Water- and heat-activated dynamic passivation for perovskite photovoltaics.

Further improvements in perovskite solar cells require better control of ionic defects in the perovskite photoactive layer during the manufacturing stage and their usage1-5. Here we report a living passivation strategy using a hindered urea/thiocarbamate bond6-8 Lewis acid-base material (HUBLA), where dynamic covalent bonds with water and heat-activated characteristics can dynamically heal the perovskite to ensure device performance and stability. Upon exposure to moisture or heat, HUBLA generates new agents and further passivates defects in the perovskite. This passivation strategy achieved high-performance devices with a power conversion efficiency (PCE) of 25.1 per cent. HUBLA devices retained 94 per cent of their initial PCE for approximately 1,500 hours of ageing at 85 degrees Celsius in nitrogen and maintained 88 per cent of their initial PCE after 1,000 hours of ageing at 85 degrees Celsius and 30 per cent relative humidity in air.

Multifunctional ytterbium oxide buffer for perovskite solar cells.

Perovskite solar cells (PSCs) comprise a solid perovskite absorber sandwiched between several layers of different charge-selective materials, ensuring unidirectional current flow and high voltage output of the devices1,2. A 'buffer material' between the electron-selective layer and the metal electrode in p-type/intrinsic/n-type (p-i-n) PSCs (also known as inverted PSCs) enables electrons to flow from the electron-selective layer to the electrode3-5. Furthermore, it acts as a barrier inhibiting the inter-diffusion of harmful species into or degradation products out of the perovskite absorber6-8. Thus far, evaporable organic molecules9,10 and atomic-layer-deposited metal oxides11,12 have been successful, but each has specific imperfections. Here we report a chemically stable and multifunctional buffer material, ytterbium oxide (YbOx), for p-i-n PSCs by scalable thermal evaporation deposition. We used this YbOx buffer in the p-i-n PSCs with a narrow-bandgap perovskite absorber, yielding a certified power conversion efficiency of more than 25%. We also demonstrate the broad applicability of YbOx in enabling highly efficient PSCs from various types of perovskite absorber layer, delivering state-of-the-art efficiencies of 20.1% for the wide-bandgap perovskite absorber and 22.1% for the mid-bandgap perovskite absorber, respectively. Moreover, when subjected to ISOS-L-3 accelerated ageing, encapsulated devices with YbOx exhibit markedly enhanced device stability.

Buried interface molecular hybrid for inverted perovskite solar cells.

Perovskite solar cells with an inverted architecture provide a key pathway for commercializing this emerging photovoltaic technology because of the better power conversion efficiency and operational stability compared with the normal device structure. Specifically, power conversion efficiencies of the inverted perovskite solar cells have exceeded 25% owing to the development of improved self-assembled molecules1-5 and passivation strategies6-8. However, poor wettability and agglomeration of self-assembled molecules9-12 cause interfacial losses, impeding further improvement in the power conversion efficiency and stability. Here we report a molecular hybrid at the buried interface in inverted perovskite solar cells that co-assembled the popular self-assembled molecule [4-(3,6-dimethyl-9H-carbazol-9-yl)butyl]phosphonic acid (Me-4PACz) with the multiple aromatic carboxylic acid 4,4',4″-nitrilotribenzoic acid (NA) to improve the heterojunction interface. The molecular hybrid of Me-4PACz with NA could substantially improve the interfacial characteristics. The resulting inverted perovskite solar cells demonstrated a record certified steady-state efficiency of 26.54%. Crucially, this strategy aligns seamlessly with large-scale manufacturing, achieving one of the highest certified power conversion efficiencies for inverted mini-modules at 22.74% (aperture area 11.1 cm2). Our device also maintained 96.1% of its initial power conversion efficiency after more than 2,400 h of 1-sun operation in ambient air.

Ligand-engineered bandgap stability in mixed-halide perovskite LEDs.

Lead halide perovskites are promising semiconductors for light-emitting applications because they exhibit bright, bandgap-tunable luminescence with high colour purity1,2. Photoluminescence quantum yields close to unity have been achieved for perovskite nanocrystals across a broad range of emission colours, and light-emitting diodes with external quantum efficiencies exceeding 20 per cent-approaching those of commercial organic light-emitting diodes-have been demonstrated in both the infrared and the green emission channels1,3,4. However, owing to the formation of lower-bandgap iodide-rich domains, efficient and colour-stable red electroluminescence from mixed-halide perovskites has not yet been realized5,6. Here we report the treatment of mixed-halide perovskite nanocrystals with multidentate ligands to suppress halide segregation under electroluminescent operation. We demonstrate colour-stable, red emission centred at 620 nanometres, with an electroluminescence external quantum efficiency of 20.3 per cent. We show that a key function of the ligand treatment is to 'clean' the nanocrystal surface through the removal of lead atoms. Density functional theory calculations reveal that the binding between the ligands and the nanocrystal surface suppresses the formation of iodine Frenkel defects, which in turn inhibits halide segregation. Our work exemplifies how the functionality of metal halide perovskites is extremely sensitive to the nature of the (nano)crystalline surface and presents a route through which to control the formation and migration of surface defects. This is critical to achieve bandgap stability for light emission and could also have a broader impact on other optoelectronic applications-such as photovoltaics-for which bandgap stability is required.

Narrow Bandgap Metal Halide Perovskites for All-Perovskite Tandem Photovoltaics.

All-perovskite tandem solar cells are attracting considerable interest in photovoltaics research, owing to their potential to surpass the theoretical efficiency limit of single-junction cells, in a cost-effective sustainable manner. Thanks to the bandgap-bowing effect, mixed tin-lead (Sn-Pb) perovskites possess a close to ideal narrow bandgap for constructing tandem cells, matched with wide-bandgap neat lead-based counterparts. The performance of all-perovskite tandems, however, has yet to reach its efficiency potential. One of the main obstacles that need to be overcome is the─oftentimes─low quality of the mixed Sn-Pb perovskite films, largely caused by the facile oxidation of Sn(II) to Sn(IV), as well as the difficult-to-control film crystallization dynamics. Additional detrimental imperfections are introduced in the perovskite thin film, particularly at its vulnerable surfaces, including the top and bottom interfaces as well as the grain boundaries. Due to these issues, the resultant device performance is distinctly far lower than their theoretically achievable maximum efficiency. Robust modifications and improvements to the surfaces of mixed Sn-Pb perovskite films are therefore critical for the advancement of the field. This Review describes the origins of imperfections in thin films and covers efforts made so far toward reaching a better understanding of mixed Sn-Pb perovskites, in particular with respect to surface modifications that improved the efficiency and stability of the narrow bandgap solar cells. In addition, we also outline the important issues of integrating the narrow bandgap subcells for achieving reliable and efficient all-perovskite double- and multi-junction tandems. Future work should focus on the characterization and visualization of the specific surface defects, as well as tracking their evolution under different external stimuli, guiding in turn the processing for efficient and stable single-junction and tandem solar cell devices.

Planar perovskite solar cells with long-term stability using ionic liquid additives.

Solar cells based on metal halide perovskites are one of the most promising photovoltaic technologies1-4. Over the past few years, the long-term operational stability of such devices has been greatly improved by tuning the composition of the perovskites5-9, optimizing the interfaces within the device structures10-13, and using new encapsulation techniques14,15. However, further improvements are required in order to deliver a longer-lasting technology. Ion migration in the perovskite active layer-especially under illumination and heat-is arguably the most difficult aspect to mitigate16-18. Here we incorporate ionic liquids into the perovskite film and thence into positive-intrinsic-negative photovoltaic devices, increasing the device efficiency and markedly improving the long-term device stability. Specifically, we observe a degradation in performance of only around five per cent for the most stable encapsulated device under continuous simulated full-spectrum sunlight for more than 1,800 hours at 70 to 75 degrees Celsius, and estimate that the time required for the device to drop to eighty per cent of its peak performance is about 5,200 hours. Our demonstration of long-term operational, stable solar cells under intense conditions is a key step towards a reliable perovskite photovoltaic technology.

Intermediate-phase engineering via dimethylammonium cation additive for stable perovskite solar cells.

Achieving the long-term stability of perovskite solar cells is arguably the most important challenge required to enable widespread commercialization. Understanding the perovskite crystallization process and its direct impact on device stability is critical to achieving this goal. The commonly employed dimethyl-formamide/dimethyl-sulfoxide solvent preparation method results in a poor crystal quality and microstructure of the polycrystalline perovskite films. In this work, we introduce a high-temperature dimethyl-sulfoxide-free processing method that utilizes dimethylammonium chloride as an additive to control the perovskite intermediate precursor phases. By controlling the crystallization sequence, we tune the grain size, texturing, orientation (corner-up versus face-up) and crystallinity of the formamidinium (FA)/caesium (FA)yCs1-yPb(IxBr1-x)3 perovskite system. A population of encapsulated devices showed improved operational stability, with a median T80 lifetime (the time over which the device power conversion efficiency decreases to 80% of its initial value) for the steady-state power conversion efficiency of 1,190 hours, and a champion device showed a T80 of 1,410 hours, under simulated sunlight at 65 °C in air, under open-circuit conditions. This work highlights the importance of material quality in achieving the long-term operational stability of perovskite optoelectronic devices.

Ultranarrow Line Width Room-Temperature Single-Photon Source from Perovskite Quantum Dot Embedded in Optical Microcavity.

Ultranarrow bandwidth single-photon sources operating at room-temperature are of vital importance for viable optical quantum technologies at scale, including quantum key distribution, cloud-based quantum information processing networks, and quantum metrology. Here we show a room-temperature ultranarrow bandwidth single-photon source generating single-mode photons at a rate of 5 MHz based on an inorganic CsPbI3 perovskite quantum dot embedded in a tunable open-access optical microcavity. When coupled to an optical cavity mode, the quantum dot room-temperature emission becomes single-mode, and the spectrum narrows down to just ∼1 nm. The low numerical aperture of the optical cavities enables efficient collection of high-purity single-mode single-photon emission at room-temperature, offering promising performance for photonic and quantum technology applications. We measure 94% pure single-photon emission in a single-mode under pulsed and continuous-wave (CW) excitation.

Understanding the Degradation of Methylenediammonium and Its Role in Phase-Stabilizing Formamidinium Lead Triiodide.

Formamidinium lead triiodide (FAPbI3) is the leading candidate for single-junction metal-halide perovskite photovoltaics, despite the metastability of this phase. To enhance its ambient-phase stability and produce world-record photovoltaic efficiencies, methylenediammonium dichloride (MDACl2) has been used as an additive in FAPbI3. MDA2+ has been reported as incorporated into the perovskite lattice alongside Cl-. However, the precise function and role of MDA2+ remain uncertain. Here, we grow FAPbI3 single crystals from a solution containing MDACl2 (FAPbI3-M). We demonstrate that FAPbI3-M crystals are stable against transformation to the photoinactive δ-phase for more than one year under ambient conditions. Critically, we reveal that MDA2+ is not the direct cause of the enhanced material stability. Instead, MDA2+ degrades rapidly to produce ammonium and methaniminium, which subsequently oligomerizes to yield hexamethylenetetramine (HMTA). FAPbI3 crystals grown from a solution containing HMTA (FAPbI3-H) replicate the enhanced α-phase stability of FAPbI3-M. However, we further determine that HMTA is unstable in the perovskite precursor solution, where reaction with FA+ is possible, leading instead to the formation of tetrahydrotriazinium (THTZ-H+). By a combination of liquid- and solid-state NMR techniques, we show that THTZ-H+ is selectively incorporated into the bulk of both FAPbI3-M and FAPbI3-H at ∼0.5 mol % and infer that this addition is responsible for the improved α-phase stability.

Thermal Management Enables Stable Perovskite Nanocrystal Light-Emitting Diodes with Novel Hole Transport Material.

The severely insufficient operational lifetime of perovskite light-emitting diodes (LEDs) is incompatible with the rapidly increasing external quantum efficiency, even as it approaches the theoretical limit, thereby significantly impeding the commercialization of perovskite LEDs. In addition, Joule heating induces ion migration and surface defects, degrades the photoluminescence quantum yield and other optoelectronic properties of perovskite films, and induces the crystallization of charge transport layers with low glass transition temperatures, resulting in LED degradation under continuous operation. Here, a novel thermally crosslinked hole transport material, poly(FCA60 -co-BFCA20 -co-VFCA20 ) (poly-FBV), with temperature-dependent hole mobility is designed, which is advantageous for balancing the charge injection of the LEDs and limiting the generation of Joule heating. The optimised CsPbI3 perovskite nanocrystal LEDs with poly-FBV realise approximately a 2-fold external quantum efficiency increase over the LED with commercial hole transport layer poly(4-butyl-phenyl-diphenyl-amine) (poly-TPD), owing to the balanced carrier injection and suppressed exciton quenching. Moreover, because of the Joule heating control provided by the novel crosslinked hole transport material, the LED utilising crosslinked poly-FBV has a 150-fold longer operating lifetime (490 min) than that utilizing poly-TPD (3.3 min). The study opens a new avenue for the use of PNC LEDs in commercial semiconductor optoelectronic devices.

Adduct-based p-doping of organic semiconductors.

Electronic doping of organic semiconductors is essential for their usage in highly efficient optoelectronic devices. Although molecular and metal complex-based dopants have already enabled significant progress of devices based on organic semiconductors, there remains a need for clean, efficient and low-cost dopants if a widespread transition towards larger-area organic electronic devices is to occur. Here we report dimethyl sulfoxide adducts as p-dopants that fulfil these conditions for a range of organic semiconductors. These adduct-based dopants are compatible with both solution and vapour-phase processing. We explore the doping mechanism and use the knowledge we gain to 'decouple' the dopants from the choice of counterion. We demonstrate that asymmetric p-doping is possible using solution processing routes, and demonstrate its use in metal halide perovskite solar cells, organic thin-film transistors and organic light-emitting diodes, which showcases the versatility of this doping approach.

Highly Absorbing Lead-Free Semiconductor Cu2AgBiI6 for Photovoltaic Applications from the Quaternary CuI-AgI-BiI3 Phase Space.

Since the emergence of lead halide perovskites for photovoltaic research, there has been mounting effort in the search for alternative compounds with improved or complementary physical, chemical, or optoelectronic properties. Here, we report the discovery of Cu2AgBiI6: a stable, inorganic, lead-free wide-band-gap semiconductor, well suited for use in lead-free tandem photovoltaics. We measure a very high absorption coefficient of 1.0 × 105 cm-1 near the absorption onset, several times that of CH3NH3PbI3. Solution-processed Cu2AgBiI6 thin films show a direct band gap of 2.06(1) eV, an exciton binding energy of 25 meV, a substantial charge-carrier mobility (1.7 cm2 V-1 s-1), a long photoluminescence lifetime (33 ns), and a relatively small Stokes shift between absorption and emission. Crucially, we solve the structure of the first quaternary compound in the phase space among CuI, AgI and BiI3. The structure includes both tetrahedral and octahedral species which are open to compositional tuning and chemical substitution to further enhance properties. Since the proposed double-perovskite Cs2AgBiI6 thin films have not been synthesized to date, Cu2AgBiI6 is a valuable example of a stable Ag+/Bi3+ octahedral motif in a close-packed iodide sublattice that is accessed via the enhanced chemical diversity of the quaternary phase space.

Chemical Control of the Dimensionality of the Octahedral Network of Solar Absorbers from the CuI-AgI-BiI3 Phase Space by Synthesis of 3D CuAgBiI5.

A newly reported compound, CuAgBiI5, is synthesized as powder, crystals, and thin films. The structure consists of a 3D octahedral Ag+/Bi3+ network as in spinel, but occupancy of the tetrahedral interstitials by Cu+ differs from those in spinel. The 3D octahedral network of CuAgBiI5 allows us to identify a relationship between octahedral site occupancy (composition) and octahedral motif (structure) across the whole CuI-AgI-BiI3 phase field, giving the ability to chemically control structural dimensionality. To investigate composition-structure-property relationships, we compare the basic optoelectronic properties of CuAgBiI5 with those of Cu2AgBiI6 (which has a 2D octahedral network) and reveal a surprisingly low sensitivity to the dimensionality of the octahedral network. The absorption onset of CuAgBiI5 (2.02 eV) barely changes compared with that of Cu2AgBiI6 (2.06 eV) indicating no obvious signs of an increase in charge confinement. Such behavior contrasts with that for lead halide perovskites which show clear confinement effects upon lowering dimensionality of the octahedral network from 3D to 2D. Changes in photoluminescence spectra and lifetimes between the two compounds mostly derive from the difference in extrinsic defect densities rather than intrinsic effects. While both materials show good stability, bulk CuAgBiI5 powder samples are found to be more sensitive to degradation under solar irradiation compared to Cu2AgBiI6.

Time-Resolved Changes in Dielectric Constant of Metal Halide Perovskites under Illumination.

Despite their impressive performance as a solar absorber, much remains unknown on the fundamental properties of metal halide perovskites (MHPs). Their polar nature in particular is an intense area of study, and the relative permittivity (εr) is a parameter widely used to quantify polarization over a range of different time scales. In this report, we have exploited frequency-dependent time-resolved microwave conductivity (TRMC) to study how εr values of a range of MHPs change as a function of time, upon optical illumination. Further characterization of charge carriers and polarizability are conducted by femtosecond transient absorption and stimulated Raman spectroscopy. We find that changes in εr are roughly proportional to photogenerated carrier density but decay with a shorter time constant than conductance, suggesting that the presence of charge carriers alone does not determine polarization.

Photoinduced Vibrations Drive Ultrafast Structural Distortion in Lead Halide Perovskite.

The success of organic-inorganic perovskites in optoelectronics is dictated by the complex interplay between various underlying microscopic phenomena. The structural dynamics of organic cations and the inorganic sublattice after photoexcitation are hypothesized to have a direct effect on the material properties, thereby affecting the overall device performance. Here, we use ultrafast heterodyne-detected two-dimensional (2D) electronic spectroscopy to reveal impulsively excited vibrational modes of methylammonium (MA) lead iodide perovskite, which drive the structural distortion after photoexcitation. Vibrational analysis of the measured data allows us to monitor the time-evolved librational motion of the MA cation along with the vibrational coherences of the inorganic sublattice. Wavelet analysis of the observed vibrational coherences reveals the coherent generation of the librational motion of the MA cation within ∼300 fs complemented with the coherent evolution of the inorganic skeletal motion. To rationalize this observation, we employed the configuration interaction singles (CIS), which support our experimental observations of the coherent generation of librational motions in the MA cation and highlight the importance of the anharmonic interaction between the MA cation and the inorganic sublattice. Moreover, our advanced theoretical calculations predict the transfer of the photoinduced vibrational coherence from the MA cation to the inorganic sublattice, leading to reorganization of the lattice to form a polaronic state with a long lifetime. Our study uncovers the interplay of the organic cation and inorganic sublattice during formation of the polaron, which may lead to novel design principles for the next generation of perovskite solar cell materials.

Facile Synthesis of Stable and Highly Luminescent Methylammonium Lead Halide Nanocrystals for Efficient Light Emitting Devices.

Metal halide perovskites are promising candidates for use in light emitting diodes (LEDs), due to their potential for color tunable and high luminescence efficiency. While recent advances in perovskite-based light emitting diodes have resulted in external quantum efficiencies exceeding 12.4% for the green emitters, and infrared emitters based on 3 D/2D mixed dimensional perovskites have exceeded 20%, the external quantum efficiencies of the red and blue emitters still lag behind. A critical issue to date is creating highly emissive and stable perovskite emitters with the desirable emission band gap to achieve full-color displays and white LEDs. Herein, we report the preparation and characterization of a highly luminescent and stable suspension of cubic-shaped methylammonium lead triiodide (CH3NH3PbI3) perovskite nanocrystals, where we synthesize the nanocrystals via a ligand-assisted reprecipitation technique, using an acetonitrile/methylamine compound solvent system to solvate the ions and toluene as the antisolvent to induce crystallization. Through tuning the ratio of the ligands, the ligand to toluene ratio, and the temperature of the toluene, we obtain a solution of CH3NH3PbI3 nanocrystals with a photoluminescence quantum yield exceeding 93% and tunable emission between 660 and 705 nm. We also achieved red emission at 635 nm by blending the nanocrystals with bromide salt and obtained perovskite-based light emitting diodes with maximum electroluminescent external quantum efficiency of 2.75%.

Efficient planar heterojunction perovskite solar cells by vapour deposition.

Many different photovoltaic technologies are being developed for large-scale solar energy conversion. The wafer-based first-generation photovoltaic devices have been followed by thin-film solid semiconductor absorber layers sandwiched between two charge-selective contacts and nanostructured (or mesostructured) solar cells that rely on a distributed heterojunction to generate charge and to transport positive and negative charges in spatially separated phases. Although many materials have been used in nanostructured devices, the goal of attaining high-efficiency thin-film solar cells in such a way has yet to be achieved. Organometal halide perovskites have recently emerged as a promising material for high-efficiency nanostructured devices. Here we show that nanostructuring is not necessary to achieve high efficiencies with this material: a simple planar heterojunction solar cell incorporating vapour-deposited perovskite as the absorbing layer can have solar-to-electrical power conversion efficiencies of over 15 per cent (as measured under simulated full sunlight). This demonstrates that perovskite absorbers can function at the highest efficiencies in simplified device architectures, without the need for complex nanostructures.

Mesoporous TiO2 single crystals delivering enhanced mobility and optoelectronic device performance.

Mesoporous ceramics and semiconductors enable low-cost solar power, solar fuel, (photo)catalyst and electrical energy storage technologies. State-of-the-art, printable high-surface-area electrodes are fabricated from thermally sintered pre-formed nanocrystals. Mesoporosity provides the desired highly accessible surfaces but many applications also demand long-range electronic connectivity and structural coherence. A mesoporous single-crystal (MSC) semiconductor can meet both criteria. Here we demonstrate a general synthetic method of growing semiconductor MSCs of anatase TiO2 based on seeded nucleation and growth inside a mesoporous template immersed in a dilute reaction solution. We show that both isolated MSCs and ensembles incorporated into films have substantially higher conductivities and electron mobilities than does nanocrystalline TiO2. Conventional nanocrystals, unlike MSCs, require in-film thermal sintering to reinforce electronic contact between particles, thus increasing fabrication cost, limiting the use of flexible substrates and precluding, for instance, multijunction solar cell processing. Using MSC films processed entirely below 150 °C, we have fabricated all-solid-state, low-temperature sensitized solar cells that have 7.3 per cent efficiency, the highest efficiency yet reported. These high-surface-area anatase single crystals will find application in many different technologies, and this generic synthetic strategy extends the possibility of mesoporous single-crystal growth to a range of functional ceramics and semiconductors.

The Phosphine Oxide Route toward Lead Halide Perovskite Nanocrystals.

We report an amine-free synthesis of lead halide perovskite (LHP) nanocrystals, using trioctylphosphine oxide (TOPO) instead of aliphatic amines, in combination with a protic acid (e.g., oleic acid). The overall synthesis scheme bears many similarities to the chemistry behind the preparation of LHP thin films and single crystals, in terms of ligand coordination to the chemical precursors. The acidity of the environment and hence the extent of protonation of the TOPO molecules tune the reactivity of the PbX2 precursor, regulating the size of the nanocrystals. On the other hand, TOPO molecules are virtually absent from the surface of our nanocrystals, which are simply passivated by one type of ligand (e.g., Cs-oleate). Furthermore, our studies reveal that Cs-oleate is dynamically bound to the surface of the nanocrystals and that an optimal surface coverage is critical for achieving high photoluminescence quantum yield. Our scheme delivers NCs with a controlled size and shape: only cubes are formed, with no contamination with platelets, regardless of the reaction conditions that were tested. We attribute such a shape homogeneity to the absence of primary aliphatic amines in our reaction environment, since these are known to promote the formation of nanocrystals with sheet/platelet morphologies or layered phases under certain reaction conditions. The TOPO route is particularly appealing with regard to synthesizing LHP nanocrystals for large-scale manufacturing, as the yield in terms of material produced is close to the theoretical limit: i.e., almost all precursors employed in the synthesis are converted into nanocrystals.

Impact of Bi3+ Heterovalent Doping in Organic-Inorganic Metal Halide Perovskite Crystals.

Intrinsic organic-inorganic metal halide perovskites (OIHP) based semiconductors have shown wide applications in optoelectronic devices. There have been several attempts to incorporate heterovalent metal (e.g., Bi3+) ions in the perovskites in an attempt to induce electronic doping and increase the charge carrier density in the semiconductor. It has been reported that inclusion of Bi3+ decreases the band gap of the material considerably. However, contrary to the earlier conclusions, despite a clear change in the appearance of the crystal as observed by eye, here we show that the band gap of MAPbBr3 crystals does not change due the presence of Bi3+ in the growth solution. An increased density of states in the band gap and use of very thick samples for transmission measurements, erroneously give the impression of a band gap shift. These sub band gap states also act as nonradiative recombination centers in the crystals.