Large Piezoelectric Coefficient Research Articles

First-principles prediction of intrinsic piezoelectricity, spin-valley splitting and magneto-crystal anisotropy in 2H-VS2 magnetic semiconductor

The piezoelectricity, valley character and magnetic properties of intrinsic ferrovalley 2H-VS2 monolayer are studied using density functional theory. The results suggest that 2H-VS2 monolayer exhibits obvious bipolar magnetic semiconductor characters with Curie temperature (TC) of 278 K, large piezoelectric coefficient d11 of 3.925 pm/V, in-plane magneto-crystal anisotropy (MA) and large valley splitting (ΔKK′) of 75.1 meV. Applying in-plane strain (-6% to 6 %) can well adjust the ΔKK′ and TC from 72 meV to 76.7 meV and from 98 K to 397 K, respectively, resulting an obvious change of electronic structures from bipolar magnetic semiconductor to spin gapless semiconductor phase. The magnetic anisotropy energy (MAE) of 2H-VS2 monolayer firstly increases and then decreases as the strain increases from −6% to 6 %, which mainly originates from the contribution of V dx2-y2 and dxy orbitals. In addition, 2H-VS2 monolayer retains a large valley-contrasting Berry curvature and non-zero anomalous Hall conductivity, indicating that the transverse velocity of carriers is opposite to the effect of in-plane longitudinal electric field. These results suggest that the 2H-VS2 monolayer can become good candidates for the spintronic and valleytronic applications.

Rock drilling performance of rotary ultrasonic tools incorporating PZT piezoceramic and Mn:PIN-PMN-PT piezocrystal

High performance Mn:PIN-PMN-PT piezocrystal material is investigated to understand if its extraordinary properties can replace the traditional hard piezoceramic material for space exploration applications. A bolted Langevin-style ultrasonic drill tool incorporating a pair of Mn:PIN-PMN-PT piezocrystal rings is built to compare with a same configuration ultrasonic drill tool actuated with a pair of hard piezoceramic rings, which are tuned to the first longitudinal mode (L1) at around 20 kHz. From the characterisation results, it is observed that the piezocrystal material presents significantly greater values of relative permittivity, electromechanical coupling coefficient, and piezoelectric charge coefficient than the hard piezoceramic material. Despite these outstanding properties, the piezocrystal driven ultrasonic drill tool shows similar displacement amplitudes to its counterpart. Nonetheless, the impedance magnitude of the piezocrystal driven ultrasonic drill tool at resonance is a magnitude lower than the piezoceramic actuated drill tool, due to the large piezoelectric charge coefficient d33. Ultrasonic rock drilling experiments suggest that the cutting force for sandstone and marble are greatly reduced, but limestone and tuff are less affected.In general, the piezocrystal driven ultrasonic drill tool demonstrates a marginally improved cutting performance than the piezoceramic actuated drill tool, in terms of lower cutting force and motor power consumption, however, the tool wear appears slightly poorer. The research outcome of this paper indicates that the thickness mode of the piezocrystal rings might not be the optimal form of excitation, which could be due to the piezoelectric losses at high excitation levels, so other excitation conditions and vibration modes will need to be explored to fully adopt the extraordinary material properties of the piezocrystal material.

The enhanced vertical piezoelectricity in Janus C3HFX (X = Si and Ge) monolayers based on the born effective charges dipole-moment

Recently, two-dimensional (2D) piezoelectric materials are widely studied, and the vertical piezoelectric properties of 2D materials are highly required to be known in the related theory research works and experiments, so it becomes very important to explore the intrinsic mechanism of piezoelectricity in the 2D materials. Herein, we systematically study the piezoelectricity of Janus C3HFX (X = Si and Ge) monolayers with semiconductor property, which are carbon-based 2D materials, using the first-principles calculation. The remarkable enhancements on the absolute values of the vertical piezoelectric coefficient of C3HFSi-1 (e33 = 11.27 × 10−10 C/m) and C3HFGe-4 (e33 = −12.78 × 10−10 C/m) are larger than that of C4HF (e33 = −2.28 × 10−10 C/m) by 5 and 6 times, respectively. It indicates that the atom replacement at appropriate positions in the multiatomic monolayer can significantly enhance the vertical piezoelectric properties based on the appropriate distribution of polarization charge. We define the concepts, the Born effective charges center (BECs-center) and the BECs-dipole-moment in this work, to explain these large vertical piezoelectric coefficients’ variation. The larger BECs-dipole-moment will enhance the vertical piezoelectricity for these C3HFX monolayers than that of the C4HF monolayer. These concepts defined in this work will deepen the understanding of the internal physical mechanism about the piezoelectricity.

Optimized electromechanical performance in Aurivillius compounds via hot-pressing

Bismuth layer-structured ferroelectrics (BLSFs) are widely demanded in high-temperature piezoelectric sensors, while their low piezoelectricity-induced low sensitivity of piezoelectric sensors is not appropriate for practical operation conditions. Texturing is an effective way to engineer the performance of piezoelectric ceramics by aligning the polar vectors and increasing poling efficiency. Herein, chemical substitution together with the hot-pressing technique is utilized to improve the piezoelectricity of BTN-based ceramics. Characterizations demonstrate that the grains with (100) orientation as shown in the {001} pole figure and the improved domain switching are the main causes of excellent ferroelectricity (Pr∼17.7 μC/cm2) and large piezoelectric coefficient (d33∼27 pC/N) in the textured BCTNTW-Per ceramic. The BCTNTW-Per ceramic also exhibits high TC (890 °C), low dielectric loss, high electrical resistivity (1.6 ×105 Ω•cm at 600 °C), and excellent thermal stability, demonstrating that the combination of the hot-pressing technique and traditional doping strategy is an effective way to prepare high-performance of BLSFs.

Large piezoelectricity with enhanced thermal stability in BiScO3-BiInO3-PbTiO3 ternary perovskite ceramics

Simultaneously achieving large piezoelectricity and excellent thermal stability in a piezoceramic is highly desired for constructing advanced high-temperature electromechanical coupling devices. Here, a large high-temperature piezoelectric coefficient (d33 = 523 pC/N at 200 °C) with a small fluctuation rate (η ≤ ±10 %) over an ultra-broaden temperature range of 48–342 °C was achieved in novel zBiScO3-xBiInO3-yPbTiO3 (zBS-xBI-yPT) ternary perovskite piezoceramics with a high Curie temperature of 440 °C. The morphotropic phase boundary (MPB) of multiphase coexistence can be driven and optimized in this system, which is mainly responsible for the enhanced piezoelectricity, and the optimal MPB composition is located at x/y/z = 0.010/0.625/0.365. The excellent temperature stability of the optimal MPB sample should be attributed to the increase in the number of thermally stable irreversible non-180° domains. zBS-xBI-yPT perovskite ceramics with excellent comprehensive high-temperature piezoelectric properties exceed many reported lead-based counterparts, and are more suitable for electromechanical coupling applications at harsh elevated temperatures.

Novel Piezo-active 2–1–2 Composites with Sets of Large Hydrostatic Parameters

A 2–1–2 composite with two single-crystal components is studied for the first time to highlight large hydrostatic piezoelectric coefficients dh * and gh *, figure of merit dh *gh *, and electromechanical coupling factor kh *. Each 2–1–2 composite contains layers of domain-engineered [011]-poled relaxor-ferroelectric (1–x)Pb(Zn1/3Nb2/3)O3 – xPbTiO3 single crystal (x = 0.0475–0.09) and heterogeneous layers being systems of aligned piezoelectric Li2B4O7 single crystal rods in polyethylene, and these rods have an elliptic cylindrical shape. New diagrams show the volume-fraction ranges wherein large values of dh *> 10−9 C/N, dh *gh *> 2.10−10 Pa−1 and kh *≈ 0.5–0.6 are observed.

First-principles study on AgBi(CrO4)2:An effective infrared nonlinear optical compound

The investigation of nonlinear optical (NLO) materials is critically important in developing laser technologies. The AgBi(CrO4)2 which crystallizes in the tetragonal lattice with a space group of I 4¯ is a potential candidate for the infrared (IR) region due to the large birefringence (Δn = 0.18), strong NLO response than the KDP crystal and the high electro-optical coefficients are justified their good performance NLO applications. The investigation of the elastic constant of AgBi(CrO4)2 indicates the ductile nature and the large piezoelectric coefficients make this crystal has great attention as bifunctional material.

Effect of acceptor–donor co‐doping on the microstructure and electrical properties of BiScO3–PbTiO3‐based ceramics

AbstractDesigning BiScO3‐PbTiO3 (BS–PT) ceramics that merge high Curie temperature (TC) and large piezoelectric coefficient (d33) has always been a significant challenge for high‐temperature applications. Doping is a commonly used and effective method for enhancing the electrical performances of piezoelectric ceramics. In this study, the Li+/W6+ acceptor–donor co‐doping method was used to enhance the piezoelectric properties of 0.36BiSc1‐xLixO3–0.64PbTi1‐yWyO3 (0.36x = 0.64y) ceramics. The optimal electrical performance was observed at x = 0.01 near morphotropic phase boundaries, with a large d33 (505 pC/N), high TC (407°C), huge remnant polarization (Pr ∼ 40.9 μC/cm2), and inverse piezoelectric coefficient (d33* = 601 pm/V). Rietveld refinement and piezoelectric force microscopy results revealed that incorporating Li+/W6+ into the BS–PT ceramics decreased the T phase proportion and domain size and increased the domain wall density. The enhancement in piezoelectricity can be attributed to the lowered energy barrier resulting from the reduced T‐phase proportion and complex domain structure, which promotes polarization rotation and facilitates domain wall motion. This work demonstrates that acceptor–donor co‐doping is a promising strategy for optimizing the electrical performance of the BS–PT ceramics.

Achieving ultrahigh electromechanical properties with high TC in PNN-PZT textured ceramics

<001> textured Pb(Ni1/3Nb2/3)O3-PbZrO3-PbTiO3 (PNN-PZT) ceramics were prepared by templated grain growth (TGG) technique using 0.36PNN-xPZ-(0.64-x)PT (x = 0.23, 0.25 and 0.27) powder matrix. Optimum template content was derived to achieve the best electromechanical properties of textured ceramics. The piezoelectric coefficient d33 = 1165 pC/N, Curie temperature TC = 197 °C, longitudinal mode electromechanical coupling factor k33 = 0.86 and a very large effective piezoelectric strain coefficient d33* = 2041 pm/V were simultaneously achieved at the morphotropic phase boundary (MPB) composition (x = 0.25) with 3 vol.% BaTiO3 (BT) templates. Domain structures of textured ceramics were analyzed in detail to reveal the origin of these high piezoelectric and electromechanical properties.

A Piezotronic and Magnetic Dual‐Gated Ferroelectric Semiconductor Transistor

AbstractPiezotronics is the coupling effect of the piezoelectric and semiconductor properties; however, the piezoelectric constant of the piezoelectric semiconductor is relatively small while the ferroelectric materials with large piezoelectric constant typically possess weak semiconductor properties, thus limiting the effective coupling coefficient of the piezotronic materials and devices. Here, a piezotronics and magnetic dual‐gated ferroelectric semiconductor transistor (PM‐FEST) is fabricated by Terfenol‐D, aluminum oxide (Al2O3), and ferroelectric semiconductor α‐In2Se3, which has a large piezoelectric coefficient, room‐temperature ferroelectricity, and dipole locking. The charge carrier transport and corresponding drain current of the PM‐FEST can be directly modulated by either the applied magnetic field or external strain. At a low magnetic field (&lt;200 mT), the maximum current on/off ratio of α‐In2Se3 based PM‐FEST is as high as 1700%. Compared with traditional piezotronic devices, the PM‐FEST demonstrates a higher gauge factor (2.3 × 104) than that of the piezoelectric semiconductors. This work provides a possibility of realizing magnetism‐modulated electronics in semiconductors by exploiting the coupling of piezotronics and magnetostriction.

Piezoelectric and magneto-optical effect of lanthanum-doped bismuth ferrite films on silicon substrate

Rhombohedral La:BiFeO3 films were successfully prepared on Si substrates by using Radio frequency magnetron sputtering method. The LaNiO3 as buffer layer is beneficial for improving the quality of the film, reducing surface roughness, and getting rid of the impure phase. The Bi0.9La0.1FeO3/LaNiO3/Si film has the largest piezoelectric coefficient with d33 reaching 4.76 pm/V, which is about 2.5 times larger than that of BiFeO3/LaNiO3/Si. The saturation magnetization and the MCD signal of BiFeO3 films are significantly enhanced by doping La3+. The MCD ellipticity of La:BiFeO3 film at 555 nm increase with the increase of La3+ concentration. Bi0.7La0.3FeO3/LaNiO3/Si film show strong magneto-optical effect with the high MCD ellipticity of 850 deg./cm, which is more than about 1.7 times larger than that of BiFeO3 film. This film is expected to be developed into a new multifunctional material with multi-field coupling of electro-opt-magnetism.

Conformally Large-Area Single-Crystal Piezocomposites with High Performance for Acoustic Transducers.

Large-area and conformal piezoelectric elements are highly desired for acoustic transducers to possess a large power source level and wide detecting range. To date, single-crystal piezocomposites attract much attention on enhancing the power source level and bandwidth for next-generation acoustic transducers, owing to their higher piezoelectric and electromechanical coupling properties compared to traditional piezocomposites. Unfortunately, it is still challenging to achieve large-area and conformal single-crystal piezocomposites because of the fragile nature, large anisotropy, and the limited grown size of piezoelectric single crystals. Here, we successfully fabricate the conformally large-area single-crystal piezocomposite with an area of 160 × 50 mm2 and a bending angle of 162° by a modified 3D-printing-assisted inserting method. The single-crystal piezocomposite exhibits a high thickness electromechanical coupling factor kt of 85% and a large piezoelectric coefficient d33 of 1150 pC/N, surpassing those of the reported large-area piezocomposites. The influence of the volume fraction and curvature radius of single-crystal PCs and acoustic transducers was investigated. Furthermore, we designed an acoustic transducer based on the conformal single-crystal piezocomposite. Benefiting from the excellent piezoelectric and electromechanical properties of the single-crystal piezocomposite, the transducer indicates a high maximum transmitting voltage response of 171.8 dB. Especially, its bandwidth (-3 dB) achieves 60 kHz with a resonant frequency of 292 kHz, which is about 1.8 times superior to the conformal acoustic transducer based on the ceramic piezocomposite with a similar resonant frequency. This work may benefit the future design and fabrication of high-performance and complex-shape piezoelectric composites as key materials for next-generation transducers.

Clamping of ferroelectric PVDF to enhance the electromechanical performance of a 1–3 PMN-PT/PVDF piezoelectric composite

A group of 1–3 type piezoelectric Pb (Mg1/3Nb2/3)O3-PbTiO3/polyvinylidene fluoride (PMN-PT/PVDF) composite sheets are prepared using a complex two-step hot-pressing method. Then the molecular structure model of piezoelectric materials and an inverse piezoelectric simulation of the composites are performed to express the horizontal compression, indicating the clamping activity of ferroelectric PVDF on PMN-PT. As such, this composite sheet possesses a high dielectric permittivity (εr) of 560 at 100 Hz for its compacted connecting of two phases. After polarization, a very large piezoelectric coefficient (d33) of 1125 pC/N and a considerable electromechanical coupling factor (kt) of 0.43 is obtained in PMN-PT/PVDF sheet with a proper aspect ratio of 1.4 and a thickness of 2.1 mm, further indicating that promoting effect of PVDF matrix on the strain in Z-direction of PMN-PT. The result shows that ferroelectric PVDF serving as polymer matrix favors the electromechanical coupling effect, and may provide a prospect of the potential application of PMN-PT/PVDF composite in sensor or transistor for matrix ultrasonic probes.

Single-atom molybdenum array bound to distorted 1 T′ ReS2 quantum dots triggers highly intrinsic piezoelectricity for hierarchical porous electret piezo-catalysis

Piezoelectricity in 2D transition metal dichalcogenides (TMDs) has gathered significant interest due to their massive exposure of unsaturated edge sites and high piezoelectric modulus. Nevertheless, the piezoelectricity in 1 T′ phase TMDs is inhibited by its center symmetry of space group. Herein, to break the shackles of piezoelectric polarization, we synthesize a piezoelectric material composed of an atomic molybdenum array bound to distorted 1 T′ ReS2 (MDR). The phase transition from 1 T′ to distorted 1 T′ (D-1 T′) removes the special Peierl's distortion of ReS2, breaking its center symmetry and allowing for piezoelectric generation. Remarkably, MDR exhibits a large piezoelectric coefficient (d33) value of 15.45 pm/V, which is an order of magnitude higher than those reported in other TMDs. Combining with excellent piezocatalytic activity, a 0D/3D di-piezoelectric porous electret featuring an enhanced quantum confinement piezoelectric effect based on the MDR quantum dots (QDs) and inverse opal g-C3N4 (IOCN) is demonstrated for high-efficiency piezoelectric catalysis.

The First Ring Enlargement Induced Large Piezoelectric Response in a Polycrystalline Molecular Ferroelectric.

Inorganic ferroelectrics have long dominated research and applications, taking advantage of high piezoelectric performance in bulk polycrystalline ceramic forms. Molecular ferroelectrics have attracted growing interest because of their environmental friendliness, easy processing, lightweight, and good biocompatibility, while realizing the considerable piezoelectricity in their bulk polycrystalline forms remains a great challenge. Herein, for the first time, through ring enlargement, a molecular ferroelectric 1-azabicyclo[3.2.1]octonium perrhenate ([3.2.1-abco]ReO4 ) with a large piezoelectric coefficient d33 up to 118 pC/N in the polycrystalline pellet form is designed, which is higher than that of the parent 1-azabicyclo[2.2.1]heptanium perrhenate ([2.2.1-abch]ReO4 , 90 pC/N) and those of most molecular ferroelectrics in polycrystalline or even single crystal forms. The ring enlargement reduces the molecular strain for easier molecular deformation, which contributes to the higher piezoelectric response in [3.2.1-abco]ReO4 . This work opens up a new avenue for exploring high piezoelectric polycrystalline molecular ferroelectrics with great potential in piezoelectric applications.

Composition design of BNBT-ST relaxor ferroelectric ceramics in superparaelectric state with ultrahigh energy density

BNT-6BT-based lead-free ceramics have gained significant attention due to their relatively large piezoelectric coefficients and tunable morphotropic phase boundary conditions. In this investigation, SrTiO3 (ST) was added to BNT-6BT ceramics to fabricate the BNT-6BT-xST (BNBT-xST) composition. The impact of ST content on the phase structure and dielectric permittivity of the BNBT-xST ceramics was studied. The XRD refinement data show that with increasing ST content, the crystal structure of BNBT-xST ceramics was transformed from the morphotropic phase structure (coexisting tetragonal (P4/mmm) and pseudo-cubic (Pmm) phase) to the pseudo-cubic phase. The dielectric permittivity data of the BNBT-80ST showed that the Tm (the maximum permittivity temperature) moved to −61.9 °C, which caused the room temperature to fall within the range of Tm < T < TB (the Burns temperature). This makes the BNBT-80ST a superparaelectric state in relaxor ferroelectrics (RFE). Furthermore, the maximum energy density and the charge-discharge efficiency of the BNBT-80ST achieved 5.48 J/cm3 and 87% at 495 kV/cm, respectively. The energy density of the BNBT-80ST was improved by 2.97-fold and 49% compared with that of the BNBT-30ST and BNBT-70ST. This is mostly attributed to weakened ferroelectricity and improved paraelectricity in the BNBT-80ST. This investigation demonstrates that BNBT-xST ceramics can be adjusted to a superparaelectric state with an ST content of 80%. This makes the material to possess both a large polarization and a high breakdown field. This material holds great promise for high energy density capacitor applications.

Enhanced piezoelectric properties in coarse-grained 0.7Bi(Fe0.9985Mn0.0015)O3-0.3BaTiO3 ceramics

The lead-free BiFeO3-BaTiO3 (BF-BT) based ceramics with large piezoelectric coefficient (d33) have been desired for promising applications in high-temperature fields. Herein, the 0.7Bi(Fe0.9985Mn0.0015)O3-0.3BaTiO3 ceramics with different grain sizes are intentionally prepared by solid-state method, and a large d33 (232 pC/N) and high Curie temperature Tc (501 °C) are simultaneously achieved in the case of large grain size (>9 µm). X-ray diffraction and Rietveld refinement analyses indicate that these coarse-grained samples possess stronger rhombohedral distortion and enlarged lattice parameter compared to fine-grained samples, which make domain switching easier and give rise to the increase in strain. As a result, the piezoelectric and ferroelectric properties of such samples are significantly improved with increasing grain size from 3.05 µm to 9.07 µm. In addition, electric domain configuration and field-induced strain further prove that the strong piezoelectric response in coarse-grained samples is attributed mainly to enhanced non-180° domain mobility. This study reveals the origin of large piezoelectric response in coarse-grained BF-BT ceramics, and proposes an effective approach to improve the piezoelectric properties of BF-BT ceramics.

Enhancing piezocatalytic H2O2 production through morphology control of graphitic carbon nitride

Piezocatalytic H2O2 production has attracted significant attention as a green alternative to traditional anthraquinone methods with heavy environmental pollution and high energy consumption. However, since the efficiency of piezocatalyst in producing H2O2 is poor, searching for a suitable method to improve the yield of H2O2 is of great interest. Herein, a series of graphitic carbon nitride (g-C3N4) with different morphologies (hollow nanotube, nanosheet and hollow nanosphere) are applied to enhance the piezocatalytic performance in yielding H2O2. The hollow nanotube g-C3N4 exhibited an outstanding H2O2 generation rate of 262 umol·g−1·h−1 without any co-catalyst, which is 1.5 and 6.2 times higher than nanosheets and hollow nanospheres, respectively. Piezoelectric response force microscopy, piezoelectrochemical tests, and Finite Element Simulation results revealed that the excellent piezocatalytic property of hollow nanotube g-C3N4 is mainly attributed to its larger piezoelectric coefficient, higher intrinsic carrier density, and stronger external stress absorption conversion. Furthermore, mechanism analysis indicated that piezocatalytic H2O2 production follows a two-step single-electro pathway, and the discovery of 1O2 furnishes a new insight into explore this mechanism. This study offers a new strategy for the eco-friendly manufacturing of H2O2 and a valuable guide for future research on morphological modulation in piezocatalysis.

Thermal conductivity of ScxAl1−xN and YxAl1−xN alloys

Owing to their very large piezoelectric coefficients and spontaneous polarizations, (Sc,Y)xAl1−xN alloys have emerged as a new class of III-nitride semiconductor materials with great potential for high-frequency electronic and acoustic devices. The thermal conductivity of constituent materials is a key parameter for design, optimization, and thermal management of such devices. In this study, transient thermoreflectance technique is applied to measure the thermal conductivity of ScxAl1−xN and YxAl1−xN (0 ≤x ≤0.22) layers grown by magnetron sputter epitaxy in the temperature range of 100–400 K. The room-temperature thermal conductivity of both alloys is found to decrease significantly with increasing Sc(Y) composition compared to that of AlN. We also found that the thermal conductivity of YxAl1−xN is lower than that of ScxAl1−xN for all studied compositions. In both alloys, the thermal conductivity increases with the temperature up to 250 K and then saturates. The experimental data are analyzed using a model based on the solution of the phonon Boltzmann transport equation within the relaxation time approximation. The contributions of different phonon-scattering mechanisms to the lattice thermal conductivity of (Sc,Y)xAl1−xN alloys are identified and discussed.

Large piezoelectric response in a Jahn-Teller distorted molecular metal halide

Piezoelectric materials convert between mechanical and electrical energy and are a basis for self-powered electronics. Current piezoelectrics exhibit either large charge (d33) or voltage (g33) coefficients but not both simultaneously, and yet the maximum energy density for energy harvesting is determined by the transduction coefficient: d33*g33. In prior piezoelectrics, an increase in polarization usually accompanies a dramatic rise in the dielectric constant, resulting in trade off between d33 and g33. This recognition led us to a design concept: increase polarization through Jahn-Teller lattice distortion and reduce the dielectric constant using a highly confined 0D molecular architecture. With this in mind, we sought to insert a quasi-spherical cation into a Jahn-Teller distorted lattice, increasing the mechanical response for a large piezoelectric coefficient. We implemented this concept by developing EDABCO-CuCl4 (EDABCO = N-ethyl-1,4-diazoniabicyclo[2.2.2]octonium), a molecular piezoelectric with a d33 of 165 pm/V and g33 of ~2110 × 10−3 V m N−1, one that achieved thusly a combined transduction coefficient of 348 × 10−12 m3 J−1. This enables piezoelectric energy harvesting in EDABCO-CuCl4@PVDF (polyvinylidene fluoride) composite film with a peak power density of 43 µW/cm2 (at 50 kPa), the highest value reported for mechanical energy harvesters based on heavy-metal-free molecular piezoelectric.