Density of states

状态密度
  • 文章类型: Journal Article
    研究人员现在专注于无毒的无机卤化物基立方金属钙钛矿,因为他们努力将钙钛矿衍生的光电产品和太阳能电池商业化。本研究探索了新型无铅化合物的性质,特别是GaGeX3(其中X=Cl,Br,andI),通过执行第一性原理密度泛函理论(DFT)来分析它们的光学,电子,机械,和压力下的结构特征。通过应用Born稳定性标准并计算形成能,可以仔细评估所有化合物的可靠性。通过弹性调查发现,这些材料表现出各向异性行为,灵活性,和优异的弹性稳定性。电子带结构,在0GPa下使用HSE06和GGA-PBE函数计算,揭示迷人的行为。然而,使用GGA-PBE计算非零压力的能带结构。这里,当卤化物Cl被Br或I改变时,导带移动到较低的能量。静水压力的应用可以导致所有化合物的带隙特性可调,例如GaGeCl3从0.779eV到0eV,GaGeBr3从0.462eV到0eV,GaGeI3从0.330eV到0eV,导致从半导体到金属。理解带隙变化的起源可以通过检查部分和总的态密度(PDOS&TDOS)来阐明。当受到压力时,所有研究的化合物都显示出吸收系数的有效增加,并且在可见光和UV区域都显示出异常的光学电导率。然而,GaGeCl3是更有效的UV吸收剂,因为其在UV区域中更强烈地吸收光。此外,GaGeI3由于其令人印象深刻的可见吸收和光学电导率而在所检查的化合物中脱颖而出,在不同的压力条件下保持一致。此外,当受到压力时,GaGeI3表现出较高的反射率,使得它们适用于UV屏蔽应用。最后,这些不含铅的金属立方卤化物钙钛矿为推进光电技术提供了有希望的机会。凭借其可调谐特性和良好的光学特性,这些材料因其在太阳能电池中的潜力而备受追捧,多节太阳能电池,和不同的光电功能。
    Researchers are now focusing on inorganic halide-based cubic metal perovskites that are not toxic as they strive to commercialize optoelectronic products and solar cells derived from perovskites. This study explores the properties of new lead-free compounds, specifically GaGeX3 (where X = Cl, Br, and I), by executing first-principles Density Functional Theory (DFT) to analyze their optical, electronic, mechanical, and structural characteristics under pressure. Assessing the reliability of all compounds is done meticulously by applying the criteria of Born stability and calculating the formation energy. As discovered through elastic investigations, these materials showed anisotropic behavior, flexibility, and excellent elastic stability. The electronic band structures, calculated using both HSE06 and GGA-PBE functionals at 0 GPa, reveal fascinating behavior. However, computed band structures with non-zero pressures using GGA-PBE. Here, the conduction band moved to the lower energy when the halide Cl was changed with Br or I. In addition, the application of hydrostatic pressure can lead to tunable band gap properties in all compounds such as from 0.779 eV to 0 eV for GaGeCl3, from 0.462 eV to 0 eV for GaGeBr3 and from 0.330 eV to 0 eV for GaGeI3, resulting transformation from semiconductor to metallic. Understanding the origins of bandgap changes can be illuminated by examining the partial and total density of states (PDOS & TDOS). When subjected to pressure, all the studied compounds showed an impactful increase in absorption coefficients and displayed exceptional optical conductivity in both the visible and UV zones. Yet, GaGeCl3 is a more effective UV absorber because it absorbs light more strongly in the UV area. Moreover, GaGeI3 stands out among the compounds examined due to its impressive visible absorption and optical conductivity, which remain consistent under varying pressure conditions. Besides, GaGeI3 exhibits higher reflectivity when subjected to pressure making them suitable for UV shielding applications. At last, these metal cubic halide perovskites without lead present promising opportunities for advancing optoelectronic technologies. With their tunable properties and favorable optical characteristics, these materials are highly sought after for their potential in solar cells, multi-junctional solar cells, and different optoelectronic functions.
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  • 文章类型: Journal Article
    催化剂性能的准确预测对于设计具有特定催化功能的材料至关重要。密度泛函理论(DFT)方法因其准确性而被广泛使用,建模异构系统,特别是支持的过渡金属,提出了重大的计算挑战。为了应对这些挑战,我们介绍了电子结构分解方法(ESDA),一种新的方法,可识别负责催化剂上吸附物相互作用和活化的特定状态密度(DOS)区域。作为一个案例研究,我们研究了α-Al2O3(0001)作为载体材料对Ru纳米颗粒(NPs)上CO吸附能和C-O键拉伸频率的影响。采用多元线性回归分析,使用来自分离的RuNP的数据训练ESDA模型,并使用支持的NP样本数据进行调整。ESDA模型准确预测CO吸附能和C-O振动频率,证明了预测值和DFT计算值之间的强线性相关性,并且对于分离的和支持的RuNP,各个吸附位点的误差都很低。除了查明负责CO吸附和C-O键活化的DOS区域外,这项研究提供了有关操纵这些DOS区域以控制CO活化的见解,从而促进CO解离。此外,与DFT计算相比,ESDA显着加速了分离和负载RuNP上CO吸附和活化的表征和预测,加快新催化材料的设计,推进催化研究。此外,ESDA对电子结构作为描述符的依赖表明其预测催化之外的各种性质的潜力,扩大其在不同科学领域的适用性。
    Accurate prediction of catalyst performance is crucial for designing materials with specific catalytic functions. While the density functional theory (DFT) method is widely used for its accuracy, modeling heterogeneous systems, especially supported transition metals, poses significant computational challenges. To address these challenges, we introduce the Electronic Structure Decomposition Approach (ESDA), a novel method that identifies specific density of states (DOS) areas responsible for adsorbate interaction and activation on the catalyst. As a case study, we investigate the influence of α-Al2O3(0001) as a support material on CO adsorption energy and the stretching frequency of the C-O bond on Ru nanoparticles (NPs). Using multiple linear regression analysis, ESDA models were trained with data from isolated Ru NPs and adjusted using supported NP sample data. The ESDA models accurately predict the CO adsorption energies and C-O vibrational frequencies, demonstrating strong linear correlations between predicted and DFT-calculated values with low errors across various adsorption sites for both isolated and supported Ru NPs. Beyond pinpointing the DOS areas responsible for CO adsorption and C-O bond activation, this study provides insights into manipulating these DOS areas to control CO activation, hence facilitating CO dissociation. Additionally, ESDA significantly accelerates the characterization and prediction of CO adsorption and activation on both isolated and supported Ru NPs compared to DFT calculations, expediting the design of new catalytic materials and advancing catalysis research. Furthermore, ESDA\'s reliance on the electronic structure as a descriptor suggests its potential for predicting various properties beyond catalysis, broadening its applicability across diverse scientific domains.
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  • 文章类型: Journal Article
    在纳米科学领域,液体在超过常规结构弛豫时间的尺度下的动力学行为,τ,展现了令人着迷的固体状特征,包括集体剪切波的传播和弹性的出现。然而,在经典的散装液体中,其中τ通常为1ps或更小,这种类似固体的行为在态密度(DOS)的低频区域仍然难以捉摸。这里,我们通过对限制在氧化石墨烯膜内的液态水和甘油中的低频DOS的非弹性中子散射测量,为短距离内液体出现的固体状性质提供了证据。特别是,在增加约束强度时,我们观察到从液体状DOS(频率ω为线性)到固体状行为的转变(德拜定律,ω2)在1-4meV的范围内。分子动力学模拟证实了这些发现,并揭示了其他类似固体的特征,包括传播集体剪切波和自扩散常数的减小。最后,我们表明,固体状动力学的开始被推向低频,同时限制时松弛过程的减慢。这种纳米约束诱导的转变,符合k-gap理论,强调了利用液体纳米限制来推进纳米级科学和技术的潜力,在流体力学和材料工程之间建立更多的联系。
    In the realm of nanoscience, the dynamic behaviors of liquids at scales beyond the conventional structural relaxation time, τ, unfold a fascinating blend of solid-like characteristics, including the propagation of collective shear waves and the emergence of elasticity. However, in classical bulk liquids, where τ is typically of the order of 1 ps or less, this solid-like behavior remains elusive in the low-frequency region of the density of states (DOS). Here, we provide evidence for the emergent solid-like nature of liquids at short distances through inelastic neutron scattering measurements of the low-frequency DOS in liquid water and glycerol confined within graphene oxide membranes. In particular, upon increasing the strength of confinement, we observe a transition from a liquid-like DOS (linear in the frequency ω) to a solid-like behavior (Debye law, ∼ω2) in the range of 1-4 meV. Molecular dynamics simulations confirm these findings and reveal additional solid-like features, including propagating collective shear waves and a reduction in the self-diffusion constant. Finally, we show that the onset of solid-like dynamics is pushed toward low frequency along with the slowing-down of the relaxation processes upon confinement. This nanoconfinement-induced transition, aligning with k-gap theory, underscores the potential of leveraging liquid nanoconfinement in advancing nanoscale science and technology, building more connections between fluid dynamics and materials engineering.
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  • 文章类型: Journal Article
    我们通过主动减去由电流-电压特性中的非线性产生的主要电流谐波来增加扫描隧道显微镜(STM)的动态范围,这些谐波可能会在低结阻抗或高增益下使电流前置放大器饱和。余弦激励电压与电流谐波之间的严格相位关系允许使用放置在前置放大器输入处的驱动补偿电容器的位移电流进行出色的消除。直流电流的去除对,并且去除一次谐波只会导致微分电导的刚性偏移,可以通过添加已知的去除电流在数值上进行反转。我们的方法不需要永久更改硬件,而只需要两个相位同步电压源和一个多频锁定放大器即可实现高动态范围的光谱和成像。•有源电力滤波器•动态范围压缩•高增益前置放大器。
    We increase the dynamical range of a scanning tunneling microscope (STM) by actively subtracting dominant current-harmonics generated by nonlinearities in the current-voltage characteristics that could saturate the current preamplifier at low junction impedances or high gains. The strict phase relationship between a cosinusoidal excitation voltage and the current-harmonics allows excellent cancellation using the displacement-current of a driven compensating capacitor placed at the input of the preamplifier. Removal of DC currents has no effect on, and removal of the first harmonic only leads to a rigid shift in differential conductance that can be numerically reversed by adding the known removal current. Our method requires no permanent change of the hardware but only two phase synchronized voltage sources and a multi-frequency lock-in amplifier to enable high dynamic range spectroscopy and imaging. • Active power filter • Dynamic range compression • High gain preamplifier.
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  • 文章类型: Journal Article
    恒定电势下的分子动力学(MD)模拟是研究电化学过程的重要工具,提供结构的微观信息,热力学,和动力学属性。尽管在电极模拟方面取得了许多进展,它们不能准确地表示石墨等材料的电子结构。在这项工作中,介绍了一种简单的参数化方法,该方法可以基于态密度(DOS)的量子化学计算来调节电极的金属性。作为第一个例子,石墨电极和两种不同液体电解质之间的界面,NaCl水溶液和纯离子液体,在不同的施加电位进行了研究。结果表明,模拟定性地再现了实验测量的电容;特别是,它们在零电荷点(PZC)产生最小的电容,这是由于量子电容(QC)的贡献。对吸附液体的结构的分析允许理解为什么尽管离子液体具有大的离子浓度,但离子液体仍显示较低的电容。除了与重要的碳质电极相关外,这种方法可以应用于任何电极材料(例如2D材料,导电聚合物,etc),从而使分子模拟研究复杂的电化学装置在未来。
    Molecular dynamics (MD) simulations at a constant electric potential are an essential tool to study electrochemical processes, providing microscopic information on the structural, thermodynamic, and dynamical properties. Despite the numerous advances in the simulation of electrodes, they fail to accurately represent the electronic structure of materials such as graphite. In this work, a simple parameterization method that allows to tune the metallicity of the electrode based on a quantum chemistry calculation of the density of states (DOS) is introduced. As a first illustration, the interface between graphite electrodes and two different liquid electrolytes, an aqueous solution of NaCl and a pure ionic liquid, at different applied potentials are studied. It is shown that the simulations reproduce qualitatively the experimentally-measured capacitance; in particular, they yield a minimum of capacitance at the point of zero charge (PZC), which is due to the quantum capacitance (QC) contribution. An analysis of the structure of the adsorbed liquids allows to understand why the ionic liquid displays a lower capacitance despite its large ionic concentration. In addition to its relevance for the important class of carbonaceous electrodes, this method can be applied to any electrode materials (e.g. 2D materials, conducting polymers, etc), thus enabling molecular simulation studies of complex electrochemical devices in the future.
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  • 文章类型: Journal Article
    通过在mBJ势内采用密度泛函理论(DFT)报告了Zn1-xCrxSe(0≤x≤1)半导体的光电和结构特征。结果表明,晶格常数随着Cr浓度的增加而减小,虽然体积模量表现出相反的趋势。ZnSe是一种直接带隙材料;然而,在Cr的存在下,已经看到了从直接电子带隙到间接电子带隙的变化。这种转变是由Cr和缺陷形成的结构改变引起的,这导致了新的光学特征,包括电子转换。电子带隙从2.769减小到0.216eV,允许声子参与并改善光吸收。较高浓度的Cr增强红外吸收,并且这些基于Cr的ZnSe(ZnCrSe)半导体还覆盖从红光到蓝光的可见范围内的较宽光谱。重要的光学参数,如反射率,光学电导率,光学带隙,消光系数,折射率,磁化因子,并讨论了能量损失函数,从理论上了解ZnCrSe半导体在光子和光电器件中的各种应用。
    The optoelectronic and structural characteristics of the Zn1-xCrxSe (0 ≤ x ≤ 1) semiconductor are reported by employing density functional theory (DFT) within the mBJ potential. The findings revealed that the lattice constant decreases with increasing Cr concentration, although the bulk modulus exhibits the opposite trend. ZnSe is a direct bandgap material; however, a change from direct to indirect electronic bandgap has been seen with Cr presence. This transition is caused by structural alterations by Cr and defects forming, which results in novel optical features, including electronic transitions. The electronic bandgap decreases from 2.769 to 0.216 eV, allowing phonons to participate and improving optical absorption. A higher concentration of Cr boosts infrared absorption and these Cr-based ZnSe (ZnCrSe) semiconductors also cover a wider spectrum in the visible range from red to blue light. Important optical parameters such as reflectance, optical conductivity, optical bandgap, extinction coefficient, refractive index, magnetization factor, and energy loss function are discussed, providing a theoretical understanding of the diverse applications of ZnCrSe semiconductors in photonic and optoelectronic devices.
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  • 文章类型: Journal Article
    对三维反射腔内光子的热态的现代教科书分析基于三个量子数,这些量子数表征了施加边界条件时出现的光子能量特征值。从量子数到连续频率的关键通道是通过引入三个离散量子数的三维连续版本来操作的,这导致了能量谱密度和熵谱密度。该标准分析掩盖了与相同本征频率相关的多个能量特征值的作用。在本文中,我们回顾了Bose熵谱密度的过去推导,并基于能量特征值的多重性对能量谱密度和熵谱密度进行了新的分析。我们的分析明确定义了能量和熵的特征频率分布,并将其用作从离散特征频率到连续频率的起点。
    The modern textbook analysis of the thermal state of photons inside a three-dimensional reflective cavity is based on the three quantum numbers that characterize photon\'s energy eigenvalues coming out when the boundary conditions are imposed. The crucial passage from the quantum numbers to the continuous frequency is operated by introducing a three-dimensional continuous version of the three discrete quantum numbers, which leads to the energy spectral density and to the entropy spectral density. This standard analysis obscures the role of the multiplicity of energy eigenvalues associated to the same eigenfrequency. In this paper we review the past derivations of Bose\'s entropy spectral density and present a new analysis of energy spectral density and entropy spectral density based on the multiplicity of energy eigenvalues. Our analysis explicitly defines the eigenfrequency distribution of energy and entropy and uses it as a starting point for the passage from the discrete eigenfrequencies to the continuous frequency.
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  • 文章类型: Journal Article
    几何结构,相对稳定性,铌碳团簇的电子和磁性,Nb7Cn(n=1-7),在这项研究中进行了调查。密度泛函理论(DFT)计算,再加上桑德斯踢全球搜索,进行了研究Nb7Cn(n=1-7)的结构性质。关于平均结合能的结果,二阶差分能量,离解能,HOMO-LUMO间隙,和化学硬度突出了Nb7C3的强大稳定性。态密度的分析表明,Nb7Cn的分子轨道主要由过渡金属Nb的轨道组成,与最小的C原子的参与。自旋密度和自然种群分析表明,Nb7Cn的总磁矩主要位于Nb原子上。Nb原子对总磁矩的贡献主要来自4d轨道,其次是5p,5s,和6s轨道。
    The geometrical structures, relative stabilities, and electronic and magnetic properties of niobium carbon clusters, Nb7Cn (n = 1-7), are investigated in this study. Density functional theory (DFT) calculations, coupled with the Saunders Kick global search, are conducted to explore the structural properties of Nb7Cn (n = 1-7). The results regarding the average binding energy, second-order difference energy, dissociation energy, HOMO-LUMO gap, and chemical hardness highlight the robust stability of Nb7C3. Analysis of the density of states suggests that the molecular orbitals of Nb7Cn primarily consist of orbitals from the transition metal Nb, with minimal involvement of C atoms. Spin density and natural population analysis reveal that the total magnetic moment of Nb7Cn predominantly resides on the Nb atoms. The contribution of Nb atoms to the total magnetic moment stems mainly from the 4d orbital, followed by the 5p, 5s, and 6s orbitals.
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  • 文章类型: Journal Article
    背景:氢已成为一种有前途的清洁能源载体,强调必须了解其吸附机制。本研究深入研究了Co-Mo-P团簇的磁性和电子性质,旨在揭示它们在制氢方面的催化潜力。采用密度泛函理论(DFT),我们优化了集群配置,并仔细检查了它们的磁行为。我们的研究揭示了ConMoP(n=1~5)集群的16种稳定构型,主要在空间形式。磁属性主要归因于Co金属原子的d轨道,与Co3MoP表现出特殊的磁特性。对状态图密度的分析揭示了自旋上升的α电子在d轨道中的普遍存在,而自旋下降的β电子削弱了整体的磁性。局部轨道(LOL)分析强调了簇内稳定的共价键,确认其催化潜力。轨道离域指数(ODI)分析揭示了不同配置轨道的不同空间分布范围,表明离域特性随着簇大小的增加而逐渐衰减。此外,红外光谱在各种构型中揭示了不同的振动峰,指示独特的红外活动。这些发现有助于对Co-Mo-P团簇进行细致的理论理解,并为旨在提高其在氢气生产中的催化效率的未来研究铺平了道路。这项研究强调了Co-Mo-P团簇作为常规Pt催化剂替代品的可行性,提供对可持续能源应用新型材料设计的见解。需要进一步的研究来探索Co-Mo-P体系在不同反应条件下的行为,促进材料和能源科学的进步。
    方法:在本研究中,我们利用ConMoP(n=1~5)团簇作为探测材料局部结构的模拟平台。我们的目标是仔细检查磁力,电子特性受这些团簇中变化的金属原子的影响。系统的探索涉及增加金属原子的数量并扩大簇的大小以阐明相应的性质变化。密度泛函理论(DFT)计算对我们的方法至关重要,采用高斯16软件包中实现的B3LYP混合功能。对ConMoP(n=1~5)簇进行了def2-tzvp量化级的优化计算和振动分析,产生具有不同自旋多重度的优化配置。为了全面表征和直观地表现稳定性,电子功能,和这些配置的催化属性,我们使用了一套计算工具。具体来说,量子化学软件GaussView和波函数分析软件Multiwfn起到了积分作用。通过综合使用这些计算工具,我们获得了对磁性的宝贵见解,ConMoP(n=1~5)团簇的电子特性,揭示它们对不同金属原子的依赖性。
    BACKGROUND: Hydrogen has emerged as a promising clean energy carrier, underscoring the imperative need to comprehend its adsorption mechanisms. This study delves into the magnetic and electronic properties of Co-Mo-P clusters, aiming to unveil their catalytic potential in hydrogen production. Employing density functional theory (DFT), we optimized cluster configurations and scrutinized their magnetic behaviors. Our investigation unveiled 16 stable configurations of the ConMoP (n = 1 ~ 5) cluster, predominantly in steric forms. The magnetic attributes were primarily ascribed to the d orbitals of Co metal atoms, with Co3MoP exhibiting exceptional magnetic characteristics. Analysis of density of state diagrams revealed the prevalence of spin-up α-electrons in d orbitals, while spin-down β-electrons attenuated overall magnetic properties. Localized orbital (LOL) analysis highlighted stable covalent bonds within the clusters, affirming their catalytic potential. Orbital delocalization index (ODI) analysis revealed diverse spatial distribution ranges for orbitals across different configurations, suggesting a progressive attenuation of off-domain properties with increasing cluster size. Furthermore, infrared spectroscopy unveiled distinct vibrational peaks in various configurations, indicative of unique infrared activities. These findings contribute to a nuanced theoretical understanding of Co-Mo-P clusters and pave the path for future research aimed at augmenting their catalytic efficiency in hydrogen production. This study underscores the viability of Co-Mo-P clusters as alternatives to conventional Pt catalysts, offering insights into the design of novel materials for sustainable energy applications. Further research is warranted to explore the behavior of the Co-Mo-P system under diverse reaction conditions, fostering advancements in materials and energy science.
    METHODS: In this study, we harnessed the ConMoP (n = 1 ~ 5) cluster as a simulation platform for probing the local structure of the material. Our aim was to scrutinize the magnetism, electronic characteristics influenced by the varying metal atoms within these clusters. A systematic exploration involved incrementing the number of metal atoms and expanding the cluster size to elucidate the corresponding property variations. Density functional theory (DFT) calculations were pivotal to our methodology, employing the B3LYP hybrid functional implemented in the Gaussian 16 software package. The ConMoP (n = 1 ~ 5) cluster underwent optimization calculations and vibrational analysis at the def2-tzvp quantization level, yielding optimized configurations with diverse spin multiplet degrees. To comprehensively characterize and visually represent the stability, electronic features, and catalytic attributes of these configurations, we employed a suite of computational tools. Specifically, quantum chemistry software GaussView and wave function analysis software Multiwfn played integral roles. Through the integrated use of these computational tools, we acquired valuable insights into the magnetism, electronic characteristics of the ConMoP (n = 1 ~ 5) cluster, shedding light on their dependency on distinct metal atoms.
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  • 文章类型: Journal Article
    为了提高CuP合金的机械性能,特别关注Cu3P阶段,本研究全面考察了各种合金元素对合金性能的影响。在本文中,利用密度泛泛函理论的第一原理和VASP5.4.4软件下的投影增强波法重新计算晶格常数,评估晶格稳定性,并探索所选掺杂元素的机械性能,如In,Si,V,Al,Bi,Nb,Sc,Ta,Ti,Y和Zr,包括剪切,刚度,压缩,和可塑性。研究表明,In和Si的战略掺杂显着提高了抗剪切性和刚度,而V的添加显着增强了抗压缩性。此外,加入Al,Bi,Nb,Sc,Ta,Ti,V,Y,和Zr具有显著提高的塑性,通过精确的合金化表明了广泛的机械增强。至关重要的是,通过Si和Sn掺杂试样的硬度实验证明了我们的计算模型的验证,证实了理论预测。此外,对状态密度的细致分析进一步证实了我们的计算方法的准确性和可靠性。这项研究强调了有针对性的合金化来定制Cu3P合金的机械性能的潜力,并建立了一个强大的理论框架来预测金属合金中掺杂的影响。本文提出的发现为材料设计和优化提供了宝贵的见解和新颖的视角,标志着朝着开发具有定制机械性能的先进材料迈出了重要的一步。
    In the quest to enhance the mechanical properties of CuP alloys, particularly focusing on the Cu3P phase, this study introduces a comprehensive investigation into the effects of various alloying elements on the alloy\'s performance. In this paper, the first principle of density universal function theory and the projection-enhanced wave method under VASP 5.4.4 software are used to recalculate the lattice constants, evaluate the lattice stability, and explore the mechanical properties of selected doped elements such as In, Si, V, Al, Bi, Nb, Sc, Ta, Ti, Y and Zr, including shear, stiffness, compression, and plasticity. The investigation reveals that strategic doping with In and Si significantly enhances shear resistance and stiffness, while V addition notably augments compressive resistance. Furthermore, incorporating Al, Bi, Nb, Sc, Ta, Ti, V, Y, and Zr has substantially improved plasticity, indicating a broad spectrum of mechanical enhancement through precise alloying. Crucially, the validation of our computational models is demonstrated through hardness experiments on Si and Sn-doped specimens, corroborating the theoretical predictions. Additionally, a meticulous analysis of the states\' density further confirms our computational approach\'s accuracy and reliability. This study highlights the potential of targeted alloying to tailor the mechanical properties of Cu3P alloys and establishes a robust theoretical framework for predicting the effects of doping in metallic alloys. The findings presented herein offer valuable insights and a novel perspective on material design and optimization, marking a significant stride toward developing advanced materials with customized mechanical properties.
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