Varying Particle Size Research Articles

Power ultrasound-assisted enhancement of granulated blast furnace slag reactivity in cement paste

The impact of the power ultrasound (PUS)-assisted preparation technique on the physicochemical and mechanical characteristics of cement-granulated blast furnace slag (GBFS) pastes was studied. Pastes containing GFBS with varying particle size fractions, partially replacing Portland cement, were tested using PUS in pulse mode in a sonoreactor with closed-circuit cooling. The best-performing cement-GBFS composite paste showed a notable increase in compressive and flexural 2-day strengths (132% and 58%, respectively), as well as Vickers hardness and modulus of elasticity (98% and 74%, respectively) when compared to conventional mixing procedures. Similarly, the BET surface area increased by about 111%, cumulative heat release increased by about 34% after 2 days, reduced substitute setting times (initial by about 32%, final by about 55%), and portlandite content decreased by about 29%. The power of this association is linked to C-S-H/C-A-S-H nucleation seeding, which can be formed via an interfacial mediator induced by PUS.

Effect of Nano Particle Size on Mechanical and Fatigue Behavior of TiO2 Particular—Reinforced Aluminum Alloy Composites

Aluminum alloys are among the most widely used materials in the parts and vehicle sectors due to their high strength-to-weight ratio and qualities such as higher corrosion and wear resistance, as well as minimal thermal growth when compared to other metals. This research involved matrix alloy AA7075 aluminum reinforced with constant 7 wt. % TiO2 (with different particle sizes 30, 70, and 100 nm). The goal of this study is to improve the mechanical (impact strength and young modulus) and fatigue properties of AA7075 alloy-based metal matrix composites, and fatigue. AA7075 composites with a constant weight percentage of 7wt.% of TiO2 and variable particle size have been successfully synthesized by the stir casting route. Microstructural examinations revealed that nanocomposites with (30nm) particle size have better distribution and less porosity compared to the other particles size. The nanocomposite having 30 nm particle size was found to have maximum improvement UTS and YS in comparison with the other nanocomposites, 20.45%, and 12.87% respectively, and minimum elongation. An increase in particle size and fatigue results indicates the decreasing trend of fatigue life and strength. The higher endurance fatigue limit was recorded to be (23.875 MPa) for (30 nm) nanocomposite.

Effect of MoS2 particle size on tribological and vibration reduction properties of thermoplastic polyurethane

The incorporation of lubricating filler can improve the self-lubricating properties of polymers and mitigate friction-induced vibration under harsh conditions. However, filler performances significantly vary depending on its size. In this study, molybdenum bisulfide (MoS2) particles of various sizes were utilized as lubricating additives to reinforce thermoplastic polyurethane (TPU). The results showed that an appropriate decrease in the particle size of MoS2 facilitated more efficient stress transfer from the polymer to the particle due to strengthened interfacial interaction, resulting in improved mechanical properties of the reinforced TPU composites. Additionally, the adsorption property of the MoS2 particle improved, extending the duration of the MoS2 tribo-film. These beneficial phenomena endow TPU composites with excellent tribological and frictional vibration reduction properties, with the 500 nm MoS2 presenting the best reinforcing effect. However, further reduction in particle size caused particle agglomeration, which adversely affected the mechanical and self-lubricating properties of the composite and eventually reduced the frictional vibration reduction properties. The findings obtained herein provide a valuable reference for developing a novel polymer with excellent friction and vibration reduction properties.

Interaction of a Dense Layer of Solid Particles with a Shock Wave Propagating in a Tube

A numerical simulation of an unsteady gas flow containing inert solid particles in a shock tube is carried out using the interpenetrating continuum model. The gas and dispersed phases are characterized by governing equations that express the concepts of mass, momentum, and energy conservation as well as an equation that shows the change of the volume fraction of the dispersed phase. Using a Godunov-type approach, the hyperbolic governing equations are solved numerically with an increased order of accuracy. The working section of the shock tube containing air and solid particles of various sizes is considered. The shock wave structure is discussed and computational results provide the spatial and temporal dependencies of the particle concentration and other flow quantities. The numerical simulation results are compared with available experimental and computational data.

The Effect of Polyethylene Microplastics on Growth and Antioxydant Response of Oscillatoria Princeps and Chlorella Pyrenoidosa.

This study investigated the impacts of polyethylene microplastics (PE-MPs) with varying particle sizes (13μm and 6.5μm) on the growth and antioxidant responses of two freshwater algae species, Oscillatoria princeps (O. princeps) and Chlorella pyrenoidosa (C. pyrenoidosa). The results revealed a significant reduction in chlorophyll a content in both algal species upon exposure to PE-MPs, indicating a disruption of photosynthesis. Furthermore, Superoxide Dismutase (SOD) activity decreased in O. princeps, while Catalase (CAT) activity increased in both species, indicating complex physiological responses to microplastic stress. Notably, phycotoxin levels in O. princeps decreased with PE-MP exposure, while those in C. pyrenoidosa increased, particularly with 6.5μm PE-MPs. These findings underscore the potential toxic effects of PE-MPs on freshwater algal growth and metabolism, as well as their influence on toxin production. This study contributes valuable insights into the ecotoxicological impacts of microplastics in freshwater environments, highlighting the need for further research on their biological effects and environmental health implications.

Excellent mechanical properties and giant room-temperature elastocaloric effect in spark plasma sintered Ni-Co-Mn-Ti shape memory alloy

All-d-metal Heusler-type Ni-Mn-Ti alloys have emerged as a research focus in the field of elastocaloric refrigeration due to their remarkable elastocaloric effect. However, the mechanical properties of these materials present a challenge for their engineering applications. In this work, Ni37Co13Mn33.5Ti16.5 alloys with varying particle sizes were successfully prepared under different conditions using spark plasma sintering. The influence of particle size on the microstructure, mechanical properties and the elastocaloric effect were systematically explored. The results indicate that smaller particle sizes can significantly enhance mechanical properties during the SPS process, primarily due to grain refinement and the presence of Ti-rich second phases within the grains. Notably, compressive strength and fracture strain reached as high as 2225 MPa and 33 %, respectively, marking an increase of 145.9 % and 312.5 % over the as-cast alloy. Additionally, an unprecedently adiabatic temperature variation of 31.2 K was obtained upon loading in the sintered Ni-(Co)-Mn-Ti shape memory alloys.

Evaluating the potential of soy protein isolate /alginate hydrogel as polyphenolic liposome carrier during gastrointestinal tract: A case study on sumac extract

Sumac seed is one of the best sources of polyphenolic compounds and natural antioxidants. This study was conducted to protect the polyphenolic compounds of sumac extract. For this purpose, the chemical composition of sumac extract (SE) was identified using LC-MS technique. Then sumac extract was trapped in liposomal structures and physicochemical properties were evaluated. The results showed that the size and specific surface areas of the liposomes influenced the entrapment efficiency of SE. The zeta potential of liposomes containing SE indicated stability between bioactive substances and liposome bilayers. In the next step, three ratios of soy protein isolate-alginate hydrogel (P1A3, P1A1, and P3A1) were applied to cover the liposome-SE. Furthermore, the flow behavior, surface morphological analysis, texture, and release of phenolic compounds from soy protein isolate-alginate hydrogels containing SE were investigated. Quantitative data showed variations in particle size, sphericity, and loading efficiency according to the SPI to ALG ratio. Fourier-transform infrared spectroscopy confirmed the interactions between the components at a molecular level. This study provided valuable insights into the design and optimization of drug delivery systems and functional food ingredients, highlighting the complexities involved in the controlled release of bioactive substances.

Promotion of antibiotic-resistant genes dissemination by the micro/nanoplastics in the gut of snail Achatina fulica

Terrestrial animal intestines are hotspots for the enrichment of micro/nano plastics (M/NPs) and antibiotic-resistant genes (ARGs). However, little is known about the further impact of M/NPs on the spread of ARGs in animal guts. This study investigates the role of M/NPs (polystyrene) with varying particle sizes (0.082, 42, and 182 μm), concentrations (10 and 100 mg/L), and exposure durations (4 and 16 days) in the ARGs dissemination via conjugation in the edible snail (Achatina fulica) gut. Combination of qPCR with 16S rRNA-based sequencing, we found that PS exposure caused intestinal cell impairment and shifts in the gut microbial community of snails. Conjugation rate increased with PS particle sizes in the snail gut. After 4 days of exposure, significantly higher conjugation rates were observed in the gut exposed to 100 mg/L PS compared to 10 mg/L, however, this trend reversed after 16 days. Consistently, the abundances of conjugation relevant genes trfA and trbB shared similar trends to the conjugation ratios in the snail gut after PS exposure. Transconjugant diversity was much lower in 10 mg/L PS groups than in 100 mg/L PS treatments. Therefore, this study suggests that the presence of M/NPs would complicate management of ARG spread. The selection pressure exerted by M/NPs may sustain or even amplify the spread of ARGs in the gut of terrestrial animals even in the absence of antibiotics. It highlights the necessity of avoiding M/NPs intake as a part of comprehensive strategy for cubing ARG dissemination in the gut of animals.

Green florescent carbon dots synthesized from various household green wastes for detection of parathion methyl pesticide

The purpose of the current study was to examine the use of green household wastes, such as lemon peel, bottle gourd peel (BG), culinary banana peel, and sugarcane bagasse, as a source for synthesizing carbon dots (C-dots) and to determine how the composition of the material affected the functional characteristics of the C-dots and its interaction behaviour for detection of pesticide. The synthesized C-dots showed green fluorescence with varying particle sizes and red shifting fluorescence with more than 100 nm Stokes shift, indicating time and excitation dependent luminescence behaviour. C-dots produced from bottle gourd (BG) peel had a positive impact on the functional characteristics with a maximum emission of 514 nm and excitation of 410 nm. The SAED and TEM pattern confirmed its amorphous structure. The hydronium ion diameter and the quantum yield were 0.99 nm and 3.1 % respectively. Contributing towards food safety, the synthesized C-dots from BG showed significant behaviour in the detection of parathion methyl (MP) like organophosphorus pesticide (OP) as it conjugated with iron and 1 ppm of parathion methyl, which exhibited “Turn-Off-On” fluorescence behaviour with noticeable changed in intensity and act as a promising qualitative tool for detection of parathion methyl in real sample. The intensity of FL and concentration of OP is directly proportional which is established by the investigated OP in vegetable, fruit and water samples. The significance of iron and MP-OP was also investigated in the presence of other metal ions and pesticides and showed that the C-dots synthesized probe solution was reliable and sensitive towards the detection of MP-OP in real samples.

Molecular dynamics mechanism of incorporating ZnO with varying particle sizes into ECTFE coatings and its impact on corrosion resistance

A composite coating of zinc oxide/chlorotrifluoroethylene copolymer (ZnO/ECTFE) was prepared on the surface of carbon steel via electrostatic spraying and heat treatment at 260 ℃. The influence of ZnO particle size variations on the anticorrosive properties of ECTFE coating was investigated by characterizing the microstructure, adhesion, hydrophilic/hydrophobic properties, electrochemical corrosion performance, as well as the dynamics simulation analysis on water molecule and chloride ions diffusion in the coating. The results show that the ECTFE coating incorporated with 100nm ZnO has the highest surface roughness (Roughness coefficient Ra = 30.6nm), the most robust adhesion (Bonding pull-out strength = 5.22MPa), and the lowest corrosion current density after a 90-day immersion (Icorr,90d = 4.05 × 10⁻⁸ A∙cm⁻²). These improvements represent an increase of 81.67% and 59.9% compared to the pure copolymer coating (Icorr,90d = 2.21 × 10⁻⁷ A∙cm⁻²) and the coating incorporated with 200nm ZnO (Icorr,90d = 1.01 × 10⁻⁷ A∙cm⁻²), respectively. This phenomenon can be attributed to the addition of small-sized ZnO, which enhances the density of the coating, induces a hydrophobic transition on its surface, strengthens the double electric layer effect, thereby improving its resistance against water molecule and chloride ions diffusion and ultimately enhances the corrosion resistance.

Mechanochemically assisted synthesis, inversion degree and magnetization of spinel compounds across the (Zn,Mg)Fe2O4 system for flexible smart devices

Magnetic spinel oxides are multifunctional materials used or under consideration for a range of applications across electronics, communication technologies, remediation and health. They can also present high magnetostriction coefficients, and are being investigated as active inorganic fillers in polymer matrix composites for flexible sensors and actuators. However, state-of-the-art materials for these later applications are NiFe2O4- and CoFe2O4-based compositions, and it is necessary to find environmentally-friendly alternatives free of toxic elements that provide comparable responses, ideally biocompatible. This work presents a study of the spinel phases across the (Zn,Mg)Fe2O4 system and of their suitability to be used as magnetic component in hybrid composites. Spinel single phase materials with variable particle size across the submicron range, down to the verge of the nanoscale, have been obtained by mechanochemically assisted synthesis for five selected compositions spanning the whole ZnFe2O4-MgFe2O4 system. Evolution of the crystal lattice and inversion degree (amount of Fe3+ at tetrahedral site) has been obtained from Rietveld refinement of synchrotron X-ray diffraction data, and correlated with the development of magnetic ordering. Ferrimagnetic compositions are identified, among which Zn0.25Mg0.75Fe2O4 stands out for its magnetization characteristics comparable to NiFe2O4. This spinel compound is thus a promising environmentally-friendly candidate for flexible devices, in principle also biocompatible.

Effect of particle size and replacement ratio on mechanical performance of cementitious mortar containing ground recycled acrylonitrile butadiene styrene (GRABS) waste plastics

While waste plastics have been used as a natural sand aggregate replacement in cementitious mortar as a sustainable option to mitigate global accumulation of plastic waste in landfills, fundamental mechanical properties like compressive, tensile, and shear must be known to advance design and practical application of these cement-concrete composites as suitable building construction materials. Experimental testing is conducted to reveal to what extent the cementitious composite properties are altered, thereby influencing their overall mechanical performance, when both ungraded and graded ground recycled acrylonitrile butadiene styrene (GRABS) plastic are employed as substitutes for natural aggregates. The novelty of this research lies in its pioneering investigation to quantify the effects of varying particle sizes and volume fractions of waste plastics acquired through mechanical recycling and their influences on the mechanical properties of mortars containing plastics as a composite material. The results from fresh and hardened material properties are compared to conventional mortar properties to examine the impact of various GRABS particle sizes and volume fractions on the overall material strength. While replacing sand with waste plastic generally reduced mechanical properties, the resulting mixes still met the minimum compressive strength (4060 psi [28 MPa]) as per ASTM C150 standards for Portland cement. Notably, graded plastic particles with sizes less than 0.024 in [0.6 mm] demonstrated an overall improvement in mechanical properties compared to ungraded particles. Failure mechanisms responsible for compressive, tensile, and shear damage development are discussed by analyzing the fracture surfaces, which provide insight into the intricate relationship between waste plastic size and distribution on the mechanical behavior of mortar. The findings indicate that GRABS waste plastics, when combined with sand at appropriate particle sizes and volume fractions, have the potential to create tailored mixes to meet minimum mix design standards for construction applications.

Experimental research on self-amplifying density waves in horizontal pipelines of two phase granular slurries: Measurements on the effect of particle diameter and concentration

Self-amplifying density waves in hydraulic transport pipelines is a scarcely researched topic. Density waves are in essence the result of a spatial redistributing effect and clustering of solids in hydraulic transport pipelines. Self-amplifying density waves are very undesirable for practical applications, as these waves increasing the risk of pipeline blockages. The two available experimental studies (Talmon et al., 2007; Matoušek and Krupička, 2013) report conflicting properties of the density waves, such as wave length and wave celerity. This new experimental research aims to shed light on the reported differences, by broadly varying particle size and concentration in a new dedicated experiment. The main highlight of this research is that two separate mechanisms were identified that can cause density waves, and Talmon et al. (2007) and Matoušek and Krupička (2013) in hindsight were studying the two different mechanism respectively. Both wave type mechanisms come into effect at mixture velocities close to the deposit limit velocity, and require a stationary bed layer to initiate. The first mechanism is caused by an imbalance of erosion and sedimentation of the bed layer, which is predominant for fine sand particles (∼242μm and ∼308μm in this research). The second mechanism occurs when the bed layer starts sliding, instead of being eroded, and is specific for larger sand sizes (∼617μm and ∼1.08mm in this research). These two mechanisms are clearly distinguishable, having different wave lengths, celerity, amplitudes and amplification rates. The results also show a clear relationship between the mean concentration of a density wave, the wave amplitude and wave celerity specific for each of the two mechanisms.

Shear characteristics of nonuniform distribution of granular materials in ring shear test and impact on landslides

Knowledge of the shear behavior of landslide soil is very important for understanding landslide dynamics. This study investigated the shear behavior of base soil particle materials using ring shear tests with glass beads. Samples with varying particle sizes and distributions were examined to explore how particle size affects shear behavior at different shear velocities. Analysis of the samples included assessment of shear stress, displacement-shear stress fluctuations, and changes in the shear stress standard deviation. Results showed that with increasing shear displacement, shear stress fluctuations stabilize. Rather large difference particle size differences lead to more uniform particle mixing and a lower shear stress standard deviation. Conversely, when smaller particles predominate, particle mixing is less uniform, resulting in a higher shear stress standard deviation. Additionally, this study discussed the shear dilation and compaction mechanisms of samples under large displacement shear.

Influence of Dy3+ doping on Mössbauer, magnetic and microwave absorption properties of M-type Ba0.5Ca0.5DyxFe12-xO19 hexaferrites

The present research paper reports a systematic study of the magnetic, and structural properties of Ba0.5Ca0.5DyxFe12-xO19 M-type hexaferrite. The dysprosium was doped @ x = 0 − 0.2, keeping Δx = 0.05, in BCDF by the sol–gel self-ignition technique. The sintering of the synthesized samples was performed for 4 h at 1050°C. The crystallographic analysis of the samples was made from the X-ray diffractograms (XRD), while the morphological and elemental analysis was made from field emission scanning electron microscopy (FESEM), and energy-dispersive X-ray spectroscopy (EDAX) profiles. The structural results revealed the formation of the M-type hexaferrite having P63/mmc as a space group along with the co-existence of a secondary Fe2O3 phase. FESEM micrographs exhibit the hexagonal platelets randomly arranged with agglomerations at some places giving rise to the random variations in particle size with varying ’x’. Magnetic measurements (VSM) show that the saturation magnetization (MS) and coercivity (HC) increase with the increasing Dy3+ doping pointing towards the fact that the Dy doping in Ba-Ca ferrite can be used to fabricate the hard ferrites with good saturation magnetization. The Mössbauer spectrum recorded at room temperature reveals five superimposed sextets representing the five Fe3+ ion sites. Investigating the Microwave absorption (MWA) characteristics in the frequency range 8 − 12 GHz (X-band), reveals that the sample with x = 0.1 having 3 mm thickness possesses good MWA power. Its minimum RL value for matching frequency 10.06 GHz is approximately −26.96 dB, indicating that more than 90 % of microwaves are absorbed. The current work offers the Dysprosium-doped BCDF hexaferrites, as promising candidatesfor microwave absorption applications.

Structure-activity relationship and deactivation behavior of iron oxide during CO2 hydrogenation

Identifying the dynamic structural evolution of iron during the thermocatalytic conversion of CO2 into liquid hydrocarbons is a promising approach for understanding the deactivation behavior and to design an efficient catalyst. Despite the understanding of the oxidation of χ-Fe5C2 to high-valent iron oxides (e.g., Fe3O4, Fe2O3) caused by water formed as the byproduct, the deactivation mechanism depending on the particle size during a long-term reaction remains unclear. Herein, the structural evolution and deactivation mechanism of Na-promoted Fe2O3 catalysts with varying particle sizes were investigated. The catalyst activity and deactivation behavior were highly dependent on the initial morphology of the calcined catalysts. The reduced iron catalyst with an average particle size (dave) of 0.52 μm maintained its domain integrity, whereas that with a dave value of 2.18 μm was severely pulverized during the CO2 hydrogenation. The pulverized particles exposed a new surface, making it highly susceptible to re-oxidation and catalyst deactivation. Conversely, maintenance of the iron integrity suppressed the re-oxidation, whereas the excess formation of graphitic carbon on the χ-Fe5C2 site was the main deactivation mechanism during long-term CO2 hydrogenation.

Investigation of the regulatory mechanism of monolayer colloidal crystals prepared by gas-liquid-solid three-phase interfacial self-assembly method

In recent years, the gas-liquid interface self-assembly method has emerged as a recognized and efficient technique for preparing two-dimensional monolayer colloidal crystals. However, challenges such as limited preparation area, dependence on complex equipment, and high costs persist in the conventional preparation process. This paper proposes a straightforward, rapid, and cost-effective method to implement a gas-liquid-solid three-phase interfacial self-assembly strategy. This approach enhances the gas-liquid interfacial self-assembly method, allowing for the preparation of large-area, high-quality single-layer colloidal crystals (>10 cm2) without using any surfactant. The gas-liquid-solid three-phase interfacial self-assembly process was analyzed in detail, and it was found that the main factors affecting the quality of the monolayer colloidal crystals were the volume ratio of PS colloidal solution to ethanol and the self-assembly temperature. It was shown that the optimal self-assembly conditions were achieved after dispersion by ultrasonic dispersion in a water bath at 32 °C–30 °C at a volume ratio of 1:2.5 of PS colloidal solution to ethanol. In addition, particles of various sizes can be prepared by this method to produce tightly arranged monolayer films that can be transferred to a variety of different substrates with great versatility. The demonstrated efficiency of this self-assembly method underscores its significant potential for application in large-scale manufacturing and practical industrialization.

A simple model incorporating foam rheology to quantify foam penetration behaviour in EPB shield tunnelling

Fulfilling the role of a soil conditioner, foam plays a pivotal role in Earth Pressure Balance (EPB) shield tunnelling by enhancing soil properties such as lowering permeability and increasing flowability. This study introduces a macro-model designed to quantify foam penetration behaviour in saturated sand, utilising rheological properties. To validate this model, experiments were conducted to replicate the foam penetration behaviour. Six sand beds characterised by varying particle sizes, along with foam having an expansion ratio of fifteen, were employed for penetration tests under different hydraulic conditions utilising a sand column device. The rheological profile of the foam is described by the power-law model, as also found by rheometer tests, although with different parameters. The flow behaviour of foam within the sand column conforms to the flow equation that governs power-law fluids in porous media. The developed model effectively predicts the foam penetration process under varying hydraulic conditions compared with the experimental results. Furthermore, the fitting results of the experimental data indicate that the flow behaviour index of the foam remains approximately 0.09 across all tests, regardless of the type of sand used. In contrast, the model-derived generalised permeability coefficient strongly correlates with the effective particle size (d10) of the sand bed. Overall, the model effectively quantifies the foam penetration behaviour, accounting for changes in infiltration velocity and pore water pressure, which is essential for understanding the transfer of support pressure in EPB shield tunnelling.

Particle Size Effect on Anaerobic Digestion of Fruit and Vegetable Waste

During the anaerobic digestion (AD) of fruit and vegetable waste (FVW), excessive particle size reduction can lead to the overproduction and inhibition of methanogenic microorganisms. This paper presents an in-depth analysis through experimental assays, modeling, and response surface analysis of the effect of particle size on methane production. A simple model was proposed considering the inhibition of the growth of methanogenic microorganisms and surface-based hydrolysis kinetics. The model parameters were estimated using experimental data from batch systems fed with FVW of varying particle sizes (ranging from 1.8 to 1000 μm). Response surface methodology establishes a statistical model for estimating methane production based on particle size and concentration. Numerical and statistical analyses were conducted using Matlab R2024a and Minitab 24 software. A model with an R2 of 0.89 was obtained, which determined an optimal concentration of 8.2 kg·m−3 and a particle size of 742.3 μm, yielding a methane production of 303.3 m3·kg−1 VS, similar to the experimentally obtained range of 300.95 to 316.7 m3·kg−1 VS.

Influence of carrier gas flow rate and particle size of AISI M2 in the laser-directed energy deposition process

ABSTRACT Additive manufacturing (AM) is a rapid prototyping technology that offers many advantages over conventional manufacturing processes. However, to make the most of the AM advantages, some requirements need to be met, such as the adjustment of process parameters and quality of the feedstock. This work assessed the influence of carrier gas flow rate and particle size of AISI M2 in the laser-directed energy deposition process (L-DED). Different carrier gas flow rates were tested for two powders with particle size of 53–150 µm (larger range) and 20–53 µm (lower range). The variation of carrier gas flow rate and particle size was assessed in single lines and layers. The results show that increasing the carrier gas flow rate provides better powder convergence in the region where there is interaction with the laser beam and faster particle velocity. The lower range tends to have greater efficiency in the deposition of single lines and layers. Regarding geometric characteristics, the aspect ratio did not show a well-defined trend as a function of the carrier gas flow rate and particle size, however, the layer height tends to be greater for the lower range, while the dilution tends to be greater for the larger range.