Homogeneous Elements Research Articles

High hydrogen permeability of Pd-Ru-In membranes prepared by electroless co-deposition

In this work, Pd-Ru-In membranes were prepared by electroless co-deposition and characterized by SEM, XRD, XPS, AES and hydrogen permeation test. The results show that defect-free 5–6 μm thick Pd-Ru-In membrane with homogeneous element distribution was successfully prepared. The composition of the membrane is Pd-Ru0.5at%-In1at% (M1) and Pd-Ru0.5at%-In2at% (M2), respectively. The hydrogen permeability of the membrane M2 reaches 1.32 × 10-8 mol·m−1·s−1·Pa−0.5 at 773 K, which is 1.6 times higher than that of a Pd-Ru0.5at% membrane prepared under the same conditions. The addition of the element In leads to a structural evolution of the membrane: the lattice parameters of the Pd-Ru-In membranes increase. This lattice expansion results in an improvement in the hydrogen permeability. Our study provides a useful reference for the fabrication of Pd-Ru-In ternary membranes with high hydrogen permeability.

Thermal Conductivity Analysis of Polymer‐Derived Nanocomposite via Image‐Based Structure Reconstruction, Computational Homogenization, and Machine Learning

Macroscopic thermal properties of engineered or inherent composites depend substantially on the composite structure and the interface characteristics. While it is acknowledged that unveiling such dependency relation is essential for materials design, the complexity involved in, e.g., microstructure representation and limited data impedes the research progress. Herein, this issue is tackled by machine learning techniques on image‐based microstructure and property data predicted from physics simulations, along with experimental validation. The methodology is demonstrated for the model system ultrahigh‐temperature ceramic nanocomposite. The structure is reconstructed from scanning electron microscope images, and is resolved by a diffuse‐interface representation, which is advantageous in handling complicated structure and interface properties. Subsequently, hierarchical finite element homogenization is carried out to evaluate the effective thermal conductivity. A thorough comparison between the computed results and experimentally measured data, conducted across diverse temperatures and varying interface thermal resistances, reveals a high level of agreement. The observed agreement allows for the inverse estimation of the interface thermal resistance, a parameter typically challenging to ascertain directly through experimental means. Utilizing comprehensive data, a machine learning surrogate model has been meticulously trained to accurately predict the effective thermal conductivity of composite structures with exceptional performance.

Simultaneous enhancement of mechanical and functional properties by heat-treatment in CuAlNi shape memory alloys fabricated by laser powder bed fusion

Laser powder bed fusion (LPBF) is a promising manufacturing method for fabricating Cu-based shape memory alloys (SMAs), but further performance improvement is needed to ensure service stability and broaden the engineering applications. To achieve simultaneous enhancement of mechanical and functional properties of CuAlNi ternary SMAs fabricated via the LPBF process, this study conducts isochronous and isothermal quenching treatments to tailor the microstructure. The heat-treated specimens with a high quenching temperature and long soaking time exhibited high ultimate tensile strength of 696 ± 10 MPa, large ductility of 8.9 ± 0.2%, and excellent recoverable strain under 2% pre-strain with a shape recovery rate of 100%, which were considerably superior than those of as-built specimens (ultimate tensile strength of 612 ± 10 MPa, elongation of 2.6 ± 0.1%, and 1.26% recoverable strain). This is attributed to the element homogenization during heat treatment, release of residual stress, and coordinated martensite network boundary. However, no significant strain platform of martensite reorientation or detwinning was found in the tensile deformation of the as-built and heat-treated samples, due to localized strain concentration in the parent grain. The microstructural evolution under different quenching treatments and the underlying mechanisms for the improvement of mechanical and functional properties are discussed in detail. This work not only reveals the unique functional response of LPBF fabricated Cu-based SMAs, but also provides a simple and effective method to improve their performance.

Electrophoretic deposition for improved trace element homogeneity in silica reference materials

Spatially-resolved analysis requires homogeneous reference materials (RMs) to make reliable quantitative measurements. We previously developed an electrophoretic deposition (EPD) method for fabrication of glassy microanalytical RMs with superior platinum-group element homogeneity **[1], and now include further dopants. For 39 trace elements, we analyzed dopant homogeneity in sintered silica (SiO2) samples consolidated either mechanically by die-pressing (DP) or by EPD. A set of EPD and DP samples was made from each of two nanoparticle feedstocks produced by variations of the Stöber process **[2]. Spatially-resolved dopant distribution was characterized in all samples by laser-ablation inductively-coupled plasma mass spectrometry (LA-ICP-MS). In both sample sets, homogeneity of most trace elements was substantially improved by EPD relative to their DP counterpart.

Modification of microstructure and mechanical properties for twin-wire directed energy deposition-arc fabricated Ti–48Al–2Cr–2Nb alloys via current regulation

Considering the advantages of low density and excellent high-temperature performance, titanium aluminide is identified as an ideal aerospace structural material. In recent years, twin-wire directed energy deposition-arc (TW-DED-arc), which possesses the characteristics of low cost but high deposition efficiency, has continuously attracted worldwide attention. However, obtaining equiaxed grains with small Al variation for titanium aluminide using TW-DED-arc method is still a key concern. In the present research, Ti–48Al–2Cr–2Nb alloy with equiaxed lamellar colonies and less than 1 at.% of Al content was successfully fabricated by regulating deposition current of TW-DED-arc. Also, the effect of deposition current on microstructure and mechanical properties was systematically investigated. The experimental results that focus on top and middle regions of as-fabricated TiAl-4822 alloys, indicate that increasing current favors in generation of equiaxed grains and γ lamellae, which leads to columnar to equiaxed transition and higher γ phase content, respectively. Also, elemental homogeneity can be significantly homogenized. As deposition current increases, tensile strength increases while degree of tensile anisotropy decreases significantly, benefiting from the equiaxed grains with satisfying size. Importantly, microstructure evolution, tensile anisotropy and fracture characteristics of TW-DED-arc fabricated TiAl-4822 alloys are discussed in detail. Generally, these findings provide an effective process method to optimize microstructure and mechanical properties of TW-DED-arc fabricated TiAl-4822 alloys.

Modelling, optimization, and testing of novel cuboidal spherical plate lattice structures

ABSTRACT This study investigates the mechanical behavior of a novel set of Cuboidal Spherical Plate Lattice (CSPL) materials. The procedure of constrained-domain topology optimization is implemented with the aim of enhancing stiffness. The micromechanical finite element homogenization approach is used to evaluate the effective elastic-plastic properties of the CSPLs and their topologically optimized counterparts, TOCSPLs (Topologically Optimized Cuboidal Spherical Plate Lattices). The TOCSPLs demonstrate higher uniaxial, shear, and bulk moduli compared to the CSPLs, with an increase of 31%, 14%, and 36% respectively. Moreover, there is an increase in the yield strengths under uniaxial, shear, and hydrostatic loading conditions, with enhancements of 103%, 55%, and 62%, respectively. The topologies are additively manufactured through Fused Deposition Modeling (FDM) out of ABS thermoplastic material. The quasi-static compression experiments demonstrate the superiority of TOCSPL 111+100 over the other topologies in terms of uniaxial modulus. The suffix 111+100 denotes the crystallographic planar orientations in which the solid plate-like disks were formed within a cubic system. The topologies proposed herein outperform certain types of Triply Periodic Minimal Surface, honeycomb, truss-, and plate-based lattice materials. The proposed topologies offer a compelling justification for their utilization in applications that require load-bearing and impact absorption capabilities.

Effect of annealing heat treatment on the microstructure and mechanical properties of laser directed energy deposited CrMnFeCoNi high entropy alloy

In this study, a thin-wall build of CrMnFeCoNi high entropy alloy (HEA) was fabricated by laser directed energy deposition (LDED) process. The effect of high-temperature annealing heat treatment at 1000 °C on the microstructure and mechanical properties of LDEDed CrMnFeCoNi HEA was investigated. The results showed that the as-deposited microstructure of CrMnFeCoNi HEA features long-strip and coarse columnar grains with plenty of tiny pores and exhibits a homogeneous elements distribution. The microstructure shows good stability when the annealing time is within 4 h. With the further increase of annealing time, recrystallized equiaxed grains with interior twins form at the original coarse columnar grain boundaries. The dislocations distinctly pile up around recrystallized equiaxed grains accompanied by interior twins and show a cluster distribution. Precipitates including Cr-rich σ phases and Cr2MnO4 oxides form and distribute uniformly in annealed microstructure. Twin boundaries across these precipitates are distorted and correspondingly form a local high-interface-energy region around these precipitates where is prone to crack. In this study, the recommended annealing time is within 4 h to avoid the crack formation and associated dramatical degeneration of tensile properties. Our results are of great importance in understanding the microstructure evolution, as well as the effect of high-temperature annealing heat treatment, in the laser directed energy deposition of CrMnFeCoNi HEA.

Enhanced mechanical properties of Fe-based hardfacing alloy with Al additions fabricated by laser cladding

Laser cladding was used to prepare an Al-containing Fe-Cr-C hardfacing alloy layer on a 316 L stainless steel substrate. The effects of Al addition on the elemental distribution, physical phase composition, and properties of the cladding layers were systematically investigated using experimental observations, finite-element simulation, and performance tests. Aluminum promoted the flow and elemental homogenization of the molten pool, leading to a more dispersed carbide distribution. Aluminum increased the thermal conductivity of the material and accelerated the cooling rate of the melt pool, which suppressed the eutectic reaction L → γ + (Fe,Cr)7C3 and promoted the peritectic reaction L + (Fe,Cr)7C3 → γ + (Fe,Cr)3C. Consequently, the (Fe,Cr)7C3 content decreased, whereas that of (Fe,Cr)3C increased. Aluminum improved the stability of ferrite and promoted its formation. The Al addition resulted in fine-grain, load-transfer, dislocation, and Orowan strengthening, thereby improving the hardness and wear resistance of the Fe-Cr-C hardfacing alloys. Dislocation and Orowan strengthening were the largest contributors, followed by fine-grain and load transfer strengthening.

Phase, microstructure, and properties of fine-grained Mo-W-Cu alloys prepared by mechanical alloying and large electric current sintering

BackgroundThe novel Mo-W-Cu alloy exhibits relatively low density and good high-temperature resistance. However, due to the poor sintering ability of the mixed powders, enhancing the densification and properties of the alloys remains a challenge. MethodsWe prepared fine-grained Mo-W-Cu alloys by a combination of mechanical alloying (MA) and large electric current sintering (LCS) at relatively low temperatures and short durations and then conducted a comprehensive systematic inquiry into the densification behavior, phase, microstructure, and properties of the resulting alloys. Significant findingsIt was revealed that the MA process did not affect the phase-type of the alloy but significantly altered its densification, microstructure, and properties. In addition to the pre-existing Mo, W, and Cu phases, XRD and TEM results unveiled three new phases formed in the alloys, namely Cu0.4W0.6 intermetallic compound, Mo-W solid solution, and Mo-Cu solid solution, none of which are present in an equilibrium state. The MA process is pivotal in refining powder particles, fostering elemental homogeneity, thereby enhancing the densification of Mo-W-Cu alloys. In comparison, the microstructure of the Mo-W-Cu alloys prepared with the MA process becomes denser and more homogeneous, accompanied by a marked improvement in both densification and properties. Notably, Mo-W-Cu alloys prepared with a ball milling time of 40 h exhibit optimal properties, achieving an approximate relative density of 98 %.

Low-Temperature controlled synthesis of nanocast mixed metal oxide spinels for enhanced OER activity

The controlled cation substitution is an effective strategy for optimizing the density of states and enhancing the electrocatalytic activity of transition metal oxide catalysts for water splitting. However, achieving tailored mesoporosity while maintaining elemental homogeneity and phase purity remains a significant challenge, especially when aiming for complex multi-metal oxides. In this study, we utilized a one-step impregnation nanocasting method for synthesizing mesoporous Mn-, Fe-, and Ni-substituted cobalt spinel oxide (Mn0.1Fe0.1Ni0.3Co2.5O4, MFNCO) and demonstrate the benefits of low-temperature calcination within a semi-sealed container at 150–200 °C. The comprehensive discussion of calcination temperature effects on porosity, particle size, surface chemistry and catalytic performance for the alkaline oxygen evolution reaction (OER) highlights the importance of humidity, which was modulated by a pre-drying step. The catalyst calcined at 170 °C exhibited the lowest overpotential (335 mV at 10 mA cm−2), highest current density (433 mA cm−2 at 1.7 V vs. RHE, reversible hydrogen electrode) and further displayed excellent stability over 22 h (at 10 mA cm−2). Furthermore, we successfully adapted this method to utilize cheap, commercially available silica gel as a hard template, yielding comparable OER performance. Our results represent a significant progress in the cost-efficient large-scale preparation of complex multi-metal oxides for catalytic applications.

Numerical and experimental characterization of high-temperature heat transfer in a ceramic foam with dual-scale porosity

In this paper, we compare numerical predictions and measurements of the high-temperature apparent thermal conductivity of an insulating alumina foam with dual-scale porosity: the foam contains ▪-sized cells and also ▪-sized pores in the highly scattering foam skeleton. Simulations of the apparent thermal conductivity are performed on tomography-reconstructed foams, with a three-part multi-scale approach to account for the dual-scale porosity. The effective phonon thermal conductivity of the foam is first computed using a finite element homogenization technique. The spectral and temperature-dependent effective radiative properties of the foam are next computed through an improved Monte Carlo ray-tracing approach, with foam skeleton scattering modeled using a physical-optics-based approach. The apparent thermal conductivity of the foam is then simulated by resolving the coupled conductive-radiative heat transfer through a semi-infinite homogeneous slab. The simulated high-temperature apparent thermal conductivity is found to be in good agreement with experimental data up to ▪, obtained by parallel hot wire measurements coupled with an improved quadrupolar model for low-density insulating materials. The large influence of scattering at the cell-skeleton interface is shown through a numerical parametric study. It is also shown that the Rosseland conductivity calculated directly from the simulated spectral radiative properties provides a good estimation of radiative heat transfer for optical thicknesses exceeding 30.

Three-dimensional dynamic homogenous modeling: The biomechanical influences of leg tissue stiffness on pressure performance of compression biomedical therapeutic textiles.

Patient compliance and therapeutic precision of compression textiles (CTs) are frequently limited by the inaccurate pressure distributions along biological bodies in physical-based compression therapy. Therefore, the biomechanical influences of physiological tissue material characteristics of lower extremities on compression generations of CTs need to be explored systematically to improve pressure management efficacy. In this study, we developed three-dimensional (3D) homogenous finite element (FE) CT-leg systems to qualitatively compare the pressure diversities along lower limbs with different biomaterial tissue properties under each external compression level. Simultaneously, through the obtained leg circumferential displacement, a contact analysis model was applied to quantitatively explore the impact mechanisms of soft leg indentations on the pressure performance of CTs. Based on the experimental validation study, the proposed FE systems could be efficiently utilized for compression performance prediction (error ratio: 7.45%). Through the biomechanical simulation and theoretical calculations, the tissue stiffness characteristics of applied bodies showed significant correlations (p < 0.05) with the body circumferential displacements but no correlations (p > 0.05) with pressure delivery differences of CTs. This study facilitates the pressure fit design principle and leg mannequin material selection guidance for the development and experimental assessment of CTs. It also provides effective simulation methods for pressure prediction and property parametric optimization of compression materials.

Importance of the drying method in crystalline phase formation and metallic elements distribution of glycine complexes

In this work, for the first time, the multi mineral complexes composed of three and four elements FeII, MnII, CuII & ZnII and CuII, MnII & ZnII, respectively) bounded to glycine have been produced to be used as a feed additive for farm animals. To the best of our knowledge, all products were synthesized for the first time as novel compounds containing several transition metals. The impact of the drying procedure on the microstructure, chemical composition and crystalline phase was evaluated using different analytical techniques. The trace element concentration distributions and homogeneity were also studied. A single crystal of dehydrated metal glycinate compound was synthesized from drying of glycine and a multi-metal sulphate solution under room temperature. On the other hand, both spray drying and spray granulation of this similar solution results to the formation of crystalline powders. The crystalline powders obtained present a typical metal-sulphate-glycinate dehydrated crystalline form and a homogeneous distribution of the metals within the product particles. The developed products have been compared and their differences have been underlined.

Thermodynamic equilibrium theory-guided design and synthesis of Mg-doped LiFe0.4Mn0.6PO4/C cathode for lithium-ion batteries

Mn-rich LiFe1−xMnxPO4 (x > 0.5), which combines the high operation voltage of LiMnPO4 with excellent rate performance of LiFePO4, is hindered by its sluggish kinetic properties. Herein, thermodynamic equilibrium analysis of Mn2+-Fe2+-Mg2+-C2O42−–H2O system is used to guide the design and preparation of in-situ Mg-doped (Fe0.4Mn0.6)1−xMgxC2O4 intermediate, which is then employed as an innovative precursor to synthesize high-performance Mg-doped LiFe0.4Mn0.6PO4. It indicates that the metal ions with a high precipitation efficiency and the stoichiometric precursors with uniform element distribution can be achieved under the optimized thermodynamic conditions. Meanwhile, accelerated Li+ diffusivity and reduced charge transfer resistance originating from Mg doping are verified by various kinetic characterizations. Benefiting from the contributions of inherited homogeneous element distribution, small particle size, uniform carbon layer coating, enhanced Li+ migration ability and structural stability induced by Mg doping, the Li(Fe0.4Mn0.6)0.97Mg0.03PO4/C exhibits splendid electrochemical performance.

Creep strength and toughness synergistic strengthening mechanism investigation of the Inconel625/ BNi-2 brazed joint

Creep strength and toughness synergistic strengthening mechanism of Inconel625/BNi-2 brazed joint is investigated based on the post-brazing solid solution heat treatment (PSSHT). The heat treatment temperature of 1150 °C is adopted. The results show that borides in brazed joint are eliminated and broken gradually with the increasing of PSSHT time, and the elements are more uniformly distributed. The brazed joint with PSSHT time of 3 h has the longest creep life and the highest toughness, followed by those with PSSHT time of 6 h and 0 h, respectively. Elements homogenization can promote the creep strength and toughness of the brazed joint. While more PSSHT time will increase the grain size of brazed joint, and thus it degenerates the creep strength and toughness of the brazed joint. Although the borides can increase the risk of joint crack failure, the proper amount of punctate borides distribute along the grain boundary or in the interior of the grain can serve as the pinning points to slow down the dislocation movement of grain boundary, so as to improve the creep strength of brazed joint. Therefore, creep strength and toughness strengthening of the brazed joint caused by PSSHT is the synergistic action of element homogenization, borides distribution and grain size. The solid solution heat treatment time of 3 h at 1150 °C is a recommended heat treatment procedure.

A Universal Approach for Controllable Synthesis of Homogeneously Alloyed PtM Nanoflowers toward Enhanced Methanol Oxidation.

Platinum (Pt)-based alloys have received considerable attention due to their compositional variability and unique electrochemical properties. However, homogeneous element distribution at the nanoscale, which is beneficial to various electrocatalytic reactions, is still a great challenge. Herein, a universal approach is proposed to synthesize homogeneously alloyed and size-tunable Pt-based nanoflowers utilizing high gravity technology. Owing to the significant intensification of micro-mixing and mass transfer in unique high gravity shearing surroundings, five typical binary/ternary Pt-based nanoflowers are instantaneously achieved at room temperature. As a proof-of-concept, as-synthesized Platinum-Silvernanoflowers (PtAg NFs) demonstrate excellent catalytic performance and anti-CO poisoning ability for anodic methanol oxidation reaction with high mass activity of 1830mA mgPt -1, 3.5 and 3.2 times higher than those of conventional beaker products and commercial Pt/C, respectively. The experiment in combination with theory calculations suggest that the enhanced performance is due to additional electronic transmission and optimized d-band center of Pt caused by high alloying degree.

Scientific and methodological aspects of the choice of discount rate in the evaluation of investment projects

The article makes a scientific research of existing methodological approaches that have been formed in management. The article also analyses the causes of the collapse of investment projects, in particular in the construction industry, which threaten the stability of the functioning of national economies. All these researches give an opportunity to find the real causes of ineffective implementation of projects. The author offers a methodological approach to the formation of a holistic organizational structure of the socio–economic system, which has the goal to solve the problem of crisis phenomens in management. The author`s approach gives an opportunity to form organizational structure in an organic combination with the economic processes that take place in it and provide the qualitative formation of the organizational structure, which makes it possible to make control over each of its economic elements and ensure an absolutely effective management.&#x0D; Based on a systemic approach, the author considers the organizational structure as a dynamic system that consists from economic elements which necessary for the effective implementation of the purpose of the created structure. This approach to considering the organizational structure is different from the traditional one, in which the structure of the organization is a static system, the elements of which are only labor resources with defined functions.&#x0D; Consideration of the organizational structure as an integral system that consists from selected homogeneous economic elements which structure on the basis of normative model in which the management and managed subsystems are allocated, and also there are the main, auxiliary and service production in the managed subsystem gives an opportunity to form a normative model of the organizational structure which provides qualitative structuring of all its elements.

Genome-wide expansion and reorganization during grass evolution: from 30 Mb chromosomes in rice and Brachypodium to 550 Mb in Avena

BackgroundThe BOP (Bambusoideae, Oryzoideae, and Pooideae) clade of the Poaceae has a common ancestor, with similarities to the genomes of rice, Oryza sativa (2n = 24; genome size 389 Mb) and Brachypodium, Brachypodium distachyon (2n = 10; 271 Mb). We exploit chromosome-scale genome assemblies to show the nature of genomic expansion, structural variation, and chromosomal rearrangements from rice and Brachypodium, to diploids in the tribe Aveneae (e.g., Avena longiglumis, 2n = 2x = 14; 3,961 Mb assembled to 3,850 Mb in chromosomes).ResultsMost of the Avena chromosome arms show relatively uniform expansion over the 10-fold to 15-fold genome-size increase. Apart from non-coding sequence diversification and accumulation around the centromeres, blocks of genes are not interspersed with blocks of repeats, even in subterminal regions. As in the tribe Triticeae, blocks of conserved synteny are seen between the analyzed species with chromosome fusion, fission, and nesting (insertion) events showing deep evolutionary conservation of chromosome structure during genomic expansion. Unexpectedly, the terminal gene-rich chromosomal segments (representing about 50 Mb) show translocations between chromosomes during speciation, with homogenization of genome-specific repetitive elements within the tribe Aveneae. Newly-formed intergenomic translocations of similar extent are found in the hexaploid A. sativa.ConclusionsThe study provides insight into evolutionary mechanisms and speciation in the BOP clade, which is valuable for measurement of biodiversity, development of a clade-wide pangenome, and exploitation of genomic diversity through breeding programs in Poaceae.

Improved hydrogen ab-/desorption performance of Ti–Cr based alloys via dual-effect of oxide reduction and element substitution by minor Al additive

Hysteresis of hydrogen storage alloys essentially hinders the compressibility and operation efficiency of metal hydride hydrogen compressors. In this work, minor Al additive was added into Ti–Cr based hydrogen compression alloys through induction levitation melting, and the apparent hysteresis was successfully ameliorated. The XRD and SEM results indicate homogeneous element distribution of a main C14 Laves phase of Ti0.96Zr0.06Cr1.0Mn0.6Fe0.4Alx (x = 0, 0.01, 0.02, 0.04, 0.08) alloys, and vanishing of a minor oxide phase in case the Al additive is introduced. As Al stoichiometry increases in the alloys, the hydrogenation plateau decreases obviously but the dehydrogenation plateau hardly changes. Meanwhile, the hydrogen capacity ascends initially but descends slightly. Additionally, no severe performance degradation is induced. The mechanism for overall performance improvement can be concluded as dual functions of Al additive: one can be oxide reduction of other elements during melting determined by XPS and ICP, and the other can be partial Al substitution for the B-side elements, leading to relieved deformation energy surrounding the vacant Al-containing interstitials. As to hydrogenation kinetics, the alloys exhibit accelerated hydrogenation rate with increased Al stoichiometry due to decreased activation energy and hydrogenation plateau. Furthermore, the first-principles calculation results indicate random Al substitution for the B-side atoms, and anisotropic expansion of the unit cell can be attributed to Al substitution at 6h sites. This work reveals a simple and effective way to enhance hydrogen storage performance of Ti–Cr based alloys.

On the Hybrid Modelling of Rigid Sonic Crystal Embedded in Plenum Chamber at Low Frequencies Using the Effective Medium Approach and Finite Element Method

This study explores the application of homogenization schemes in modelling acoustic wave propagation in a finite array of circular scatterers embedded into a 2D cavity. The cavity is integrated into the 2D waveguide attached to the cavity inlet and outlet. Square-lattice sonic crystal (SC), composed of rigid and radially symmetric circular cylinders, is used to represent the finite array in this study. The model is aimed at informing the novel designs of plenum windows with superior soundproofing performance. The sound transmission performance is analysed with hybrid numerical simulation using the Finite Element Method (FEM) and homogenization scheme. A theoretical homogenization method based on the Effective Medium Approach (EMA) is reviewed and implemented on the modelling of the SC array inside the cavity at low frequencies and then implemented in FEM. Comparison of the transmission loss (TL) reveals a high degree of matching between settings with and without homogenization at low-frequency range. It is observed that performance of the hybrid model maintains a high degree of matching provided the cavity modes are dominated by a single characteristic scale in the low frequency. This includes the case of a narrow plenum chamber with only a single cylinder placed inside the cavity with a width of one lattice constant. This homogenization method is proven to be more computationally efficient in FEM compared to the modelling of exact geometry of the problem.