Multiple Lattice Research Articles

Multiple surface lattice resonances in symmetric nanocuboid dimer arrays

Abstract Surface lattice resonances based on nanoparticle arrays have significant characteristics such as localized field enhancement and high quality factor, and can be applied in fields such as optical sensors and lasers. In this work, we propose a symmetric Si/SiO2 nanocuboid dimer array that can generate and regulate two surface lattice resonances. One of the surface lattice resonances (named SLR1) is mainly due to the coupling between the electric dipole resonance of single Si/SiO2 nanocuboid dimers and the diffraction waves perpendicular to the applied electric field. Another surface lattice resonance (named SLR2) mainly originates from the coupling between the magnetic dipole resonance of single Si/SiO2 nanocuboid dimers and the diffraction waves parallel to the direction of the applied electric field. The research results indicate that the polarization direction of the incident field, the period of the array, the gap between the nanocuboids in the dimer, particle size, and the medium environment are all important for regulating the two surface lattice resonances. The sensing application of multiple surface lattice resonances is also investigated. The results show that under appropriate structural parameters, SLR1 can provide good stability for sensing applications, its sensitivity and figures of merit are 472 nm/RIU and 104, respectively. However, SLR2 is very weak or suppressed when the refractive index of the medium environment is greater than or equal to 1.2. This characteristic limits the application range of SLR2 in sensing. This work is of great significance for the design of micro-nano photonic devices based on multiple surface lattice resonances.

Biomechanical analysis of partial mandibular implants with various lattice designs of different material properties: In vitro study and finite element analysis

For patients with mandibular bone defects, although reconstruction plates can be used for repair, achieving both occlusal function and facial aesthetics is challenging. In the present study, in vitro experiments and finite element analysis (FEA) were conducted to determine the biomechanical characteristics of multiple porous lattice structures of varying shapes and diameters that were used for mandibular implants. Additionally, an abutment designed to carry occlusal forces was added to the top of the implants. The stress distribution of four lattice designs (tetrahedron, quad-diametral-cross, hex-star, and hex-vase) of three sizes (2.5, 3.0, and 3.5 mm) in cubic porous models were analyzed by FEA. Subsequently, two optimal designs for 3D-printed titanium alloy were selected. These designs, featuring different lattice diameters (0.5, 0.7, and 0.9 mm), were tested to determine their elastic modulus, which was used in another FEA of a mandibular implant designed for a patient with a malignant tumor in the right mandible. This model, which included an abutment design, was subjected to a vertical force of 100 N and muscle forces generated by biting. This analysis was conducted to determine the elastic modulus of the implant and the values of stress and strain on the implant and surrounding bone. The lattice designs of quad-diametral-cross and hex-vase exhibited smaller high-stress regions than those of tetrahedron and hex-star. In vitro tests revealed that the elastic modulus of the lattices increased with the rod diameter. When these values were applied to mandibular implants, Young’s modulus decreased, which in turn increased the frictional stress observed at the interface between the abutment and the implant. However, the implant’s maximum stress remained below its yield strength (910 MPa), and the strain on the surrounding bone varied between 1500 and 3000 μstrain. As indicated by Frost’s theory, these implants are unlikely to damage the surrounding bone tissue and are likely to support bone growth.  

The Composition of Graded Dental Zirconias

Zirconia dental ceramics have evolved from uniform blocks of 3 mol.% yttria (3Y) to strength- and color-graded blocks containing 3 mol.% and 5 mol.% components. Relatively little is known about the graded materials’ compositions and microstructures. Concerns have been raised about aging and degradation. This study investigated the microstructure, elemental composition, and phase content of different zones of strength- and color-graded zirconia blocks using scanning electron microscopy, x-ray fluorescence, and x-ray diffraction. Specimens were made from green-state blocks using CAD/CAM machining and sintering. Two strength- and color-graded zirconia materials had different grain sizes, elemental compositions, and phase contents between their top and bottom zones, these data being internally consistent as well as being broadly consistent with prior compositional physical property data. A color-graded zirconia material did not exhibit substantial differences between its top and bottom zones, consistent with expectations and previously published data. Modeling phase content for complex yttria-doped zirconia crystal systems with multiple heterogeneous crystal lattices from XRD data was inherently difficult, which may account for the ranges among previously published data; authors should describe detailed methodologies. Detailed compositional data at the scale of the microstructure is needed to relate composition to phase content, physical behavior, including crack evolution.

Hierarchical triply periodic minimal surface shell lattices with superior isotropic elasticity: Design guidelines, fabrication, and validation

Hierarchical triply periodic minimal surface (TPMS) shell lattices exhibit a wide range of tailorable properties that can be fine-tuned by lattice design. Recent advances in additive manufacturing towards high resolution enable the precise fabrication of hierarchical TPMS lattices. However, the isotropic behavior of hierarchical TPMS lattices has received little attention. In this study, we focus on the design of hierarchical TPMS lattices to explore their superior isotropic elasticity. By considering three unique geometric parameters of hierarchical TPMS: cell length ratio, relative density, and order number, multiple representative isotropic hierarchical TPMS lattices can be achieved at the same given relative density, which significantly expands its design space. The resultant lattices retain a minimal mid-surface and exhibit a large range of tailorable stiffness. To validate their isotropic elasticity, high-precision laser powder bed fusion was adopted to fabricate representative isotropic lattices and their anisotropic counterparts. Morphology observation and micro-CT scan show that the fabricated samples are dense, and their geometries are highly consistent with the designed models. Quasi-static compression tests further confirm the isotropic elasticity in the new designs. Moreover, a prediction rule was proposed to assess whether an isotropic hierarchical TPMS lattice can be obtained from two selected single-level lattices, which significantly enhances the design efficiency. As a result, the design method and principles can be summarized in this study to provide effective design guidelines to swiftly create hierarchical shell lattices with superior isotropic elasticity.

Can unilateral lattice dystrophy be triggered by cataract surgery in an elderly patient?

ABSTRACT Purpose Aim is to report unilateral lattice corneal dystrophy (LCD) possibly triggered after cataract surgery in an elderly patient and to demonstrate anterior segment optic coherence tomography (AS-OCT) findings. Case Report A 77-year-old male presented with irritation and photophobia in the left eye. His medical history revealed that the patient had undergone cataract surgery on the left eye 5 months ago and his symptoms exaggerated after the surgery. Best corrected visual acuity (BCVA) was 20/32 in OD and 20/63 in OS. Slit lamp examination indicated clear cornea with nuclear sclerosis in the right eye, multiple fine lattice lines at the level of middle stroma in the left eye. The lattice lines extended radially but did not involve the limbus. The overlying epithelium was intact. AS-OCT was consistent with LCD in the left eye with the presence of hyperreflective material at the level of the middle stroma. In contrast, AS-OCT in the right eye showed a normal, healthy cornea. Conclusion LCD is an inherited disease that can rarely present with unilateral involvement. Apart from its unilaterality and lack of limbal-limbal extension, the time of onset of the lattice lines is another distinguishing feature of this case report. Herein, clinical findings appeared at an older age compared to the literature. In addition, the occurrence of findings after phacoemulsification surgery has raised the question that environmental factors may trigger the emergence of unilateral LCD in patients with genetic predisposition. It is not yet known whether unilateral LCD is an asymmetric and asynchronous presentation of bilateral LCD or a different entity triggered by external factors. AS-OCT enables to demonstrate the corneal microstructural changes, and confirm the diagnosis of unilateral LCD by showing that the fellow eye is healthy.

One stone three birds: Natural mineral enhancing thermoelectric properties in Cu2Se-based composites

Copper selenide can be used in thermoelectric applications since it has the features of a superionic conductor. Nevertheless, improving its electrical and thermal transport properties using facile fabrication is challenging. Herein, a one-stone and three-bird strategy was proposed for enhancing the thermoelectric performance of Cu2Se-based composites. Natural verdigris was used as an additive to construct a porous structure simultaneously while introducing Cu vacancies and multiscale Cu2O precipitates in the Cu2-xSe material. The carrier concentration was tailored to optimize the electrical transport properties of the bulk composites. Additionally, multiple lattice defects were generated in the bulk composites, benefiting the significantly reduced thermal conductivity. Ultimately, the Cu2Se-based composite achieved a peak ZT value of 1.25 at 873 K. This study provided a simple approach of adding a natural mineral to regulate the composition and microstructure of the material, which may be worth promoting in other systems.

Numerical simulation of combined effects of a vertical magnetic field and thermal radiation on natural convection of non-Newtonian fluids confined between circular and square concentric cylinders

BackgroundThis study addresses magnetohydrodynamic (MHD) natural convection involving non-Newtonian fluids. Focusing on the annular region between concentric circular and square cylinders, the research examines the impact of a vertical magnetic field and thermal radiation. MethodsThe Multiple Relaxation Time Lattice Boltzmann Method (MRT-LBM) is employed to simulate momentum and energy interactions in non-Newtonian fluid. Control parameters like Rayleigh number, Hartmann number, Radiation parameter, aspect ratio, square cylinder subdivision, and power-law index are systematically varied, while maintaining a constant Prandtl number. Significant findingsUsing shear-thinning fluid (n < 1) significantly improves cooling, particularly in conjunction with radiation effect. Correlations for the mean Nusselt number are established, offering insights. Results emphasize the substantial influence of parameters like Ra, Rd, and AR. High values of the latter promote the flow intensity and heat evacuation. For n < 1, increasing Ra from 103 to 5 × 104 results in a substantial increase in the heat transfer rate reaching 65 %. For shear-thickening fluid, the heat transfer rate is reduced by 25.31 % at Ra = 5 × 104 when Ha is increased from 0 to 50 in the absence of radiation. In addition, radiation enhances the heat transfer rate by 71.41 % by incrementing Rd from 0 to 0.8 for Ha = 0. The most pronounced effect of the radiation parameter is observed in the cases of Newtonian and shear-thickening fluids. Conversely, Ha and n act by reduction effects on the outputs of the problem. The attenuating effect of the magnetic field is more pronounced in the case of shear-thinning fluids. The plot of mean Nusselt number vs. AR shows an hysteresis phenomenon due to the existence of multiple steady solutions in a range of this parameter. In the latter range of AR, heat transfer induced by multicellular flow is higher than that induced by bicellular one. Heat transfer is somewhat enhanced by the RC configuration, compared to SC one.

A new curved road lattice model integrating the multiple prediction effect under V2X environment

In order to explore the driver's multiple prediction effects of flux changes (MPEFC) on traffic flow on a curved road, parameters of the weighted flow gradient of multiple lattices ahead are introduced to characterize the MPEFC effect on a curved road. On this basis, combined with the characteristics of a curved road, a lattice model considering the drive's MPEFC effects is proposed under the V2X environment. The stability criterion is obtained. Through the reduced perturbation method, the density wave equation and its solution used to describe the propagation law of traffic congestion near the critical point are derived. The results show that the stability of traffic flow on a curved road increases along with the increase in radian, and that considering the MPEFC effects simultaneously has a significant stabilizing effect for traffic flow on a curved road. It is also discovered that under the V2X environment, the traffic flow is optimally stabilized by considering the information of just two lattices ahead.

Chiral symmetry restoration at finite temperature in a model with manifest confinement

Multiple lattice evidences support the existence of a confining but chirally symmetric regime of QCD above the chiral symmetry restoration crossover at Tch≃155 MeV. This regime is characterised by an approximate chiral spin symmetry of the partition function, which is a symmetry of the colour charge and the confining electric part of the QCD Lagrangian. It is traditionally believed that confinement should automatically induce spontaneous breaking of chiral symmetry, which would preclude the existence of a confining but chirally symmetric regime of QCD at high temperatures. We employ a well-known solvable quark model for QCD in 3+1 dimensions that is chirally symmetric and manifestly confining and argue that while confinement indeed induces dynamical breaking of chiral symmetry at T=0, a chiral restoration phase transition takes place at some critical temperature Tch. Above this temperature, the spectrum of the model consists of chirally symmetric hadrons with approximate chiral spin symmetry.

Synergistically optimized electron and phonon transport in high-performance copper sulfides thermoelectric materials via one-pot modulation

Optimizing thermoelectric conversion efficiency requires the compromise of electrical and thermal properties of materials, which are hard to simultaneously improve due to the strong coupling of carrier and phonon transport. Herein, a one-pot approach realizing simultaneous second phase and Cu vacancies modulation is proposed, which is effective in synergistically optimizing thermoelectric performance in copper sulfides. Multiple lattice defects, including nanoprecipitates, dislocations, and nanopores are produced by adding a refined ratio of Sn and Se. Phonon transport is significantly suppressed by multiple mechanisms. An ultralow lattice thermal conductivity is therefore obtained. Furthermore, extra Se is added in the copper sulfide for optimizing electrical transport properties by inducing generating Cu vacancies. Ultimately, an excellent figure of merit of ~1.6 at 873 K is realized in the Cu1.992SSe0.016(Cu2SnSe4)0.004 bulk sample. The simple strategy of inducing compositional and structural modulation for improving thermoelectric parameters promotes low-cost high-performance copper sulfides as alternatives in thermoelectric applications.

Transformable lattice with in-situ changeable elastic modulus arising from structural interaction

Many efforts have been made for lattice design and fabrication for various applications, but most lattices possess fixed elastic modulus after fabrication, which impedes the development of multifunctional lattices. Here we propose a new lattice type that enables in-situ structural transformation and changeable elastic modulus. The structural interaction arises from opposite rotations of the rings from Yin and Yang patch of a lattice under compressive force. The distance between the Yin and Yang patch determines if interaction occurs and the lattice elastic modulus, which is decoupled with volume fraction. Here, numerical and experimental investigation were carried out to reveal the relationship between the interaction type, distance and stress-strain curve. Results show that the ratio of maximum to minimum elastic modulus of a lattice is 81.4 with six interaction bars on the ring, and we can obtain an exponential number of reprogrammable elastic moduli when combining multiple lattices as units to construct a cellular structure. Our work shows a potential for constructing intelligent lattices that can adapt to the surroundings.

Integrated multi-material and multi-scale optimization of compliant structure with embedded movable piezoelectric actuators

Piezoelectric actuators embedded in compliant structures have many potential applications, which call for effective design approaches. Existing optimization driven design methods focus on the piezoelectric actuator location or the macro topology of the host compliant structure while ignoring the possibility to exploit the use of multiple materials and hierarchical material design. In this study, an integrated, density-based multi-material and multi-scale optimization method for compliant structures with embedded movable piezoelectric actuators is proposed. The design variables in the optimization represent the location of the piezoelectric actuators and the layout of the macro/micro host structures. To mitigate the risk of suboptimal designs, the three sets of design variables are simultaneously optimized using gradient-based optimization where the gradients are computed using the adjoint method. A material interpolation model that describes the piezoelectric actuators, multiple lattice materials of the host structure as well as their coating layer is proposed. To illustrate the formulation, several compliant structures embedded with movable piezoelectric actuators are designed such that the displacement at an output port is maximized. Macro and micro volume fractions, and overlapping of piezoelectric actuators are constrained in the optimization.

Twisting two-dimensional iron sulfide layers into coincident site superlattices via intercalation chemistry.

Layered van der Waals (vdW) materials are susceptible not only to various stacking polymorphs through translations but also twisted structures due to rotations between layers. Here, we study the influence of such layer-to-layer twisting through the intercalation of ethylenediamine (EDA) molecules into tetragonal iron sulfide (Mackinawite FeS). Selected area electron diffraction patterns of intercalated FeS display reflections corresponding to multiple square lattices with a fixed angle between them, contrary to a single square lattice seen in the unintercalated phase. The observed twist angles of 49.13° and 22.98° result from a superstructure formation well described by the coincident site lattice (CSL) theory. According to the CSL theory, these measured twist angles lead to the formation of larger coincident site supercells. We build these CSL models for FeS using crystallographic group-subgroup transformations and find simulated electron diffraction patterns from the model to agree with the experimentally measured data.

Dynamic behaviors and heat transfer characteristics of impacting droplets on heated superhydrophobic surfaces with randomly distributed rough structures: Numerical simulation and theoretical analysis

Due to the extensive usage of superhydrophobic surfaces, numerous studies have investigated the dynamics and heat transfer of a droplet impacting on superhydrophobic surfaces. However, previous studies did not consider the actual superhydrophobic surfaces with randomly distributed rough structures, especially so in heat transfer of droplet impacting on superhydrophobic surfaces with random rough structures. To address this issue, a multiple distribution function phase-field lattice Boltzmann model was developed to model the droplet impacting on randomly rough surfaces. After experimental validation, this model was used in the analysis of the impacting dynamics and heat transfer characteristics. The differences between actual randomly rough surface and ideal smooth surface were revealed. Herein, random rough structures significantly influence the wetting state and heat transfer of impacting droplet on solid surface. Moreover, the effects of roughness on droplet bouncing ability and the total transferred heat were evaluated. The results show that the random rough surface with smaller skewness, a kurtosis of 3.0, and a standard deviation of 0.3 μm could simultaneously promote impacting droplet to rebound from the surface and to reduce the total transferred heat. Subsequently, the predictive correlation for total transferred heat was proposed based on the roughness parameters. This work provides novel insights into the design of rough structures on functional superhydrophobic surfaces.

Bouncing modes and heat transfer of impacting droplets on textured superhydrophobic surfaces

Superhydrophobic modifications could effectively minimize heat exchange at the interfaces of impacting droplets and solid surfaces. Previous studies have lacked numerical explorations regarding the effect of bouncing modes on the heat transfer characteristics during droplets impacting on textured superhydrophobic surfaces with micro-pillars. To address this issue, a multiple distribution function phase-field lattice Boltzmann model is developed to numerically study dynamic behaviors and heat transfer during droplet impact. Comparisons between the simulations and previous experimental results validate the computation model. Subsequently, the dynamic behaviors of impacting droplets and the effects on the heat transfer were studied using the proposed model. The effects of the textured surface structural parameters on the dynamics and heat transfer are discussed in detail. The numerical results indicate four possible bouncing modes of the impacting droplets: Cassie bouncing, partially penetrated bouncing, pancake bouncing and Wenzel bouncing. These modes depend on the surface energy stored in the penetrating droplet in the microstructures cavities of the surface. Moreover, the synergistic effects of contact time and contact area affect the heat transfer performance. Further, the developed theoretical model to predict the total transferred heat is based on the identified droplet dynamics. Finally, the effects of roughness parameters on total transferred heat are studied, and the design principles of textured superhydrophobic surfaces for heat transfer suppression are given for two application scenarios. The results demonstrate that the control of microstructures would be crucial for the dynamics and heat transfer of impacting droplets on textured superhydrophobic surfaces.

Multiple Skew-Orthogonal Polynomials and 2-Component Pfaff Lattice Hierarchy

Multiple Skew-Orthogonal Polynomials and 2-Component Pfaff Lattice Hierarchy

Multiple lattice sites occupied AlTaO4:Cr3+ phosphor for luminescence ratiometric thermometry and NIR light source

Cr3+-doped near infrared (NIR) phosphors have promising applications in NIR light sources and optical temperature detection. The development of materials with high relative sensitivity and efficient broadband NIR luminescence is the key. In this paper, we report a new multifunctional NIR phosphor AlTaO4:Cr3+, which contains both narrow-band emission associated with 2Eg→4A2 g transition and broadband emission induced by the 4T2 g→4A2 g transition owing to Cr3+ occupies both AlO6 and TaO6 lattice sites. The R-line (2Eg→4A2 g) emission and its anti-Stokes phonon sideband emission follow the Boltzmann distribution, and the thermometer constructed accordingly reaches a maximum Sr of 1% K−1 at 110 K. Under 425 nm excitation, the broad emission band (FWHM = 200 nm) reaches maximum at 880 nm with an internal quantum efficiency of 62.8%. The NIR LEDs prepared with AlTaO4:Cr3+ confirm the application value in NIR light sources.

Multiple surface lattice resonances of overlapping nanoparticle arrays with different lattice spacing.

Multiple surface lattice resonances generated with nanoparticle arrays are promising to enhance light-matter interactions at different spectral positions simultaneously, and it is important to tailor these resonances to desired frequencies for practical applications such as multi-modal nanolasing. To this end, this study proposes to generate multiple surface lattice resonances using overlapping nanoparticle arrays with different lattice spacing. Both full-wave numerical simulations and analytical coupled dipole approximation calculations reveal that for the overlapping structures composed with two different gold nanosphere arrays, both surface lattice resonances for the element structures are effectively excited. Considering that the optical responses are governed by the dipole-dipole interactions between the nanoparticles, it is interesting to find that the multiple surface lattice resonances are almost invariant by adjusting the relative shifts between the two arrays, which can be useful to tailor the high-quality factor resonances to desired spectral positions. In addition, due to the same reason, it is also shown that the multiple surface lattice resonances can be further finely tuned by selectively removing specific nanoparticles in the array. We anticipate that the tolerance to generate multiple surface lattice resonances and the flexible tunability make the overlapping nanoparticle arrays useful to design high performance linear and nonlinear nanophotonic devices.

Study on the stable and efficient white-emitting Bi/Tb/Eu tridoped single-phase borate Sr3YB3O9 phosphors

Several series of novel broad band white light emitting Bi/Tb/Eu tridoped in multiple lattice sites of single-phase Sr3YB3O9 (SYBO) borate phosphors, which covered almost all visible range through mixing the separate blue, green and red emissions from dopants of Bi, Tb and Eu, respectively, were successfully obtained by using the facile and conventional solid-state reaction method under air condition. Rietveld refinements based on XRD data together with the combination match of charge and ion radius for dopants of Bi, Tb, Eu and lattice cations of Sr, Y and B show that Bi is more inclined to replace the Sr site while Tb/Eu are more likely to enter the Y site, respectively. Through spectrum analysis of photoluminescence excitation (PLE), PL and decay lifetime, the efficient energy transfer (ET) from the Bi to both Tb and Eu, and from Tb to Eu are all testified via the dipole-dipole interactions, indicating that the non-rare-earth activator Bi is acting both as the blue luminescence center and ET sensitizer, while the Tb contributes both as ET bridge and green luminescence center to better connect the Bi and Eu. The optimal tridoped white emission SYBO phosphor appears good thermal stability, which could continue to have its PL intensity above 75% at 150 °C as compared with the original room temperature PL intensity. Altogether, the single-component SYBO:Bi/Tb/Eu phosphor could be well served as potential white light phosphor for n-UV pumped wLED devices.

Modeling Mesoporous 3D-Printed Lattice Electrodes for Energy Storage

3D printing could offer the versatility to design and manufacture energy storage devices on demand. The precision and material flexibility of 3D printing is ideal for integrating porous electrodes that can enhance electrochemical performance[1]. This work analyzes the electrical conductivity of 3D-printed mesoscale strut lattices at the 100 μm – 1 mm scale with 40 – 90 % volumetric porosity to develop optimal electrodes for energy storage devices. We use a graph-theory-based model[2] to compute the conductivity of multiple 3D lattice types with either solid conducting struts or struts coated with conductive material. These structures show 3 – 5X higher conductivity than random conductive foams that lack an internal periodic mesostructure[3]. Using microstereolithography, we 3D print samples with high-resolution struts (< 70 µm) that maintain their shape and achieve high conductivity after carbonization at 700 ˚C. By tuning the lattice architecture, we manipulate the tradeoff between conductivity, weight, and porosity, validating our simulations with experimental measurements. These results demonstrate that that body-centered cubic (BCC) strut lattices have optimal conductivity per weight compared with other lattice types. Implementing these 3D-printed conductive lattices as supercapacitor electrodes, we see that the lattice architecture impacts the gravimetric capacitance of the devices as well as the mechanical strength, with octet structures outperforming both cubic and BCC lattices. Electrochemical impedance spectroscopy (EIS) shows that 3D-printed electrodes with higher porosity exhibit higher gravimetric double layer capacitance and lower charge transfer resistance, making them ideal candidates for use in supercapacitor electrodes as free-standing 3D hosts for active materials. CV characterization of the electrodes also illustrates how our graph theory-based model for 3D lattices can predict the optimal structure for energy storage. This model can also serve to predict electrode performance and tailor design for integration of higher surface area nanoporous materials on these conductive 3D printed scaffolds. This allows us to guide the design of 3D printed electrodes to minimize charge transfer resistance and achieve an optimal balance between gravimetric and volumetric energy density for device applications.[1] J. Zhao, Y. Zhang, X. Zhao, R. Wang, J. Xie, C. Yang, J. Wang, Q. Zhang, L. Li, C. Lu, Y. Yao, Advanced Functional Materials 2019, 29, 1900809.[2] J. E. Huddy, M. S. Rahman, A. B. Hamlin, Y. Ye, W. J. Scheideler, Cell Reports Physical Science 2022, 3, 100786.[3] F. G. Cuevas, J. M. Montes, J. Cintas, P. Urban, J Porous Mater 2008, 16, 675. Figure showing (a) designed octet (blue), cubic (orange), and BCC (red) lattice types as well as (b) SEM images of their experimental 3D-printed counterparts and (c) measured electrical resistance. Figure 1