Prior to the onset of the ferromagnetic transition in semimetallic $\mathrm{Eu}{\mathrm{B}}_6$, unusual magnetic and electric behavior have been reported. Using a highly sensitive magneto-optical imaging (MOI) technique, we visualize the behavior of magnetic domains in a $\mathrm{Eu}{\mathrm{B}}_6$ single crystal. The transformation from a paramagnetic to a ferromagnetic state is shown to be non-Curie-Weiss-like and proceeds via multiple breaks in the curvature of the temperature-dependent local magnetization. From our experiments, we identify three characteristic boundaries, $T^{*}\left(H\right),T_{c1}^{*}\left(H\right)$, and $T_{c2}\left(H\right)$, in a field-temperature magnetic phase diagram. Using scaling and a modified Arrott's plot analysis of isothermal bulk magnetization data, we determine the critical exponents $\beta =0.22\pm 0.01,\gamma =0.88\pm 0.05$ and $\delta =5.0\pm 0.1$ and a $\mathrm{critical}\mathrm{transition}\mathrm{temperature}=12.0\pm 0.2\mathrm{K}$, which is found to be equal to $T_{c2}$. The critical exponents are close to those associated with the universality class of tricritical mean field model. The absence of a model with which the exponents correspond with directly, suggests the presence of large critical fluctuations in this system. The critical fluctuations in this system are sensitive to the applied magnetic field, which leads to field dependence of boundaries in the magnetic phase diagram. Deep inside the ferromagnetic state at $T$ below $T_{c2}$, we observe the presence of large magnetized domains along with the observation of Barkhausen-like jumps in local magnetization. With increasing $T$ the magnetic domains disintegrate into finger-like patterns before fragmenting into disjoint magnetized puddles at $T_{c1}^{*}$ and ultimately disappearing at T*. At $T_{c1}^{*}$ we observe a significant increase in the spatial inhomogeneity of the local magnetic field distribution associated with the magnetic domain structure disintegrating into smaller magnetized structures. We explain our results via the formation of magnetic polaronic clusters and their coalescing into larger domains.

The superionic electrical conductor ${\mathrm{Ag}}_4\mathrm{SSe}$ is reported to undergo an unusual first-order structural phase transition at $\sim 260\mathrm{K}$ with concomitant anomalous electronic properties. Single-crystal x-ray diffraction reveals that the crystal undergoes a structural transition from monoclinic $\alpha \text{−}{\mathrm{Ag}}_4\mathrm{SSe}$ to an orthorhombic crystal structure below 260 K. The new low-temperature phase is denoted as $\delta \text{−}{\mathrm{Ag}}_4\mathrm{SSe}$, and it is found to be isostructural to $\alpha \text{−}{\mathrm{Ag}}_2\mathrm{Se}$. The diamagnetic magnetic susceptibility is of larger magnitude in the low-temperature $\delta$ phase than in $\alpha \text{−}{\mathrm{Ag}}_4\mathrm{SSe}$. A diamagnetic susceptibility of larger magnitude is usually related to a lower density of states at the Fermi level which leads to a decrease in the Pauli paramagnetic susceptibility. However, we find $\delta \text{−}{\mathrm{Ag}}_4\mathrm{SSe}$ to be metallic with a much lower resistivity than semiconducting $\alpha \text{−}{\mathrm{Ag}}_4\mathrm{SSe}$. As a consequence, the $\alpha \text{−}\delta$ structural phase transition of ${\mathrm{Ag}}_4\mathrm{SSe}$ causes an unusual Fermi surface reconstruction with an increased mobility of charge carriers and unexpected metallic behavior in $\delta \text{−}{\mathrm{Ag}}_4\mathrm{SSe}$. Band structure calculations substantiate such a claim. In addition, we also observe spontaneous voltage generation (SVG) at the phase transition, which has previously been observed only in a few magnetic materials.

We report the magnetotransport properties of $\alpha \text{−}{\mathrm{Bi}}_4{\mathrm{I}}_4$ single crystals, which have a crystal structure similar to that of the quasi-one-dimensional topological insulator $\beta \text{−}{\mathrm{Bi}}_4{\mathrm{I}}_4$. Prominent Shubnikov–de Hass oscillations and weak antilocalization effect are observed in all measured samples. The angular-dependent magnetoresistance indicates that the behavior of Shubnikov–de Hass oscillations is two-dimensional (2D) in $n$-type samples, while it is three-dimensional (3D) in $p$-type samples. First-principles calculations show that the $n$-type samples have a 2D Fermi surface, while the $p$-type samples have a 3D Fermi surface. Considering the similar carrier density and mobility, we infer that the transport behaviors in both types of samples come from bulk electron contributions. In addition, a large negative magnetoresistance with a transverse configuration is observed in the $n$-type sample A1. All the results indicate that $\alpha \text{−}{\mathrm{Bi}}_4{\mathrm{I}}_4$ is an important material platform for investigation of novel and interesting phenomena. Our work may also provide important references for studying the topological surface transport properties in $\beta \text{−}{\mathrm{Bi}}_4{\mathrm{I}}_4$ in the future.

In ${\mathrm{CsW}}_2{\mathrm{O}}_6$, which undergoes a metal-insulator transition (MIT) at 213 K, the emergence of exotic properties associated with rattling motion of Cs is expected owing to its characteristic $\beta$-pyrochlore-type structure. However, a hurdle for crystal growth hampers elucidation of detailed properties and mechanisms of the MIT. Here we report on the epitaxial growth of $\beta$-pyrochlore-type ${\mathrm{CsW}}_2{\mathrm{O}}_6$ films and their electronic properties across the MIT. Using pulsed-laser deposition technique, we grew single-crystalline ${\mathrm{CsW}}_2{\mathrm{O}}_6$ films exhibiting remarkably lower resistivity compared with a polycrystalline bulk and sharp MIT around 200 K. Negative magnetoresistance and a positive Hall coefficient were found, which became pronounced below 200 K. The valence-band and core-level photoemission spectra indicated the drastic changes across the MIT. In the valence-band photoemission spectrum, the finite density of states was observed at the Fermi level in the metallic phase. In contrast, an energy gap appeared in the insulating phase. The split of $\mathrm{W}4f$ core-level spectrum suggested the charge disproportionation of ${\mathrm{W}}^{5+}$ and ${\mathrm{W}}^{6+}$ in the insulating phase. The change of spectral shape in the $\mathrm{Cs}4d$ core levels reflected the rattling motion of ${\mathrm{Cs}}^{+}$ cations. These results strongly suggest that ${\mathrm{CsW}}_2{\mathrm{O}}_6$ is an exotic material in which MIT is driven by the charge disproportionation associated with the rattling motion.

Adsorption of $\mathrm{C}{\mathrm{O}}_2$ on a semiconductor surface is a prerequisite for its photocatalytic reduction. Owing to superior photocorrosion resistance, nontoxicity, and suitable band-edge positions, $\mathrm{Ti}{\mathrm{O}}_2$ is considered to be the most efficient photocatalyst for facilitating redox reactions. However, due to the absence of adequate understanding of the mechanism of adsorption, the $\mathrm{C}{\mathrm{O}}_2$ conversion efficiency on $\mathrm{Ti}{\mathrm{O}}_2$ surfaces has not been maximized. While anatase $\mathrm{Ti}{\mathrm{O}}_2$ (101) is the most stable facet, the (001) surface is more reactive, and it has been experimentally shown that the stability can be reversed and a larger percentage (up to $\sim 89\%)$ of the (001) facet can be synthesized in the presence fluorine ions. Therefore, through density functional calculations we have investigated the $\mathrm{C}{\mathrm{O}}_2$ adsorption on $\mathrm{Ti}{\mathrm{O}}_2$ (001) surfaces. We have developed a three-state quantum-mechanical model that explains the mechanism of chemisorption, leading to the formation of a tridentate carbonate complex. The electronic structure analysis reveals that the $\mathrm{C}{\mathrm{O}}_2\text{−}\mathrm{Ti}{\mathrm{O}}_2$ interaction at the surface is uniaxial and long ranged, which gives rise to anisotropy in binding energy (BE). It negates the widely perceived one-to-one correspondence between coverage and BE and infers that the spatial distribution of $\mathrm{C}{\mathrm{O}}_2$ primarily determines the BE. A conceptual experiment is devised where the $\mathrm{C}{\mathrm{O}}_2$ concentration and flow direction can be controlled to tune the BE within a large window of $\sim 1.5\mathrm{eV}$. The experiment also reveals that a maximum of $50\%$ coverage can be achieved for chemisorption. In the presence of water, the activated carbonate complex forms a bicarbonate complex by overcoming a potential barrier of $\sim 0.9\mathrm{eV}$.

We use density functional theory (DFT) to compute the core structures of $a_0\left[100\right]\left(010\right)$ edge, $a_0\left[100\right]\left(011\right)$ edge, $a_0/2\left[\overline{1}\overline{1}1\right]\left(1\overline{1}0\right)$ edge, and $a_0/2\left[111\right]\left(1\overline{1}0\right){71}^{\circ }$ mixed dislocations in body-centered cubic (bcc) Fe. The calculations are performed using flexible boundary conditions (FBC), which effectively allow the dislocations to relax as isolated defects by coupling the DFT core to an infinite harmonic lattice through the lattice Green function (LGF). We use the LGFs of the dislocated geometries in contrast to most previous FBC-based dislocation calculations that use the LGF of the bulk crystal. The dislocation LGFs account for changes in the topology of the crystal in the core as well as local strain throughout the crystal lattice. A simple bulklike approximation for the force constants in a dislocated geometry leads to dislocation LGFs that optimize the core structures of the $a_0\left[100\right]\left(010\right)$ edge, $a_0\left[100\right]\left(011\right)$ edge, and $a_0/2\left[111\right]\left(1\overline{1}0\right){71}^{\circ }$ mixed dislocations. This approximation fails for the $a_0/2\left[\overline{1}\overline{1}1\right]\left(1\overline{1}0\right)$ dislocation, however, so in this case we derive the LGF from more accurate force constants computed using a Gaussian approximation potential. The standard deviations of the dislocation Nye tensor distributions quantify the widths of the dislocation cores. The relaxed cores are compact, and the local magnetic moments on the Fe atoms closely follow the volumetric strain distributions in the cores. We also compute the core structures of these dislocations using eight different classical interatomic potentials, and quantify symmetry differences between the cores using the Fourier coefficients of their Nye tensor distributions. Most of the core structures computed using the classical potentials agree well with the DFT results. The DFT core geometries provide benchmarking for classical potential studies of work-hardening, as well as substitutional and interstitial sites for computing solute-dislocation interactions that serve as inputs for mesoscale models of solute strengthening and solute diffusion near dislocations.

The accelerated exploration of the materials space in order to identify configurations with optimal properties is an ongoing challenge. Current paradigms are typically centered around the idea of performing this exploration through high-throughput experimentation/computation. Such approaches, however, do not account for—the always present—constraints in resources available. Recently this problem has been addressed by framing materials discovery as an optimal experiment design. This work augments earlier efforts by putting forward a framework that efficiently explores the materials design space not only accounting for resource constraints but also incorporating the notion of model uncertainty. The resulting approach combines Bayesian model averaging within Bayesian optimization in order to realize a system capable of autonomously and adaptively learning not only the most promising regions in the materials space but also the models that most efficiently guide such exploration. The framework is demonstrated by efficiently exploring the MAX ternary carbide/nitride space through density functional theory (DFT) calculations.

Layered structure and peculiar electronic properties of two-dimensional (2D) materials foster the concept of utilizing them as main components of lithium-ion batteries. Understanding basic physical mechanisms governing the interaction of Li with 2D crystals is of key importance to succeeding in a rational design of cathode and anode materials with superior functionalities. In this study density functional theory was applied to reveal the microscopic picture of Li interaction with 15 2D crystals, including several transition metal oxides and dichalcogenides, carbides of Group XIV elements, functionalized graphene, silicene, and germanene, as well as black phosphorus and ${\mathrm{Ti}}_2\mathrm{C}$ MXene. We found that the general trend in Li binding can be estimated from positions of conduction band minima of 2D materials, since the energy of the lowest empty electronic states shows a nice correlation with the strength of Li adsorption. At variance to the majority of studied surfaces where the electron transferred from Li is spread across the substrate, in monolayers of carbides of Group XIV elements the interaction with Li and the charge transfer are well localized. This gives rise to their capability to accommodate Li structures with a nearly constant binding energy of alkaline atoms over Li coverages ranging from well-separated adatoms to a full monolayer.

We measure the thermal time constants of suspended single-layer molybdenum disulfide drums by their thermomechanical response to a high-frequency modulated laser. From this measurement, the thermal diffusivity of single-layer ${\mathrm{MoS}}_2$ is found to be $1.14\times {10}^{-5}{\mathrm{m}}^2/\mathrm{s}$ on average. Using a model for the thermal time constants and a model assuming continuum heat transport, we extract thermal conductivities at room temperature between 10 to $40\mathrm{W}{\mathrm{m}}^{-1}{\mathrm{K}}^{-1}$. Significant device-to-device variation in the thermal diffusivity is observed. Based on a statistical analysis we conclude that these variations in thermal diffusivity are caused by microscopic defects that have a large impact on phonon scattering but do not affect the resonance frequency and damping of the membrane's lowest eigenmode. By combining the experimental thermal diffusivity with literature values of the thermal conductivity, a method is presented to determine the specific heat of suspended 2D materials, which is estimated to be $255\pm 104\mathrm{J}{\mathrm{kg}}^{-1}{\mathrm{K}}^{-1}$ for single-layer ${\mathrm{MoS}}_2$.

The experimental realization of quasi-two-dimensional hole gas at the complex oxide interface has long been a grand challenge that may open up new possibilities for oxide-based electronics. ${\mathrm{SrTiO}}_3$ (STO)-capped ${\mathrm{LaAlO}}_3$ (LAO)/${\mathrm{SrTiO}}_3$ (100) is a potential candidate that has been recently demonstrated to show possible electron-hole bilayer conducting channels near the interfaces of the heterostructure. In this work we present a systematic investigation on the structural and magnetotransport properties of STO-capped and uncapped LAO/STO (100) samples that were grown by an oxide molecular beam epitaxy system. The STO/LAO/STO (100) samples exhibit metallic interfaces down to $T$ = 2 K even with a LAO thickness of merely 3 unit cells (3-uc). On the contrary for uncapped LAO(5-uc)/STO (100) samples the conducting interface becomes insulating at lower temperatures due to the surface adsorbate on top of the LAO as revealed from x-ray photoelectron spectroscopy measurements. The magnetotransport data at different back-gate voltages for STO-capped and uncapped LAO/STO (100) samples were analyzed and compared to each other using the two-band model. The presence of two types of charge carriers with opposite signs is uniquely found for STO/LAO/STO (100) samples which is in big contrast to the uncapped LAO/STO (100) samples with only electron-type carriers. Our results support the coexistence of electron-type and hole-type carriers in the STO/LAO/STO (100) heterostructure where their sheet densities and mobilities can be tuned significantly by electrical gating effect and the layer thickness of the heterostructure.

The search for large-band-gap quantum spin Hall (QSH) insulators, in which the dissipationless gapless edge states lie inside the bulk gap, is critical for their practical applications at room temperature. Based on first-principles calculations, we propose a sort of QSH insulator in a rectangular structure, i.e., AuSb, AuAs, and CuAs monolayers, which exhibits sizable bulk gaps up to 258 meV. These compounds host unexpected topological Rashba-like edge states, which exhibit strong dispersion with a nearly-free-electron feature. Such nontrivial edge states originate from spin-orbital coupling and an abrupt discontinuous potential across the surface. Furthermore, we argue that the AuSb monolayer can be epitaxially grown on a rutile $\mathrm{Ti}{\mathrm{O}}_2\left(110\right)$ surface. Importantly, the thermodynamic stability of AuSb is enhanced while the topological features are perfectly preserved due to the weak van der Waals interaction at the interface. Our findings provide promising large-gap QSH candidates with exotic topological Rashba-like edge states that are in favor of experimental realization at room temperature.

While ${\mathrm{ZnGeN}}_2$ and GaN are closely lattice matched and have almost equal band gaps around 3.5 eV, their band offset is of order 1 eV. This situation suggests that there could be an opportunity for tuning the band gap in the alloy system. In particular, we examine here the 50 at. % composition, ${\mathrm{ZnGeGa}}_2{\mathrm{N}}_4$. It is shown that there are two 16-atom unit cell ordered structures, with space groups $Pmn{2}_1$ and $P1n1$, that obey the octet rule, with each N bound to two Ga, one Zn, and one Ge. The $Pmn{2}_1$ structure is a superlattice along the orthorhombic $b$ direction of the ${\mathrm{ZnGeN}}_{2}Pbn{2}_1$ structure, in which half the cell is replaced by GaN; consequently, octet-rule-preserving polytypes spanning the entire range of composition can be formed based upon this structure. Two other structures that do not obey the octet rule are also considered for comparison. These are superlattices consisting of 1/2 cell GaN and 1/2 cell ${\mathrm{ZnGeN}}_2$ along the orthorhombic $a$ or $c$ direction. By means of fully relaxed density functional calculations, we find that the structures that obey the octet rule have significantly lower total energy than the ones that do not. Detailed crystallographic data on these four structures: space group, lattice constants, relaxed Wyckoff positions, and predicted x-ray diffraction spectra, are provided. The lowest energy structure is found to have a negative energy of formation, comparable to those of ${\mathrm{ZnGeN}}_2$ and GaN. However, the mixing energy is slightly positive, indicating a tendency toward phase separation into ${\mathrm{ZnGeN}}_2$ and GaN even when only considering low energy octet-rule-preserving structures. The band gaps of the octet-rule-preserving structures, calculated using the quasiparticle self-consistent $GW$ method, are found to be slightly higher than those of ${\mathrm{ZnGeN}}_2$ and GaN. This result can be explained in terms of size quantization effects compensating the reduced interface band gap.

To understand superconductivity in Chevrel phase compounds and guide the search for interesting properties in materials created with Chevrel phase molecules as building blocks, we use ab initio methods to study the properties of single ${\mathrm{Mo}}_6{X}_8$ molecules with $X=\text{S}$, Se, Te as well as the bulk solid ${\mathrm{PbMo}}_6{\mathrm{S}}_8$. In bulk ${\mathrm{PbMo}}_6{\mathrm{S}}_8$, the different energy scales from strong to weak are the band kinetic energy, the intramolecular Coulomb interaction, the on-molecule Jahn-Teller energy, and the Hund's exchange coupling. The metallic state is stable with respect to Mott and polaronic insulating states. The bulk compound is characterized by a strong electron-phonon interaction with the largest coupling involving phonon modes with energies in the range from 11 to 17 meV and with a strong intermolecule (Peierls) character. A two-band Eliashberg equation analysis shows that the superconductivity is strong coupling, with different gaps on the two Fermi surface sheets. A Bergman-Rainer analysis of the functional derivative of the transition temperature with respect to the electron-phonon coupling reveals that the Peierls modes provide the most important contribution to the superconductivity. This work illustrates the importance of intermolecular coupling for collective phenomena in molecular solids.

We demonstrate the integration of a two-dimensional electron gas (2DEG) oxide structure composed of $\mathrm{LaTi}{\mathrm{O}}_3/\mathrm{SrTi}{\mathrm{O}}_3$ (LTO/STO) on undoped Si(001) that possesses the attractive attributes of high charge density from the oxide and high mobility of silicon. Key to this approach is modification of the oxygen content at the STO-Si interface, which tunes the band alignment and induces electron carriers to move from the oxide 2DEG to form a 2DEG in the silicon substrate. As a consequence, the overall mobility of the heterostructure increases by two orders of magnitude compared to that in the oxide 2DEG to up to $100\mathrm{c}{\mathrm{m}}^2{\mathrm{V}}^{-1}{\mathrm{s}}^{-1}$ at room temperature, with a carrier density of $\sim 1\times {10}^{13}\mathrm{c}{\mathrm{m}}^{-2}$. This approach can be applied to technologies that require both high carrier and high carrier mobility for applications in plasmonics and high power electronics.

It has been recently demonstrated that yttrium oxyhydride (YHO) films can exhibit reversible photochromic properties when exposed to illumination at ambient conditions. This switchable optical property enables their utilization in many technological applications, such as smart windows, sensors, goggles, and medical devices. However, how the composition of the films affects their optical properties is not fully clear and therefore demands an investigation. In this paper, the composition of YHO films manufactured by reactive magnetron sputtering under different conditions is deduced in a ternary diagram from time-of-flight elastic recoil detection analysis. The results suggest that stable compounds are formed with a specific chemical formula—$\mathrm{Y}{\mathrm{H}}_{2\text{−}\delta }{\mathrm{O}}_{\delta }$. In addition, optical and electrical properties of the films are investigated, and a correlation with their compositions is established. The corresponding photochromic response is found in a specific oxygen concentration range ($0.45<\delta <1.5$) with maximum and minimum of magnitude on the lower and higher border, respectively.

Bismuth-antimony ($\mathrm{B}{\mathrm{i}}_{100\text{−}x}\mathrm{S}{\mathrm{b}}_x$) alloys have the highest thermoelectric figure of merit of all $n$-type thermoelectric materials below 200 K. They are the only Te-free thermoelectric alternatives to the tetradymite materials for applications at and below room temperature. Single-crystal $\mathrm{B}{\mathrm{i}}_{100\text{−}x}\mathrm{S}{\mathrm{b}}_x$ alloys show the maximum figure of merit $zT\sim 0.5$ at 200 K along the trigonal axis crystallographic direction, but the cost associated with single-crystal growth and the tendency of single crystals to cleave preclude their use. Mechanically robust polycrystalline $\mathrm{B}{\mathrm{i}}_{100\text{−}x}\mathrm{S}{\mathrm{b}}_x$/$\mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3$ nanocomposites are shown here to be able to reach competitive $zT$ values. Two compositions are investigated, $\mathrm{B}{\mathrm{i}}_{82}\mathrm{S}{\mathrm{b}}_{18}$ and $\mathrm{B}{\mathrm{i}}_{88}\mathrm{S}{\mathrm{b}}_{12}$. Thermal and electrical transport properties confirm significant reduction of lattice thermal conductivity in the nanocomposite samples, but the concurrent loss of electrical conductivity leads to an unfavorable net effect on $zT$. In contrast, a large increase in thermopower is observed in the $\mathrm{B}{\mathrm{i}}_{82}\mathrm{S}{\mathrm{b}}_{18}$/$\mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3$ nanocomposite system, which is attributed to a better optimized doping level. Accordingly, the $zT$ of a $\mathrm{B}{\mathrm{i}}_{82}\mathrm{S}{\mathrm{b}}_{18}$/$\mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3$ nanocomposite sample is shown to reach $zT\sim 0.4$ at 240 K, which rivals that of single crystals. Near room temperature, the $zT$ of the nanocomposite sample is improved by $\sim 60\%$ over that of the single-crystalline sample. Galvano- and thermomagnetic analysis suggests a strong effect of carrier concentration on the $zT$ of ${\mathrm{Bi}}_{100\text{−}x}{\mathrm{Sb}}_x/{\mathrm{Al}}_2{\mathrm{O}}_3$ nanocomposite samples.

Many bulk-metallic-glass (BMG) forming melts undergo a rather abrupt fragile-to-strong transition (FST), at which density and local structure appear to change only continuously. In this study, we reproduce similar results for a ternary BMG former (${\mathrm{Zr}}_{0.606}{\mathrm{Cu}}_{0.29}{\mathrm{Al}}_{0.104}$) using computer simulations. The results include a smooth evolution of radial distribution functions at small distances through the FST. However, the long-range density correlation length increases (quasi)discontinuously at the FST as revealed by an Ornstein-Zernike-based analysis of the radial distribution function. Likewise, the temperature derivative of $a_{\mathrm{Zr}-\mathrm{Zr}}\left(T\right)$ decreases (quasi)discontinuously at the FST. These observations add to the rich phenomenology of FSTs lacking a theoretical understanding.

The role of grain boundaries in limiting irradiation damage in nanocrystalline materials is often correlated with the grain boundary sink efficiency. Here, we demonstrate on a tungsten material system (which has very distinct vacancy and interstitial mobilities) that sink efficiency does not unequivocally describe how grain boundaries impact irradiation damage. Rather, it reflects a particular defect diffusion equation that can change if any of the bulk conditions change. Even when denuded zone formation does not occur and grain boundaries have zero sink efficiencies, grain boundaries still impact the performance of nanocrystalline materials under irradiation by acting as a saturable defect storage site. However, denuded zone formation can occur under a necessary requirement of extra defect recombination at the grain boundaries (which, for example, is not possible when vacancy migration does not occur). These insights provide answers to several outstanding questions regarding the sink efficiency of a grain boundary and assist in parametrizing the role of grain boundaries in limiting irradiation damage in nanocrystalline materials.