Mismatch Of Coefficients Research Articles

Integrating mesh adaptivity and digital image correlation for full-field displacement evaluation of cracked bodies

The study of crack initiation and propagation is primary to the fracture mechanics domain and essential for developing new materials. Such a study is relevant for refractory ceramics adopted as thermal insulators in high-temperature industrial applications. In particular, mechanical and thermal tests are essential in measuring properties and contribute to the material selection process. Such tests can be assisted using non-intrusive measurement techniques, in particular, by the Digital Image Correlation (DIC) technique, which enables to obtain full-field information concerning the displacement and strain fields in a loaded configuration. Identifying the crack location is a challenge for DIC techniques and requires special treatment of the correlation process to get reasonable resolution around the crack. Global DIC approaches can benefit from mesh refinement strategies to improve the identification of the displacement field and, consequently, the crack's location. In this context, the present article introduces mesh refinement strategies to improve the image correlation, allowing to identify the crack location in cracked specimens better. The adaptivity approach is developed using Correli framework and the Application Programming Interface (API) of the GMsh software, which has several features to control the element mesh size distribution, particularly by controlling mesh size parameters using strain and local gray-level residue. Herein, the mesh strategies are applied in a model composite system submitted to temperature variation. The composite consists of a brass inclusion surrounded by an alumina matrix. The thermal expansion coefficient mismatch between the phases leads to a radial crack pattern when the material is heated. The evaluation of the mesh refinement algorithm is established in terms of reducing global gray-level residual in the correlation procedure, and the enhanced definition of the crack location. The present article contributes to the DIC processing, getting more information on specific regions based on strain and gray level residual information, and also furnishes information to verify computational fracture mechanics tools.

Dynamic strain sensing using Doppler-shift-immune phase-sensitive OFDR with ultra-weak reflection array and frequency-tracking

In distributed fiber-optic sensing based on optical frequency domain reflectometry (OFDR), Doppler frequency shifts due to the changes of disturbances during one sweep period introduce demodulation errors that accumulate along both the distance and time, impairing the sensing performance. Here, we report distributed dynamic strain sensing using Doppler-shift-immune phase-sensitive OFDR based on frequency-tracking and spectrum-zooming with an ultra-weak reflection array. A theoretical study has been carried out with the introduction of the mismatch coefficient, unveiling quantitatively the impact of the Doppler shift. Following a numerical analysis of the proposed method, a retained precision has been experimentally verified regardless of the position mismatch due to the Doppler effect. Doppler-shift-immune sensing for dynamic strains covering continuous spatial resolution over a distance of 1000 m with a 2.5 cm sensing spatial resolution has been demonstrated, verifying the high fidelity promised by the proposed method.

Solving the puzzle of higher photoluminescence yield at the edges of MoS2 monolayers grown by chemical vapor deposition

Higher photoluminescence yield from the boundaries as compared to the interiors in monolayer (1L) islands of transition metal dichalcogenides grown by chemical vapor deposition (CVD) has been frequently documented in the literature. However, the detailed understanding of this phenomenon is still lacking. Here, we investigate the effect observed in CVD grown 1L-MoS2 islands on c-sapphire substrates. The study reveals a blue shift of the A-excitonic feature from the interiors to the edges of the monolayers, suggesting the release of the tensile strain, which is resulting in the interiors due to lattice and/or thermal expansion coefficient mismatch between the layer and the substrate, toward the boundaries. The degree of valley polarization is also found to increase at the edges. However, when the as-grown monolayers are transferred on a SiO2 surface, the intensity, position, and valley polarization of the A-excitonic peak do not show any inhomogeneity over the surface. The study attributes the decrease in PL intensity and the valley polarization in the interiors as compared to the edges of these as-grown islands to the reduction of the energy gap between the Γ- and K-valley valence band maxima with the increase in the tensile strain in the layer. First principles density functional theory based calculations for the geometry optimization are performed on a 1L-MoS2 flake residing on a (0001) sapphire surface, which indeed shows the relaxation of tensile strain toward the edges.

Self‐Assembled Composite Cathodes with TEC Gradient for Proton‐Conducting Solid Oxide Fuel Cells

AbstractOne of the key challenges for high‐performance proton‐conducting solid oxide fuel cells (H‐SOFCs) is the mismatch in thermal expansion coefficients (TEC) between the cathode and electrolyte. While incorporating negative thermal expansion (NTE) materials can mitigate this issue, mechanical mixing often weakens cathode strength. To address this, a TEC gradient cathode is proposed and successfully implemented by co‐sintering PrBa(Co0.7Fe0.3)2O5‐δ(PBCF) with Y2W3O12 (YWO) in this work. In this work, Ba atoms at the A‐site of PBCF migrated from the lattice, generating A‐site defects. The resulting BaWO4 and Y10W8O21 phases, which have low TEC, are uniformly distributed between PBCF and YWO, forming a TEC gradient composite cathode. In addition, the transition phase captures the A‐site element Ba in the electrolyte layer, optimizing the electrolyte‐cathode interface. The composite cathode exhibits a reduced TEC, closely matching that of the electrolyte, significantly enhancing interface bonding, thereby providing a lower ohmic resistance of 0.051 Ω cm2 and a higher power density of 1.88 W cm−2 at 700 °C. Remarkably, thermal cycling tests conducted under temperature switching conditions demonstrate the composite cathode's long‐term thermal and chemical stability.

Continuously tunable negative pressure for engineering high-symmetry nanocrystalline phases

In this work, the phenomenon of strain induced by a mismatch in thermal expansion coefficients between a thin film and its substrate is harnessed in a new context, replacing the canonical planar support with a three-dimensional (3-D), nanoconfining scaffold in which we embed a material of interest. In this manner, we demonstrate a general approach to exert a continuously tunable, triaxial, tensile strain, defying the Poisson ratio of the embedded material and achieving the exotic condition of "negative pressure." This approach is hypothetically generalizable to materials of low modulus and high thermal expansion coefficient, and we use it here to achieve negative pressure in perovskite-phase CsPbI3 embedded within the cylindrical pores of anodic aluminum oxide membranes. Through controlled thermal hysteresis, the perovskite crystal structure can be continuously tuned toward higher symmetry when confined in a scaffold with pore size <40 nm, in contrast with the symmetry-reducing action of any other mechanical perturbation. We use this effect to control the octahedral rotation angle that is critical to the remarkable photovoltaic attributes of halide perovskites. Under hundreds of megapascals of apparent negative pressure, the bandgap tunability is observed to follow the same quantitative trend observed for hydrostatic positive pressure, exploring the negative pressure region and demonstrating the relative dominance of bond stretching effects over average octahedral rotation angle on electronic structure. This study reveals and quantifies the structural and electronic consequences of 3D tensile strain present by design and provides a framework for understanding adventitious strain present in all nanocomposite materials.

The effects of in-situ SiAlON on the properties and fracture behavior of alumina-based castables: Based on microcrack toughening mechanism

This study investigates the effect of adding Si powder on the microstructure and fracture behavior of in-situ SiAlON bonded alumina-based castables and clarifies the toughness improvement mechanism. The in-situ SiAlON bonded alumina-based castables were obtained using a nitriding reaction method with Si powder as the precursor. The fracture behavior of the specimens was characterised using the wedge-splitting test (WST) and digital image correlation technique (DIC). It was found that introducing in-situ SiAlON bonding phases can significantly improve the fracture behavior and toughness. The toughness parameter (GF/σNT) increased from 18.9 μm to 38.6 μm as the addition of Si powder increased from 0 wt% to 6 wt%. The primary toughness mechanism of the castables is microcrack toughening. The formation of microcracks is the consequence of a mismatch in the thermal expansion coefficients (CTE) of the corundum and in-situ SiAlON phases.

Achieving enhanced strength-ductility synergy in Mg-6Zn-1Mn alloy by introducing deformable Ti particles

The Mg-based composites have been considered as an efficacious method to enhance the strength of Mg matrix. How to concurrently augment the strength and ductility of the Mg matrix composites remains a pivotal concern. In this work, Mg-6Zn-1Mn (ZM61) composites, reinforced with varying contents of deformable Ti particles, were successfully manufactured employing a method of semi-solid stirring coupled with ultrasonic treatment, subsequently followed by hot extrusion. The outcomes demonstrated marked enhancement in strength and ductility of composites. The interfacial reaction between Ti and Mg matrix minimized the precipitation of MgZn2 and α-Mn in the matrix. Ti particles boosted the dynamic recrystallization (DRX) behavior effectively. The TEM characterizations revealed that MgZn2 nucleated on the Ti particle and Mn diffusion layer was formed in the Ti particle. The 2Ti/ZM61 composite achieved superior comprehensive mechanical properties, marked by the YS of 288 MPa, the UTS of 383 MPa, and the elongation to 22.1 %. The augmented strength was primarily owning to the grain boundary strengthening and the mismatch coefficient of thermal expansion (CTE) between Ti and Mg. The synergistic deformation of Ti particles was the main reason of improving the ductility.

Robust deadbeat predictive current control for unipolar sinusoidal excited SRM with multi-parameter mismatch compensation

In the control of unipolar sinusoidal excited switched reluctance motors (SRMs), deadbeat predictive current controllers (DPCCs) have gained attention for their enhanced dynamic performance. However, periodic disturbances caused by mismatches between the predictive model’s nominal and actual system parameters degrade the control performance of SRMs. To address this issue, a robust DPCC with multi-parameter compensation is proposed to improve dq0-axes current control performance. By analyzing the impact of parameter mismatches, a Kalman filter (KF) is developed to compensate for inductance coefficient mismatches, mitigating periodic disturbances. Additionally, a disturbance estimator with measurement noise suppression is integrated into the DPCC for both state and disturbance estimation to handle residual uncertainties, including winding resistance mismatches, magnetic saturation, and unmodeled dynamics. Compared simulation and experimental results validate the effectiveness of the proposed robust DPCC.

Enhancing sapphire/Kovar alloy brazed joint through combined effect of TiB whisker reinforcement and surface micro-nano structures

The brazed joining between Kovar alloy and sapphire was successfully achieved by using TiB whisker reinforcement and applying the surface micro-nano structure. We systematically studied the composition and mechanical properties of Kovar/Sapphire joint. The typical interfacial structure of the joint brazed at 825 °C for 10 min was determined as Sapphire/ γ-TiO/ Ti3(Cu,Al)3O/ Ag(s,s) + Cu(s,s) + TiB/ Ti2Cu + TiFe2 + TiNi3/ Kovar alloy. The addition of B forms tiny TiB whisker reinforcement phase in situ, which refines the interface structure. The presence of micro-nano structures improves the interface products on the sapphire side: reducing the generation of Ti3(Cu,Al)3O and replacing it with γ-TiO. This makes the phase transition on the sapphire side smoother and reduces thermal expansion coefficient mismatch, thereby enhancing joint strength. Under suitable brazing parameters, the maximum shear strength of the joint is 137 MPa. This study provides new insights for optimizing and improving connections between sapphire ceramics and metals, with potential applications in more ceramic/metal joining.

Improved SOFC performance by enhancing cathode/electrolyte bonding and grain refinement of cathode with thermal expansion offset

The thermal expansion coefficient (TEC) mismatch between the cathode and electrolyte presents significant challenge to the thermo-mechanical stability of commercial solid oxide fuel cells (SOFCs). Here a thermal expansion offset composite cathode designated as Ba0.5Sr0.5FeO3-δ (BSF)-xNdMnO3-δ (NM) (x = 0–40 wt%) is developed to address this issue. For the first time, the phase boundary between heterogeneous oxides and the grain size of composite cathode are quantitatively studied with the electron backscatter diffraction (EBSD) technology. For x = 20 wt%, the TEC of cathode decreases by 41 % while the peeling strength of cathode/electrolyte interface increases by 87 %. The highest peak power density (PPD) is achieved for BSF-20NM cathode (1266 mW cm−2 at 650 °C), which is 81 % higher than that for BSF one. Meanwhile, markedly enhanced long-term and thermal cycling stability is obtained. The comprehensive results suggest that both the increased TPB length by enhanced cathode/electrolyte bonding and grain refinement of composite cathode should be responsible for the markedly improved performance and stability.

The effect of in situ-synthesized Y2SiO5 on the thermal shock resistance of Y2O3 ceramic materials

Y2O3 ceramics are increasingly recognized for their excellent vacuum stability and high-temperature chemical stability in the field of functional materials research. However, their poor thermal shock resistance renders them susceptible to spalling and damage during use, thus restricting further applications. To address this issue, the low thermal expansion coefficients of Y2SiO5 materials were leveraged. Through an in situ reaction between SiO2 and Y2O3, a Y2SiO5 phase was generated that induced a thermal expansion mismatch with Y2O3, thereby enhancing the thermal shock resistance of the ceramic. Using Y2O3 fine powder as the primary material, silica sol and nano-SiO2 were selected as reactive silicon sources to prepare Y2O3–Y2SiO5 composite ceramics at 1750 °C. The impact of the different silicon sources and Y2SiO5 phase content on the microstructure, mechanical, and thermal properties of the composite ceramics was studied. The results demonstrated that the in situ formation of Y2SiO5 significantly improved the thermal shock resistance of the composite ceramic. Specifically, increasing the SiO2 content led to a gradual rise in the volume fraction of Y2SiO5 formed between Y2O3 grains, thereby increasing the residual flexural strength and enhancing the hardness and elastic modulus. The low thermal expansion coefficient of Y2SiO5 reduced the overall thermal expansion coefficient of the composite material, thereby improving the thermal shock resistance. Moreover, the thermal expansion coefficient mismatch between the Y2O3 and Y2SiO5 phases induced numerous microcracks within the material, providing thermal stress relief within the microcracks and markedly improving the resistance of the ceramic to thermal shock.

Experimental and numerical study on the material constraint effect in pipeline steel welded joint

An in-depth analysis of the material constraint effect is crucial for accurately determining the constitutive relationship and safety evaluation of pipeline steel welded joint. Therefore, this work combines experiments and finite element simulations to study the constraint effect. Through the welding method, the weld specimens with different sizes and strength mismatch conditions are prepared. The microstructure and hardness distribution of the specimens are measured, and tensile tests based on the digital image correlation (DIC) technology are conducted. Finite element models of the weld specimens with different sizes and material parameters are established, followed by tensile simulations and detailed analysis. Based on the experiments and numerical simulations, the tensile strain responses, stress-strain curves, and material parameters of different weld specimens are obtained. The results show that the smaller the weld width, the more significant the effect of the material constraint. For undermatched welds, the calculated stress of the weld metal (WM) increases with the decrease of the weld width. Additionally, the calculated stress of WM also increases with the decrease of the mismatch coefficient, where the mismatch coefficient refers to the ratio of the yield strength of WM to that of the base metal (BM). Conversely, for overmatched welds, the calculated stress of WM decreases with the decrease of the weld width. The material constraint effect is also influenced by the mismatch condition of the weld. An increase in the mismatch coefficient reduces the effective range of the stress-strain curve obtainable for WM. To analyze the effect of the mismatch condition, it is necessary to comprehensively compare the yield strength and strain hardening capacity of each material. The width-to-thickness ratio of the weld specimen has little effect on the calculated stress of WM. The finite element simulation method can be used to correct the stress-strain curves obtained from the tests to achieve accurate constitutive relationships.

Mechanical property analysis and optimization of nano-hydroxyapatite coated carbon fiber reinforced hydroxyapatite composites

Carbon fiber (CF) is one of ideal reinforcements to hydroxyapatite (HA) owing to its unique structure, excellent biocompatibility and high mechanical properties. However, the mechanical property of CF reinforced HA (CF/HA) composites cannot be effectively improved due to the mismatch in surface properties and thermal expansion coefficients between CF and HA. In order to solve the problems, nano-hydroxyapatite (nHA) coating with different thickness was fabricated on the CF surface. The effect of the coating thickness on mechanical property of nHA-coated CF/HA composites was studied by finite element analysis. The CF with proper nHA coating thickness was subsequently used to reinforce HA. The compressive strength of nHA-coated CF/HA composites was approximately 97.3 % and 164.6 % higher than those of the uncoated CF/HA composites and pure HA ceramics, respectively. The interface properties and crack propagation were analyzed by cohesive element in the finite element analysis. The toughening mechanism of the composites included interfacial debonding, crack deflection, crack branching, and crack bridging. The mechanical properties of nHA-coated CF/HA composites were enhanced due to the strong interfacial bonding strength and reducing cracking in HA matrix. The prepared nHA-coated CF/HA composites satisfy the requirement of the mechanical properties of human load-bearing bone. It can be used to prepare cages, plates, screws, pins and other compact bone substitute parts in bone grafting. The study provided a method for construction of nHA-coated CF/HA composites with the designed properties by adjusting the nHA coating on the fiber and can be used to design other fibers reinforced ceramic matrix composites.

High-performance GaN ultraviolet polarization-sensitive photodetector based on ferroelectric polarization LiNbO3

High responsivity ultraviolet (UV) photodetectors (PDs) are essential for abundant civilian and military applications. Gallium nitride (GaN) has emerged as an ideal material for UV PD fabrication due to its favorable properties. However, the quality of GaN epitaxial layers significantly impacts device performance and reliability. Sapphire-based GaN epitaxial growth technology enables the realization of high-quality GaN epitaxial layers, making it the preferred choice for GaN substrates. Nonetheless, the thermal expansion coefficient mismatch between sapphire and GaN can lead to crystal mismatch and stress accumulation at high temperatures, affecting device performance and reliability. In contrast, lithium niobate (LiNbO3) exhibits similar coefficients of thermal expansion to GaN, mitigating crystal mismatch and stress accumulation issues. Here, we report the realization of a GaN UV PD by laminating GaN membrane onto ferroelectric LiNbO3 through selective electrochemical etching of the sapphire-based GaN epitaxial film. The LiNbO3-based GaN PD achieves a specific high on/off ratio of 107. At a 5 V bias voltage, the device exhibits a high peak responsivity of 1.712 × 103 A/W under 325 nm laser illumination. Furthermore, the device demonstrates excellent performance for polarization light detection, with a polarization ratio of approximately 54.95. Exploiting the local ferroelectric polarization of x-cut LiNbO3, the photogenerated electron–hole pairs in GaN are efficiently separated by the electrostatic field from the polarization of ferroelectric LiNbO3, resulting in enhanced light-to-electric conversion efficiency. Our work presents a method for fabricating high responsivity GaN-based UV PD, showcasing the potential of integrating ferroelectric LiNbO3 to enhance device performance.

Experimental demonstration of quantum encryption in phase space with displacement operator in coherent optical communications

We provide experimental validation of quantum encryption in phase space using displacement operators in coherent states (DOCS) in a conventional coherent optical communication system. The proposed encryption technique is based on displacing the information symbols in the phase space using random phases and amplitudes to achieve encryption randomly and provide security at the physical layer. We also introduce a dual polarization encryption approach where we use two different and random DOCS to encrypt the X and Y polarizations separately. The experimental results show that only authorized users can decrypt the signal correctly, and any mismatch in the displacement operator coefficients, amplitudes, or phases will lead to a bit error ratio (BER) of approximately 50%. We also compare the performance of the system with and without encryption over 80 km of standard-single mode fiber (SSMF) transmission to assess the added penalty of such encryption. The achieved net bit rates are 224, 448, and 560 Gb/s for QPSK, 16QAM, and 32QAM modulation formats, respectively. The experimental results showcase the efficacy of the DOCS encryption technique in resisting various decryption attempts, demonstrating its effectiveness in ensuring the security and confidentiality of transmitted data in a real-world transmission scenario.

Cold Gas Spraying Copper Metal On AlN Ceramics as an Alternative to Thick DBC Substrates for Power Electronics

Abstract This study investigates the use of cold gas spraying (CGS) as a low-temperature additive manufacturing method to bond copper onto aluminum nitride (AlN) substrates for electronic packaging of high-power applications. While direct bond copper (DBC) technique is commonly used, it has limitations due to the large mismatch in coefficient of thermal expansion, which affects substrate reliability. This work employed cold gas spraying (CGS) to mechanically bond Cu on AlN. The study explores the effect of multiple sprays, spray angle and spraying direction on deposition thickness, coating surface roughness, and deposited volume through a factorial design of experiments (DOE). The results, based on optical and scanning electron microscopy combined with profilometry data, showed that coatings sprayed at a 60° angle had a smoother profile topography and less surface roughness than those sprayed at a 90° angle. After depositing 10 layers, a surface roughness (Sa) of around 30 µm and a coating thickness of over 300 µm were successfully attained. These findings provide valuable insights into the processing factors affecting the growth and quality of copper coatings on AlN substrates via multiple sprays, thus enabling the realization of CGS technology as a potential solution to DBC substrates for electronic packaging of wide-bandgap semiconductors.

Giant Thermomechanical Bandgap Modulation in Quasi‐2D Tellurium

AbstractLattice deformation via substrate‐driven mechanical straining of 2D materials can profoundly modulate their bandgap by altering the electronic band structure. However, such bandgap modulation is typically short‐lived and weak due to substrate slippage, which restores lattice symmetry and limits strain transfer. Here, it is shown that a non‐volatile thermomechanical strain induced during hot‐press synthesis results in giant modulation of the inherent bandgap in quasi‐2D tellurium nanoflakes (TeNFs). By leveraging the thermal expansion coefficient (TEC) mismatch and maintaining a pressure‐enforced non‐slip condition between TeNFs and the substrate, a non‐volatile and anisotropic compressive strain is attained with ε = −4.01% along zigzag lattice orientation and average biaxial strain of −3.46%. This results in a massive permanent bandgap modulation of 2.3 eV at a rate S (ΔEg) of up to 815 meV/% (TeNF/ITO), exceeding the highest reported values by 200%. Furthermore, TeNFs display long‐term strain retention and exhibit robust band‐to‐band blue photoemission featuring an intrinsic quantum efficiency of 80%. The results show that non‐volatile thermomechanical straining is an efficient substrate‐based bandgap modulation technique scalable to other 2D semiconductors and van der Waals materials for on‐demand nano‐optoelectronic properties.

Photo‐Directed Growth of Surface Micro‐Patterns on Photosensitive Semicrystalline Polymers

AbstractPatterning polymeric materials with controllable microstructures can meet diversified requirements and realize promising applications. Exploring micro‐/nano‐pattern methodology offers possibilities for future techniques, however, the self‐organized growth of polymeric materials has some limitations and the development of direct and noncontact patterning processes is still challenging. In this work, the study presents a facile strategy for endowing polymers with spatially regulated microstructures by direct photo‐printing, which incorporates both advantages of typical top‐down and bottom‐up approaches. By employing the photodimerization of anthracene‐containing semi‐crystallized polymers, the gradient crosslinking results in a mismatch of thermal expansion coefficients between the crosslinked surface and the uncrosslinked bottom layer. After heating treatment, constrained by the crosslinked surface, the uncrosslinked bottom polymer of the molten state in the exposed region tends to flow and migrate toward the unexposed region, similar to a volcanic eruption, which accurately determines the height and morphology of pattern. Besides, the well‐defined patterns can controllably grow upon thermal treatment due to phase transformation and migration. The versatility of the proposed strategy not only provides a brand‐new reliable platform to pattern functional materials with photo‐regulated and reversible microstructures, but also promotes the development of smart materials that can find applications in information safety, reversible microfluidics, and electronic devices.

High-temperature tribological behavior of high-entropy sublattice oxide, nitride, and diboride coatings

The tribological performance of sputtered (Al,Cr,Nb,Ta,Ti)N, ▪ , and ▪ coatings on steel substrates was compared against TiN in dry ball-on-disk and scratch tests in ambient air at 20°C, 400°C and 700°C. The (Al,Cr,Nb,Ta,Ti)N and TiN perform similar in all tests, with (Al,Cr,Nb,Ta,Ti)N showing higher oxidation and abrasion resistance. The adhesion of (Al,Cr,Nb,Ta,Ti)N is superior to TiN at 20°C, but worse at elevated temperature due to an earlier onset of recovery processes that increase the mismatch in coefficient of thermal expansion with the substrate. The ▪ is the most abrasion resistant coating at room temperature owing to its high hardness, but suffers from oxidation in hot air. Scratch tests yield a similar adhesion strength to TiN at 20°C, but the anisotropic lattice expansion and shrinkage of the hexagonal structure at elevated temperatures lead to early delamination in the scratch test. The ▪ also adheres poorly on the steel, resulting in quick delamination during all tests.

Negative Thermal Expansion in ABC(MoO4)3 Compounds.

Negative thermal expansion (NTE) compounds provide a solution for the mismatch of coefficients of thermal expansion in highly integrated device design. However, the current NTE compounds are rare, and how to effectively design new NTE compounds is still challenging. Here, a new concept is proposed to design NTE compounds, that is, to increase the flexibility of framework structure by expanding the space in framework structure compounds. Taking the parent compound NaZr2(PO4)3 as a case, a new NTE system AIBIICIII(MoO4)3 (A = Li, Na, K, and Rb; B = Mg and Mn; C = Sc, In, and Lu) is designed. In these compounds, the large volume of MoO4 tetrahedron is used to replace the small volume of PO4 tetrahedron in NaZr2(PO4)3 to enhance structural space and NTE performance. Simultaneously, a joint study of temperature-dependent X-ray diffraction, Raman spectroscopy, and the first principles calculation reveals that the NTE in AIBIICIII(MoO4)3 series compounds arise from the coupled oscillation of polyhedral. Large-radius ions are conducive to enhancing the space and softening the framework structure to achieve the enhancement of NTE. The current strategy for designing NTE compounds is expected to be adopted in other compounds to obtain more NTE compounds.