Soft Lattice Research Articles

Two-dimensional halide perovskite lateral epitaxial heterostructures.

Epitaxial heterostructures based on oxide perovskites and III-V, II-VI and transition metal dichalcogenide semiconductors form the foundation of modern electronics and optoelectronics1-7. Halide perovskites-an emerging family of tunable semiconductors with desirable properties-are attractive for applications such as solution-processed solar cells, light-emitting diodes, detectors and lasers8-15. Their inherently soft crystal lattice allows greater tolerance to lattice mismatch, making them promising for heterostructure formation and semiconductor integration16,17. Atomically sharp epitaxial interfaces are necessary to improve performance and fordevice miniaturization.However, epitaxial growth of atomically sharp heterostructures of halide perovskites has not yet been achieved, owing to their high intrinsic ion mobility, which leads to interdiffusion and large junction widths18-21, and owing to their poor chemical stability, which leads to decomposition of prior layers during the fabrication of subsequent layers. Therefore, understanding the origins of this instability and identifying effective approaches to suppress ion diffusion are of great importance22-26. Here we report an effective strategy to substantially inhibit in-plane ion diffusion in two-dimensional halide perovskites by incorporating rigid π-conjugated organic ligands. We demonstrate highly stable and tunable lateral epitaxial heterostructures, multiheterostructures and superlattices. Near-atomically sharp interfaces and epitaxial growth are revealed by low-dose aberration-corrected high-resolution transmission electron microscopy. Molecular dynamics simulations confirm the reduced heterostructure disorder and larger vacancy formation energies of the two-dimensional perovskites in the presence of conjugated ligands. These findings provide insights into the immobilization and stabilization of halide perovskite semiconductors and demonstrate a materials platform for complex and molecularly thin superlattices, devices and integrated circuits.

α-level Fuzzy Soft Sets

In this paper, based on soft lattices, with the help of fuzzy level (cut) set, -level fuzzy soft sets and -level fuzzy soft lattices are defined, and the structure and characteristics of our definitions are explained with examples, at the same time, their di erences and relations are compared with classic soft set.

Facile Strategy for Facet Competition Management to Improve the Performance of Perovskite Single-Crystal X-ray Detectors.

Methylammonium lead tribromide perovskite single crystals have been demonstrated to be good candidates as sensitive X-ray detectors in direct detection mode in recent years. However, its X-ray detection performance based on the orientation of different facets is still not clear. Here, we developed a facile strategy to chemically expose the [110] facet of single crystals from low-cost solution processes by tailoring the nonstoichiometry of feeding ions to selectively suppress the growth of the [100] facet. In contrast to physically cutting and sawing single-crystal ingots, this avoids damage to the fragile single crystals as well as orientation errors, more suitable for the naturally soft lattice. Compared to the [100] facet, the exposed [110] facet of perovskite single crystals exhibits a smaller trap density and excellent charge carrier transportation properties, leading to an improved sensitivity of 3928.3 μC/Gyair/cm2 to 120 keV hard X-rays, which potentially outperforms the currently dominating CsI scintillator of a commercial digital radiography (DR) medical imager for a routine health check.

Lattice Superdeformation as the Synergy of Two Martensitic Transformations in Titanium Nickelide Alloys

The uniqueness of titanium nickelide alloys consists in the binary B2 → R, B2 → B19) martensitic instability of the isotropically soft B2 lattice and in the synergetic effects induced by the superposition of these two transformations, which form the synergetic B19' lattice with martensitic superdeformation formed in the transformations B2 → R → B19', B2 → B19', and B2 → B19 → B19'. The effects of synergy of the two martensitic transformations are observed during the relay B2 → B19 → B19', and the superdeformation effects are most pronounced at the stage B19 → B19'.

Energy transfer and wavelength tunable lasing of single perovskite alloy nanowire

Single perovskite alloy nanowire capable of emitting lasing broadly and continuously is highly desirable for the miniaturization and integration of all-photonic devices. However, due to the limitation of a soft and dynamic crystal lattice and the synthesized strategy, single perovskite nanowire with single-band lasing emission is mostly observed. Here, we propose a solid-solid anion-diffusion process to construct single CsPbCl3-3xBr3x perovskite alloy nanowire with a widely tunable bandgap from 2.41 to 2.82 eV and a regularly geometrical structure. We realized a broadly and continuously tunable nanolaser from 480 to 525 nm in single CsPbCl3-3xBr3x nanowire, as different spots along the length serve as a gain medium and microcavity simultaneously. The kinetics and atomic-scale mechanism of solid-solid anion diffusion were analyzed by a quantitative study and theoretical calculations, giving a small activation energy of halide migrations. The dynamics of carrier transportations revealed the energy transfer in single CsPbCl3-3xBr3x alloy nanowire, that's why broadly tunable lasers are difficult to realize in single isolated nanowire. Our work proposes a new strategy to construct single perovskite alloy nanowire for achieving a broadly and continuously tunable laser, clarifies the mechanism and kinetics of anion diffusion in perovskite alloy nanowires.

Compressive behavior of soft lattice structures and their application to functional compliance control

Lattice structures are advantageous in terms of their high specific stiffness and strength, and have been applied to the design of lightweight structures owing to the recent development of additive manufacturing (AM). The unique design flexibility of AM has enabled the fabrication of a functionally graded lattice (FGL) by gradually changing the lattice size and enhancing structural efficiency of lattice structures. Although FGLs have been generally designed to reduce the compliance (i.e., to increase the stiffness), this study aims to develop soft polymeric lattices to widen the range of compliance for the development of FGLs. To develop soft lattice structures, various lattices were designed and fabricated using a photo-polymerization type 3D printer and photo-curable polyurethane resin. Compression tests were conducted on these lattices, and their deformation behaviors were analyzed experimentally. The effects of various lattice design parameters and the curing time were also investigated, and the resulting changes in the compliance were analyzed. As a consequence, the compressive stiffness can vary widely, within a range of 10−3 to 102 N/mm. Two types of FGLs, which enabled the self-positioning and self-guided moving functions, were then developed by varying the lattice direction, strut diameter and curing time effectively.

Soft Lattice and Defect Covalency Rationalize Tolerance of β-CsPbI3 Perovskite Solar Cells to Native Defects.

Although all-inorganic metal halide perovskites (MHPs) have shown tremendous improvement, they are still inferior to the hybrid organic-inorganic MHPs in efficiency. Recently, a conceptually new β-CsPbI3 perovskite reached 18.4 % efficiency combined with good thermodynamic stability at ambient conditions. We use ab initio non-adiabatic molecular dynamics to show that native point defects in β-CsPbI3 are generally benign for nonradiative charge recombination, regardless of whether they introduce shallow or deep trap states. These results indicate that MHPs do not follow the simple models used to explain defect-mediated charge recombination in the conventional semiconductors. The strong tolerance is due to the softness of the perovskite lattice, which permits separation of electrons and holes upon defect formation, and only allows carriers to couple to the low-frequency vibrations. Both factors decrease notably the non-adiabatic coupling and slow down the dissipation of energy to heat.

Soft Lattice and Defect Covalency Rationalize Tolerance of β‐CsPbI3 Perovskite Solar Cells to Native Defects

AbstractAlthough all‐inorganic metal halide perovskites (MHPs) have shown tremendous improvement, they are still inferior to the hybrid organic–inorganic MHPs in efficiency. Recently, a conceptually new β‐CsPbI3 perovskite reached 18.4 % efficiency combined with good thermodynamic stability at ambient conditions. We use ab initio non‐adiabatic molecular dynamics to show that native point defects in β‐CsPbI3 are generally benign for nonradiative charge recombination, regardless of whether they introduce shallow or deep trap states. These results indicate that MHPs do not follow the simple models used to explain defect‐mediated charge recombination in the conventional semiconductors. The strong tolerance is due to the softness of the perovskite lattice, which permits separation of electrons and holes upon defect formation, and only allows carriers to couple to the low‐frequency vibrations. Both factors decrease notably the non‐adiabatic coupling and slow down the dissipation of energy to heat.

Soft valuation on a generalized soft lattice

Lattice theory play an important role in mathematics as well as in other disciplines such as computer science, engineering, cryptography, etc. In this paper, we introduce the concept of generalized soft lattice (gs lattice) and investigate some of its fundamental properties. Further we define soft valuation on a generalized soft lattice (gs lattice) and study its major properties. In the last section we discuss the notion of soft distance function and express it in terms of soft valuation. Here we discuss the notions of soft pseudo metric lattice and soft metric lattice.

High-pressure polymorphism in pyridine.

Single crystals of the high-pressure phases II and III of pyridine have been obtained by in situ crystallization at 1.09 and 1.69 GPa, revealing the crystal structure of phase III for the first time using X-ray diffraction. Phase II crystallizes in P212121 with Z' = 1 and phase III in P41212 with Z' = ½. Neutron powder diffraction experiments using pyridine-d5 establish approximate equations of state of both phases. The space group and unit-cell dimensions of phase III are similar to the structures of other simple compounds with C 2v molecular symmetry, and the phase becomes stable at high pressure because it is topologically close-packed, resulting in a lower molar volume than the topologically body-centred cubic phase II. Phases II and III have been observed previously by Raman spectroscopy, but have been mis-identified or inconsistently named. Raman spectra collected on the same samples as used in the X-ray experiments establish the vibrational characteristics of both phases unambiguously. The pyridine molecules interact in both phases through CH⋯π and CH⋯N interactions. The nature of individual contacts is preserved through the phase transition between phases III and II, which occurs on decompression. A combination of rigid-body symmetry mode analysis and density functional theory calculations enables the soft vibrational lattice mode which governs the transformation to be identified.

Tailoring liquid crystal honeycombs by head-group choice in bird-like bent-core mesogens

New non-centrosymmetric soft honeycomb lattices and superlattices are generated by self-assembly of novel mesogens promising applications as SHG and ferroelectric materials.

First-principles soft-mode lattice dynamics of PbZr0.5Ti0.5O3 and shortcomings of the virtual crystal approximation

A comparative study between PbTiO$_3$, PbZrO$_3$, and the solid solution PbZr$_{0.5}$Ti$_{0.5}$O$_3$ is performed on the soft mode lattice dynamics within the first Brillouin Zone. We consider the six unique B-site orderings for PbZr$_{0.5}$Ti$_{0.5}$O$_3$ representable within the 2$\times$2$\times$2 primitive perovskite supercell as well as the virtual crystal approximation (VCA) to extract the phonon dispersion relations of a high-symmetry cubic-constrained form using density functional perturbation theory. We find that the most unstable modes in the rock-salt ordered structure and the VCA, like pure PbZrO$_3$, are antiferrodistortive (AFD) whilst lower symmetry arrangements are dominated by $\Gamma$-point ferroelectric (FE) instabilities like pure PbTiO$_3$. Despite similarities in the phonon dispersion relations between the rock-salt ordered supercell and the VCA, the character of modes at high symmetry points are found to be different. In particular, the a$^{0}$a$^{0}$c$^{-}$ & a$^{0}$a$^{0}$c$^{+}$ AFD instabilities of the rock-salt ordering are replaced with a$^{-}$b$^{-}$c$^{-}$ & a$^{+}$b$^{+}$c$^{+}$ instabilities within the VCA. Such a rotation pattern is not seen in any of the supercell-based calculations thus serving as a quantitative example of the inability of the method to represent accurately local structural distortions. Single modes are found exhibiting dual order parameters. At the zone centre, some arrangements show mixed FE & antipolar soft modes (due to Pb motion tansverse to the polar axis) and at long wavelengths all arrangements have soft modes of a mixed antipolar & AFD character. These are described with direct analysis of the eigendisplacements.

THE WAY-BELOW SOFT SET RELATION

Order is used frequently in mathematical objects and related fields. We use order in the soft set that is introduced by Molodtsov [1]. Babitha and Sunil [2] gave the definition of soft set relation, then Babitha and Sunil [3] defined partially ordered soft set. We introduced directed soft sets in [4]. Moreover, definition of soft lattice, complete soft lattice were given in [5]. We made a presentation, whose abstract was published only in the Abstract Book, in ICRAPAM 2014 [6] about the way-below soft set relation. In this paper, this study is extended and the proofs of all results of our presentation is given. Moreover, continuous soft lattices, L-soft domain are defined, and some important results are obtained and proved in this study.

Reversible Thermochromism and Strong Ferromagnetism in Two-Dimensional Hybrid Perovskites.

Two-dimensional (2D) hybrid perovskites have shown many attractive properties associated with their soft lattices and multiple quantum well structure. Herein, we report the synthesis and characterization of two new multifunctional 2D hybrid perovskites, (PED)CuCl4 and (BED)2 CuCl6 , which show reversible thermochromic behavior, dramatic temperature-dependent conductivity change, and strong ferromagnetism. Upon temperature change, the (PED)CuCl4 and (BED)2 CuCl6 crystals exhibit a reversible color change between yellow and red-brown. The associated structural changes were monitored by in situ temperature-dependent powder X-ray diffraction (PXRD). The (BED)2 CuCl6 exhibits superior thermal stability, with a thermochromic working temperature up to 443 K. The conductivity of (BED)2 CuCl6 changes over six orders of magnitude upon temperature change. The 2D perovskites exhibit ferromagnetic properties with Curie temperatures around 13 K.

Reversible Thermochromism and Strong Ferromagnetism in Two‐Dimensional Hybrid Perovskites

AbstractTwo‐dimensional (2D) hybrid perovskites have shown many attractive properties associated with their soft lattices and multiple quantum well structure. Herein, we report the synthesis and characterization of two new multifunctional 2D hybrid perovskites, (PED)CuCl4 and (BED)2CuCl6, which show reversible thermochromic behavior, dramatic temperature‐dependent conductivity change, and strong ferromagnetism. Upon temperature change, the (PED)CuCl4 and (BED)2CuCl6 crystals exhibit a reversible color change between yellow and red‐brown. The associated structural changes were monitored by in situ temperature‐dependent powder X‐ray diffraction (PXRD). The (BED)2CuCl6 exhibits superior thermal stability, with a thermochromic working temperature up to 443 K. The conductivity of (BED)2CuCl6 changes over six orders of magnitude upon temperature change. The 2D perovskites exhibit ferromagnetic properties with Curie temperatures around 13 K.

Monitoring Electron-Phonon Interactions in Lead Halide Perovskites Using Time-Resolved THz Spectroscopy.

Lead halide perovskite semiconductors have low-frequency phonon modes within the lead halide sublattice and thus are considered to be soft. The soft lattice is considered to be important in defining their interesting optoelectronic properties. Electron-phonon coupling governs hot-carrier relaxation, carrier mobilities, carrier lifetimes, among other important electronic characteristics. Directly observing the interplay between free charge carriers and phonons can provide details on how phonons impact these properties (e.g., exciton populations and other collective modes). Here, we observe a delicate interplay among carriers, phonons, and excitons in mixed-cation and mixed-halide perovskite films by simultaneously resolving the contribution of charge carriers and phonons in time-resolved terahertz photoconductivity spectra. We are able to observe directly the increase in phonon population during carrier cooling and discuss how thermal equilibrium populations of carriers and phonons modulate the carrier transport properties, as well as reduce the population of carriers within band tails. We are also able to observe directly the formation of free charge carriers when excitons interact with phonons and dissociate and to describe how free carriers and exciton populations exchange through phonon interactions. Finally, we also time-resolve how the carriers are screened via the Coulomb interaction at low and room temperatures. Our studies shed light on how charge carriers interact with the low-energy phonons and discuss implications.

First-Principles Investigation of Spin-Phonon Coupling in Vanadium-Based Molecular Spin Quantum Bits.

Paramagnetic molecules can show long spin-coherence times, which make them good candidates as quantum bits (qubits). Reducing the efficiency of the spin-phonon interaction is the primary challenge toward achieving long coherence times over a wide temperature range in soft molecular lattices. The lack of a microscopic understanding about the role of vibrations in spin relaxation strongly undermines the possibility of chemically designing better-performing molecular qubits. Here we report a first-principles characterization of the main mechanism contributing to the spin-phonon coupling for a class of vanadium(IV) molecular qubits. Post-Hartree-Fock and density functional theory methods are used to determine the effect of both intermolecular and intramolecular vibrations on modulation of the Zeeman energy for four molecules showing different coordination geometries and ligands. This comparative study provides the first insight into the role played by coordination geometry and ligand-field strength in determining the spin-lattice relaxation time of molecular qubits, opening an avenue to the rational design of new compounds.

Manipulating efficient light emission in two-dimensional perovskite crystals by pressure-induced anisotropic deformation.

The hybrid nature and soft lattice of organolead halide perovskites render their structural changes and optical properties susceptible to external driving forces such as temperature and pressure, remarkably different from conventional semiconductors. Here, we investigate the pressure-induced optical response of a typical two-dimensional perovskite crystal, phenylethylamine lead iodide. At a moderate pressure within 3.5 GPa, its photoluminescence red-shifts continuously, exhibiting an ultrabroad energy tunability range up to 320 meV in the visible spectrum, with quantum yield remaining nearly constant. First-principles calculations suggest that an out-of-plane quasi-uniaxial compression occurs under a hydrostatic pressure, while the energy is absorbed by the reversible and elastic tilting of the benzene rings within the long-chain ligands. This anisotropic structural deformation effectively modulates the quantum confinement effect by 250 meV via barrier height lowering. The broad tunability within a relatively low pressure range will expand optoelectronic applications to a new paradigm with pressure as a tuning knob.

Self-Trapped Excitons in All-Inorganic Halide Perovskites: Fundamentals, Status, and Potential Applications.

Photoluminescence is a radiative recombination process of electron-hole pairs. Self-trapped excitons (STEs), occurring in a material with soft lattice and strong electron-phonon coupling, emit photons with broad spectrum and large Stokes shift. Recently, series halide perovskites with efficient STE emission have been reported and showed promise for solid-state lighting. In this Perspective, we present an overview of various photoluminescence phenomena with the emphasis on the mechanism and characteristics of emission derived from STEs. This is followed by the introduction of STE emission in hybrid halide perovskites. We then introduce all-inorganic STE emitters and focus in particular on the mechanism of STEs in double-perovskite Cs2AgInCl6 and strategies for efficiency improvement. Finally, we summarize the current photoluminescence and electroluminescence applications of STE emitters as well as the potential in luminescent solar concentrators and provide an overview of future research opportunities.

Guanidinium and Mixed Cesium-Guanidinium Tin(II) Bromides: Effects of Quantum Confinement and Out-of-Plane Octahedral Tilting.

Hybrid organic–inorganic main-group metal halide compounds are the subject of intense research owing to their unique optoelectronic characteristics. In this work, we report the synthesis, structure, and electronic and optical properties of a family of hybrid tin (II) bromide compounds comprising guanidinium [G, C(NH2)3+] and mixed cesium–guanidinium cations: G2SnBr4, CsGSnBr4, and Cs2GSn2Br7. G2SnBr4 has a one-dimensional structure that consists of chains of corner-sharing [SnBr5]2– square pyramids and G cations situated in between the chains. Cs+ exhibits a pronounced structure-directing effect where a mixture of Cs+ and G cations forms mono- and bilayered two-dimensional perovskites: CsGSnBr4 and Cs2GSn2Br7. Furthermore, the flat shapes of the guanidinium cations induce anisotropic out-of-plane tilts of the [SnBr6]4– octahedra in the CsGSnBr4 and Cs2GSn2Br7 compounds. In G2SnBr4, the Sn lone pair is highly stereoactive and favors non-octahedral, that is, square pyramidal coordination of Sn(II). G2SnBr4 exhibits bright broad-band emission from self-trapped excitonic states, owing to its soft lattice and electronic localization. This emission in G2SnBr4 is characterized by a photoluminescence (PL) quantum yield of 2% at room temperature (RT; 75 ± 5% at 77 K) and a fast PL lifetime of 18 ns at room temperature.