Ultrathin Layer Research Articles

PLANE PROBLEMS ABOUT THE ACTION OF OSCILLATING LOAD ON THE BOUNDARY OF AN ELASTIC ISOTROPIC LAYER IN THE PRESENCE OF SURFACE STRESSES

In this paper, symmetric and antisymmetric plane problems about the action of oscillating load on the boundary of an elastic isotropic nanothin layer are considered. The nanoscale layer thickness is considered by introducing surface stresses in accordance with the Gurtin-Murdoch theory. According to this theory, it is assumed that, in addition to external loads, surface stresses act on the layer boundaries, which are described by Hooke's “surface” law. As a result, the properties of the elastic material of the layer with nanoscale thickness become different from the properties of the material of a regular-sized body, which is typical for nanomechanics problems. A standard technique was used for the solution of formulated problems, including the application of limiting absorption principle, the Fourier transform over infinitely extended coordinate and the theory of residues for finding the inverse Fourier transform. It is shown how it is possible to obtain solutions in the form of series in natural waves, in which the wave numbers are defined as the roots of the corresponding dispersion equations. For a specific example, dispersion relations were studied and graphs of the first dispersion curves were plotted. The behavior of barrier frequencies, changes in wave numbers and zones of existence of backward waves at different nanoscale layer thicknesses are analyzed. The results of the analysis showed that for an ultrathin layer, surface effects have a significant impact on the dispersion relations, and the trends in the dispersion curves can differ significantly for different modes and layer thicknesses.

Liquid-solid interfacial polymerization of thin-film composite nanofiltration membrane

Interfacial polymerization prepared polyamide (PA) nanofiltration membranes are widely used for desalination and wastewater recovery due to their lower operating pressure compared to reverse osmosis desalination and ease of scalability. The diffusion behavior of amine (PIP) and acyl chloride (TMC) monomers make a significant impact on PA structure and performance. In this paper, through freezing the aqueous amine reactive solution which turned the liquid–liquid reaction process into liquid–solid and regulated the amine monomer diffusion behavior, an ultra-thin, defect-free PA layer was achieved. The effect of PIP solution temperature in the range of −15 to 25 °C on membrane morphology, chemical composition and surface properties was investigated. The results indicated that PIP diffusion rate had a positive effect on the crosslinking degree of formed PA layer. However, frozen amine solution effectively inhibited the diffusion rate of PIP and hydrolysis of TMC which simultaneously improve the permeability and selectivity. The fabricated membrane by liquid–solid reaction process showed hydrophilic, dense and ultrathin PA layer with a high pure water permeance (23.7 L·m−2·h−1·bar−1) and good retention of salt (95.4 % for Na2SO4). Also, the good selectivity to divalent cation and anion, and excellent stability of the membrane prefigured its potential in application of various water treatment fields.

“Fe-locking” effect by g-C3N4 stabilizing lithium iron oxide pre-lithiation additives

Li5FeO4 (LFO) is an ideal cathode pre-lithiation reagent to improve on lithium-ion batteries due to its high irreversible capacity, cheapness and suitable de-lithiation platform. However, the transition metal (iron) dissolution during cycling hinders its further application. Here, the correlation between the degree of dissolution of iron upon cycling and battery performance is deeply disclosed. More importantly, an effective strategy of ultrathin C3N4 protective layers on the LFO surface is also proposed in this regard. In conjunction with theoretical analyses, it is found that the protective layer formed on LFO is not only conducive to the lithium ions diffusion but also effectively suppressing the dissolution of iron. Consequently, the full-cell capacity is increased by 37.7 mAh g−1 when C3N4@Li5FeO4 (C3N4@LFO) is introduced into LiNi0.8Co0.1Mn0.1O2 cathode material. This work offers a rational viewpoint and a widely applicable strategy for boosting battery performance.

Epitaxial Ultrathin Pt Atomic Layers on CrN Nanoparticle Catalysts.

The construction of platinum (Pt) atomic layers is an effective strategy to improve the utilization efficiency of Pt atoms in electrocatalysis, thus is important for reducing the capital costs of a wide range of energy storage and conversion devices. However, the substrates used to grow Pt atomic layers are largely limited to noble metals and their alloys, which is not conducive to reducing catalyst costs. Herein, low-cost chromium nitride (CrN) is utilized as a support for the loading of epitaxial ultrathin Pt atomic layers via a simple thermal ammonolysis method. Owing to the strong anchoring and electronic regulation of Pt atomic layers by CrN, the obtained Pt atomic layerscatalyst (containing electron-deficient Pt sites) exhibits excellent activity and endurance for the formic acid oxidation reaction, with a mass activity of 5.17AmgPt -1 that is 13.6 times higher than that of commercial Pt/C catalyst. This novel strategy demonstrates that CrN can replace noble metals as a low-cost substrate for constructing Pt atomic layers catalysts.

Wax appearance temperature in crude oils measured by surface plasmon resonance

To predict and quantify the wax appearance temperature in crude oils, we proposed and implemented a well-explored sensing method known as surface plasmon resonance. This phenomenon occurs when an incident light beam couples into a metallic surface. As sensing method, this phenomenon has been widely used in biosensing applications. In this research, we showed the effectiveness of the surface plasmon resonance sensing technique in hydrocarbon sensing in general and in crude oil wax appearance prediction in particular. To the authors knowledge, this is the first exploration of monitoring wax deposition events from crude oil using surface plasmon resonance measurements. A compact optical sensor was developed from an ultra-thin layer of gold deposited on a sapphire prism and supported by a new data analyzing metric to analyze the acquired reflected beam intensity profile and detect the precipitation of crude oil wax or other hydrocarbon particles under varying-temperature and low-pressure conditions. The obtained wax appearance temperatures using the introduced on-site method were found to be comparable with the literature measurements using the common in-lab Cross-Polarization Microscopy method.

Surface-Modified Carbon Nanotubes with Ultrathin Co3O4 Layer for Enhanced Oxygen Evolution Reaction.

Alkaline water electrolysis is a vital technology for sustainable and efficient hydrogen production. However, the oxygen evolution reaction (OER) at the anode suffers from sluggish kinetics, requiring overpotential. Precious metal-based electrocatalysts are commonly used but face limitations in cost and availability. Carbon nanostructures, such as carbon nanotubes (CNTs), offer promising alternatives due to their abundant active sites and efficient charge-transfer properties. Surface modification of CNTs through techniques such as pulsed laser ablation in liquid media (PLAL) can enhance their catalytic performance. In this study, we investigate the role of surface-modified carbon (SMC) as a support to increase the active sites of transition metal-based electrocatalysts and its impact on electrocatalytic performance for the OER. We focus on Co3O4@SMC heterostructures, where an ultrathin layer of Co3O4 is deposited onto SMCs using a combination of PLAL and atomic layer deposition. A comparative analysis with aggregated Co3O4 and Co3O4@pristine CNTs reveals the superior OER performance of Co3O4@SMC. The optimized Co3O4@SMC exhibits a 25.6% reduction in overpotential, a lower Tafel slope, and a significantly higher turnover frequency (TOF) in alkaline water splitting. The experimental results, combined with density functional theory (DFT) calculations, indicate that these improvements can be attributed to the high electrocatalytic activity of Co3O4 as active sites achieved through the homogeneous distribution on SMCs. The experimental methodology, morphology, composition, and their correlation with activity and stability of Co3O4@SMC for the OER in alkaline media are discussed in detail. This study contributes to the understanding of SMC-based heterostructures and their potential for enhancing electrocatalytic performance in alkaline water electrolysis.

Fast Near-Infrared Photodetectors Based on Nontoxic and Solution-Processable AgBiS2.

Solution-processable near-infrared (NIR) photodetectors are urgently needed for a wide range of next-generation electronics, including sensors, optical communications and bioimaging. However, it is rare to find photodetectors with >300kHz cut-off frequencies, especially in the NIR region, and many of the emerging inorganic materials explored are comprised of toxic elements, such as lead. Herein, solution-processed AgBiS2 photodetectors with high cut-off frequencies under both white light (>1MHz) and NIR (approaching 500kHz) illumination are developed. These high cut-off frequencies are due to the short transit distances of charge-carriers in the ultrathin photoactive layer of AgBiS2 photodetectors, which arise from the strong light absorption of this material, such that film thicknesses well below 120nm are sufficient to absorb >65% of NIR to visible light. It is also revealed that ion migration plays a critical role in the photo-response speed of these devices, and its detrimental effects can be mitigated by finely tuning the thickness of the photoactive layer, which is important for achieving low dark current densities as well. These outstanding characteristics enable the realization of air-stable, real-time heartbeat sensors based on NIR AgBiS2 photodetectors, which strongly motivates their future integration in high-throughput systems.

Enhanced separation performance of composite nanofiltration membranes via electrostatic air spray PSS/PEI interlayer

Thin-film composite (TFC) membranes with an interlayer were prepared extensively for desalination, but the hydrophilicity and permeability were not well improved. In this work, a smooth and hydrophilic interlayer was constructed by electrostatic air spray deposition (EASD) of poly (sodium 4-styrenesulfonate) (PSS) and polyethyleneimine (PEI) on the polyethersulfone substrate and an ultra-thin separation layer was prepared using interfacial polymerization of piperazine (PIP) and trimesoyl chloride (TMC) to acquire high-performance composite nanofiltration (NF) membranes. The polymer solution was atomized into tiny particles under a high-pressure electrostatic air spray effect, facilitating the deposition of PSS/PEI with good homogeneity and enabling a denser and smoother interlayer surface. The introduction of PSS/PEI enhanced the hydrophilicity of TFC membranes and increased the repulsion of divalent cations to improve the salt rejection. The impacts of PEI concentration and EASD time on the separation performance of NF membrane were explored. The optimized TFC-3 NF membrane had a permeate flux of 74.5 ± 1.6 L·m−2·h−1 under 0.5 MPa, which was 2.5 times higher than the water flux of conventional TFC-0 membrane, while retaining up to 99.2 ± 0.5 % of Na2SO4. This work provides a prospective strategy to develop high-performance TFC membranes with great extensive progress for seawater purification.

MXene-Based Mixed Conductor Interphase for Dendrite-Free Flexible Al Organic Battery.

Al batteries are promising post-Li battery technologies for large-scale energy storage applications owing to their low cost and high theoretical capacity. However, one of the challenges that hinder their development is the unsatisfactory plating/stripping of the Al metal anode. To circumvent this issue, an ultrathin MXene layer is constructed on the surface of Al by in situ chemical reactions at room temperature. The as-prepared flexible MXene film acts like armor to protect the Al-metal by its high ionic conductivity and high mechanical flexibility. The MXene endow the Al anode with a long cyclic life of more than 5000 h at ultrahigh current density of 50 mA cm-2 for Al//Al batteries and a retention of 100% over 200 cycles for 355 Wh kg-1 PTO//Al batteries. This work provides fresh insights into the formation and regulation of stable electrode-electrolyte interfaces as well as effective strategies for improving Al metal batteries.

Fatigue behavior of short-headed studs embedded in Ultra-high Toughness Cementitious Composites (UHTCC)

The multi-cracking and strain-hardening capacities of Ultra-high Toughness Cementitious Composites (UHTCC) make it feasible for orthotropic steel bridge decks (OSBDs) applications to control crack width. In this composite bridge deck, shear connectors play an important role in providing good shear strength and ensuring structural service performance. To evaluate the shear resistance of short-headed studs embedded in ultra-thin UHTCC layer, three series of push-out tests were conducted in this study. The test results including shear strength, fatigue strength, failure modes, dynamic slip, stiffness degradation, plastic slip and residual mechanical properties were all considered and carefully discussed. In this study, the shear force of shear connectors was calculated and compared with current codes. The stress amplitude-fatigue life (S-N) relationship of studs was fitted by different codes. Then the empirical formulation was developed to predict the load-slip behavior and stiffness degradation of studs during fatigue loading. The relationship between plastic slip and fatigue life was established and normalized. Furthermore, based on post-fatigue static test results and test results in previous research, a new machine learning model was proposed to predict the residual shear strength of studs and contrasted with previous model. Then Analysis of Variance (ANOVA) with two parameters (i.e. load amplitude, maximum repeated force) was conducted and revealed that the peak load significantly impacted the residual shear strength of push-out specimens compared with load amplitude. Moreover, a parametric study was conducted to further investigate the degradation of studs under various working conditions. By experimental and theoretical analysis, UHTCC could fully develop the shear strength of studs embedded in ultra-thin cover thickness. And related models were established to predict the static and fatigue behavior of steel-UHTCC push-out specimen.

Vertical β-Ga2O3 metal–insulator–semiconductor diodes with an ultrathin boron nitride interlayer

In this work, we demonstrate the high performance of β-Ga2O3 metal–insulator–semiconductor (MIS) diodes. An ultrathin boron nitride (BN) interlayer is directly grown on the Ga2O3 substrate by pulsed laser deposition. X-ray photoelectron spectroscopy, Raman spectroscopy, and high-resolution transmission electron microscopy confirm the existence of a 2.8 nm BN interlayer. Remarkably, with the insertion of the ultrathin BN layer, the breakdown voltage is improved from 732 V for Ga2O3 Schottky barrier diodes to 1035 V for Ga2O3 MIS diodes owing to the passivated surface-related defects and reduced reverse leakage currents. Our approach shows a promising way to improve the breakdown performance of Ga2O3-based devices for next-generation high-power electronics.

Improving the Device Performance of CZTSSe Thin-Film Solar Cells via Indium Doping.

Cation incorporation emerges as a promising approach for improving the performance of the kesterite Cu2ZnSn(S,Se)4 (CZTSSe) device. Herein, we report indium (In) doping using the chemical bath deposition (CBD) technique to enhance the optoelectronic properties of CZTSSe thin-film solar cells (TFSCs). To incorporate a small amount of the In element into the CZTSSe absorber thin films, an ultrathin (<10 nm) layer of In2S3 is deposited on soft-annealed precursor (Zn-Sn-Cu) thin films prior to the sulfo-selenization process. The successful doping of In improved crystal growth and promoted the formation of larger grains. Furthermore, the CZTSSe TFSCs fabricated with In doping exhibited improved device performance. In particular, the In-CZTSSe-2-based device showed an improved power conversion efficiency (PCE) of 9.53%, open-circuit voltage (Voc) of 486 mV, and fill factor (FF) of 61% compared to the undoped device. Moreover, the small amount of In incorporated into the CZTSSe absorber demonstrated reduced nonradiative recombination, improved carrier separation, and enhanced carrier transport properties. This study suggests a simple and effective way to incorporate In to achieve high efficiency and low Voc loss.

Asymmetric Triple-Functional Janus Membrane for Blood Oxygenation.

The oxygenation membrane, a core material of extracorporeal membrane oxygenation (ECMO), is facing challenges in balancing anti-plasma leakage, gas exchange efficiency, and hemocompatibility. Here, inspired by the asymmetric structural features of alveolus pulmonalis, a novel triple-functional membrane for blood oxygenation with a Janus architecture is proposed, which is composed of a hydrophobic polydimethylsiloxane (PDMS) layer to prevent plasma leakage, an ultrathin polyamide layer to enhance gas exchange efficiency with a CO2 :O2 permeance ratio of ≈10.7, and a hydrophilic polyzwitterionic layer to improve the hemocompatibility. During the simulated ECMO process, the Janus oxygenation membrane exhibits excellent performance in terms of thrombus formation and plasma leakage prevention, as well as adequate O2 transfer rate (17.8 mL min-1 m-2 ) and CO2 transfer rate (70.1 mL min-1 m-2 ), in comparison to the reported oxygenation membranes. This work presents novel concepts for the advancement of oxygenation membranes and demonstrates the application potential of the asymmetric triple-functional Janus oxygenation membrane in ECMO.

Achieving superior anticoagulation of endothelial membrane mimetic coating by heparin grafting at zwitterionic biocompatible interfaces

Thrombosis and bleeding are common complications of blood-contacting medical device therapies. In this work, an endothelium membrane mimetic coating (PMPCC/Hep) has been created to address these challenges. The coating is fabricated by multi-point anchoring of a phosphorylcholine copolymer (poly-MPC-co-MSA, PMPCC) with carboxylic side chains and end-group grafting of unfractionated heparin (Hep) onto polydopamine precoated blood-contacting material surfaces. The PMPCC coating forms an ultrathin cell outer membrane mimetic layer to resist protein adsorption and platelet adhesion. The tiny defects/pores of the PMPCC layer provide entrances for heparin end-group to be inserted and grafted onto the sub-layer amino groups. The combination of the PMPCC cell membrane mimetic anti-fouling nature with the grafted heparin bioactivity further enhances the anticoagulation performance of the formed endothelium membrane mimetic PMPCC/Hep coating. Compared to conventional Hep coating, the PMPCC/Hep coating further decreases protein adsorption and platelet adhesion by 50 % and 90 %, respectively. More significantly, the PMPCC/Hep coating shows a superior anticoagulation activity, even significantly higher than that of an end-point-attached heparin coating. Furthermore, the blood coagulation function is well preserved in the PMPCC/Hep coating anticoagulation strategy. All the results support that the PMPCC/Hep coating strategy has great potential in developing more efficient and safer blood-contacting medical devices.

Facile Synthesis of Core-Shell Nanoparticles Silver/Cr2O3 Embedded with Ultrathin MoS2 Layers, Microstructure Analysis and Biocompatibility Enhancement by in vitro Evaluation of Antiproliferation and Antibacterial Activities

Cost-effective methods were employed in this study to synthesize core-shell nanoparticles of silver/Cr2O3 (SM) embedded with ultrathin MoS2 layers (SM1) to increase the properties and biocompatibility of the nanomaterials. For structural and morphological investigation, powder XRD, TEM, SEM, EDAX and XPS were used. Magnetic behaviour of SM and SM1 nanoparticles investigated by VSM was shown to be ferromagnetic, and when MoS2 nanosheets were injected, their magnetism decreased. The zeta potential of SM1 was also analyzed. This nanomaterial was synthesized to test the biocompatibility effectiveness of anticancer and antibacterial compounds. In MCF-7 adenocarcinoma (breast cancer) and HepG-2 hepatocellular carcinoma (liver cancer) cell lines, SM1 was investigated for antiproliferation effectiveness. The MCF-7 and HepG-2 cell lines both showed strong cytotoxic potential. Antimicrobial activity was observed against Staphylococcus aureus and Escherichia coli. This study provides strong evidence to support the development of cytotoxicity and antimicrobial properties for significant biomedical compatibility by demonstrating a key to understanding the Ag/Cr2O3 nanoparticle embedded in 2D MoS2 nanosheets on forming a unique interaction as well as the strategy for achieving in vitro efficiency.

Corrosion resistance and earth-abundance FeS-based heterojunction catalyst for seawater splitting at industrial grade density

The strategic progression toward highly efficient transition metal electrocatalytic electrodes is crucial to achieving efficiency and long-term stability in hydrogen production from authentic seawater sources. This work reports the development of a self-supporting, heterogeneous and corrosion-resistant iron sulfur-based catalytic electrode via a streamlined, one-step process involving sulfide etching and electroless plating on an iron foam substrate (IF). This new electrode, named NiS-FeS@IF, involves a nanostructured NiS-FeS catalytic material that combines in situ, resulting in a thin, ultrathin nanospherical layer on the IF. This construction has low overpotentials of merely 322 mV for the hydrogen evolution reaction (HER) and 563 mV for the oxygen evolution reaction (OER) with a current density of 500 mA cm−2 in alkaline simulated seawater electrolytes. Importantly, the NiS-FeS@IF electrode enduring more than 500 h at an industrial grade high current density of 1 A cm−2 without noteworthy performance deterioration. The unique and uniformly dispersed morphology of NiS-FeS facilitates intensified interfacial electron transfer, optimizes active site exposure and provides efficient channels for the rapid release and mass transfer of gas bubbles. This work introduces a novel approach for the facile preparation of efficient electrode materials.

Large voltage-controlled magnetic anisotropy effect in magnetic tunnel junctions prepared by deposition at cryogenic temperatures

We investigated the influence of the buffer material and a cryogenic temperature deposition process on the voltage-controlled magnetic anisotropy (VCMA) effect for an ultrathin CoFeB layer in bottom-free type MgO-based magnetic tunnel junctions prepared by a mass production sputtering process. We used Ta and TaB buffers and compared the differences between them. The TaB buffer enabled us to form a flat and less-contaminated CoFeB/MgO interface by suppressing the diffusion of Ta with maintaining a stable amorphous phase. Furthermore, the introduction of cryogenic temperature deposition for the ultrathin CoFeB layer on the TaB buffer improved the efficiency of the VCMA effect and its annealing tolerance. Combining this with interface engineering employing an Ir layer for doping and a CoFe termination layer, a large VCMA coefficient of −138 ± 3 fJ/Vm was achieved. The developed techniques for the growth of ultrathin ferromagnet and oxide thin films using cryogenic temperature deposition will contribute to the development of high-performance spintronic devices, such as voltage-controlled magnetoresistive random access memories.

Steady state thermokinetic of ultra-thin Mo2C/G heterostructures grown on the prior-graphitized cu/graphene biasing

In this work, the chemical vapor deposition synthesis of the Mo2C/graphene heterostructure above the melting temperature of Cu bias (1356 K) is studied. Two sets of Mo2C growth experiments at high CH4 flow rates (5 SCCM ≥ 3 SCCM) are performed, either using prior-graphene synthesis or having in situ graphitization, for three different Cu bias thicknesses. Raman mappings taken from all six-test samples show graphene covers not only over the Mo2C pillars but also over their untransformed Cu bias substrate regions. The only difference is that the Mo2C pillar grows over the prior graphene bias; on the other hand, the in situ graphene grown Mo2C pillar nucleates and grows over the fresh Cu bias surfaces. A steady-state laminate model for flows of Mo and C species with phase transformations is developed for the radial and vertical growth kinetics of synthesized Mo2C/graphene heterostructure. The computer simulation reproduces those experimental observations performed recently in our laboratories on the prior or no-prior graphitized (G) test modules with Cu/G bias, having three different thicknesses at 1363 K. AFM-topography and SEM photos for a prior graphitized test module of 25 µm thick Cu and 4.72 Å graphene bias show a three layered Mo2C/graphene heterostructure; the first layer is almost perfect hexagonal flat, and the other two circular shaped layers constitute the whole pillar of 140 nm height. This may be compared to a 250 µm thick Cu/4.7 Å graphene bias sample, which furnishes an ultra-thin single flat layer of 10–13 nm thick Mo2C crystallites having a perfect planar hexagonal structure.

High-speed metasurface modulator using perfectly absorptive bimodal plasmonic resonance

Free-space electro-optic (EO) modulators operating at gigahertz and beyond are attractive for a wide range of emerging applications, including high-speed imaging, free-space optical communication, microwave photonics, and diffractive computing. Here, we experimentally demonstrate a high-speed plasmonic metasurface EO modulator operating in a near-infrared wavelength range with a gigahertz modulation bandwidth. To achieve efficient intensity modulation of reflected light from an ultrathin metasurface layer, we utilize the bimodal plasmonic resonance inside a subwavelength metal–insulator–metal grating, which is precisely tuned to satisfy the critical coupling condition. As a result, perfect absorption of −27 dB (99.8%) and a high quality (Q) factor of 113 are obtained at a resonant wavelength of 1650 nm. By incorporating an EO polymer inside the grating, we achieve a modulation depth of up to 9.5 dB under an applied voltage of ±30 V. The 3-dB modulation bandwidth is confirmed to be 1.25 GHz, which is primarily limited by the undesired contact resistance and the output impedance of the driver. Owing to the high electrical conductivity of metallic gratings and a compact device structure with a minimal parasitic capacitance, the demonstrated device can potentially operate at several tens of gigahertz, which opens up exciting opportunities for ultrahigh-speed active metasurface devices in various applications.

Ultra-thin silicon oxide tunnel layer passivated contacts for screen-printed n-type industry solar cells

Effects of the ultra-thin silicon oxide (SiOx) on tunnel oxide passivated contact solar cells (TOPCon) are investigated in this paper. The experiment is fabricated to study the TOPCon electrical performance with different SiOx thickness and the champion efficiency is achieved by the TOPCon with a 1.5 nm SiOx layer, with Voc 698.93 mV, Jsc 40.14 mA/cm2, FF 81.03 and efficiency 22.73 %. For futher understanding, EDNA2 and AFORS-HET are used to simulate the relationship between the SiOx thickness, rear SRV and the doping concentration in n+ layer. It indicates that the total J0 at the SiOx-(c-Si) interface (J0, interface) can be affected by the phosphorus concentration at the SiOx-(c-Si) interface. Besides, due to the variation of SRV or P-doped concentration, different recombination mechanisms, including auger recombination and surface recombination, will dominant the total J0, interface. In addition, the sensitivity of TOPCon solar cells electrical performance to SiOx thickness can be affected by rear SRV, and the sensitivity of TOPCon solar cells electrical performance to rear SRV can be affected by SiOx thickness.