PHYSICAL REVIEW B 98, 174111 (2018) Heterogeneity governs diameter-dependent toughness and strength in SiC nanowires Fazle Elahi, Ling Ma, and Zubaer M. Hossain * Department of Mechanical Engineering, Laboratory of Mechanics & Physics of Heterogeneous Materials, University of Delaware, Newark, Delaware 19716, USA (Received 27 August 2018; revised manuscript received 9 November 2018; published 27 November 2018) Using a combination of density functional theory and molecular dynamics simulations, this paper reveals the atomistic origin of diameter-dependent extreme mechanical behavior of [111] 3C-SiC nanowires obtained from an energy-based framework. Our results suggest that heterogeneity in atomic stress and variations in diameter-dependent potential-energy density have a profound impact on extreme mechanical properties in the nanowires. The heterogeneity in stress evolves from the nonuniform bond lengths mediated by low coordinated surface atoms—and it penetrates the entire cross section in thinner nanowires and constitutes the atomistic basis for their large reduction in fracture strain, toughness, and strength. Although stress heterogeneity is substantially higher in ultrathin nanowires, its intensity drops and saturates rapidly in larger nanowires following a nonlinear dependence on diameter. The maximum stress heterogeneity in a cross section localizes crack nucleation at the core in ultrathin nanowires but near the surface in larger nanowires. Moreover results show that stiffness, toughness, strength, and fracture strain of the nanowires increase nonlinearly with increasing diameter and saturate at a lower value compared to bulk SiC. In addition to resolving wide discrepancies in the reported values of the first-order elastic modulus in SiC nanowires, the findings highlight heterogeneity as a critical factor for inducing diameter-dependent extreme mechanical behavior in brittle nanowires. DOI: 10.1103/PhysRevB.98.174111 I. INTRODUCTION Strength and toughness are two crucial mechanical prop- erties of a solid that dictate its ability to function reliably under extreme conditions. For brittle solids (such as SiC, Si, Ge, or SiO 2 ) the ideal strength is defined by the maximum stress and the toughness by the maximum elastic energy density that the solid can withstand prior to failure. These are well-defined intensive properties for a bulk solid, but they act like an extensive property in nanostructured solids due to the presence of surfaces which alter the energetics of the material and associated mechanical behavior [1–15]. Until recently, it was believed that the evolution of sur- face stress in nanowires (NWs) is the key factor for in- ducing a variety of diameter-dependent (d -dependent) me- chanical and structural features in nanowires. Although a surface can set up various interconnected effects including surface stress [12], surface potential [13], surface energy [16], charge density [14], chemical reactions [17], and atomic reconstruction [15], it is generally surface stress that is used to explain various mechanisms in nanowires including self- healing, surface reorientation, phase transformation, yield- ing, failure, and ductile-to-brittle transition [1–11]. Recent findings nonetheless contradict several surface-stress-based explanations. For instance, softening or stiffening behavior of metallic nanowires is shown to be controlled by the orientation-dependent nonlinear elasticity at the core alone [18]. Also, instability to plastic shear has been shown ex- perimentally to originate mainly from the surface energy * zubaer@udel.edu [19], which violates several surface-stress-based interpreta- tions [11,20–22] that are mostly built upon the assumption of isotropy and homogeneity in material properties [12]. Additionally, substantial efforts have been devoted to pre- dict the first-order elastic modulus in a range of nanowires [23–30]; but analogous efforts remain missing for the higher- order elastic properties of nanowires and their failure mech- anisms that can reveal the atomistic processes responsible for the nucleation of defects causing catastrophic failure under practical conditions. Extreme mechanical properties of nanowires and their atomistic basis therefore continue to puzzle scientists and engineers, invoking novel insight and understanding on the subject [31,32]. Here, we focus on SiC nanowires which are brittle in character and have a variety of important applications in stretchable absorbers, fast-response ultraviolet detectors, pres- sure sensors, aerogels, biosensors, transistors, and reinforce- ments in composites due to high-temperature heat resistance, recoverability, chemical resistance, and lightweightness [33– 37]. Silicon carbide has a number of polytypes, such as a-SiC, 6H-SiC, 4H-SiC, 2H-SiC, and 3C-SiC [37]. Among these polytypes, 3C-SiC nanowires have drawn wide attention due to their exceptional properties. Using ab initio simulations, it has been reported that 3C-SiC nanowires show remarkable d - dependent electronic properties with increased optical activity and electron mobility [27,38–41]. In the context of mechani- cal properties, it has been shown that the first-order elastic modulus depends strongly on diameter [29,41,42]. Nonethe- less, the reported values cover a wide range of variations ranging from 150 to 700 GPa without any clear trend on it diameter-dependent behaviors [30]. The large discrepancy is attributed to several factors including: The way the diameter 2469-9950/2018/98(17)/174111(12) 174111-1 ©2018 American Physical Society