Atomic Coordinates Research Articles

Optimization of Crystal Structures in Polylithionite Concentrate: A Molecular Dynamics Approach to Lithium Extraction Efficiency

Molecular dynamics (MD) techniques offer significant potential for optimizing mineral extraction processes by simulating economically or physically restrictive conditions at the laboratory level. Lithium, a crucial metal in the electromobility era, exemplifies the need for ongoing re-evaluation of extraction techniques. This research aims to simulate the crystal structures of mineral species present in a polylithionite mineral concentrate [KLi2Al(Si4O10)(F,OH)2] using crystallographic data obtained from X-ray diffraction analysis. This study focuses on optimizing these structures, validating them through density comparisons, and determining the interaction parameter between the identified phases and lithium oxide (Li2O). The X-ray diffraction analysis revealed five predominant mineral phases: quartz (SiO2), calcite [Ca(CO3)], pyrite (FeS2), cassiterite (SiO2), and a compound Pb6O2(BO3)2SO4. Structural data, including lattice parameters, space groups, and atomic coordinates, were used to construct the crystal structures with Materials Studio 8.0, employing the Crystal Builder module. Optimization was performed using the Forcite module with the Smart optimization algorithm and the Universal force field. The interaction parameter (χ) indicated an affinity between lithium oxide and pyrite, as well as between calcite and quartz.

Chemical space-informed machine learning models for rapid predictions of x-ray photoelectron spectra of organic molecules

Abstract We present machine learning models based on kernel-ridge regression for predicting X-ray photoelectron spec- tra of organic molecules originating from the ionization energies of 1s electrons in carbon (C), nitrogen (N), oxygen (O), and fluorine (F) atoms. We constructed training dataset through high-throughput calculations of core-electron binding energies (CEBEs) for 12,880 small organic molecules in the bigQM7ω dataset, employing the ∆-SCF formalism coupled with meta-GGA-DFT and a variationally converged basis set. The models are cost-effective, as they require the atomic coordinates of a molecule generated using universal force fields while estimating the target-level CEBEs corresponding to DFT-level equilibrium geometry. We explore transfer learning by utilizing the atomic environment feature vectors learned using a graph neural network framework in kernel-ridge regression. Additionally, we enhance accuracy using the ∆-machine learning framework by leveraging inexpensive baseline spectra derived from Kohn–Sham eigenvalues. Upon application to 208 com- binatorially substituted uracil molecules, larger than those in the training set, our analyses reveal that while the models may not yield quantitatively accurate predictions of CEBEs on a molecule-by-molecule basis, they do exhibit a strong linear correlation, which proves valuable for virtual high-throughput screening purposes. We present the dataset and models as the Python module, cebeconf, to facilitate further explorations.

Out-of-plane coordination of iridium single atoms with organic molecules and cobalt-iron hydroxides to boost oxygen evolution reaction.

Advancements in single-atom-based catalysts are crucial for enhancing oxygen evolution reaction (OER) performance while reducing precious metal usage. A comprehensive understanding of underlying mechanisms will expedite this progress further. Here we report Ir single atoms coordinated out-of-plane with dimethylimidazole (MI) on CoFe hydroxide (Ir1/(Co,Fe)-OH/MI). This Ir1/(Co,Fe)-OH/MI catalyst, which was prepared using a simple immersion method, delivers ultralow overpotentials of 179 mV at a current density of 10 mA cm-2 and 257 mV at 600 mA cm-2 as well as an ultra-small Tafel slope of 24 mV dec-1. Furthermore, Ir1/(Co,Fe)-OH/MI has a total mass activity exceeding that of commercial IrO2 by a factor of 58.4. Ab initio simulations indicate that the coordination of MI leads to electron redistribution around the Ir sites. This causes a positive shift in the d-band centre at adjacent Ir and Co sites, facilitating an optimal energy pathway for OER.

Crystal and Local Structures of Pr2Co7Dx during Its Deuterium Absorption Process Determined by Neutron Diffraction.

We investigated crystal and local structures of Pr2Co7, Pr2Co7D2.7 and Pr2Co7D7.2 by neutron diffraction. The determined structural model of Pr2Co7D2.7 was the Ce2Ni7-type structure by Rietveld refinement, where the deuterium atoms occupied both the CaCu5-type (I) and the MgZn2-type cells. The deuterium contents in these cells were 0.10 and 0.80 D/M, respectively. The expansions of the lattice parameters of Pr2Co7D2.7 from the original intermetallics were Δa = 0.3% and Δc = 7.3%. The crystal structure transformed in the order Ce2Ni7-type Pr2Co7 → Ce2Ni7-type Pr2Co7D2.7 → orthorhombic Pr2Co7D7.2. The expansions of the lattice parameters of Pr2Co7D7.2 from the original intermetallics were Δa = 5.9%, Δb = 6.2%, and Δc = 6.4%; nearly isotropic expansion was observed. The deuterium contents in the MgZn2-type, CaCu5-type (I), and CaCu5-type (II) cells were 1.11, 0.44, and 0.83 D/M, respectively. The refined structural parameters by a pair distribution function (PDF) analysis on Pr2Co7 (0.18 < r < 5.0 nm) and Pr2Co7D2.7 (0.13 < r < 5.0 nm) obtained were consistent with those obtained by Rietveld refinement. The Rietveld refinement results of the refined lattice parameters of Pr2Co7D7.2 corresponded with the PDF analysis results in the region of 0.13 < r < 5.0 nm, whereas the refined atomic coordinates of the atoms D1, D2, D4, D6, and D9 obtained by the two methods differed. The refined structural parameters of the short-range structure (0.13 < r < 1.0 nm) in Pr2Co7D7.2 did not correspond to those of the long-range structure (0.13 < r < 5.0 nm). The local distortion within the domain of approximately 1.0 nm in size exists in Pr2Co7D7.2.

Kinetic origin of hysteresis and the strongly enhanced reversible barocaloric effect by regulating the atomic coordination environment

Hysteresis is an inherent property of first-order transition materials that poses challenges for solid-state refrigeration applications. Extensive research has been conducted, but the intrinsic origins of hysteresis remain poorly understood. Here, we report a study of the kinetic origin of hysteresis and the enhanced barocaloric effect (BCE) in MnCoGe-based alloys with ~2% nonmagnetic In atoms. First-principles calculations demonstrate that substituting In atoms at Ge sites rather than Co sites results in a lower energy barrier, indicating a narrower hysteresis for the former. Combining neutron powder diffraction (NPD) with magnetic and calorimetric measurements completely verified the theoretical prediction. Electron local function (ELF) calculations further reveal the atomic coordination origin of regulated hysteresis due to weaker Co–Ge bonds when In atoms replace Ge, which is opposite to Co sites. Moreover, we experimentally investigate the BCE and find that although MnCo(Ge0.98In0.02) has a lower barocaloric entropy change ΔSP than does Mn(Co0.98In0.02)Ge, the reversible ΔSrev of the former is advantageous owing to a smaller hysteresis. The maximum ΔSrev of MnCo(Ge0.98In0.02) is 1.7 times greater than that of Mn(Co0.98In0.02)Ge. These results reveal the atomic-scale mechanism regulating hysteresis and provide insights into tailoring the functional properties of novel caloric refrigeration materials.

Reverse hierarchical DED assembly in the cFLIP-procaspase-8 and cFLIP-procaspase-8-FADD complexes

cFLIP, a master anti-apoptotic regulator, targets the FADD-induced DED complexes of procaspase-8 in death receptor and ripoptosome signaling pathways. Several tumor cells maintain relatively high levels of cFLIP in achieving their immortality. However, understanding the three-dimensional regulatory mechanism initiated or mediated by elevated levels of cFLIP has been limited by the absence of the atomic coordinates for cFLIP-induced DED complexes. Here we report the crystal plus cryo-EM structures to uncover an unconventional mechanism where cFLIP and procaspase-8 autonomously form a binary tandem DED complex, independent of FADD. This complex gains the ability to recruit FADD, thereby allosterically modulating cFLIP assembly and partially activating caspase-8 for RIPK1 cleavage. Our structure-guided mutagenesis experiments provide critical insights into these regulatory mechanisms, elucidating the resistance to apoptosis and necroptosis in achieving immortality. Finally, this research offers a unified model for the intricate bidirectional hierarchy-based processes using multiprotein helical assembly to govern cell fate decisions.

Investigation on mechanism of mechanical activation and chemical reactions in CMP of diamond assisted by hydroxyl free radicals

Chemical mechanical polishing (CMP) is a crucial manufacturing process for diamond substrate applications. However, due to the extremely high hardness and chemical stability of diamond, its CMP efficiency is extremely low. This study aims to achieve microscopic simulation of atomic oxidation removal at the three-phase interface between diamond abrasive particle, diamond substrate, and hydroxyl free radicals (∙OH) aqueous solution. The mechanical activation behavior, microscopic mechanism, and feasibility of elementary reactions in the ∙OH aqueous solution environment was studied using various perspectives of radial distribution function, central atomic coordination state, atomic bonding and removal forms, energy, electron orbitals, and density functional theory (DFT). The simulation results indicate that during the process of diamond atomic oxidation removal, the atomic density at the first adjacent position centered on one atom decreases, and the stable covalent bond structure is disrupted, resulting in an amorphous phase transition. The chemical adsorption reaction generates C-O and C–H bonds. The C atoms mainly separate from the diamond substrate by the forming products such as carbon monoxide (CO), carbon dioxide (CO2), and carbon chains. The mechanical activation behavior indirectly reduces the activation energy of chemical reactions, while increasing the absolute value of adsorption energy and improving the ability of chemical adsorption solution atoms H and O, as well as ∙OH groups. Based on DFT, it has been verified that the intrusion process of ∙OH groups in the elementary reactions involving the typical product C*O2 is an exothermic reaction that can occur spontaneously, and the energy barrier needs to be overcome by the mechanical action of abrasive particles. At the same time, the energetics of the oxidation of diamond C atoms to generate C*O2 have successfully confirmed that the combined action of ∙OH and diamond abrasive particles is expected to achieve efficient oxidation removal and finishing polishing of diamond atoms.

Velocity Effect in Synthesis of Noncircular Nanopores by Etching Tracks of Swift Heavy Ions in Olivine

The velocity effect was studied in the synthesis of nanopores with a noncircular cross section by etching tracks of swift heavy ions in olivine. The developed atomistic model for the etching of olivine irradiated with swift heavy ions predicts the possibility of synthesizing nanopores with a noncircular cross section in it. The model consists of connected blocks that describe the sequential stages of track formation and etching. The TREKIS Monte Carlo model describes the initial electronic and lattice excitations in the nanoscale vicinity of the trajectory of an incident ion. These results are used as initial conditions for molecular dynamics simulation of structural changes along the ion trajectory. The obtained atomic coordinates after cooling of the structurally damaged area serve as the initial data for the original atomistic model of track etching in olivine. The results of the model application show that it is possible to control the cross section of these pores by changing the orientation of the crystal relative to the direction of irradiation. The presented simulation results for Xe ions demonstrate that the size of the resulting pores depends on the velocity of the incident ion, and not only on its linear energy loss.

Insights of the Multimode Orientation-Dependent Initial Oxidation of Aluminum by First-Principles Theory Calculations.

A fundamental understanding of the oxidation mechanisms of aluminum (Al) alloys is of great importance for its applications in corrosion, catalysis, sensors, etc. In this work, we systematically investigated the first-stage oxidation behaviors of three low-index Al facets with O coverage up to two monolayers (ML) by using density-functional theory (DFT). The large negative adsorption energies indicated favorable oxidation on all three facets. However, distinctive structural and electronic changes induced by the adsorption of oxygen have led to different oxidation modes. More specifically, the oxidation process proceeded by "intercalating" into the subsurface region along the (111) plane out of the (110) facet with spontaneous O ingress into (110) far below one ML, as revealed by the electron density distribution, whereas the oxide ad-layer grew in a "layer-by-layer" mode on Al(111) and (001) facets. Moreover, various Al-O complexes with different atomic coordination numbers (CN), configurations, and sizes may be indicators of the tendency of an Al surface to be oxidized. Besides, the oxide phases formed on (111)/(001) and (110) assembled the Al-O bond distribution within α-Al2O3 and γ-Al2O3, respectively.

Atomically dispersed iron sites from eco-friendly microbial mycelium as highly efficient hydrogenation catalyst

Iron, one of the most abundant elements on earth and an essential element for living organisms, plays a crucial role in our daily metabolism. In the field of catalysis, the development of high-performance catalysts based on less toxic iron element is also of significant importance for green chemistry and a sustainable future. To construct Fe-based heterogeneous catalysts with excellent hydrogenation performance, precise modulation of the atomic coordination structure is a key strategy for enhancing catalytic activity. In this study, we present an in-situ coating method for applying a zeolitic imidazolate framework (ZIF) onto the surface of fungal hyphae. The asymmetric coordination structure of Fe1-N3P1 was precisely tailored by utilizing the phosphorus source from the fungus and the nitrogen source in the ZIFs. Detailed characterizations and density functional theory calculations revealed that the incorporation of ZIFs not only increased the specific surface area of catalysts, but also facilitated the dispersion of Fe2P nanoparticles into the Fe1-N3P1 center, making the lowest reaction energy barrier and resulting in the best performance for nitrobenzene hydrogenation when compared to the Fe2P nanoparticles and clusters. This research introduces a novel design concept for constructing asymmetric monoatomic configuration based on the inherent characteristics of natural microorganisms and the exogenous porous coordination polymers.

Effects of Dynamic Surface Transformation on the Activity and Stability of Mixed Co‐Mn Cubic Spinel Oxides in the Oxygen Evolution Reaction in Alkaline Media

AbstractAn atomic‐scale understanding of how electrocatalyst surfaces reconstruct and transform during electrocatalytic reactions is essential for optimizing their activity and longevity. This is particularly important for the oxygen evolution reaction (OER), where dynamic and substantial structural and compositional changes occur during the reaction. Herein, a multimodal method is developed by combining X‐ray fine structure absorption and photoemission spectroscopy, transmission electron microscopy, and atom probe tomography with electrochemical measurements to interrogate the temporal evolution of oxidation states, atom coordination, structure, and composition on Co2MnO4 and CoMn2O4 cubic spinel nanoparticle surfaces upon OER cycling in alkaline media. Co2MnO4 is activated at the onset of OER due to the formation of ≈2 nm Co‐Mn oxyhydroxides with an optimal Co/Mn ratio of ≈3. As OER proceeds, Mn dissolution and redeposition occur for the CoMn oxyhydroxides, extending the OER stability of Co2MnO4. Such dynamic dissolution and redeposition are also observed for CoMn2O4, leading to the formation of less OER‐active Mn‐rich oxides on the nanoparticle surfaces. This study provides mechanistic insights into how dynamic surface reconstruction and transformation affect the activity and stability of mixed CoMn cubic spinels toward OER.

Determining the chemical ordering in nanoalloys by considering atomic coordination types.

The energetically most favorable chemical ordering of bimetallic nanoparticles can be characterized by combining global optimization algorithms and surrogate energy models. The latter approximate the energy of nanoalloys relying on structural descriptors, training models, and data. Here, we systematically evaluate the performance of highly data-efficient topological descriptors [Kozlov et al., Chem. Sci. 6, 3868 (2015)] for predicting the energies of metal nanoalloys with different chemical orderings. We also introduce a new descriptor based on atomic coordination types, which results in a less data-efficient and interpretable approach, but improves the general accuracy and the quantification of orderings in the inner parts of nanoparticles. The capacity of both the original and new approaches in combination with a basin hopping algorithm is illustrated by generating convex hulls of PdZn nanoalloys and predicting the resulting active surface site distribution as a function of particle composition. Finally, we show how these approaches can be combined with machine-learning adsorption models in electrocatalysis studies for a fast evaluation of the reactivity landscape of targeted nanoalloys.

Identifying crystal structures beyond known prototypes from x-ray powder diffraction spectra

The large amount of powder diffraction data for which the corresponding crystal structures have not yet been identified suggests the existence of numerous undiscovered, physically relevant crystal structure prototypes. In this paper, we present a scheme to resolve powder diffraction data into crystal structures with precise atomic coordinates by screening the space of all possible atomic arrangements, i.e., structural prototypes, including those not previously observed, using a pre-trained machine learning (ML) model. This involves (i) enumerating all possible symmetry-confined ways in which a given composition can be accommodated in a given space group, (ii) ranking the element-assigned prototype representations using energies predicted using the Wyckoff representation regression ML model [Goodall , ], (iii) assigning and perturbing atoms along the degree of freedom allowed by the Wyckoff positions to match the experimental diffraction data, and (iv) validating the thermodynamic stability of the material using density-functional theory. An advantage of the presented method is that it does not rely on a database of previously observed prototypes and is, therefore capable of finding crystal structures with entirely new symmetric arrangements of atoms. We demonstrate the workflow on unidentified x-ray diffraction spectra from the ICDD database and identify a number of stable structures, where a majority turns out to be derivable from known prototypes. However, at least two are found not to be part of our prior structural data sets. Published by the American Physical Society 2024

The impact of amorphous-crystal interface on photoresponse in oxide semiconductor InGaZnO4

The photoresponse of an oxide semiconductor is influenced by lattice distortion, which can be adjusted through atomic coordination status. Typically, the modulation of atomic coordination and photoresponse involves introducing oxygen vacancy (VO) density. In addition to VO, the interface exhibits varying degrees of lattice distortion and may offer an efficient means for modulating photoresponse. Therefore, investigating the interface dependence of photoresponse is both warranted and lacking in current research. Herein, we utilize an amorphous-crystal interface in an InGaZnO4 film to modulate its photoresponse. Compared to films without such interfaces, those with interfaces demonstrate a higher illumination-to-dark current ratio and a slower decay rate of photocurrent upon removal of illumination.

Shape controlled synthesis and crystal facet dependent gas sensitivity of tungsten oxide

Gas sensors can achieve remarkable functionality through the optimization of particle size, shapes, crystal facets, and oxygen defects, resulting in unsaturated coordination atoms, high charge densities, and enhanced bond energies. In this study, WO2.72 nanourchins, WO3-x nanowires, and WO3 nanorods/nanocube with (010), (001), (200), and (002) dominant crystal facets were synthesized and used as gas sensing materials. It was found that WO2.72 nanourchins exhibit an excellent response of Ra/Rg=21 to 100 ppm acetone with good selectivity among other sensors as-fabricated. First-principle calculations of Density Functional Theory were performed on acetone's adsorption on different crystal planes of tungsten oxide. The results verify spontaneous and fast adsorption on the (010) crystal plane than on the (001) and (200) planes. Further characterizations indicate that WO2.72 nanourchins with (010) crystal facets contain more reactive sites with high surface energy, facilitating charge separation, increasing charge carrier mobility, and enabling the redox reactions to occur independently at different rates. Moreover, their richer electron-donor surface oxygen defects, smaller feature sizes, and higher surface area (SBET) with hierarchical porous structures, all contribute to the enhanced acetone sensing. Our work provides a strategy for improved acetone sensing based on optimizing the particle shape with different crystal facets and oxygen vacancy density. We further expect our strategy to be applicable in designing other sensor materials with efficient charge separation and fast surface redox reactions to detect toxic gases.

Insight into the polysulfides conversion kinetics and its activation energy relationship on ultrafine V8C7 in Li-S batteries

Catalytic conversion of lithium polysulfides (LiPSs) is regarded as an effective approach to boosting kinetics and suppressing shuttling effect in lithium-sulfur (Li-S) batteries, but developing efficient catalysts and understanding of its catalytic mechanism still remain challenges. Herein, the ultrafine V8C7 nanocrystals embedded into the porous N-doped carbon frameworks (V8C7/NC) was designed for accelerating the LiPSs catalytic-conversion kinetics toward high-performance Li-S batteries. We propose that the ultrafine V8C7 nanocrystals with abundant unsaturated coordination atoms increase the active sites for catalytic-conversion of LiPSs and also accelerate the corresponding kinetics by reducing its reaction activation energy, meanwhile the interlinked nano-channels of V8C7/NC can effectively confine LiPSs and also promote electron/ion transfer. These attributes enable the Li-S cell equipped with V8C7/NC to deliver a large discharge capacity of 1393.3 mAh g−1 at 0.2 C, excellent rate capability (496.0 mAh g−1 at 10 C), and robust cycling stability (1000 cycles with a negligible capacity decay rate of 0.019 % per cycle even at 5 C). The innovative concept of ultrafine V8C7 nanocrystals embedded into the porous carbon toward improved LiPSs catalytic-conversion kinetics could be extended to develop other electrocatalytic hosts for high-performance Li-S batteries.

Enhancing Activity and Stability of Pd-on-TiO2 Single-Atom Catalyst for Low-Temperature CO Oxidation through in Situ Local Environment Tailoring.

The development of efficient Pd single-atom catalysts for CO oxidation, crucial for environmental protection and fundamental studies, has been hindered by their limited reactivity and thermal stability. Here, we report a thermally stable TiO2-supported Pd single-atom catalyst that exhibits enhanced intrinsic CO oxidation activity by tunning the local coordination of Pd atoms via H2 treatment. Our comprehensive characterization reveals that H2-treated Pd single atoms have reduced nearest Pd-O coordination and form short-distanced Pd-Ti coordination, effectively stabilizing Pd as isolated atoms even at high temperatures. During CO oxidation, partial replacement of the Pd-Ti coordination by O or CO occurs. This unique Pd local environment facilitates CO adsorption and promotes the activity of the surrounding oxygen species, leading to superior catalytic performance. Remarkably, the turnover frequency of the H2-treated Pd single-atom catalyst at 120 °C surpasses that of the O2-treated Pd single-atom catalyst and the most effective Pd/Pt single-atom catalysts by an order of magnitude. These findings open up new possibilities for the design of high-performance single-atom catalysts for crucial industrial and environmental applications.

Atomistic study of selenium doping effects on the mechanical properties of zinc-blende and wurtzite CdTe nanowires

CdSexTe1–x semiconductor materials, having potential to be used to design dependable and reproducible nanowire devices, require an extensive study of their mechanical behaviors. The uniaxial tensile deformation mechanism of CdSexTe1–x nanowires (NWs) with different Se dopant concentration are yet to be explored. By integrating theoretical analysis with computational simulation, this research demonstrated that Se doping in CdTe NWs influences the mechanical response and failure modes. Ultimate tensile strength (UTS) and elastic modulus (EM) were studied for both zinc-blende (ZB) and wurtzite (WZ) structures with different crystal orientations. The findings revealed that these mechanical properties increase linearly with increasing Se concentration in all cases. In addition, the WZ structures exhibited similar mechanical properties under both zigzag and armchair loadings, unlike the ZB structures, which exhibited a strong dependence on the crystal orientation. The [111]-oriented ZB structures showed the highest EM and UTS whereas [100]-oriented ZB structures showed lowest EM and UTS. The failure mechanism was explored for CdSe50Te50 to underscore the influence of the dopant on the NWs failure for tensile loading. In both the cases of WZ structure, the failure planes were perpendicular to the loading direction. Furthermore, the failure plane varied with the Se content in ZB CdSexTe1–x. Atomic coordination and bond length affected by doping defined the alterations of mechanical properties and the preferred modes of failure. The significance of the interaction between doping elements and nanowire structures offers insights that unite material science and mechanics, contributing to the scientific understanding of solid materials’ behavior.

Data-Driven Design of Single-Atom Electrocatalysts with Intrinsic Descriptors for Carbon Dioxide Reduction Reaction

The strategic manipulation of the interaction between a central metal atom and its coordinating environment in single-atom catalysts (SACs) is crucial for catalyzing the CO2 reduction reaction (CO2RR). However, it remains a major challenge. While density-functional theory calculations serve as a powerful tool for catalyst screening, their time-consuming nature poses limitations. This paper presents a machine learning (ML) model based on easily accessible intrinsic descriptors to enable rapid, cost-effective, and high-throughput screening of efficient SACs in complex systems. Our ML model comprehensively captures the influences of interactions between 3 and 5d metal centers and 8 C, N-based coordination environments on CO2RR activity and selectivity. We reveal the electronic origin of the different activity trends observed in early and late transition metals during coordination with N atoms. The extreme gradient boosting regression model shows optimal performance in predicting binding energy and limiting potential for both HCOOH and CO production. We confirm that the product of the electronegativity and the valence electron number of metals, the radius of metals, and the average electronegativity of neighboring coordination atoms are the critical intrinsic factors determining CO2RR activity. Our developed ML models successfully predict several high-performance SACs beyond the existing database, demonstrating their potential applicability to other systems. This work provides insights into the low-cost and rational design of high-performance SACs.

Electromechanical properties and piezoelectric potentials of one-dimensional GaN nanostructures: A bond relaxation investigation

From the viewpoint of atomic bond relaxation, an analytical approach was put forward to elucidate the physical origins of crystal size and cross-sectional shape dependency of piezoelectric potentials in GaN nanowires and nanotubes. It is demonstrated that (i) size-induced increase in piezoelectric potential is attributed to the coupling effect of the rising piezoelectric coefficient and both the reducing dielectric constant and elastic constant caused by the surface atomic coordination number loss, bond energy perturbation, and surface-to-volume ratio rising; (ii) as the number of sides for polygonal nanowires or nanotubes with the same equivalent radius decreases, the surface-to-volume ratio rises, and the piezoelectric potential increases; and (iii) the nanotubes can generate a piezoelectric potential higher than their nanowire counterparts due to their larger surface-to-volume ratios. The proposed formulation offers a scientific basis for the fabrication, optimization, and modulation of one-dimensional GaN-based piezoelectric nanometer devices.