Fundamental Material Properties Research Articles

Manipulation and Characterization of Submillimeter Shearing Contacts in Graphite by the Micro-Dome Technique.

Manipulation techniques are the key to measuring fundamental properties of layered materials and their monolayers (2D materials) on the micro- and nanoscale as well as a necessity to the solution of relevant existing challenges. An example is the challenge against upscaling structural superlubricity, a phenomenon of near-zero friction and wear in solid contacts. To date, the largest single structural superlubric contact only has a size of a few tens of micrometers, which is achieved on graphite mesa, a system that has shown microscale superlubricity. The first obstacle against extending the contact size is the lack of suitable manipulation techniques. Here, a micro-dome technique is demonstrated on graphite mesas by shearing contacts 2500 times larger in area than previously possible. With this technique, submillimeter graphite mesas are opened, characterized for the first time, and compared to their microscale counterparts. Interfacial structures, which are possibly related to the failure of superlubricity, are observed: commensurate grains, external steps, and carbon aggregates. Furthermore, a proof-of-concept mechanical model is developed to understand how the micro-dome technique works and to predict its limits. Finally, a dual-axis force measuring device is developed and integrated with the micro-dome technique to measure the normal and lateral forces when shearing submillimeter mesas. These results provide a platform technique for future research on structural superlubricity on different scales and manipulation of structures of layered materials in general.

Low temperature epitaxial growth of Cantor-nitride thin films by magnetic field assisted magnetron sputtering

Low-temperature epitaxial growth of multicomponent alloy-based thin films remains an outstanding challenge in materials science and is important for established fundamental properties of these complex materials. Here, Cantor nitride (CrMnFeCoNi)N thin films were epitaxially grown on MgO(100) substrates at low deposition temperature by magnetic-field-assisted dc-magnetron sputtering, a technique where a magnetic field is applied to steer the dense plasma to the substrate thereby influencing the flux of Ar-ions bombarding the film during growth. Without ion bombardment, the film displayed textured growth. As the ion flux was increased, the films exhibited epitaxial growth. The epitaxial relationship between film and substrate was found to be cube on cube (001)film||(001)MgO, [100]film||[100]MgO. The epitaxy was retained up to a thickness of approximately ∼100 nm after which the growth becomes textured with a 002 out-of-plane orientation. The elastic constants determined by Brillouin inelastic light scattering were found to be C11 = 320 GPa, C12 = 125 GPa, and C44 = 66 GPa, from which the polycrystalline Young’s modulus was calculated as 204 GPa and Poisson's ratio = 0.32, whereas available elastic properties still remained very scarce.

High-Temperature Piezoelectric Resonators: Electroacoustic Properties and Applications of Langasite-Type Crystals

Piezoelectric devices based on high-temperature stable single crystals are of increasing interest due to a wide range of potential applications, such as actuators and resonant gravimetric sensors. The latter require highly accurate resonant-frequency measurements at temperatures as high as 1000 °C, and this can only be achieved with narrow resonance peaks and correspondingly low acoustic loss at these temperatures. Relevant atomistic defects in langasite (La3Ga5SiO14, LGS) and catangasite (Ca3TaGa3Si2O14, CTGS) are reviewed with respect to their impact on electrical conductivity and acoustic loss. The focus on these crystals also enables a comparison of electroacoustic properties of partially disordered (LGS) and ordered (CTGS) crystals and the formulation of approaches for reducing acoustic loss and enhancing device performance.Starting with defect chemistry models for LGS and CTGS, electrical conductivities as a function of temperature and oxygen partial pressure are considered. One result of this analysis is that contributions of oxygen ions to the total conductivity are determined to be relatively small in the studied crystals. Temperature-dependent acoustic loss of LGS and CTGS crystals is also studied. Two independent techniques, contact resonant piezoelectric spectroscopy, and a contactless tone-burst excitation technique, are applied. Contributions to the measured acoustic loss are determined by fitting loss-related functions for point defects and conductivity-related relaxations. The extracted fit parameters, in particular the activation energies of the processes, are discussed and compared with that of the electrical conductivity. The losses are caused by a superposition of several mechanisms including conductivity-related relaxations, point-defect relaxations and intrinsic phonon-phonon loss.The long-term stability of the crystals is also evaluated at 1000 °C with respect to fundamental materials properties including electrical conductivity and resonant frequency.After one year of thermal treatment, the resonance frequency of CTGS resonators from different crystal sources is found to decrease by no more than 0.4 %. Thus, the applicability of CTGS as a piezoelectric resonator that operates for long periods at extreme temperatures, such as a resonant nanobalance, is demonstrated.Application examples to be presented include resonant nanobalances for in-situ monitoring of non-stoichiometry and phase transformations in thin films during growth at high temperatures. In this context, the key application properties of the sensors at high temperatures, such as mass sensitivity and resolution, are discussed. As an application example, the attached figure shows the oxygen non-stoichiometry x of thin praseodymium-cerium oxide films (Pr0.1Ce0.9O2-x) at 700 °C as a function of oxygen partial pressure determined by LGS and CTGS nanobalances, which agrees very well with literature data (chemical capacitance: D. Chen et al., Chem. Mater. 2014, 26, 22, 6622–6627). Figure 1

Pr‐ and Co‐substitution in rare earth nickelates: Application as SOEC air electrodes

AbstractIn this work, fundamental material properties of compounds in the system (La,Pr)2(Ni,Co)O4+δ as well as their performance as air electrodes in solid oxide electrolysis cells were investigated. Nickelates co‐doped with Pr and Co were characterized on a material basis by means of X‐ray diffraction and thermogravimetry. Conductivity and conductivity relaxation measurements were performed in order to obtain the electronic conductivity as well as the chemical surface exchange coefficient and the chemical diffusion coefficient of oxygen as a function of temperature and oxygen partial pressure. These parameters can be regarded as the most essential properties at the material level required to assess the suitability of mixed ionic‐electronic conducting ceramics for application as air electrode in solid oxide cells. The electrode performance of the materials was then tested on fuel electrode‐supported button cells at 800°C. The electrodes were applied by screen‐printing and the effect of varying the Pr‐content and Co‐content of the electrode powder was investigated. Cell tests were performed by means of current‐voltage measurements in electrolysis mode. While no significant impact of Pr‐doping on the investigated material properties was observed, the electrode performance of Pr‐containing materials was significantly better than for the Pr‐free compound, which has been discussed in detail.

Lattice Vacancy Induced Energy Renormalization of Photonic Quasiparticles in Two-Dimensional Semiconductors.

Coulomb interactions among dense charges and quasiparticle energy renormalization are at the center of quantum science because they significantly reshape the fundamental electronic and photonic properties of materials. While lattice vacancies are ubiquitous in solid materials, their physical effect on the Coulomb interaction among quasiparticles is normally weak and negligible. Here we show that in atomically thin semiconductors the presence of lattice vacancies emerges as an important but unexplored origin for the nontrivial renormalization of quasiparticle binding energies, due to the subtle modification of overall dielectric functions at low dimensionality. Such a renormalization effect leads to unusual reduction in the energy scales of photonic quasiparticles and red shifts of photoluminescence as the density of lattice vacancies increases. With strict configurative form factors derived, a dielectric screening model is also established for the generalized trilayer systems to capture the fine modification in the energy scales of quasiparticles and to elucidate the dielectric functions versus realistic Bohr lengths. This finding highlights the essential but commonly neglected role of lattice vacancies and deciphers the longstanding enigma of unpredictable photoluminescent line shifts in low-dimensional systems.

A simple figure of merit to identify the first layer to degrade and fail in dual layer SiOx/HfO2 gate dielectric stacks

Understanding the degradation dynamics and the breakdown sequence of a bilayer high-k (HK) gate dielectric stack is crucial for the improvement of device reliability. We present a new Figure of Merit (FoM), the IL/HK Degradation Index, that depends on fundamental materials properties (the dielectric breakdown strength and the dielectric constant) and can be used to easily and quickly identify the first layer to degrade and fail in a bilayer SiO2/HK dielectric stack. Its dependence on IL and HK material parameters is investigated and its validity is demonstrated by means of accurate physics-based simulations of the degradation process. The proposed FoM can be easily used to understand the degradation dynamics of the gate dielectric stack, providing critical insights for device reliability improvement.

A modified approach for measuring the air permeability of ultra-high performance concrete (UHPC) under vacuum conditions

This study proposes a novel test method of the air permeability measurement under extreme vacuum condition to examine the performance of materials for Hyperloop tubes. Tests on cement-based materials demonstrated that the developed test setup was effective in measuring air permeability in extreme vacuum conditions. The results show that ultra-high performance concrete (UHPC) has significantly lower air permeability (10–18 m2) in vacuum conditions than other cement-based materials (10–16 m2) due to its dense microstructure and reduced pore size, which were within the range of previous results (10-18-10-16 m2). The measured porosity results had a strong correlation with air permeability (R2 > 0.97), validating the suitability of the proposed method for measuring the air permeability of cement-based materials in vacuum conditions. These findings provide fundamental material properties for the design of Hyperloop tube structures.

Analyzing Fundamental Properties of Two-Dimensional Materials by Raman Spectroscopy from Microscale to Nanoscale.

Analyzing Fundamental Properties of Two-Dimensional Materials by Raman Spectroscopy from Microscale to Nanoscale.

The Projectile Perforation Resistance of Materials: Scaling the Impact Resistance of Thin Films to Macroscale Materials.

From drug delivery to ballistic impact, the ability to control or mitigate the puncture of a fast-moving projectile through a material is critical. While puncture is a common occurrence, which can span many orders of magnitude in the size, speed, and energy of the projectile, there remains a need to connect our understanding of the perforation resistance of materials at the nano- and microscale to the actual behavior at the macroscale that is relevant for engineering applications. In this article, we address this challenge by combining a new dimensional analysis scheme with experimental data from micro- and macroscale impact tests to develop a relationship that connects the size-scale effects and materials properties during high-speed puncture events. By relating the minimum perforation velocity to fundamental material properties and geometric test conditions, we provide new insights and establish an alternative methodology for evaluating the performance of materials that is independent of the impact energy or the specific projectile puncture experiment type. Finally, we demonstrate the utility of this approach by assessing the relevance of novel materials, such as nanocomposites and graphene for real-world impact applications.

Controllable pore size of super-hydrophobic magnetic core-shell nanospheres with dendritic architecture and their pore-dependent performances in oil/water separation

The fundamental properties of porous materials strongly rely on their pore sizes. Pore-size-dependent performances play significant roles in their applications like catalysis, adsorption, delivery, and so forth. In this work, a feasible pore-expanding approach has been successfully explored to control the pore size of magnetic core–shell nanospheres with dendritic architecture (Fe3O4@DMSNs). The size can be adjusted from ca. 10 nm to 25 nm and further to 60 nm in an unprecedented wide range. Further, a concise modification route has been adopted to endow Fe3O4@DMSNs particles with super-hydrophobic abilities by the usage of a long-chain silane (Fe3O4@DMSNs-OTES). The as-prepared nanospheres with magnetic response function can not only form magnetic liquid marbles (MLMs) easily, but also separate n-hexane in oil–water mixtures or oil-in-water emulsions rapidly and efficiently. However, the above three particles display certain differences in their basic properties (like pore volume) and application performances (like oil removal efficiency). Most importantly, Fe3O4@DMSNs-OTES with 60 nm pores exhibit the best super-hydrophobicity in contact angles of H2O and MLMs, Fe3O4@DMSNs-OTES with 25 nm pores possess the maximum adsorption capacity, while the ones with 10 nm pores show the quickest adsorption rate (removal efficiency). The relationship between the performances and the pore size has been thoroughly revealed and well deciphered by wettability theory (e.g., Cassie-Baxter equation) and surface tension theory. In a word, all Fe3O4@DMSNs-OTES hold promising potentials as candidates for the practical wastewater purification on the basis of their characteristics.

Novel octa-graphene-like structures based on GaP and GaAs.

The discovery of graphene gave way to the search for new two-dimensional structures. In this regard, octa-graphene is a carbon allotrope consisting of 4- and 8-membered rings in a single planar sheet, drawing the research community's attention to study their inorganic analogs. Considering the promising properties of octa-graphene-like structures and the role of GaAs and GaP in semiconductor physics, this study aims to propose, for the first time, two novel inorganics buckled nanosheets based on the octa-graphene structure, the octa-GaAs and octa-GaP. This work investigated the structural, electronic, and vibrational properties of these novel octa-graphene-based materials. The octa-GaP and octa-GaAs have an indirect band gap transition with a valence band maximum between M and Г points and a conduction band minimum at Г point with energy of 3.05 eV and 2.56 eV, respectively. The QTAIMC analysis indicates that both structures have incipient covalent in their bonds. The vibrational analysis demonstrates the occurrence of ΓRaman = 6Ag + 6Bg and ΓRaman = 12A' + 12B″ for octa-GaP and octa-GaAs, respectively. The symmetry reduction of octa-GaAs leads to activating inactive modes observed in the octa-GaP structure. The frontier crystalline orbitals are composed by Ga(px) and P(py and pz) orbitals for octa-GaP and Ga(px and py) and As(s, py, and pz) for octa-GaAs in the valence bands while in the conduction bands by Ga(py, pz, and s) for both compounds and P(px and pz) and As(py). The phonon bands demonstrate the absence of the negative frequency modes and the structural stability of these new nanosheets. This report aims to reveal the fundamental properties of both newfound materials for stimulating experimental research groups in the search for synthesis routes to obtain this structure. This work used the DFT/B3LYP approach implemented in the CRYSTAL17 computational package. Ga, As, and P atomic centers were described by triple-zeta valence with polarization (TZVP) basis set. The vibrational analysis was carried out via coupled-perturbed Hartree-Fock/Kohn Sham (CPHF/KS) method, and the chemical bonds were evaluated via the quantum theory of atoms in molecules and crystals (QTAIMC).

Ultrafast Photocurrent Detection in Low‐Dimensional Materials

Photocurrent generation from photon absorption to electron collection involves various physical processes and reflects the whole life of excited charge carriers. The investigation of photocurrent enables the revelation of fundamental material properties and improvement of electronic device performance. Recently, with the development of ultrafast optics, the time‐resolved photocurrent (TRPC) technique is innovated as a photocurrent detection method with a time resolution down to subpicosecond, which allows exploring the ultrafast carrier dynamics and the photodetector intrinsic response highly efficiently. Herein, the advancement of TRPC studies in low‐dimensional materials is focused on. First, the TRPC technique is first introduced, including the setup composition and its measurement mechanism, and compared with the conventional transport‐based method to demonstrate its uniqueness. Then, the TRPC studies in various low‐dimensional materials including 2D graphene, transition metal dichalcogenides and black phosphorus, 1D nanowires, and 0D nanocrystals are discussed, where the originations of their ultrafast photocurrent are analyzed. Finally, an outlook is given on the research prospects of this powerful technique. The TRPC measurement is highlighted as a significant tool to analyze the ultrafast carrier dynamics in the generation of photocurrent and to instruct the structure design of a new generation of ultrafast photodetectors.

Effect of the Preparation Methodology of Polydopamine-Containing Systems over Light-to-Thermal Energy Conversion Performance

Polydopamine (PDA) is an attractive material utilized for a wide range of scientific purposes, including light-to-thermal energy conversion, because of presenting plenty of advantages. The proper integration way of PDA into a system is critical to benefit from the PDA content in maximum. Here, the two main PDA-containing composite preparation methods were compared in terms of fundamental material properties and the light-to-thermal energy conversion ability of the final product. For this purpose, the classical emulsion polymerization method first synthesized an aqueous dispersion of polystyrene nanoparticles (PS). PDA was then integrated into the system via two different preparation methods: coating the surfaces of polystyrene nanoparticles with a PDA layer while PS is in a dispersion state (PS@PDA) and adding separately synthesized PDA nanoparticles into the PS dispersion medium (PS–PDA). Two prepared composite systems were fundamentally characterized by dynamic light scattering (DLS), ultraviolet–visible (UV–vis) spectroscopy, and scanning electron microscopy (SEM) while in their dispersion state, and by differential scanning calorimetry (DSC), thermogravimetric analysis (TGA), Fourier-transform infrared (FTIR) spectroscopy, and X-ray diffraction (XRD) while in their solid state, which was obtained after the water evaporated. As the targeted property, the solid forms of these were investigated in terms of light-to-thermal energy conversion performance with solar and laser light exposure under 1 SUN and at 808 nm, respectively. The results showed that the composite system prepared by coating surfaces of PS nanoparticles with the PDA layer had higher light-to-thermal energy conversion under both conditions than those prepared by separately added PDA nanoparticles into the dispersion system. To show one of the possible applications of the prepared composites, in addition to the main target, the solid form of the composite system, which was prepared by coating surfaces of PS nanoparticles with the PDA layer, was also evaluated in detail concerning the latent heat-storage ability with incorporation of PEG 4000 as a phase-change material (PCM) into the system. It was found that the prepared shape-stable phase-change composite with a ratio of 1:3 between PS@PDA and PEG 4000 resulted in a latent heat of 126.9 J/g.

A general methodology to measure the light-to-heat conversion efficiency of solid materials

Light-to-heat conversion has been intensively investigated due to the potential applications including photothermal therapy and solar energy harvesting. As a fundamental property of materials, accurate measurement of light-to-heat conversion efficiency (LHCE) is of vital importance in developing advanced materials for photothermal applications. Herein, we report a photothermal and electrothermal equivalence (PEE) method to measure the LHCE of solid materials by simulating the laser heating process with electric heating process. The temperature evolution of samples during electric heating process was firstly measured, enabling us to derive the heat dissipation coefficient by performing a linear fitting at thermal equilibrium. The LHCE of samples can be calculated under laser heating with the consideration of heat dissipation coefficient. We further discussed the effectiveness of assumptions by combining the theoretical analysis and experimental measurements, supporting the obtained small error within 5% and excellent reproducibility. This method is versatile to measure the LHCE of inorganic nanocrystals, carbon-based materials and organic materials, indicating the applicability of a variety of materials.

Electromagnetic Radiation Effects on MgO-Based Magnetic Tunnel Junctions: A Review.

Magnetic tunnel junctions (MTJs) have been widely utilized in sensitive sensors, magnetic memory, and logic gates due to their tunneling magnetoresistance. Moreover, these MTJ devices have promising potential for renewable energy generation and storage. Compared with Si-based devices, MTJs are more tolerant to electromagnetic radiation. In this review, we summarize the functionalities of MgO-based MTJ devices under different electromagnetic irradiation environments, with a focus on gamma-ray radiation. We explore the effects of these radiation exposures on the MgO tunnel barriers, magnetic layers, and interfaces to understand the origin of their tolerance. This review enhances our knowledge of the radiation tolerance of MgO-based MTJs, improves the design of these MgO-based MTJ devices with better tolerances, and provides information to minimize the risks of irradiation under various irradiation environments. This review starts with an introduction to MTJs and irradiation backgrounds, followed by the fundamental properties of MTJ materials, such as the MgO barrier and magnetic layers. Then, we review and discuss the MTJ materials and devices' radiation tolerances under different irradiation environments, including high-energy cosmic radiation, gamma-ray radiation, and lower-energy electromagnetic radiation (X-ray, UV-vis, infrared, microwave, and radiofrequency electromagnetic radiation). In conclusion, we summarize the radiation effects based on the published literature, which might benefit material design and protection.

Influence of the aspect ratio of the micro-cantilever on the determined Young’s modulus using the Euler-Bernoulli equation

Micro-cantilever bending experiments can be used to determine fundamental material properties, such as fracture stress and fracture toughness. Furthermore, the Young’s modulus can be calculated from the slope of the load-displacement curve using the classical Euler-Bernoulli equation. However, in literature it can be frequently found that applying this technique, the Young’s modulus is significantly underestimated, especially when using micro-cantilevers with aspect ratios (bending length/width) < 6. In order to investigate the influence of the aspect ratio on the determination of the Young’s modulus, SiO2 and single crystalline α-Al2O3 micro-cantilevers with aspect ratios ranging from ∼ 3.5–6.5 were fabricated using focused ion beam milling and tested with a nanoindenter system. In addition to the quasi-static tests, dynamic micro-cantilever bending tests were performed by using an excitation frequency on top of a quasi-static loading and the results of both techniques were compared to each other. Finally, finite element analysis was used to simulate the static-micro-cantilever bending experiments and investigate the influence of shear deformation, flexing of the support and the geometry of the micro-cantilever on the load-displacement curves.

Case Studies of Asphalt Pavement Quality Assurance Specifications, Performance-Related Specifications, and Performance-Based Specifications

Quality assurance (QA) specifications for asphalt pavement construction measure quality characteristics to adjust payments. The measured quality characteristics are assumed to empirically relate to performance. The validity of this assumption, however, has been questioned in recent years; thus, there has been increased interest in finding ways to more directly evaluate the performance of the as-constructed materials. One proposed method to meet this need involves using the Asphalt Mixture Performance Tester (AMPT) and its associated test methods, which measure fundamental material properties that are then used to calculate the fatigue cracking performance index, Sapp, and a rutting strain index (RSI). These indices can be used in performance-related specification (PRS) or performance-based specification (PBS) frameworks to determine the pay adjustments during the construction of asphalt pavement. While PBS requires measured indices, PRS uses index-volumetrics relationships (IVRs) to predict Sapp and RSI based on conventional acceptance quality. Payment can then be based on a percent within limits (PWL) approach. This paper demonstrates how pay adjustments can be made for a paving project in Indiana following three different QA specification frameworks: the current QA specifications framework in the Indiana Department of Transportation, a PRS framework using IVRs, and a PBS framework that employs measured Sapp and RSI. For each framework, the main elements of the specification were identified and determined. The specification limits for Sapp and RSI and weight factors in composite pay factor equations were determined such that the resulting pay factors are comparable to pay factors obtained from the current QA practices.

Real-space observation of ultraconfined in-plane anisotropic acoustic terahertz plasmon polaritons.

Thin layers of in-plane anisotropic materials can support ultraconfined polaritons, whose wavelengths depend on the propagation direction. Such polaritons hold potential for the exploration of fundamental material properties and the development of novel nanophotonic devices. However, the real-space observation of ultraconfined in-plane anisotropic plasmon polaritons (PPs)-which exist in much broader spectral ranges than phonon polaritons-has been elusive. Here we apply terahertz nanoscopy to image in-plane anisotropic low-energy PPs in monoclinic Ag2Te platelets. The hybridization of the PPs with their mirror image-by placing the platelets above a Au layer-increases the direction-dependent relative polariton propagation length and the directional polariton confinement. This allows for verifying a linear dispersion and elliptical isofrequency contour in momentum space, revealing in-plane anisotropic acoustic terahertz PPs. Our work shows high-symmetry (elliptical) polaritons on low-symmetry (monoclinic) crystals and demonstrates the use of terahertz PPs for local measurements of anisotropic charge carrier masses and damping.

Direct Observation of Group-V Dopant Substitutional Defects in CdTe Single Crystals.

Point defect chemistry strongly affects the fundamental properties of materials and has a decisive impact on device performance. The Group-V dopant is prominent acceptor species with high hole concentration in CdTe; however, its local atomic structure is still not clear owing to difficulties in definitive measurements and discrepancies between experimental observations and theoretical models. Herein, we report on direct observation of the local structure for the As dopant in CdTe single crystals by the X-ray fluorescence holography (XFH) technique, which is a powerful tool to visualize three-dimensional atomic configurations around a specific element. The XFH result shows the As substituting on both Cd (AsCd) and Te (AsTe) sites. Although AsTe has been well known as a shallow acceptor, AsCd has not attracted much attention and been discussed so far. Our results provide new insights into point defects by expanding the experimental XFH study in combination with theoretical first-principles studies in II-VI semiconductors.

Design of hierarchical microstructures with isotropic elastic stiffness

Elastic stiffness is one of the most fundamental properties of materials. Design of the microstructures with isotropic stiffness has been an attractive area in the field of metamaterials for over three decades. Despite many classes of isotropic microstructures, exploring novel isotropic microstructures based on innovative mechanics principles has attracted great and continuing interests. This paper presents a novel family of isotropic hierarchical microstructures (Iso-HMs). These hierarchical microstructures are modeled by replacing the solid parts of prescribed single-level microstructures with arrayed microstructures in the second level, where the key task is to identify the correct geometries of the second-level microstructures by conducting parameter space exploring. These Iso-HMs realize isotropic stiffness based on synergistic deformations of the members in the two levels, which is essentially different from existing isotropic microstructures replying on deformations of the members in a single level. Two categories of Iso-HMs with rectangular holes and Vidergauze-type struts are designed. Considering the large size difference in the designed Iso-HMs, additive manufacturing becomes a unique technique for manufacturing the designed Iso-HMs, where the size ratio between the 3D-printed specimens and the minimal features reaches 400:1. Both numerical and experimental results validate the isotropic stiffness of the designed Iso-HMs. Furthermore, the results of a microstructural instability analysis show that the designed Iso-HMs can gain improved buckling strength up to a hundred times higher than their single-level counterparts. The hierarchical design provides a new way to identify novel functional microstructures for applications, and the hierarchical configurations expand the space of the already-known families of isotropic microstructures.