), and the first layer and the fifth layer form interlayers between neighboring perovskite sheets, wherein: the perovskite sheet has a composition comprising A′.sub.2AB.sub.2X.sub.5X′.sub.2.

2. The perovskite sheet of claim 1, further comprising: a sixth layer comprising AX, and a seventh layer comprising BX.sub.2, wherein: the second AX layer and the third BX.sub.2 are positioned between the first layer and the fifth layer, the first layer is adjacent to a first BX.sub.2 layer, the fifth layer is adjacent to a second BX.sub.2 layer, and the BX.sub.2 layers and AX layers alternate positions in the sheet, wherein: the perovskite sheet has a composition comprising A′.sub.2A.sub.2B.sub.3X.sub.8X′.sub.2.

3. The perovskite sheet of claim 2, further comprising: n BX.sub.2 layers, wherein: n is greater than three, and the outer layers, the BX.sub.2 layers, and the AX layers result in a stoichiometry defined by A′.sub.2A.sub.n-1B.sub.nX.sub.3n-1X′.sub.2.

4. The perovskite sheet of claim 3, wherein 4≤n≤10,000.

5. The perovskite sheet of claim 1, wherein B further comprises at least one of tin or germanium.

6. The perovskite sheet of claim 1, wherein X further comprises at least one of fluoride, chloride, or iodide.

7. The perovskite sheet of claim 1, wherein X′ further comprises a charged form of at least one of a phosphonate group, a carboxylate group, a thiolate, a thiocyanate, an isocyanate, a carbonate, a chromate, a phosphate, a sulfite, a hydroxide, a nitrite, or a percholorate.

8. The perovskite sheet of claim 7, wherein X′ comprises at least one of acetate, propionate, butyrate, phenolate, formate, an alkylphosphonate, or an alkylthiolate.

9. The perovskite sheet of claim 1, wherein the perovskite sheet comprises a nanocrystal.

10. The perovskite sheet of claim 9, wherein the nanocrystal is suspended in a solution comprising a solvent.

11. The perovskite sheet of claim 10, wherein the solution further comprises a ligand comprising a binding group, where the binding group is physically associated with a surface of the nanocrystal.

12. The perovskite sheet of claim 11, wherein the nanocrystal emits light when exposed to UV light.

13. The perovskite sheet of claim 12, wherein the light is at an energy level between about 1.7 eV and about 3.0 eV.

14. A perovskite network comprising: a first perovskite sheet having the stoichiometry of A′.sub.2A.sub.n-1B.sub.nX.sub.3n-1X′.sub.2, and a second perovskite sheet having the stoichiometry of A′.sub.2A.sub.m-1B.sub.mX.sub.3m-1X′.sub.2, wherein: B is a first cation comprising lead, A′ is a second cation comprising at least one of hydrogen, methylammonium (MA), formamidinium (FA), or cesium, A is a third cation comprising at least one of MA, FA, or cesium, X is a first anion comprising bromide, X′ is a second anion comprising at least one of bromide or acetate, the first perovskite sheet and the second perovskite sheet each comprise an A′X′ layer, the A′X′ layer of the first perovskite sheet is physically associated with the A′X′ layer of the second perovskite sheet, and m does not equal n, m is greater than or equal to zero, and n is greater than or equal to one.

15. A perovskite network comprising: a first perovskite sheet having the stoichiometry of A′.sub.2A.sub.n-1Pb.sub.nBr.sub.3n-1X″, and a second perovskite sheet having the stoichiometry of A′.sub.2A.sub.m-1Pb.sub.mBr.sub.3m-1X″, wherein: B is a first cation comprising lead, A′ is a second cation comprising at least one of hydrogen, methylammonium (MA), formamidinium (FA), or cesium, A is a third cation comprising at least one of MA, FA, or cesium, X is a first anion comprising bromide, X″ is a second anion comprises terephthalate, the first perovskite sheet and the second perovskite sheet are physically associated by sharing at least one X″, and m does not equal n, m is greater than or equal to zero, and n is greater than or equal to one.

16. A method for making a perovskite, the method comprising: removing A and X from a first nanocrystal comprising ABX.sub.3, resulting in the forming of a second nanocrystal comprising BX.sub.2; and contacting the second nanocrystal with A′X′, resulting in the forming of a third nanocrystal comprising A′.sub.2A.sub.n-1B.sub.nX.sub.3n-1X′.sub.2, wherein: n is greater than or equal to two, the third nanocrystal includes a perovskite sheet comprising: a first layer comprising A′X′; a second layer comprising BX.sub.2; a third layer comprising AX; a fourth layer comprising BX.sub.2; and a fifth layer comprising A′X′, B is a first cation comprising lead, A′ is a second cation comprising at least one of hydrogen, methylammonium (MA), formamidinium (FA), or cesium, A is a third cation comprising at least one of MA, FA, or cesium, X is a first anion comprising bromide, X′ is a second anion comprising at least one of bromide or acetate, and the first layer and the fifth layer form interlayers between neighboring perovskite sheets.

17. The method of claim 16, wherein: the removing is achieved by immersing the first nanocrystal in a first solution comprising a first solvent, the first solution has a first solubility for the A and the X, the first solution has a second solubility for the second nanocrystal, and the first solubility is higher than the second solubility.

18. The method of claim 17, wherein the first solvent comprises at least one of water, an alcohol, ether, a halogenated alkane, a halogenated benzene, a ketone, an alkylnitrile, or an ester.

19. The perovskite sheet of claim 1, wherein the first layer and the fifth layer are substantially free of a ligand.

20. The perovskite sheet of claim 19, wherein the ligand comprises at least one of oleic acid, oleylamine, oleylammonium, phenylammonium, or dodecylammonium.

21. The perovskite sheet of claim 1, comprising at least one of MA.sub.2CsPb.sub.2Br.sub.5Ac.sub.2, FA.sub.2CsPb.sub.2Br.sub.5Ac.sub.2, H.sub.2CsPb.sub.2Br.sub.5Ac.sub.2, MA.sub.2CsPb.sub.2Br.sub.7, FA.sub.2CsPb.sub.2Br.sub.7, H.sub.2CsPb.sub.2Br.sub.7, Cs.sub.3Pb.sub.2Br.sub.7, Cs.sub.3Pb.sub.2Br.sub.5Ac.sub.2, Cs.sub.3Pb.sub.2Br.sub.5Ac.sub.2, or Cs.sub.3Pb.sub.2Br.sub.5Ac.sub.2.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) Embodiments are illustrated in referenced figures of the drawings. It is intended that the embodiments and figures disclosed herein are to be considered illustrative rather than limiting.

(2) FIG. 1 illustrates a perovskite crystal having the general formula of ABX.sub.3, according to some embodiments of the present disclosure.

(3) FIG. 2 illustrates a method for making a perovskite crystal, according to some embodiments of the present disclosure.

(4) FIG. 3 illustrates transformations of perovskite crystals based on a first treating, resulting in the extraction of CsBr salt from a CsPbBr.sub.3 (ABX.sub.3) starting perovskite nanocrystals to form PbBr.sub.2 (BX.sub.2) intermediate nanocrystals that are subsequently converted into A′.sub.2A.sub.n-1Pb.sub.nBr.sub.3n-1X′.sub.2 NCs via A′X′ addition, according to some embodiments of the present disclosure.

(5) FIG. 4A illustrates structural analysis of perovskite nanocrystals (NCs) during a nanocrystal transformation process, according to some embodiment of the present disclosure, specifically XRD patterns of CsPbBr.sub.3 (ABX.sub.3), PbBr.sub.2 (BX.sub.2), and A′.sub.2A.sub.n-1Pb.sub.nBr.sub.3n-1X′.sub.2 NCs synthesized with A′=MA.sup.+, v.sub.HOAc=0.06, and NC volume fractions of v.sub.NC=0.4 and v.sub.NC=0.2. Simulated powder diffraction patterns of the corresponding crystals are shown below each pattern. The broad scattering feature centered at 25° is due to amorphous organic ligand species and glass. Patterns are normalized and offset for clarity. Dashed vertical lines in the XRD patterns of the converted A′.sub.2A.sub.n-1Pb.sub.nBr.sub.3n-1X′.sub.2NCs highlight peaks that cannot be attributed to (MA)PbBr.sub.3.

(6) FIG. 4B illustrates structural analysis of perovskite nanocrystals during a nanocrystal transformation process, according to some embodiment of the present disclosure, specifically TEM images of: (Panel a) an individual CsPbBr.sub.3 NC, and (Panel b) array of CsPbBr.sub.3 NCs. (Panel c) TEM image of an individual PbBr.sub.2 NC, and (Panel d) an array of PbBr.sub.2NCs. (Panel e) TEM image of an individual A′.sub.2A.sub.n-1Pb.sub.nBr.sub.3n-1X′.sub.2 NC, and (Panel f) an array of A′.sub.2A.sub.n-1Pb.sub.nBr.sub.3n-1X′.sub.2 NCs synthesized with v.sub.NC=0.4 (Panel g) TEM image of an individual A′.sub.2A.sub.n-1Pb.sub.nBr.sub.3n-1X′.sub.2 NC, and (Panel h) an array of A′.sub.2A.sub.n-1Pb.sub.nBr.sub.3n-1X′.sub.2 NCs synthesized with v.sub.NC=0.2. Scale bars are 10 nm except (Panel c) and (Panel e), which are 5 nm.

(7) FIG. 5A illustrates a schematic of a layered A′.sub.2A.sub.n-1Pb.sub.nBr.sub.3n-1X′.sub.2 compound, according to some embodiments of the present disclosure.

(8) FIG. 5B illustrates a modified schematic of the one shown in FIG. 5A, of a layered A′.sub.2A.sub.n-1Pb.sub.nBr.sub.3n-1X′.sub.2 compound, according to some embodiments of the present disclosure.

(9) FIG. 6 illustrates FTIR data corresponding to the conversion of nanocrystals, according to some embodiments of the present disclosure. FTIR spectra of starting perovskite nanocrystals CsPbBr.sub.3 (ABX.sub.3), intermediate nanocrystals PbBr.sub.2 (BX.sub.2), and final perovskite nanocrystals A′.sub.2A.sub.n-1Pb.sub.nBr.sub.3n-1X′.sub.2 NCs synthesized with A′=FA.sup.+ (formamidinium), v.sub.HOAc=0.06, and NC volume fractions of v.sub.NC=0.4 and v.sub.NC=0.2. Spectra of neat OAm and OA are provided for reference. R.sup.1=oleyl. Spectra are normalized to the most intense peak and offset vertically for clarity.

(10) FIG. 7A illustrates photoluminescence of A′.sub.2A.sub.n-1Pb.sub.nBr.sub.3n-1X′.sub.2 final perovskite nanocrystals, according to some embodiments of the present disclosure, specifically PL spectra of the starting CsPbBr.sub.3 perovskite nanocrystals and A′.sub.2A.sub.n-1Pb.sub.nBr.sub.3n-1X′.sub.2 final perovskite nanocrystals for the three different cations investigated in this study (A′=Cs.sup.+, FA.sup.+, and MA.sup.+). v.sub.NC=0.4 and v.sub.HOAc=0.06 for each spectrum. Spectra are normalized and offset for clarity.

(11) FIG. 7B illustrates a photograph of the starting solution of CsPbBr.sub.3 perovskite nanocrystals (Panel A) and solutions of the A′.sub.2A.sub.n-1Pb.sub.nBr.sub.3n-1X′.sub.2 final perovskite nanocrystals (A=MA.sup.+) with n decreasing from left to right (Panel B).

(12) FIG. 7C illustrates time-resolved PL of A′.sub.2A.sub.n-1Pb.sub.nBr.sub.3n-1X′.sub.2 NCs (A′=MA.sup.+) at varying v.sub.NC values for (Panel A) v.sub.HOAc=0.08, (Panel B) v.sub.HOAc=0.06, and (Panel C) v.sub.HOAc=0.04. Each set of time-evolution spectra are normalized in intensity and offset vertically for clarity. The light-colored spectrum in each set is the initial spectrum, and the darkest color is the final spectrum. The spectra are taken from t=0 to t=180 min in 30-min intervals. Gray dashed vertical lines indicate n values.

(13) FIG. 8 provides a comparison of transformations of perovskite crystals based on a first treating, resulting in the extraction of CsBr salt from a CsPbBr.sub.3 starting perovskite nanocrystals to form PbBr.sub.2 intermediate nanocrystals that are re-formed into A′.sub.2A.sub.n-1Pb.sub.nBr.sub.3n-1X′.sub.2 NCs via AX′ addition, to a photograph of the corresponding NC solutions, according to some embodiments of the present disclosure, as explained for FIG. 7B.

REFERENCE NUMBERS

(14) 100 . . . perovskite crystal 110 . . . A-cation 120 . . . B-cation 130 . . . X-anion 200 . . . method 210 . . . starting materials 220 . . . synthesizing 230 . . . starting perovskite crystals 240 . . . first treating 242 . . . starting solution components 244 . . . starting solution containing intermediate crystals 250 . . . second treating 252 . . . salt solution components 254 . . . salt solution containing final perovskite crystals

DETAILED DESCRIPTION

(15) The present disclosure may address one or more of the problems and deficiencies of the prior art discussed above. However, it is contemplated that some embodiments as disclosed herein may prove useful in addressing other problems and deficiencies in a number of technical areas. Therefore, the embodiments described herein should not necessarily be construed as limited to addressing any of the particular problems or deficiencies discussed herein.

(16) The present disclosure relates to perovskite crystals and method for making perovskite crystals. In some embodiments of the present disclosure, CsBr (AX) salt may be selectively extracted from CsPbBr.sub.3 (ABX.sub.3) perovskite crystals (e.g. nanocrystals (NC)) to yield PbBr.sub.2 (BX.sub.2) crystals. The PbBr.sub.2 (BX.sub.2) crystals may then be exposed to different salt solutions (e.g. glacial acetic acid) to yield a variety of emissive perovskite compounds with the generic structure A′.sub.2A.sub.n-1Pb.sub.nBr.sub.3n-1X′.sub.2, where A=cesium (Cs.sup.+), methylammonium (MA.sup.+), formamidinium (FA.sup.+); A′=A or H.sup.+; X=Br.sup.−, and X′=X or acetate (CH.sub.3COO.sup.−); and n is the number of BX.sub.2 layers (see FIG. 1 below), where n=1, 2, 3, . . . ∞. In some examples, the ratios of PbBr.sub.2:ABr:CH.sub.3COOH may be systematically varied and show that certain ratios result in single-phase A′PbX′.sub.3 perovskite crystals—an effective A-site cation exchange and X-site anion exchange, where A=Cs.sup.+, A′=Cs.sup.+ MA.sup.+, or FA.sup.+, and X=Br.sup.− and X′=Cl.sup.−, Br.sup.−, or I.sup.−. In some embodiments of the present disclosure, the salt solution concentration may be increased relative to that of the PbBr.sub.2 crystals, such that time-resolved photoluminescence (PL) spectroscopy shows the dynamic evolution of many blue-shifted emission peaks due to the formation of n=1, 2, 3, 4, & 5 two-dimensional 2D networks in which CH.sub.3COO.sup.− (X′) anions and Br.sup.− (X) anions compete for the c-axis anion sites in A′.sub.2A.sub.n-1Pb.sub.nBr.sub.3n-1X′.sub.2 NCs (see FIG. 5). Further, it is shown herein that the degree of CH.sub.3COO.sup.− (X′) incorporation, and thus the thickness of the 2D network (as defined by the number of sheets of octahedra stacked on one another), and emission energy, may be controlled by kinetic factors. After a longer time (˜3 hours), thermodynamic forces dictated by Le Chatelier's principle may tune the structure in A′.sub.2A.sub.n-1Pb.sub.nBr.sub.3n-1X′.sub.2NCs from exclusively n=1 to n=∞.

(17) FIG. 1 illustrates that perovskites crystals 100 may organize into cubic crystalline structures, as well as other crystalline structures such as tetragonal and orthorhombic, and may be described by the general formula ABX.sub.3, where X (130) is an anion and A (110) and B (120) are cations, typically of different sizes (A typically larger than B). Referring to the generic structure described above, A′.sub.2A.sub.n-1Pb.sub.nBr.sub.3n-1X′.sub.2, lead is an example of a B-cation 120 and bromine is an example of an anion X (130). Thus, the generic structure may also be represented by A′.sub.2A.sub.n-1B.sub.nX.sub.3n-1X′.sub.2, where A′ and A are different or the same A-cations 110, B is a B-cation 120, and X and X′ are the same or different X anions 130, but where A′ and X′ represent ions that have been exchanged with the ions present in the starting perovskite material, ABX.sub.3. Finally, n is the number of BX.sub.2 layers within the structure between A′X′ layers, which is also equal to the number of octahedral sheets stacked on one another. FIG. 1 illustrates that a perovskite 100 may also be visualized as a cubic unit cell, where the B-cation 120 resides at the eight corners of a cube, while the A-cation 110 is located at the center of the cube and with 12 X-anions 130 centrally located between B-cations 120 along each edge of the unit cell. Typical inorganic perovskites include calcium titanium oxide (calcium titanate) minerals such as, for example, CaTiO.sub.3 and SrTiO.sub.3. In some embodiments of the present disclosure, the A-cation 110 may include a nitrogen-containing organic compound such as an alkylammonium compound. The B-cation 120 may include a metal and the X-anion 130 may include a halogen.

(18) Additional examples for the A-cation 110 include organic cations and/or inorganic cations. Organic A-cations 110 may be an alkylammonium cation, for example a C.sub.1-20 alkylammonium cation, a C.sub.1-6 alkylammonium cation, a C.sub.2-6 alkylammonium cation, a C.sub.1-5 alkylammonium cation, a C.sub.1-4 alkylammonium cation, a C.sub.1-3 alkylammonium cation, a C.sub.1-2 alkylammonium cation, and/or a C.sub.1 alkylammonium cation. Further examples of organic A-cations 110 include methylammonium (CH.sub.3NH.sub.3.sup.+), ethylammonium (CH.sub.3CH.sub.2NH.sub.3.sup.+), propylammonium (CH.sub.3CH.sub.2 CH.sub.2NH.sub.3.sup.+), butylammonium (CH.sub.3CH.sub.2CH.sub.2CH.sub.2NH.sub.3.sup.+), formamidinium (NH.sub.2CH═NH.sub.2.sup.+), and/or any other suitable nitrogen-containing organic compound. In other examples, an A-cation 110 may include an alkylamine. Thus, an A-cation 110 may include an organic component with one or more protonated amine groups. For example, an A-cation 110 may be an alkyl diamine such as formamidinium (NH.sub.2CH═NH.sub.2.sup.+). Thus, the A-cation 110 may include an organic constituent in combination with a nitrogen constituent. In some cases, the organic constituent may be an alkyl group such as straight-chain or branched saturated hydrocarbon group having from 1 to 20 carbon atoms. In some embodiments, an alkyl group may have from 1 to 6 carbon atoms. Examples of alkyl groups include methyl (C.sub.1), ethyl (C.sub.2), n-propyl (C.sub.3), 1-methyl-1-ethyl (C.sub.3), n-butyl (C.sub.4), 1-methyl-1-propyl (C.sub.4), 2-methyl-1-propyl (C.sub.4), 1,1-dimethyl-1-ethyl (C.sub.4), n-pentyl (C.sub.5), 1-methyl-1-butyl (C.sub.5), 1-ethyl-1-propyl (C.sub.5), 2-methyl-1-butyl (C.sub.5), 3-methyl-1-butyl (C.sub.5), 1,1-dimethyl-1-propyl (C.sub.5), 2,2-dimethyl-1-propyl (C.sub.5), and n-hexyl (C.sub.6). Additional examples of alkyl groups include n-heptyl (C.sub.7), n-octyl (C.sub.8) and the like. In some embodiments, the organic constituent may be an alkyl group such as a straight-chain or branched unsaturated group having from 1 to 20 carbon atoms. Examples of unsaturated alkyl groups include ethenyl (C.sub.2), 1-propenyl (C.sub.3), 2-propenyl (C.sub.3), 1-butenyl (C.sub.4), 2-butenyl (C.sub.4), 3-butenyl (C.sub.4), 2-methyl-1-propenyl (C.sub.4), 2-methyl-2-propenyl (C.sub.4), 1-pentenyl (C.sub.5), 2-pentenyl (C.sub.5), 3-pentenyl (C.sub.5), 4-pentenyl (C.sub.5), 1-methyl-1-butenyl (C.sub.5), 2-methyl-1-butenyl (C.sub.5), 3-methyl-1-butenyl (C.sub.5), 1,2-dimethyl-1-propenyl (C.sub.5), 1,2-dimethyl-2-propenyl (C.sub.5), and 1-hexenyl (C.sub.6). Additional examples of alkyl groups include 1-heptenyl (C.sub.7), 1-octenyl (C.sub.8) and the like. In addition, the A-cation 110 may include an unsaturated species with a nitrogen constituent. In some cases, the nitrogen-containing organic group may be an aryl group having from 3 to 20 carbon atoms. Examples of aryl groups include pyridine (C.sub.5H.sub.5N), pyridazine (1,2-C.sub.4H.sub.4N.sub.2), pyrimidine (1,3-C.sub.4H.sub.4N.sub.2), pyrazine (1,4-C.sub.4H.sub.4N.sub.2), triazine (1,2,3-1,2-C.sub.3H.sub.3N.sub.3; 1,2,4-1,2-C.sub.3H.sub.3N.sub.3; 1,3,5-1,2-C.sub.3H.sub.3N.sub.3), bipyridine (2,2′-C.sub.10H.sub.8N.sub.2; 2,3′-C.sub.10H.sub.8N.sub.2; 2,4′-C.sub.10H.sub.8N.sub.2; 3,3′-C.sub.10H.sub.8N.sub.2; 3,4′-C.sub.10H.sub.8N.sub.2; and 4,4′-C.sub.10H.sub.8N.sub.2), phenanthroline (1,10-C.sub.12H.sub.8N.sub.2 and other isomers), terpyridine (2,2′;6′,2″-C.sub.15H.sub.11N.sub.3 and other isomers) and the like. In the cases where more than one nitrogen is present, the A-cation may be multivalent, i.e., di-cation, tri-cation, etc. by pronating the amine groups to form ammoniums. In addition, instead of protonation, covalent bonds can be formed to one or more amine nitrogen atoms to give ammoniums. For example, 4,4′-bipyridine can be doubly methylated to form N,N′-dimethyl-4,4′-bipyridinium [(C.sub.5H.sub.4NCH.sub.3).sub.2].sup.2+, the dichloride salt of which is commonly known as paraquat. In these cases of multivalent cations, the stoichiometry of the A′.sub.2A.sub.n-1Pb.sub.nBr.sub.3n-1X′.sub.2 structure changes since fewer A-cations are required for charge balance. In the di-cation paraquat example, only one A-cation is required to charge-balance two perovskite layers, generating a structure A″A.sub.n-1Pb.sub.nBr.sub.3n-1X′.sub.2 where A″=[(C.sub.5H.sub.4NCH.sub.3).sub.2].sup.2+.

(19) Examples of metal B-cations 120 include, for example, lead, tin, germanium, and or any other 2+ valence state metal that can charge-balance the perovskite crystal 100. Examples for X-anions 130 include halogens: e.g. fluorine, chlorine, bromine, and/or iodine. In some cases, the perovskite crystal 100 may include more than one type of X-anion 130, for example pairs of halogens; chlorine and iodine, bromine and iodine, and/or any other suitable pairing of halogens. In other cases, the perovskite crystal 100 may include two or more halogens of fluorine, chlorine, bromine, iodine, and/or astatine.

(20) Thus, the A-cation 110, the B-cations 120, and X-anion 130 may be selected within the general formula of ABX.sub.3 to produce a wide variety of perovskite crystals 100, including, for example, methylammonium lead triiodide (CH.sub.3NH.sub.3PbI.sub.3), and mixed halide perovskites such as CH.sub.3NH.sub.3PbI.sub.3-xCl.sub.x and CH.sub.3NH.sub.3PbI.sub.3-xBr.sub.x. Thus, a perovskite crystal 100 may have more than one halogen element, where the various halogen elements are present in non-integer quantities; e.g. x is not equal to 1, 2, or 3. In addition, perovskite crystals may form three-dimensional (3D), two-dimensional (2D), one-dimensional (1D) or zero-dimensional (0D) networks, possessing the same unit structure (BX.sub.6.sup.4− octahedra).

(21) In a perovskite crystal 100, the negative charge of the metal halide octahedra (X-anions 130 in FIG. 1) may be balanced by monovalent A-cations 110, for example, by alkali metal and/or organic cations, as described above. Thus, FIG. 1 illustrates eight octahedra surrounding a single A-cation 110, where each octahedra shares six X-anions 130 positioned at the corners of the octahedra, with neighboring octahedra, and each grouping of six X-anions 130 surround a centrally positioned B-cation 120. Referring again to FIG. 1, the perovskite crystal 100 may be visualized as having a first sheet of four octahedra in the XY plane, positioned on a second sheet of four octahedra, also positioned in the XY plane. The size of the cations may influence the emission properties of the perovskite crystal 100 by changing the bonding, dimensionality, and/or tilt angle of the octahedra. Cations with ionic radii that satisfy the “tolerance factor” will form three-dimensional, isotropic crystals with the general crystal structure of ABX.sub.3 as shown in FIG. 1, where the A-cation 110 may include cesium (Cs.sup.+), methylammonium (MA.sup.+), and/or formamidinium (FA.sup.+). Larger A-cations may lead to layered compounds with blue-shifted emission due to two-dimensional network (2DN) quantum confinement.

(22) It is demonstrated herein that CsPbBr.sub.3 (ABX.sub.3) perovskite nanocrystals may be utilized to produce A-cation-exchanged and X-anion exchanged A′.sub.2A.sub.n-1B.sub.nX.sub.3n-1X′.sub.2 perovskite nanocrystals, as well as 2D layered perovskites within the original nanocrystal framework, for example where A=Cs.sup.+ is exchanged with A′=FA.sup.+, MA.sup.+, Cs.sup.+ and/or H.sup.+. In some embodiments of the present disclosure, these transformations may be achieved by converting CsPbBr.sub.3 (ABX.sub.3) nanocrystals into PbBr.sub.2 (BX.sub.2) nanocrystals by extracting CsBr (AX) with a water-ethanol solution. Subsequently, ion pairs (A′ X′) may be reinserted into the PbBr.sub.2 (BX.sub.2) nanocrystals to yield an array of compounds with the generic structure of A′.sub.2A.sub.n-1Pb.sub.nBr.sub.3n-1X′.sub.2, where A=Cs.sup.+, MA.sup.+, FA.sup.+; A′=A or H.sup.+; X=Br.sup.−; X′=X.sup.− or acetate (CH.sub.3COO.sup.−); and n is equal to the number of octahedral sheets and is proportional to the thickness of the exchanged nanocrystals, where n=1, 2, 3, . . . ∞. In some embodiments, depending on the conditions, perovskite nanocrystal solutions with similar size and emission properties to the parent CsPbBr.sub.3 (ABX.sub.3) nanocrystals were synthesized, showing that the salt extraction and reinsertion processes do not disrupt the original nanocrystal framework, e.g. the PbBr.sub.2 (BX.sub.2) nanocrystal framework. In some examples, compounds with blue-shifted emission were synthesized, where the blueshift may be due to the formation of two-dimensional quantum-confined sheets in which CH.sub.3COO.sup.− (X′) and Br.sup.− (X) anions compete for the c-axis anion sites in A′.sub.2A.sub.n-1Pb.sub.nBr.sub.3n-1X′.sub.2 NCs. Without wishing to be bound by theory, the larger size of X′=CH.sub.3COO.sup.− vs X=Br.sup.− may disrupt the 3-dimensional perovskite crystal lattice, resulting in 2D sheets. It is demonstrated herein, that the degree of CH.sub.3COO.sup.− (X′) incorporation, and thus the 2D layer thickness and emission energy, may be tuned using Le Chatelier's Principle from exclusively n=1 to n=∞ in the A′.sub.2A.sub.n-1Pb.sub.nBr.sub.3n-1X′.sub.2 structure. This approach highlights both the benefits and challenges associated with the solution environment of perovskite nanocrystals and enables chemistries inaccessible in conventional synthetic strategies of nanostructured and bulk perovskites.

(23) In some embodiments of the present disclosure, CsPbBr.sub.3 (ABX.sub.3) perovskite nanocrystals were synthesized using a hot injection technique. After the nanocrystals were purified to remove excess reactants and size-selected using centrifugation, the resultant solid starting perovskite nanocrystals (ABX.sub.3) were treated to extract CsBr (AX) to yield intermediate nanocrystals, PbBr.sub.2 (BX.sub.2). Although centrifugation was used here, other physical means of separation may be used, including filtration and/or gravity settling. This was achieved by exploiting selective solubility of CsBr (AX) versus PbBr.sub.2 (BX.sub.2) in a starting solution of wet ethanol (EtOH), oleic acid, and oleylamine (CsBr is highly soluble in water and alcohols, whereas PbBr.sub.2 is not). Other suitable solvents, in addition to or instead of water/ethanol, include ones with strong ability to dissolve the AX salt but not the BX.sub.2 salt. This includes at least one of an alcohol, ether, a halogenated alkane, a halogenated benzene, a ketone, an alkylnitrile, and/or an ester. For example, a water/n-butanol or water/chlorobenzene mixture will work. Oleic acid and oleylamine are ligands that are used to either coordinate to the nanocrystal surface as ligands and/or induce other ligands to coordinate. Other suitable ligands include molecules with four or more carbons (e.g. branched and/or straight-chained saturated and/or unsaturated hydrocarbons) and a binding group. The binding group may include at least one of a hydroxyl group, an epoxide, an aldehyde, a ketone, a carboxylic acid, an acid anhydride, an ester, an amide, an acyl halide, an amine, a nitrile, an imine, an isocyanate, and/or a thiol. In some embodiments of the present disclosure, the binding group may be charged. For example, a ligand may include a negatively-charged oleate (e.g. deprotonated oleic acid). Another example of a charged binding group is ammonium containing compound (e.g. protonated amine) such as at least one of oleylammonium, phenylammonium, and/or dodecylammonium.

(24) The presence of oleylamine (8.3 vol %) and oleic acid (2.8 vol %) as well as water (5 vol %) in the hydrated ethanol solution help to maintain the PbBr.sub.2 (BX.sub.2) nanocrystals during the process. The PbBr.sub.2 (BX.sub.2) intermediate nanocrystals were then solvated in a nonpolar solvent such as hexane, toluene, or benzene. A solution of A′X′=CsBr in glacial acetic acid yielded a solution with A-cations as well as X-anions (Br—) and acetate (X′=CH.sub.3COO.sup.−) anions. This is shown in FIG. 3. Alternatives to acetic acid are formic acid, other carboxylic acids, or any solvent that does not dissolve the PbBr.sub.2 (BX.sub.2) nanocrystals but dissolves the A′X′ salt such as toluene, halogenated arenes, ketones, nitriles, etc. Anions like acetate may also be directly added to the solution as a salt, A′X′, where X′=acetate, formatethiocyanate, isocyanate, carbonate, chromate, phosphate, sulfate, sulfite, hydroxide, nitrate, nitrite, percholorite, etc.

(25) In some embodiments of the present disclosure, a salt of formula A′.sub.2X″ where X″=dianions such as terephthalate [C.sub.6H.sub.4(COO.sup.−).sub.2], derived from terephthalic acid [C.sub.6H.sub.4(COOH).sub.2], may be used. These cases result in slight stoichiometry changes, compared to the examples described above, such that A′.sub.2A.sub.n-1Pb.sub.nBr.sub.3n-1X″ (versus A′.sub.2A.sub.n-1Pb.sub.nBr.sub.3n-1X′.sub.2) where X″=[C.sub.6H.sub.4(COO.sup.−).sub.2] are formed. The salts may be used in combination to form a solution with many cations and anions. The salt solution modifies the PbBr.sub.2 intermediate nanocrystals. Depending on the volume fractions of the PbBr.sub.2 starting solution (0.1 to 0.4) and acetic acid salt solution (0.04 to 0.08), as described in detail below, the method yielded final perovskite nanocrystals have the general structure described above; A′.sub.2A.sub.n-1Pb.sub.nBr.sub.3n-1X′.sub.2 nanocrystals with n=1, 2, 3, . . . ∞. In some embodiments of the present disclosure, volume fractions and ratios will change depending on the salt solution chosen for a particular application and/or final product. In other words, the volume fractions and/or ratios to yield n=1 and n=infinity may vary significantly depending on the components used (e.g. A, X′, etc.) and other treating conditions and/or parameters (e.g. whether acetic acid or other solvents are used).

(26) The method described above is summarized in FIG. 2. The method 200 may begin with the synthesizing 220 of starting perovskite crystals 230 having the structure ABX.sub.3 (e.g. CsPbBr.sub.3, CsPbI.sub.3, CsSnI.sub.3, CsPbI.sub.2Br, (CH.sub.3NH.sub.3).sub.1-xCs.sub.xPbI.sub.3-yCl.sub.y, (CH.sub.3NH.sub.3).sub.1-xCs.sub.xPbI.sub.3-yCl.sub.y, (NH.sub.2CHNH.sub.3).sub.1-xCs.sub.xPbI.sub.3, (NH.sub.2CHNH.sub.3).sub.1-xCs.sub.xPb.sub.ySn.sub.1-yI.sub.3, and (NH.sub.2CHNH.sub.3).sub.1-xCs.sub.xPb.sub.ySn.sub.1-yI.sub.3-zCl.sub.z) using the appropriate starting materials 210. The starting perovskite crystals 230 may be directed to a first treating 240, where the starting perovskite crystals 230 (e.g. CsPbBr.sub.3) may be contacted with various starting solution components 242 in the first treating 240, resulting in the removal of at least a portion of the A-cation (e.g. A=Cs.sup.+, MA.sup.+, FA.sup.+, or H.sup.+) and/or X-anion (e.g. at least one halogen) to produce a starting solution 244 containing intermediate crystals (not shown), having a structure that includes BX.sub.2 (e.g. PbBr.sub.2, SnI.sub.2, PbCl.sub.2, Sn.sub.1-xPb.sub.xI.sub.2 (where 0≥x≥1), PbI.sub.2-yBr.sub.y (where 0≥y≥2)). In some embodiments of the present disclosure, the starting solution components 242 may include a combination of solvents known to dissolve CsBr (AX) but not PbBr.sub.2 (BX.sub.2) in conjunction with ligands known to coordinate to nanocrystal surfaces, where the combination may result in the preferential removal of the A-cation from the starting ABX.sub.3 perovskite crystals 230, resulting in the formation of the intermediate BX.sub.2 crystals (not shown in FIG. 2) contained in the starting solution 244. The method 200 may proceed with a second treating 250 of the starting solution 244 by contacting the starting solution 244 containing the intermediate crystals with a salt solution 252 to produce a salt solution 254 containing final perovskite crystals (not shown in FIG. 2). In some embodiments of the present disclosure, the salt solution 252 may include on organic solvent (e.g. toluene, hexanes, chloroform), a carboxylic acid (e.g. acetic acid), and a salt A′X′ [e.g. cesium bromide, methylammonium acetate, formamidinium formate, rubidium isocyanate, cesium thiocyanate, methylammonium carbonate, formamidinium chromate, etc.], resulting in the formation the salt solution 254 containing the final perovskite crystals (not shown in FIG. 2), where the final perovskite crystals have the general structure A′.sub.2A.sub.n-1B.sub.nX.sub.3n-1X′.sub.2 with n=1, 2, 3, . . . ∞. In some embodiments of the present disclosure, A′ is different than A, or A′ is the same as A. In some embodiments of the present disclosure, X′ is different than X, or X′ is the same as X.

(27) The three types of perovskite nanocrystals described above are shown in FIG. 3: a starting perovskite nanocrystal ABX.sub.3 (CsPbBr.sub.3), an intermediate nanocrystal BX.sub.2 (PbBr.sub.2), and a final perovskite nanocrystal A′.sub.2A.sub.n-1Pb.sub.nBr.sub.3n-1X′.sub.2 Cs.sub.2Cs.sub.n-1Pb.sub.nBr.sub.3n-1CH.sub.3COO.sub.2. FIG. 4A shows exemplary X-ray diffraction (XRD) patterns for examples of the three different perovskite nanocrystals depicted in FIG. 3. The XRD pattern of the starting CsPbBr.sub.3 (ABX.sub.3) perovskite nanocrystals exhibit the cubic (Pm3m) perovskite crystal phase, which is shown in the simulated pattern below the data. FIG. 4B illustrates transmission electron microscopy (TEM) images of an individual CsPbBr.sub.3 NC (ABX.sub.3) (Panel a) and an array of NCs (Panel b) shows the starting perovskite nanocrystals are faceted in shapes having characteristic lengths between about 6 nm and about 20 nm. Upon CsBr (AX) extraction by the first treating, the PbBr.sub.2 (BX.sub.2) intermediate nanocrystals exhibit the orthorhombic (Pmnb) crystal structure with broadened XRD peaks (see PbBr.sub.2 (BX.sub.2) spectrum in FIG. 4A), consistent with Scherrer broadening due to the significant reduction in crystallite volume associated with the loss of CsBr (AX). The reduction in crystallite size upon salt extraction is confirmed by the TEM images shown in (Panels b and c) of FIG. 4B, where the PbBr.sub.2 (BX.sub.2) intermediate nanocrystals are spherical with a diameter between about 5 nm and about 10 nm.

(28) In this example, the structure of the final perovskite nanocrystals, A′.sub.2A.sub.n-1Pb.sub.nBr.sub.3n-1X′.sub.2, was controlled by changing the volume fractions of the PbBr.sub.2 (BX.sub.2) intermediate nanocrystals in the organic solvent, e.g. toluene (v.sub.NC), and acetic acid (v.sub.HOAc). A salt solution of (MA)Br (A′=MA.sup.+, X′=X=Br.sup.−) was used with v.sub.HOAc=0.06 as the example. Upon conversion of the PbBr.sub.2 (BX.sub.2) intermediate nanocrystals using v.sub.NC=0.4 and v.sub.HOAc=0.2, XRD peaks consistent with the formation of (MA)PbBr.sub.3 (A′BX′.sub.3) with cubic (Pnma) crystal structure were clearly observed (see FIG. 4A). The peak broadness in the final perovskite nanocrystals is similar to that of the starting CsPbBr.sub.3 perovskite nanocrystals, and the characteristic (MA)PbBr.sub.3 (A′BX′.sub.3) (110) peak at 2θ=14.9° of final perovskite nanocrystals is slightly shifted from the 2θ=15.1° location for the parent CsPbBr.sub.3 (ABX.sub.3). These observations confirm MA.sup.+α(A′) incorporation has occurred and suggest a similar nanocrystal size between the starting perovskite nanocrystals and the converted final perovskite nanocrystals. Low-angle reflections in the final perovskite nanocrystals also appear at 2θ=7.1° for v.sub.NC=0.4—corresponding to a spacing of 6.2 Å—and at 2θ=6.5° for v.sub.NC=0.2—corresponding to a spacing of 6.8 Å—that are absent from the starting CsPbBr.sub.3 (ABX.sub.3) perovskite nanocrystals and are not expected for (MA)PbBr.sub.3 (A′BX′.sub.3) nanocrystals with conventional surfactant ligands.

(29) The large spacings of 6.2 and 6.5 Å that give rise to these low-angle reflections is inconsistent with a 3D (MA)PbBr.sub.3 (A′BX′.sub.3) structure and indicates a 2D material structure where the ≥6.2 Å spacing reflects the distance between layered, stacked perovskite sheets. Similar low angle XRD reflections are characteristic of related 2D perovskite materials, for example (C.sub.6H.sub.5C.sub.2H.sub.4NH.sub.3).sub.2PbBr.sub.4 (phenylethylammonium), (C.sub.4H.sub.9NH.sub.3).sub.2(MA).sub.n-1Pb.sub.nI.sub.3n+1 (butylammonium), and Cs.sub.2[C(NH.sub.2).sub.3]Pb.sub.2Br.sub.7. Without wishing to be bound by theory, formation of low-dimensional perovskite networks may be achieved by slicing the 3-dimensional ABX.sub.3 perovskite crystal along specific lattice planes. Slicing along the (001) plane may result in the 2D structure type A′.sub.2A.sub.n-1B.sub.nX.sub.3n+1, (X=Cl.sup.−, Br.sup.−, I.sup.−) where n corresponds to the number of BX.sub.2 layers in the structure. Thus, n=1 for (C.sub.6H.sub.5C.sub.2H.sub.4NH.sub.3).sub.2PbBr.sub.4 and n=2 for Cs.sub.2[C(NH.sub.2).sub.3]Pb.sub.2Br.sub.7 in the above examples.

(30) As describe herein, CsBr (AX) salt extraction from the starting CsPbBr.sub.3 (ABX.sub.3) perovskite nanocrystals by a first treating and reaction of the resulting intermediate PbBr.sub.2 (BX.sub.2) nanocrystals by a second treating gives final perovskite nanocrystals that are of comparable shape and dimension to the starting CsPbBr.sub.3 (ABX.sub.3) perovskite nanocrystals (see TEM images in (Panels a-h) of FIG. 4B). These data suggest that complete disruption of the PbBr.sub.2 (BX.sub.2) intermediate nanocrystals into discrete, isolated 2D perovskite sheets is unlikely since a broad size distribution of the converted nanocrystals would be expected. Therefore, it is proposed herein that the A′X′ salt used in the second treating (A=Cs.sup.+; A′=A, MA.sup.+, FA.sup.+; X=Br.sup.−; X′=X, CH.sub.3COO.sup.−) transforms the intermediate PbBr.sub.2 (BX.sub.2) nanocrystal into a A′.sub.2A.sub.n-1Pb.sub.nBr.sub.3n-1X′.sub.2 (or more generally into A′.sub.2A.sub.n-1B.sub.nX.sub.3n-1X′.sub.2) layered final 2D perovskite nanocrystal network as shown in FIG. 5A. In this complex structure, the starting bromides from the intermediate PbBr.sub.2 (BX.sub.2) nanocrystals are bridging along the a- and b-axes (Pb.sup.2+, Br.sup.− in FIG. 5A), whereas the new X′ anion is located along the c-axis and terminates the 2D sheets. Without wishing to be bound by theory, it is posited that the acetate—from the glacial acetic acid solution, which is in large excess relative to the 0.01 M CsBr (AX) salt—may be the kinetically preferred initial X′ anion that infiltrates along a single (001) plane of the intermediate PbBr.sub.2 (BX.sub.2) nanocrystals to form A′.sub.2A.sub.n-1Pb.sub.nBr.sub.3n-1X′.sub.2 layered final perovskite nanocrystals. Similarly, it is also possible that the initial interlayer A′ cations are H.sup.+, which is why those are distinguished from the intralayer A cation (Cs.sup.+, MA.sup.+, FA.sup.+) in FIG. 5A. Finally, it is worth noting that another potential complicating factor in our structure is that the charge-balancing ligands on the surface of the nanocrystals may be different than those of the A′ or X′ interlayers. For example, in FIG. 5A the interlayer groups are shown as A′=A or H.sup.+, whereas oleylammonium groups that provide colloidal stability may be present at the nanocrystal surface. Likewise, interlayer anions X′=Br.sup.− or CH.sub.3COO.sup.− may be substituted for oleate at the nanocrystal surface.

(31) Referring again to FIG. 5A, it illustrates a layered 2D perovskite nanocrystal network made according to some embodiments described herein. The methods described herein may result in a final perovskite nanocrystal network constructed of two or more 2D sheets, where each sheet is composed of a combination of BX.sub.2 layers and AX layers positioned between two layers of A′X′. Referring to FIG. 5A, for example, a final 2D perovskite network may be constructed of one or more first sheets where each sheet contains a single BX.sub.2 layer positioned between two layers of A′X′, resulting in one or more sheets having the overall stoichiometry of A′.sub.2BX.sub.2X′.sub.2 (n=1). This same 2D perovskite network may also contain one or more sheets where each sheet contains two BX.sub.2 layers and an AX layer positioned between the BX.sub.2 layers, with the BX.sub.2 layers and the AX layer positioned between two A′X′ layers, resulting in one or more sheets having the overall stoichiometry of A′.sub.2AB.sub.2X.sub.5X′.sub.2 (n=2). This same 2D perovskite network may also contain one or more first sheets where each contains three BX.sub.2 layers and two BX.sub.2 layers, with all of these positioned between two A′X′ layers, resulting in one or more sheets having the overall stoichiometry of A′.sub.2A.sub.2B.sub.3X.sub.8X′.sub.2 (n=2).

(32) Referring again to FIG. 5A, in general, the sheets of a 2D perovskite nanocrystal network, according to some embodiments of the present disclosure, may be defined by A′.sub.2A.sub.n-1B.sub.nX.sub.3n-1X′.sub.2, where A′ is a first cation, B is a second cation, A is a third cation, X is first anion, X′ is a second cation, n is the number of BX.sub.2 layers contained in the perovskite sheet, (n−1) is the number of AX layers positioned between BX.sub.2 layers, and the number of A′X′ layers is two. According to some embodiments of the present disclosure, n may be between greater than zero and 10, between greater than zero and 100, between greater than zero and 1,000, or between greater than zero and 10,000. In some embodiments of the present disclosure, n may be larger than 10,000. Further, these sheets may associate with other sheets to form 2D perovskite networks. Thus, the A′X′ of a may be physically associated with the A′X′ layers of adjacent sheets, forming A′X′ interlayers between neighboring sheets of the perovskite network. The physical association may be by at least one of ionic bonds, van der Waals forces, dipole moments, and/or hydrogen bonds.

(33) FIG. 5B illustrates a layered 2D perovskite nanocrystal network made according to some embodiments described herein, as shown in FIG. 5A, but with the perovskite stoichiometry shown in an alternate way. The methods described herein may result in a final perovskite nanocrystal network constructed of two or more 2D sheets, where each sheet is composed of a combination of octahedral layers of at least one of A′BX′X.sub.2 and/or ABX.sub.3 and an additional layer of A′X′. Referring to FIG. 5B, for example, a final 2D perovskite network may be constructed of one or more first sheets where each sheet contains a single octahedral layer of A′BX′X.sub.2 and a neighboring layer of A′X′, resulting in one or more sheets having the overall stoichiometry of A′.sub.2BX.sub.2X′.sub.2 (n=1). This same 2D perovskite network may also contain one or more sheets where each sheet contains an octahedral layer of A′BX′X.sub.2, an octahedral layer of ABX.sub.3, and a layer of A′X′, resulting in one or more sheets having the overall stoichiometry of A′.sub.2AB.sub.2X.sub.5X′.sub.2 (n=2). This same 2D perovskite network may also contain one or more first sheets where each has a single layer of an octahedral layer of A′BX′X.sub.2, two layers octahedral layers of ABX.sub.3, and a layer of A′X′, resulting in one or more sheets having the overall stoichiometry of A′.sub.2A.sub.2B.sub.3X.sub.8X′.sub.2 (n=3).

(34) Referring again to FIG. 5B, in general, the sheets of a 2D perovskite nanocrystal network, according to some embodiments of the present disclosure, may be defined by A′.sub.2A.sub.n-1B.sub.nX.sub.3n-1X′.sub.2, where A′ is a first cation, B is a second cation, A is a third cation, X is first anion, X′ is a second cation, n is the total number of octahedral layers (ABX.sub.3 and A′BX′X.sub.2), the number of A′BX′X.sub.2 layers is one, and the number A′X′ layers is one. In some embodiments of the present disclosure, n may be between greater than zero and 10, between greater than zero and 100, between greater than zero and 1,000, or between greater than zero and 10,000. In some embodiments of the present disclosure, n may be larger than 10,000. Further, these sheets may associate with other sheets to form 2D perovskite networks. Thus, the A′X′ of a may be physically associated with the A′X′ layers of adjacent sheets, forming A′X′ interlayers between neighboring sheets of the perovskite network. The physical association may be by at least one of ionic bonds, van der Waals forces, dipole moments, and/or hydrogen bonds.

(35) Fourier transform infrared (FTIR) spectroscopy was used to elucidate additional insight into the chemical conversion of PbBr.sub.2 (BX.sub.2) to A′.sub.2A.sub.n-1Pb.sub.nBr.sub.3n-1X′.sub.2 layered nanocrystals. The top spectrum in FIG. 6 is of the starting CsPbBr.sub.3 (ABX.sub.3) perovskite nanocrystals, which may be dominated by resonances of the surface ligands. The alkyl chains of the ligands are clearly seen with the hydrocarbon stretching, ν(C—H.sub.x)=2925 cm.sup.−1, and methylene deformation modes at δ(C—H.sub.2)=1464 cm.sup.−1. Vinylic proton resonances are also clearly observed at ν(C═C—H)=3007 cm.sup.−1. The nature of ligand binding to the nanocrystal surface are also visible in the FTIR spectra. The peak centered at ν(R.sup.1N—H.sub.3.sup.+)=3132 cm.sup.−1 is due to stretching modes from oleylammonium, showing that the ligands may be cationically charged to balance the negative surface termination of the lead halide octahedra or oleate ligands in the parent CsPbBr.sub.3 (ABX.sub.3) NCs. Oleylamine (OAm) is provided for reference in FIG. 6. Excess oleic acid (OA) may be present in excess of the CsPbBr.sub.3 starting perovskite nanocrystal solutions to drive oleate onto the NC surface. Excess OA is observed in the CsPbBr.sub.3 (ABX.sub.3) starting perovskite nanocrystal spectrum (which drives oleate onto the nanocrystal surface that engenders colloidal stability), as evidenced by the broad baseline from hydroxyl stretching spanning ν(O—H)=2400-3400 cm.sup.−1 and the carbonyl at ν(C═O)=1707 cm.sup.−1 of the carboxylic acid group. In addition, oleyl carboxylate (oleate) ligands are easily identified by the absence of the broad hydroxyl peak and new peaks characteristic of carboxylate, which are the symmetric, ν.sub.s(COO.sup.−)=1407 cm.sup.−1, and asymmetric, ν.sub.as(COO.sup.−)=1538 cm.sup.−1, stretching modes. Neat OA is included for reference in FIG. 6.

(36) Referring again to FIG. 6, upon extraction of CsBr (AX) by the first treating, the FTIR spectrum of the resulting PbBr.sub.2 (BX.sub.2) intermediate nanocrystals show significantly different surface chemistry. A new resonance at ν(N—H.sub.2)=3511 cm.sup.−1 suggests OAm binds to a Pb (B) surface atoms as a neutral L-type ligand. The PbBr.sub.2 also are free from excess OA based on the absence of ν(C═O)=1707 cm.sup.−1 of the carboxylic acid group. A small feature at ˜3250 cm.sup.−1 could be due to the ν(R.sup.1N—H.sub.3.sup.+) stretch from a charge-balanced oleylammonium-oleate salt complex, which could also be the source of the minor features near 1407 and 1538 cm.sup.−1 from oleate ν(COO.sup.−) symmetric and asymmetric stretching modes, respectively.

(37) For conversion studies, FA.sup.+-based solutions were probed since FA.sup.+ (A′) has a characteristic resonance at ν(C=N)=1718 cm.sup.−1 that is convenient for monitoring this cationic species. Incorporation of FA.sup.+ (A′) upon reaction with PbBr.sub.2 (BX.sub.2) intermediate nanocrystals is clearly observed in FIG. 6 for final perovskite nanocrystals with both v.sub.NC=0.4 and v.sub.NC=0.2. A new ammonium stretching peak is observed at ν(N—H.sub.3.sup.+)=3276 cm.sup.−1 in addition to the ν(C=N) resonance that further confirms FA.sup.+ (A′) incorporation. It is proposed herein that acetate is incorporated into the final perovskite nanocrystal structure A′.sub.2A.sub.n-1Pb.sub.nBr.sub.3n-1X′.sub.2 following conversion of the PbBr.sub.2 (BX.sub.2) intermediate nanocrystals based on these FTIR spectra: nanocrystals converted with v.sub.NC=0.4 show two small peaks due to the symmetric and asymmetric carboxylate peaks appearing at ν.sub.s(COO.sup.−)=1413 cm.sup.−1 and ν.sub.as(COO.sup.−)=1526 cm.sup.−1, respectively. Notably, the energies of these peaks provide strong evidence that acetate binds to Pb(II) in a bidentate fashion by comparison to the coordination mode of metal acetate complexes, providing additional evidence that the X′=CH.sub.3COO.sup.− c-axis ligands terminate (rather than bridge) haloplumbate(II) layers. When v.sub.NC=0.2, these new peaks associated with acetate greatly increase in intensity relative to the ν(C=N) mode, indicating increased acetate incorporation into the A′.sub.2A.sub.n-1Pb.sub.nBr.sub.3n-1X′.sub.2 NC relative to that from v.sub.NC=0.4. This observation is consistent with the slight shift toward lower angle (larger lattice spacing suggesting greater acetate content) for the low angle XRD peak from v.sub.NC=0.4 versus that from v.sub.NC=0.2 (see FIG. 4A).

(38) Provided herein is a detailed account of the emission properties of these nanocrystals during the salt exchange process (e.g. second treating). The photoluminescence (PL) peak from the starting CsPbBr.sub.3 (ABX.sub.3) perovskite nanocrystals exhibits a full-width at half maximum (FWHM) value of 82 meV at an emission energy of 2.4 eV. Following CsBr (AX) extraction and addition of A′X′ solution (v.sub.NC=0.4), we observe A′.sub.2A.sub.n-1Pb.sub.nBr.sub.3n-1X′.sub.2 final perovskite nanocrystal solutions (A′=Cs.sup.+, MA.sup.+, FA.sup.+) with emission energies near that of the starting CsPbBr.sub.3 (ABX.sub.3) perovskite nanocrystals (2.39 eV for A=Cs.sup.+; 2.32 eV for A=FA.sup.+; 2.35 eV for A=MA.sup.+) with FWHM values remaining at 82 meV in all cases. These data show that the overall cation exchange process retains the size and size distribution of the starting CsPbBr.sub.3 (ABX.sub.3) perovskite nanocrystals and provides additional evidence that the PbBr.sub.2 (BX.sub.2) intermediate nanocrystals are derived directly from salt extraction from the starting perovskite nanocrystals without loss or gain of Pb′ cations. This also suggests that isolated 2DN sheets are not formed upon salt solution addition, with acetate simply binding to and separating some of the haloplumbate(II) layers and/or terminating the surface of A′.sub.2A.sub.n-1Pb.sub.nBr.sub.3n-1X′.sub.2 NCs. Photographs of UV-illuminated solutions of the starting CsPbBr.sub.3 (ABX.sub.3) nanocrystals (see Panel A of FIG. 7B) and A′.sub.2A.sub.n-1Pb.sub.nBr.sub.3n-1X′.sub.2 final perovskite nanocrystals with conditions that yield similar emission (leftmost cuvette, n=Panel B of FIG. 7B) and blue-shifted emission resulting from 2D layers within the nanocrystals (right 3 cuvettes, of Panel B of FIG. 7B). The required volume fraction for complete conversion to a homogeneous A′.sub.2A.sub.n-1Pb.sub.nBr.sub.3n-1X′.sub.2 final perovskite nanocrystal product may be monitored by simply titrating 0.01 M CsBr (AX) salt solutions into each PbBr.sub.2 (BX.sub.2) intermediate nanocrystal solution.

(39) Because both the perovskite nanocrystals and ligand concentrations can influence the structure of perovskite NCs in solution, a series of conversion experiments (e.g. second treating steps) were performed using (MA)Br (A′X′) salt solutions in which the total reaction solution volume, ligand concentration, and salt concentration were held constant, and v.sub.NC and v.sub.HOAc are varied. Panel A of FIG. 7C shows high acetic acid conditions (v.sub.HOAc=0.08). At v.sub.NC=0.1, a single emission peak at 2.85 eV is observed, which does not appreciably evolve over the course of 3 hours. When the volume fraction of perovskite nanocrystals was increased from v.sub.NC=0.2-0.4, a variety of PL peaks were observed, and the peaks evolved with time. Time-resolved spectra taken at t=0 and every 30 minutes following salt solution addition revealed it took ˜3 hours to reach an equilibrium perovskite nanocrystal composition at ambient temperature. Several interesting features are observed upon close inspection of the time-resolved PL spectra. Immediately after the (MA)Br solution was added to the PbBr.sub.2 intermediate nanocrystal solution, for all v.sub.NC>0.1, additional peaks emerged at lower energies. The same trend was observed at lower volume fractions of acetic acid, v.sub.HOAc=0.06 (Panel B of FIG. 7C) and v.sub.HOAc=0.04 (Panel C of FIG. 7C). Under these lower acetic acid concentration conditions, even more complex temporal evolution was seen, with high-energy peaks evolving into lower energy peaks with time.

(40) These data provide convincing evidence that greater acetate incorporation (lower n values in A′.sub.2A.sub.n-1Pb.sub.nBr.sub.3n-1X′.sub.2 final perovskite nanocrystals) results from higher v.sub.HOAc and lower v.sub.NC. This is consistent with the trends uncovered by XRD and FTIR data, which show increased acetate incorporation in A′.sub.2A.sub.n-1Pb.sub.nBr.sub.3n-1X′.sub.2 final perovskite nanocrystals at lower v.sub.NC. Unlike the XRD and FTIR data, however, the PL data provides temporal evidence that acetate incorporation is preferred kinetically (stronger blueshift at early times in the time-resolved spectra in Panels A-C of FIG. 7C), whereas bromide incorporation into the perovskite nanocrystal lattice is preferred thermodynamically (redshift toward lower energy 2D structures and eventually 3D structures at later times). This kinetic preference for acetate incorporation is likely due to the significantly higher concentration of acetate relative to bromide since 0.01 M CsBr (AX) salt solutions are made in glacial acetic acid and, as discussed above, likely exist as AX′ with X′=Br.sup.− or CH.sub.3COO.sup.−. Since evolution toward higher n values occurs over time, we conclude that the Pb(II)-Br (B—X) bond is slightly more favorable thermodynamically than the bidentate CH.sub.3COO—Pb(II) (B—X′) bond. Thus, though kinetics favor acetate incorporation at early times, Le Chatelier's principle ultimately governs structure obtained at equilibrium, and a high v.sub.HOAc relative to the number of PbBr.sub.2 intermediate nanocrystals can shift the equilibrium sufficiently toward complete conversion to a single-layer n=1 A′.sub.2PbBr.sub.2X′.sub.2 phase. Alternatively, decreasing v.sub.HOAc results in shifting the equilibrium toward the all-bromide 3D CsPbBr.sub.3 (ABX.sub.3) perovskite nanocrystal. Further tuning of the reaction conditions using variable temperature may be able to modulate the product distribution toward the several-layer A′.sub.2A.sub.n-1Pb.sub.nBr.sub.3n-1X′.sub.2 final perovskite nanocrystal structures.

(41) Finally, the presence of protons also may aid acetate versus bromide incorporation at early times (pK.sub.a 4.76 for HOAc vs. −9 for HBr in aqueous solution). The physical parameters affecting the degree of acetate incorporation is likely highly complex since evolution does not progress through isosbestic points in the time-resolved PL spectra. However, if acetate preferentially incorporates into the A′.sub.2A.sub.n-1Pb.sub.nBr.sub.3n-1X′.sub.2 final perovskite nanocrystals along single planes (as suggested by XRD results above), this would result in electrically isolated 2D perovskite layers with discrete emission properties within the larger perovskite A′.sub.2A.sub.n-1Pb.sub.nBr.sub.3n-1X′.sub.2 final perovskite nanocrystals. Without wishing to be bound by theory, it is hypothesized that the discrete blueshifted PL peaks at 2.49, 2.54, 2.62, 2.73, 2.85 eV result from 5, 4, 3, 2, and 1 2DN perovskite layers. For example, combining PbBr.sub.2 (BX.sub.2) with 2-(aminomethyl)pyridine (2-AMP) resulted in a 2D sheets made of (H.sub.22-AMP)PbBr.sub.4 that exhibited an excitonic absorption feature at 2.87 eV, very close to the 2.85 eV emission peak observed here.

(42) Experimental Methods

(43) Cs-Oleate Precursor Synthesis:

(44) CsCO.sub.3 (814 mg, 2.50 mmol, Aldrich, ReagentPlus, 99%), octadecene (ODE, 40 mL, Aldrich, Technical Grade, 90%), and oleic acid (2.5 mL, 7.9 mmol, Aldrich, Technical Grade, 90%) were placed in a 250 mL round-bottom flask (RBF). The mixture was heated under vacuum (10.sup.−2 Torr) at 120° C. for 1 hour, then at 150° C. under N.sub.2 while stirring with a magnetic stir bar. Heating was continued until a transparent, colorless solution was formed (˜20 minutes). The temperature of the solution was 100° C. for injection.

(45) PbBr.sub.2 (BX.sub.2) Precursor Synthesis:

(46) 0.274 g PbBr.sub.2 (Aldrich, ≥98%) and 30 mL ODE were placed in a separate RBF. The mixture was dried under vacuum by heating at 120° C. for 1 h while stirring with a magnetic stir bar. Under N.sub.2, 2 mL dry oleylamine (Aldrich, Technical Grade, 70%) and 2 mL oleic acid was injected through the septum using a syringe. Oleyamine and oleic acid were dried using 3 Å molecular sieves. After all the bulk PbBr.sub.2 reacted, a transparent, colorless solution formed, at which point the temperature was raised to 170° C.

(47) CsPbBr.sub.3 (ABX.sub.3) Starting Perovskite Nanocrystal Synthesis (e.g. Synthesizing Step 220 of FIG. 2):

(48) 1.6 mL of the 100° C. Cs-oleate precursor was injected with a syringe through a septum into the 170° C. PbBr.sub.2 (BX.sub.2) precursor to yield a bright yellow solution. The RBF was immediately removed from heat, and the reaction was quenched using an ice bath. The solution turned green and brightly luminescent upon cooling. When the temperature of the solution reached 30° C., the CsPbBr.sub.3 (ABX.sub.3) starting perovskite nanocrystal solution was transferred to a centrifuge tube and the CsPbBr.sub.3 (ABX.sub.3) starting perovskite nanocrystal solution was centrifuged at 10,000×g for 3 min. The light green supernatant was discarded, and the CsPbBr.sub.3 (ABX.sub.3) starting perovskite nanocrystals were dispersed in hexanes (˜10 mL), then centrifuged again at 6,600×g for 3 min. The green solids were discarded. An antisolvent solution was formed by combining 1.6 mL oleic acid and 1.6 mL oleylamine with 37.5 mL acetone. 20 mL of the antisolvent solution was used to precipitate the starting perovskite nanocrystals from the hexane solution, and the cloudy suspension was centrifuged at 10,000×g for 3 min. The transparent, colorless supernatant was discarded, leaving a green precipitate.

(49) PbBr.sub.2 (BX.sub.2) Intermediate Nanocrystal Preparation (e.g. First Treating Step of FIG. 2):

(50) A CsBr (AX) extraction solution was formed by combining 9 mL ethanol (dried over 3 Å molecular sieves), 0.75 mL dry oleylamine, and 0.25 mL dry oleic acid, and 0.40 mL deionized water. We found that the variable amounts of water present in non-dried reagents did not provide reproducible results, and a known amount of water had to be added to successfully achieve PbBr.sub.2 intermediate nanocrystals. The extraction solution was added to the solid CsPbBr.sub.3 (ABX.sub.3) starting perovskite nanocrystals and shaken or sonicated until the green powder turned white. Remaining CsPbBr.sub.3 (ABX.sub.3) starting perovskite nanocrystals were easily identified by green emission under UV illumination; if green emission was observed, additional shaking or sonication was performed. The resulting cloudy, white mixture was centrifuged at 10,000×g for 3 min, and the supernatant was discarded. The solid PbBr.sub.2 (BX.sub.2) intermediate nanocrystals were solvated in 10 mL dry toluene to yield a colorless solution. PbBr.sub.2 (BX.sub.2) intermediate nanocrystals solutions were stored on a Schlenk line under N.sub.2 until used for further transformations.

(51) X-Ray Diffraction:

(52) XRD measurements were performed on a Bruker D8 Discover X-ray Diffraction system with a 2.2 kW sealed Cu X-ray source. Patterns were acquired by depositing precipitated NCs onto a glass slide and scanning over 2θ using a beam voltage and current of 40 kV and 35 mA, respectively. Simulated powder diffraction patterns were generated using VESTA version 3.4 with .cif files from references.sup.32-34.

(53) A′.sub.2A.sub.n-1Pb.sub.nBr.sub.3n-1X′.sub.2 Synthesis (e.g. Second Treating 250 Step of FIG. 2):

(54) 0.01 M solutions of A′X′ salts were formed in glacial acetic acid. Transformation of PbBr.sub.2 (BX.sub.2) intermediate nanocrystals was performed by combining 0.1 mL A′X′ solution with 0.025 mL oleylamine, 0.025 mL oleic acid, and varying amounts of additional acetic acid and PbBr.sub.2 (BX.sub.2) intermediate nanocrystals solution as described above. Toluene was added to reach a total volume of 2.5 mL, which was held constant for all transformations. Each reagent was stored over 3 Å molecular sieves overnight before use.

(55) Transmission Electron Microscopy (TEM):

(56) Images were acquired on an FEI ST30 TEM operated at 300 kV. Samples were prepared by dropping dilute toluene solutions of NCs onto ultrathin carbon film/holey carbon, 400 mesh copper TEM grids.

(57) Fourier Transform Infrared Spectroscopy (FTIR):

(58) Spectra were acquired on a Bruker Alpha FTIR spectrometer inside an Ar-atmosphere glovebox. Spectra of NC samples were obtained in diffuse reflectance mode. Samples were prepared by depositing centrifuged powder onto an aluminum- or gold-coated Si wafer. Spectra were collected by averaging 50 scans at 2 cm.sup.−1 resolution. Spectra of neat oleic acid and oleylamine liquids were acquired in attenuated total reflectance mode on the same spectrometer by depositing a drop of the liquid onto a diamond ATR crystal and collecting spectra by averaging 50 scans at 2 cm.sup.−1 resolution.

(59) Photoluminescence Spectroscopy:

(60) Emission measurements were acquired using an OceanOptics OceanFX fiber-optically coupled Silicon CCD array. The OceanFX was controlled with custom LabVIEW software that allows extremely long averaging times (from ms to h) while maintaining a correct dark signal by using a light on-off acquisition sequence with a shutter cycle time of a few hundred ms. A ThorLabs M405FP1 fiber coupled 405 nm LED provided the light source, controlled by a ThorLabs DC2200 high power LED Driver. Typical output power after coupling was around 250 mW, which was allowed to have two passes through the sample by the use of a mirror on the back side of the cuvette. Typical acquisition times for photoluminescence were an integration time of 100 ms and an averaging time of a few min. The spectral sensitivity of the detector was calibrated against the HL2000-HP tungsten halogen lamp, assuming it is a perfect blackbody with a temperature of 3000 K.

COMPOSITION EXAMPLES

Example 1

(61) A perovskite sheet comprising: two outer layers, each comprising A′X′; and a first layer comprising BX.sub.2, wherein: B is a first cation, A′ is a second cation, X is a first anion, X′ is a second anion, and the first BX.sub.2 layer is positioned between the two outer layers.

Example 2

(62) The perovskite sheet of Example 1, further comprising: a first layer comprising AX; and a second BX.sub.2 layer, wherein: A is a third cation, the second BX.sub.2 layer is positioned between the outer layers, and the first AX layer is positioned between the first BX.sub.2 layer and the second BX.sub.2 layer.

Example 3

(63) The perovskite sheet of Example 2, further comprising: a second AX layer, and a third BX.sub.2 layer, wherein: the second AX layer and the third BX.sub.2 are positioned between the outer layers, each outer layer is adjacent to a BX.sub.2 layer, and the BX.sub.2 layers and AX layers alternate positions in the sheet.

Example 4

(64) The perovskite sheet of Example 3, further comprising: n BX.sub.2 layers, wherein: n is greater than three, and the outer layers, the BX.sub.2 layers, and the AX layers result in a stoichiometry defined by A′.sub.2A.sub.n-1B.sub.nX.sub.3n-1X′.sub.2.

Example 5

(65) The perovskite sheet of Example 1, wherein A comprises at least one of an alkylammonium cation, formamidinium (NH.sub.2CH═NH.sub.2.sup.+), H.sup.+, or Cs.sup.+.

Example 6

(66) The perovskite sheet of Example 5, wherein the alkylammonium cation comprises at least one of methylammonium (CH.sub.3NH.sub.3.sup.+), ethylammonium (CH.sub.3CH.sub.2NH.sub.3.sup.+), propylammonium (CH.sub.3CH.sub.2CH.sub.2NH.sub.3.sup.+), or butylammonium (CH.sub.3CH.sub.2CH.sub.2CH.sub.2NH.sub.3.sup.+).

Example 7

(67) The perovskite sheet of Example 1, wherein A′ comprises at least one of an alkylammonium cation, formamidinium (NH.sub.2CH═NH.sub.2.sup.+), H.sup.+, or Cs.sup.+.

Example 8

(68) The perovskite sheet of Example 7, wherein the alkylammonium cation comprises at least one of methylammonium (CH.sub.3NH.sub.3.sup.+), ethylammonium (CH.sub.3CH.sub.2NH.sub.3.sup.+), propylammonium (CH.sub.3CH.sub.2CH.sub.2NH.sub.3.sup.+), or butylammonium (CH.sub.3CH.sub.2CH.sub.2CH.sub.2NH.sub.3.sup.+).

Example 9

(69) The perovskite sheet of Example 1, wherein B comprises at least one of lead, tin, or germanium.

Example 10

(70) The perovskite sheet of Example 1, wherein X comprises at least one of fluorine, chlorine, bromine, or iodine.

Example 11

(71) The perovskite sheet of Example 1, wherein X′ comprises at least one of fluorine, chlorine, bromine, iodine, or acetate.

Example 12

(72) The perovskite sheet of Example 1, wherein X′ comprises a charged form of at least one of a phosphonate group, a carboxylate group, a thiolate, a thiocyanate, an isocyanate, a carbonate, a chromate, a phosphate, a sulfite, a hydroxide, a nitrite, a percholorate.

Example 13

(73) The perovskite sheet of Example 12, wherein X′ comprises at least one of includes acetate, propionate, butyrate, phenolate, formate, an alkylphosphonate, or an alkylthiolate.

Example 14

(74) The perovskite sheet of Example 12, wherein X′ comprises at least one of methylphosphonate, ethylphosphonate, phenylphosphonate, butanethiolate, hexanethiolate, or phenylthiolate.

Example 15

(75) The perovskite sheet of Example 1, wherein A′X′ is cesium acetate.

Example 16

(76) The perovskite sheet of Example 1, wherein AX is cesium bromide.

Example 17

(77) The perovskite sheet of Example 1, wherein BX.sub.2 is PbBr.sub.2.

Example 18

(78) The perovskite sheet of Example 4, wherein A′.sub.2A.sub.n-1B.sub.nX.sub.3n-1X′.sub.2 is Cs.sub.1-nPb.sub.nBr.sub.3n-1(CH.sub.3O.sub.2).sub.2.

Example 19

(79) The perovskite sheet of Example 4, wherein 4≤n≤10,000.

Example 20

(80) The perovskite sheet of Example 19, wherein 4≤n≤1,000.

Example 21

(81) The perovskite sheet of Example 20, wherein 4≤n≤100.

Example 22

(82) The perovskite sheet of Example 1, wherein the perovskite sheet comprises a nanocrystal.

Example 23

(83) The perovskite sheet of Example 22, wherein the nanocrystal has a characteristic length between about 1 nm and about 50 nm.

Example 24

(84) The perovskite sheet of Example 23, wherein the characteristic length is between about 6 nm and about 20 nm.

Example 25

(85) The perovskite sheet of Example 22, wherein the nanocrystal is suspended in a solution comprising a first solvent.

Example 26

(86) The perovskite sheet of Example 25, wherein: the first solvent has a first solubility for A′X′, the first solvent has a second solubility for BX.sub.2, the first solubility is higher than the second solubility.

Example 27

(87) The perovskite sheet of Example 26, wherein the first solvent comprises at least one of an alcohol, a carboxylic acid, a ketone, a nitrile, water, or toluene.

Example 28

(88) The perovskite sheet of Example 27, wherein the first solvent comprises at least one of acetic acid or formic acid.

Example 29

(89) The perovskite sheet of Example 25, wherein the solution further comprises a second solvent.

Example 30

(90) The perovskite sheet of Example 29, wherein the second solvent comprises a nonpolar solvent.

Example 31

(91) The perovskite sheet of Example 30, wherein the nonpolar solvent comprises at least one of hexane, toluene, or benzene.

Example 32

(92) The perovskite sheet of Example 29, wherein the solution further comprises a ligand comprising a binding group, where the binding group is physically associated with a surface of the nanocrystal.

Example 33

(93) The perovskite sheet of Example 32, wherein the physical association comprises at least one of an ionic bond, a hydrogen bond, or van der Waals forces.

Example 34

(94) The perovskite sheet of Example 32, wherein the ligand comprises a hydrocarbon having four or more carbon atoms.

Example 35

(95) The perovskite sheet of Example 32, wherein the binding group comprises a neutral group comprising at least one of a hydroxyl group, an epoxide, an aldehyde, a ketone, a carboxylic acid, an acid anhydride, an ester, an amide, an acyl halide, an amine, a nitrile, an imine, an isocyanate, or a thiol.

Example 36

(96) The perovskite sheet of Example 35, wherein the binding group comprises a charged form of the neutral group.

Example 37

(97) The perovskite sheet of Example 36, wherein the ligand comprises at least one of oleylamine, oleylammonium, phenylammonium, or dodecylammonium.

Example 38

(98) The perovskite sheet of Example 32, wherein the nanocrystal emits light when exposed to UV light.

Example 39

(99) The perovskite sheet of Example 38, wherein the light is at an energy level between about 1.7 eV and about 3.0 eV.

Example 40

(100) The perovskite sheet of Example 39, wherein the energy level is between about 2.2 eV and about 2.5 eV when A′ and A both comprise Cs.sup.+.

Example 41

(101) The perovskite sheet of Example 39, wherein the energy level is between about 2.15 eV and about 2.45 eV when A′ comprises FA.sup.+ and A comprises Cs.sup.+.

Example 42

(102) The perovskite sheet of Example 39, wherein the energy level is between about 2.10 eV and about 2.40 eV when A′ comprises MA.sup.+ and A comprises Cs.sup.+.

Example 43

(103) A perovskite sheet comprising: a first outer layer comprising A′X′; and a second outer layer comprising A′.sub.2BX.sub.2X′.sub.2, wherein: B is a first cation, A′ is a second cation, X is a first anion, X′ is a second anion, and the first outer layer and the second outer layer are adjacent to one another.

Example 44

(104) The perovskite sheet of Example 43, further comprising a first ABX.sub.3 layer positioned between the two outer layers, wherein A is a third cation.

Example 45

(105) The perovskite sheet of Example 44, further comprising a second ABX.sub.3 layer positioned between the two outer layers.

Example 46

(106) The perovskite sheet of Example 45, further comprising: (n−1) ABX.sub.3 layers, wherein: n is greater than three, and the outer layers and the ABX.sub.3 layers result in a stoichiometry defined by A′.sub.2A.sub.n-1B.sub.nX.sub.3n-1X′.sub.2.

Example 47

(107) A perovskite network comprising: a first perovskite sheet having the stoichiometry of A′.sub.2A.sub.n-1B.sub.nX.sub.3n-1X′.sub.2, and a second perovskite sheet having the stoichiometry of A′.sub.2A.sub.m-1B.sub.mX.sub.3m-1X′.sub.2, wherein: B is a first cation, A′ is a second cation, A is a third cation, X is a first anion, and X′ is a second anion, the first perovskite sheet and the second perovskite sheet each comprise an A′X′ layer, the A′X′ layer of the first perovskite sheet is physically associated with the A′X′ layer of the second perovskite sheet, and m does not equal n, m is greater than or equal to zero, and n is greater than or equal to one.

Example 48

(108) The perovskite of Example 47, wherein the physical association comprises at least one an ionic bond, a hydrogen bond, or van der Waals forces.

Example 49

(109) A perovskite network comprising: a first perovskite sheet having the stoichiometry of A′.sub.2A.sub.n-1Pb.sub.nBr.sub.3n-1X″, and a second perovskite sheet having the stoichiometry of A′.sub.2A.sub.m-1Pb.sub.mBr.sub.3m-1X″, wherein: B is a first cation, A′ is a second cation, A is a third cation, X is a first anion, and X″ is a second anion, the first perovskite sheet and the second perovskite sheet are physically associated by sharing at least one X″, and m does not equal n, m is greater than or equal to zero, and n is greater than or equal to one.

Example 50

(110) The perovskite of Example 49, wherein the physical association comprises at least one an ionic bond, a hydrogen bond, or van der Waals forces.

METHOD EXAMPLES

Example 1

(111) A method for making a perovskite, the method comprising: removing A and X from a first nanocrystal comprising ABX.sub.3, resulting in the forming of a second nanocrystal comprising BX.sub.2; contacting the second nanocrystal with A′X′, resulting in the forming of third nanocrystal comprising A′.sub.2A.sub.n-1B.sub.nX.sub.3n-1X′.sub.2, wherein: B is a first cation, A′ is a second cation, A is a third cation, X is a first anion, and X′ is a second anion.

Example 2

(112) The method of Example 1, wherein: the removing is achieved by immersing the first nanocrystal in a first solution comprising a first solvent, the first solution has a first solubility for the A and the X, the first solution has a second solubility for the second nanocrystal, and the first solubility is higher than the second solubility.

Example 3

(113) The method of Example 2, wherein the first solvent comprises at least one of water, an alcohol, ether, a halogenated alkane, a halogenated benzene, a ketone, an alkylnitrile, or an ester.

Example 4

(114) The method of Example 3, wherein the first solvent comprises water and ethanol.

Example 5

(115) The method of Example 2, wherein the first solution further comprises a ligand comprising a binding group associated with a surface of the first nanocrystal.

Example 6

(116) The method of Example 5, wherein the ligand comprises a hydrocarbon having four or more carbon atoms.

Example 7

(117) The method of Example 5, wherein the ligand comprises a hydrocarbon having four or more carbon atoms.

Example 8

(118) The method of Example 5, the binding group comprises a neutral group comprising at least one of a hydroxyl group, an epoxide, an aldehyde, a ketone, a carboxylic acid, an acid anhydride, an ester, an amide, an acyl halide, an amine, a nitrile, an imine, an isocyanate, or a thiol.

Example 9

(119) The method of Example 8, wherein the binding group comprises a charged form of the neutral group.

Example 10

(120) The method of Example 9, wherein the ligand comprises at least one of oleylamine, oleylammonium, phenylammonium, or dodecylammonium.

Example 11

(121) The method of Example 1, wherein the removing is performed by at least one of filtration, centrifugation, or gravity separation.

Example 12

(122) The method of Example 1, wherein: the contacting is performed by adding the A′X′ in a second solution comprising a second solvent, the second solvent has a third solubility for A′X′, the second solvent has a fourth solubility for BX.sub.2, and the third solubility is higher than the fourth solubility.

Example 13

(123) The method of Example 12, wherein the second solvent comprises at least one of a carboxylic acid, a halogenated arene, a ketone, a nitrile, or toluene.

Example 14

(124) The method of Example 13, wherein the second solvent comprises at least one of acetic acid or formic acid.

Example 15

(125) The method of Example 12, wherein the second solution further comprises a nonpolar solvent.

Example 16

(126) The method of Example 15, wherein the nonpolar solvent comprises at least one hexane, toluene, or benzene.

(127) The foregoing discussion and examples have been presented for purposes of illustration and description. The foregoing is not intended to limit the aspects, embodiments, or configurations to the form or forms disclosed herein. In the foregoing Detailed Description for example, various features of the aspects, embodiments, or configurations are grouped together in one or more embodiments, configurations, or aspects for the purpose of streamlining the disclosure. The features of the aspects, embodiments, or configurations, may be combined in alternate aspects, embodiments, or configurations other than those discussed above. This method of disclosure is not to be interpreted as reflecting an intention that the aspects, embodiments, or configurations require more features than are expressly recited in each claim. Rather, as the following claims reflect, inventive aspects lie in less than all features of a single foregoing disclosed embodiment, configuration, or aspect. While certain aspects of conventional technology have been discussed to facilitate disclosure of some embodiments of the present invention, the Applicants in no way disclaim these technical aspects, and it is contemplated that the claimed invention may encompass one or more of the conventional technical aspects discussed herein. Thus, the following claims are hereby incorporated into this Detailed Description, with each claim standing on its own as a separate aspect, embodiment, or configuration.