Increasing Shell Thickness Research Articles

Improvement of the magnetization and heating ability of CoFe2O4/ NiFe2O4 core/shell nanostructures

Abstract In this study, the effect of the shell thickness on the structural and magnetic properties of the CoFe2O4/NiFe2O4 core/shell is studied. A single-phase core/shell nanocomposite was prepared by the hydrothermal method. The shell thickness was found to control the magnitudes of saturation magnetization and coercive field of the prepared samples. The thickness of the NiFe2O4, which covered cubic CoFe2O4 particles of 15 nm, was 1.8 nm, leading to an increase in the saturation magnetization by 26% and a decrease in the coercive field by 50% compared to bare CoFe2O4. However, a further increase in shell thickness caused interfacial dislocations due to the lattice mismatch between the core and the shell. Finally, the heating ability at high frequency was measured for all samples. Comparing the temperature rise under the influence of AC magnetic field, which indicates power loss, relative to bare CoFe2O4, it was enhanced by 100% for a shell thickness of 26 nm. The results of this study point to potential applications for these samples in the field of magnetic hyperthermia for cancer therapy and drug delivery.

Mesoporous N-doped hierarchical porous materials derived from core-shell MOFs: A promising strategy for eliminating sulfamethoxazole using 1O2

Slfamethoxazole (SMX) has been considered as one kind of important micropollutants in water which need to be removed effectively. Developing one kind of material for effectively removing SMX in water is crucial in treatment process. In this study, core–shell structured metal–organic frameworks (MOFs) with increasing shell thickness (5, 10, and 20-ZIF-8@ZIF--67 s) were selected as an ideal platform to develop water-stable hierarchical porous carbons (HPCs) using one-step calcination, showing the dual functionals of both adsorption and catalysis by producing large amount of acitve species (1O2). These novel HPCs systematically optimized at increasing temperatures and ratios of two metals. The 10-Co-NHPC-900 at optimal conditions shows highest adsorption capacities and initial adsorption rates, which are 4.56 and 10.35 times higher than those of calcinated ZIF-67 s. The decomposition mechanisms based on PMS were systematically studied by analyzing oxidant consumption, reactive oxygen species and by-products of SMX. In addition, Co ions leached amount of 10-Co-NHPC-900 was 63.6 times lower than that of MOF precursor, indicating that the cobalt-based porous carbon have higher water stabilities. This study offers an efficient approach for reducing micropollutants risk using water-stable hierarchical porous carbons.

Surface plasmon-induced various characteristics of Gold@Copper oxide nanostructures

The combined effect of metal incorporated semiconductor nanostructures (NSs) provides hybrid, proficient and more functional properties that are difficult to be provided by single component NSs in modern applications and industry. A facile seed growth method is adapted for the synthesis of gold coated by cuprous oxide (Au@Cu2O) core@shell NSs that are functionalized in their shell thickness and surface states. As synthesized Au@Cu2O core@shell cubic NSs contain single cubic Au as a core material with varying Cu2O shell thickness, confirmed by their microscopic analysis. Various spectroscopic analyses are is accomplished to confirm the chemical structure, crystallinity, oxidation state and binding energy of the concerned material over the core's surface. Optical absorption properties of core@shell NSs are greatly affected causing a shift in the surface plasmon resonance (SPR) peaks intensities with increase of the shell size. Photoluminescence (PL) spectra explain influence of Cu2O shell morphology over the emission characteristics that an increasing shell thickness caused an enhancement in PL emission peak along with red-shift of the peak. The elemental quantifying is done by XPS technique to provide a detailed surface reaction chemistry about oxidation states of copper. The charge-transfer at the metal-semiconductor interface results in highly intense and selective enhanced SERS signals via PL quenching, using Rhodamine-6G as the probe. The results provide useful information for preparation of various Au@Cu2O NSs for applications involving charge-transfer and SPR based interaction.

Contrasting shell thickness-dependent magnetic behaviors of CoFe2O4@Fe3O4 and Fe3O4@CoFe2O4 core/shell nanoparticles

The magnetic properties of bi-magnetic core/shell nanoparticles (NPs) have been a subject of extensive investigation. Yet, the role of shell thickness in hard/soft and soft/hard core/shell NPs, corresponding to conventional and inverse structures, remains incompletely elucidated. In this study, we synthesized two sets of core/shell NPs, namely Fe3O4@CoFe2O4 (IF@CF) and CoFe2O4@Fe3O4 (CF@IF), featuring a fixed core diameter of approximately 11 nm and varying shell thicknesses up to 5 nm. These NPs were synthesized via a seed-mediated particle growth approach. The formation of the core/shell configuration of typical NPs in both sets was directly verified through scanning transmission electron microscopy-energy dispersive X-ray spectroscopy (STEM-EDS) imaging. Notably, the saturation magnetization (MS) of IF@CF NPs exhibited a significant increase compared to that of the IF core across all shell thickness variations, whereas it remained largely unchanged for CF core and CF@IF NPs. Conversely, the coercivity (HC) showed an opposite trend in the two structures with increasing shell thickness. We observed the emergence of a transition from constricted to smooth hysteresis loops in the conventional structure when the shell thickness reached 5 nm. The systematic evolution of hysteresis loops with escalating shell thickness in both structures closely correlates with distinct magnetic reversal mechanisms, influenced significantly by interparticle interactions. Our study presents a pathway for modulating the magnetic properties of bi-magnetic core/shell NPs, thereby opening avenues for advanced applications in magnetic imaging, sensing, drug delivery, and magnetic hyperthermia.

Experimental study on fragmentation characteristics of molten stainless steel discharged into liquid Lead-Bismuth Eutectic pool

The LFR is a candidate for the Generation-IV nuclear systems, where the process of MFCI differs from that occurred in LWRs and SFRs. In the absence of experimental study and widely applied theoretical models for LFRs, experiments on the interaction between molten SS and liquid LBE are conducted in this study under eight conditions. The morphological characteristics and fragment sizes of the products are analyzed based on the hydrodynamic effect parameter (We) and thermal effect parameter (Tic). Simplified thermal fragmentation models are established, where the innermost layer of the solidified shell is subjected to the maximum tangential compressive stress, while the outermost layer is subjected to the maximum tangential tensile stress. As the shell thickness increases, the total tangential stress of the outermost layer decreases. The fragmentation will occur when the maximum tangential stress on the shell exceeds the shell tensile strength.

Encapsulation of octadecane through crosslinking of cellulose nanofibrils at the interface of Pickering emulsion: Effect of ionic strength on cellulose assembly and capsule shell properties

Emulsion interfacial polymerization is a versatile approach for the encapsulation of organic phase-change materials to improve their stability and prevent their elution and leakage. Herein, we report the successful octadecane encapsulation by the preparation of Pickering emulsions stabilized with carboxylated cellulose nanofibrils (CNF) at various ionic strengths of the dispersive medium. The stable capsule shells were obtained through the formation of amide bonds in the reaction with polymeric isocyanate dissolved in the oil phase. The addition of 5–200 mM NaCl resulted in different adsorption behaviors of carboxylated CNF, which led to an increase in capsule shell thickness (up to 530 nm), improved octadecane encapsulation efficiency (up to 78 %) and thermal stability, as well as reduced elution in organic medium with increasing ionic strength. The study presents a new strategy for the encapsulation of phase-change materials by surfactant-free emulsion interfacial polymerization into containers with defined and adjustable properties.

Numerical simulations of the optical properties of SiO2@Au core–shell nanoparticles: The effect of geometrical parameters on the tunability and sensitivity of their plasmon response

Based on systematic numerical simulations, the effect of geometrical parameters of SiO2@Au core-shells (nanoshells) on the tunability and sensitivity of their optical response was elucidated. The surface plasmon resonance (SPR) of nanoshells experiences a blueshift-redshift crossover with the increase in shell thickness, and this phenomenon is ascribed to the competition between the two effects, that is, the hybridization effect dominated in the thin shells and the retardation effect dominated in the thick shells. The relative strength of absorption/scattering in the extinction spectra and the relative strength of dipolar/multipolar modes can be selectively tuned by controlling the total volume of nanoshells. The sensitivity of the SPR peak wavelength to the shell thickness is primarily dependent on the core-to-shell ratio; the higher this ratio is, the larger the sensitivity. The tailorable properties of nanoshells make them promising and well-suited platforms in various applications.

LOAD-LOADING CAPACITY AND CRACK FORMATION OF REINFORCED CONCRETE CYLINDRICAL SHELL WHEN CHANGING ITS THICKNESS

The results of experimental studies of long cylindrical shells with the aim of determining their stress-strain state, load-bearing capacity and crack resistance when the thickness of the shell changes are described. A special stand was developed by the authors to implement the task. 4 models of a cylindrical shell made of reinforced concrete (samples RC1-RC4) were manufactured and tested. The thickness of the samples was 45, 50, 55, 60 mm, and the cross-sectional dimensions of the side elements were changed accordingly. The distributed load (vertical) was applied in four strips, each 13 cm wide, and only the body of the shell, i.e. the side members were not loaded. The shell hinges from the corners on 100x100mm plates. Inside each side element are two reinforcing rods with a diameter of 10 mm. In order to obtain a complete and reliable picture of the deformation of the shell surface, 4 hour-type indicators are attached to each of the three zones located between the load chains. In addition to indicators, strain gauges were pasted on the shell, which were used to monitor deformations on the upper and lower surfaces. The loading process ended when the tested shell lost its ability to resist the external load. The magnitude of the load corresponding to this moment was taken as the bearing capacity of the shell. Simultaneously with the shell samples, control samples of prisms and cubes were made to determine the physical and mechanical characteristics of concrete. Graphs of the dependence of the relative deformation on the load were constructed. The bearing capacity of the shells and the load at which the first crack formed were determined. By the time of loss of bearing capacity, cracks with the same initial opening width of 0.05 mm had formed in all shells. The final crack opening width, as well as the load-bearing capacity, slightly increased with increasing shell thickness. However, the load at the beginning of crack formation turned out to be the largest for the two average values of the shell thickness – 50 and 55 mm. The general pattern of cracking of all samples is almost the same. The test methodology and the developed stand are universal in nature and will be used for further research.

Threshold investigation of shell thickness for enhanced mechanical and tribological performance in 3D-printed curved sandwich structures

Global prominence has been attained by additive manufacturing technology in recent years, driven by its environmental benefits and machining advantages when compared to traditional subtractive methods. Fused deposition modeling (FDM) technology, primarily utilized in polymer and polymer composite 3D printing, allows for precise control of material distribution within components. In this study, mechanical and tribological behaviors of 3D-printed structures are investigated, yielding valuable insights applicable to practical scenarios. The study identifies threshold limits for layer thickness ratios in three-layered curved sandwich structures, which directly impact their specific load capacity. Stress distribution within 3D-printed PLA discs can be accurately predicted by a saturation function dependent on shell thickness, with material-specific constants. Beyond a critical shell thickness, the impact of increased shell thickness on local tribological properties is found to be negligible. These findings generalize effectively to structures characterized by robust outer shells and weaker inner infills. Connections are drawn between tribological behavior and contact mechanical properties, opening avenues for future research involving nonlinear material modeling and advanced simulations. This study contributes to a deeper understanding of 3D printing and polymer tribology while highlighting the transformative potential of additive manufacturing in various industries, offering cost-effective and resource-efficient solutions for optimized mechanical performance.

Stiffening patterns for freeform composite shell structures

This paper investigates innovative approaches for enhancing the structural integrity of form-found shell structures with a focus on rib-based reinforcements. It discusses the significance of ribs in enhancing stability and addressing the sensitivity of form-found structures to various loads. Traditional methods such as increasing shell thickness or introducing supports often compromise efficiency and aesthetics. A more intelligent approach involves reinforcing the shell with ribs and advanced materials. Diverse rib patterns are presented, including geometric, biomimetic, and topological optimization-inspired designs, each adhering to a 50 % volume constraint, when compared to the original shell. Physical testing and numerical simulations demonstrate that these rib patterns significantly increase stiffness and buckling resistance. The findings presented in the paper suggest that combining form-finding methodologies with well-designed rib patterns can create sustainable and resilient structures, contributing to a reduction in both the consumption of materials and the environmental impact of these structures.

Parametric Optimization of System Modes for Nozzle Turbine Vane by Means of Costimulated Artificial Immune System

One requirement posed by customers is to achieve adequate durability levels as described in technical requirement documents. Modal analysis is one of the design assessments aimed at identifying the risks of high cycle fatigue (HCF). This article presents a novel application of an artificial immune system (AIS) in the optimization of a nozzle guide vane’s modal characteristics. The aim is to optimize the system’s natural frequencies in the vibration vane and adjacent hardware (turbine casing). The geometrical characteristics accounted for in the optimization process include the shell thicknesses on the turbine casing side and the nozzle outer band features (hook thickness, leaning and position). The optimization process is based on a representative model established from FEM analysis results. The framework is robust because of the applied metamodel and does not require time-consuming FEM analysis in order to evaluate the fitness function. The aim is to minimize the model area (a derivative of the system weight) with constraints imposed on the frequency (a penalty function). The optimum design is given as the solution with an increased shell thickness in the turbine casing and leaning nozzle outer band hooks to obtain the maximum stiffness of the system. The results obtained by means of the artificial immune system (AIS) and a novel variant based on an additional costimulation procedure (CAIS) are compared with the solution obtained by means of a genetic algorithm implemented in the commercial CAE software (Ansys version 19.2).

Electron-donor-impurity polarizability in a semiconductor nanostructure under electric field: Geometrical effects in ellipsoidal quantum dots

The features of electron-impurity polarizability in a quantum nanostructure are investigated from the knowledge of allowed electron states coupled to a shallow-donor impurity. The influence of geometry on the carrier confinement and the presence of external probes such as electric fields are explicitly considered. For the sake of illustration, the example of CdS/ZnSe-based prolate ellipsoidal core/shell quantum dot (PECSQD) configuration is chosen. This problem allows to consider a finite confinement potential model, employing both the finite element method and the effective mass approximation. Within this framework, impurity-related energies and associated polarizability for the lowest states were determined as functions of the shell thickness, core dimensions, impurity position, and applied electric field strength - while keeping the shell dimensions fixed. Electron-impurity energies are largely affected by electric field values. Under thinner shell conditions, polarizability shows variations with field strength that include “anomalous” negative values for certain states. Then, the increase in shell thickness causes a significant increment in the polarizabilities, regardless impurity position.

Enhancing Mechanical Characteristics of PETG Carbon Fiber Composite through Various Shell Thickness in FDM Processing

The utilization of PETG (Polyethylene Terephthalate Glycol) carbon fiber composites in Fused Deposition Modelling (FDM) processes has gained significant attention due to their enhanced mechanical properties compared to traditional PETG filaments. This study focuses on investigating the impact of varying shell thickness on the mechanical characteristics of PETG carbon fiber composites fabricated through FDM. The objective is to optimize the shell thickness to achieve superior mechanical performance while maintaining printing efficiency. A series of PETG carbon fiber composites with different shell thicknesses were manufactured using an FDM 3D printer. Mechanical tests, including tensile strength, flexural strength, and impact resistance, were conducted to evaluate the performance of the fabricated specimens. Additionally, micro-structural analysis was performed to understand the influence of shell thickness on the interfacial bonding between PETG matrix and carbon fibers. Preliminary results indicate that increasing shell thickness positively affects the mechanical properties of PETG carbon fiber composites. Tensile and flexural strength show a noticeable improvement with an increase in shell thickness, attributed to enhanced interlayer adhesion and improved load-bearing.

Study on Carrying Capacity of Square shell and Parameter analysis

Square shell is one structural type which is quite common to be seen in engineering. This paper focuses on the carrying capacity of square shell, and studies the influence of round radius and shell thickness on the ratio of mass to external volume and load factor under linear buckleing of shell. Numerical results show that, With the increase of round radius, the ratio will first decrease, then increase and approach that of circular shell, while the load factor will also increase. With the increase of shell thickness, the ration of shell will increase and the load factor will rapidly increase. This will help to better design of pressure hull of submarines.

S-HGMS coupling with alkali precipitation for the scale inhibition in recirculating cooling water with high hardness: Performance, mechanism and field application

Recirculating cooling water (RCW) contains various scale-forming ions, such as Ca2+ and Mg2+, which tend to form the hard scale in the heat transfer process. In this study, a novel method via superconducting high-gradient magnetic separation (S-HGMS) coupling with alkali precipitation for scale inhibition in RCW was proposed, which could achieve efficient removal of total hardness (91.64 %). The scale inhibition mechanism of the S-HGMS coupling is attributed to the increase of ionic hydration shell thickness and the formation of hydrogen bonds, enhancing the solubility of scale-forming ions and diminishing their nucleation rate. Furthermore, this coupling induces a crystalline transformation from recalcitrant calcite to looser aragonite, contributing to the separation of scale from the pipe wall. Significantly, the proposed method was implemented in the field application by establishing a pilot-scale system with a capacity of 800–1000 L/h, which realized a stable reduction in the total hardness of the RCW from 1270 mg/L to below 127 mg/L at a magnetic flow ratio of 0.05 T·s/m. Moreover, the heat exchanger surface scaling was effectively controlled after 71 days of continuous treatment. This study helps promote the industrial application of S-HGMS technology for scale inhibition in high-hardness water.

Surface Cross-Linking by Macromolecular Tethers Enhances Virus-like Particles' Resilience to Mucosal Stress Factors.

Virus-like particles (VLPs) are emerging as nanoscaffolds in a variety of biomedical applications including delivery of vaccine antigens and cargo such as mRNA to mucosal surfaces. These soft, colloidal, and proteinaceous structures (capsids) are nevertheless susceptible to mucosal environmental stress factors. We cross-linked multiple capsid surface amino acid residues using homobifunctional polyethylene glycol tethers to improve the persistence and survival of the capsid to model mucosal stressors. Surface cross-linking enhanced the stability of VLPs assembled from Acinetobacter phage AP205 coat proteins in low pH (down to pH 4.0) and high protease concentration conditions (namely, in pig and mouse gastric fluids). Additionally, it increased the stiffness of VLPs under local mechanical indentation applied using an atomic force microscopy cantilever tip. Small angle X-ray scattering revealed an increase in capsid diameter after cross-linking and an increase in capsid shell thickness with the length of the PEG cross-linkers. Moreover, surface cross-linking had no effect on the VLPs' mucus translocation and accumulation on the epithelium of in vitro 3D human nasal epithelial tissues with mucociliary clearance. Finally, it did not compromise VLPs' function as vaccines in mouse subcutaneous vaccination models. Compared to PEGylation without cross-linking, the stiffness of surface cross-linked VLPs were higher for the same length of the PEG molecule, and also the lifetimes of surface cross-linked VLPs were longer in the gastric fluids. Surface cross-linking using macromolecular tethers, but not simple conjugation of these molecules, thus offers a viable means to enhance the resilience and survival of VLPs for mucosal applications.

Epoxy resin mechanical properties in composition with copper (I) oxide particles, encapsulated by polylactide with variable thickness

The required functional and mechanical properties are necessary for design the polymer compositions with dispersed fillers. The mechanical properties of such polymer composition can be changed by encapsulated filler particles shell thickness varying. The paper shows that the presence of polylactide polymer shell and its thickness on the surfaces of copper (I) oxide particles significantly affect the strength of polymer composite material based on ED-20 epoxy resin. That is due to the interaction between encapsulated particles and the matrix polymer, in contrast to noncapsulated particles. In addition, a change in particle size due to increasing shell thickness also affects the strength properties of the composition. It is shown that the elastic modulus of the filled epoxy composite does not depend on the shell thickness on the particle surfaces.

Использование новых кормовых добавок из местных растительных ресурсов в рационах кур-несушек

Purpose. To establish the effect of extruded grain of amaranth (Amaranthus hybridus chlorostachys) with and without the addition of a complex of enzymes, sunflower polysaccharide extract (hereinafter referred to as SPE), sunflower and pumpkin fuses in combination with bischofite on economic, biological, hematological indicators and the immune status of laying hens. Materials and Methods. The experiment was carried out on laying hens of the industrial herd of the Hayseks brown cross at the breeding enterprise of the Volgograd region of the Svetloyarsky district on the basis of Agricultural enterprise "Svetly" JSC "Agrofirm Vostok". Blood biochemical parameters were determined according to the methods of JSC "Deacon-DS" using the appropriate set of biochemical reagents on automatic biochemical analyzers URIT-800Vet, URIT-3020, other studies – on certified equipment in the complex analytical laboratory of VRIMMP (Volgograd, Russia). The obtained results were processed using software, calculating the mean value (M), standard errors of the mean value (±SEM) and determination of the Student-Fisher test for the significance of the difference. Results. The positive dynamics of cholesterol reduction by 6.87% was proved with the addition of 10% amaranth and by 9.86% with the addition of 10% amaranth and 250 g/t of the multienzyme complex. The use of sunflower polysaccharide extract in feeding laying hens – a by-product of sunflower oil production – in the amount of 3; 5 and 7% contributed to an increase in the yield of hatching eggs, respectively, by 88, 239 and 149 pcs. regarding control, increase in the intensity of egg production, feed conversion. The highest efficiency in the production of hatching eggs was achieved when using sunflower polysaccharide extract at a dosage of 5.0% in the diet structure. A significant increase in the productivity of chickens of all experimental groups by a value of 2.00 to 3.94% (P≤0.001) was established with the addition of pumpkin, sunflower phosphatides and bischofite, while the upper value was recorded with the addition of sunflower phosphatides and bischofite. The addition of pumpkin phosphatides contributed to the greatest increase in the weight of the laid egg relative to the control by 2.7 g (4.38%). Feeding both types of phosphatides contributed to the economy of feed, lowering cholesterol levels by 2 to 3.6%. The use of bischofite was manifested in a significant increase in the thickness of the shell, respectively, by a value from 13.0 to 21.2 microns. Conclusion. The greatest reduction in cholesterol levels (by 9.86%) and efficiency in the production of eggs was achieved with the addition of 10% amaranth and 250 g/t of the multi-enzyme complex. The best economic and biological indicators of poultry were recorded when using sunflower polysaccharide extract at a dosage of 5.0% in the diet structure. The addition of sunflower phosphatides in the amount of 3% and 2.6% bischofite contributed to a significant increase in the productivity of chickens by 3.94% (P≤0.001). The addition of pumpkin phosphatides contributed to the greatest increase in the weight of the laid egg relative to the control by 2.7 g (4.38%). The inclusion of bischofite in the diet of laying hens resulted in a significant increase in shell thickness by 13.0 to 21.2 µm.

Addition of Bacillus subtilis BN Strain Probiotic on Chicken Eggs Quality

The addition of probiotics is one effort to increase the chicken's appetite. There are many probiotics that can be mixed into feed to help improve the digestive and reproductive systems, including Bacillus subtilis, which has the function of increasing egg quality, including increasing shell thickness, increasing egg volume, increasing egg yolk and white index. This reseacrh aims to find out the effect of probiotic administration of Bacillus subtilis BN Strain on shell thickness, white index and chicken yolk index. This research used 38-week-old layer laying hens as many as 24 heads, randomized into four treatments with eight replays. Based on the analysis of statistical data, the Analysis Of Variance (ANOVA) test showed no noticeable difference (p>0.05) to the thickness of the shell, white index or egg yolk index. The results showed that the addition of probiotic Bacillus subtilis BN Strain as many as 0.005 grams/kg of feed, 0.01 grams/kg of feed and 0.02 kg/kg of feed had no noticeable effect on the increase in egg shell thickness, egg white index and egg yolk index.

The Effect of the Mid‐Shell Thickness on the Charge‐Carrier Dynamics of the Green‐Light Emitting InP/ZnSe/ZnS Core‐Shell Quantum Dots

AbstractUltrafast charge carrier dynamics of green‐light emitting InP/ZnSe/ZnS core–shell quantum dots (QDs) with three different ZnSe thickness of 2.0 nm (gQD‐20), 2.4 nm (gQD‐24), or 3.3 nm (gQD‐33) are interrogated by femtosecond transient absorption (TA) and femtosecond stimulated Raman spectroscopy (FSRS). Auger‐type cooling of hot electron into the band‐edge level of InP is clearly manifested in the TA spectra, giving its time constant of ≈222, 300, or 349 fs for gQD‐20, gQD‐24, or gQD‐33, respectively, indicating that the state‐filling to the 1S(e) of InP is significantly slowed down with the increase of the mid shell thickness. The global analysis of the whole TA spectra turns out to be extremely useful to explain the dynamic behavior of the heterogeneous ensemble of single and/or bi‐ (or multi‐) excitons in the presence of the Stark‐shift. The hole‐relaxation dynamics into the band‐edge 1S (h) of the core InP is revealed in the bleaching dynamics of the FSR bands corresponding to the phonon mode of InP or ZnSe, giving the estimated lifetime of 1.0–1.4 ps for gQD‐20. The hole‐relaxation dynamics by the phonon emission seem to be little sensitive to the ZnSe shell thickness.