Close-packed Crystals Research Articles

A simple and accurate method to determine fluid-crystal phase boundaries from direct coexistence simulations.

One method for computationally determining phase boundaries is to explicitly simulate a direct coexistence between the two phases of interest. Although this approach works very well for fluid-fluid coexistences, it is often considered to be less useful for fluid-crystal transitions, as additional care must be taken to prevent the simulation boundaries from imposing unwanted strains on the crystal phase. Here, we present a simple adaptation to the direct coexistence method that nonetheless allows us to obtain highly accurate predictions of fluid-crystal coexistence conditions, assuming that a fluid-crystal interface can be readily simulated. We test our approach on hard spheres, the screened Coulomb potential, and a 2D patchy-particle model. In all cases, we find excellent agreement between the direct coexistence approach and (much more cumbersome) free-energy calculation methods. Moreover, the method is sufficiently accurate to resolve the (tiny) free-energy difference between the face-centered cubic and hexagonally close-packed crystal of hard spheres in the thermodynamic limit. The simplicity of this method also ensures that it can be trivially implemented in essentially any simulation method or package. Hence, this approach provides an excellent alternative to free-energy based methods for the precise determination of phase boundaries.

Ab initio investigation of electronic structure and magnetic transformation during the bcc to hcp transition in Fe induced by pressure

The pressure-induced structural transition from a body-centered cubic (bcc) to a hexagonal close-packed (hcp) crystal in Fe is studied through ab initio electronic structure calculations, combining with the thermodynamic and kinetic phase-transition methods. According to the energy-volume relationship and thermodynamic criterion, the reasonable phase transition pressure is calculated to be about 13.88 GPa. The SSNEB method is employed to examine kinetic structural and barrier changes along bcc-hcp transition under various pressures. The transformation path involves the deformation of (110)bcc into the tightly packed (0001)hcp, accompanied by the relative slip of (110)bcc along the [1̅10]bcc direction, leading to the formation of the hcp structure. Our results indicate a reduction in the transition barrier of bcc-hcp with increasing pressure. Under the thermodynamic phase transition pressure, the bcc-hcp phase transition barrier is still as high as 140 meV, implying that pure hydrostatic pressure is not a sufficient condition to drive the phase transition. In addition, different from the continuous change of volume, the magnetism of the structure undergoes a magnetic mutation at the transition state, and the phase transition process involves complex magnetic transitions.

In situ observation of the atomic shuffles during the {112¯1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{11}}\\bar{{{2}}}{{1}}$$\\end{document}} twinning in hexagonal close-packed rhenium

Twinning, on par with dislocations, is critically required in plastic deformation of hexagonal close-packed crystals at low temperatures. In contrast to that in cubic-structured crystals, twinning in hexagonal close-packed crystals requires atomic shuffles in addition to shear. Though the twinning shear that is carried by twinning dislocations has been captured for decades, direct experimental observation of the atomic shuffles, especially when the shuffling mode is not unique and does not confine to the plane of shear, remains a formidable challenge to date. Here, by using in-situ transmission electron microscopy, we directly capture the atomic mechanism of the 112¯1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\left\\{11\\bar{2}1\\right\\}$$\\end{document} twinning in hexagonal close packed rhenium nanocrystals. Results show that the 112¯1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\left\\{11\\bar{2}1\\right\\}$$\\end{document} twinning is dominated by the (b1/2, h1/2) twinning disconnections. In contrast to conventional expectations, the atomic shuffles accompanying the twinning disconnections proceed on alternative basal planes along 1/6 11¯00\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\left\\langle 1\\bar{1}00\\right\\rangle$$\\end{document}, which may be attributed to the free surface in nanocrystal samples, leading to a lack of mirror symmetry across the 112¯1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\left\\{11\\bar{2}1\\right\\}$$\\end{document} twin boundary.

Divergence among Local Structure, Dynamics, and Nucleation Outcome in Heterogeneous Nucleation of Close-Packed Crystals.

Heterogeneous crystal nucleation is the dominant mechanism of crystallization in most systems, yet its underlying physics remains an enigma. While emergent interfacial crystalline order precedes heterogeneous nucleation, its importance in the nucleation mechanism is unclear. Here, we use path sampling simulations of two model systems to demonstrate that crystalline order in its traditional sense is not predictive of the outcome of the heterogeneous nucleation of close-packed crystals. Consequently, structure-based collective variables (CVs) that reliably describe homogeneous nucleation can be poor descriptors of heterogeneous nucleation. This divergence between structure and nucleation outcome is accompanied by an intriguing dynamical anomaly, wherein low-coordinated crystalline particles outpace their liquid-like counterparts. We use committor analysis, high-throughput screening, and machine learning to devise CV optimization strategies and present suitable structural heuristics within the metastable fluid for CV prescreening. Employing such optimized CVs is pivotal for properly characterizing the mechanism of heterogeneous nucleation in metallic and colloidal systems.

Anisotropic functionalized platelets: percolation, porosity and network properties.

Anisotropic functionalized platelets are able to model the assembly behaviour of molecular systems in two dimensions thanks to the unique combination of steric and bonding constraints. The assembly scenarios can vary from open to close-packed crystals, finite clusters and chains, according to the features of the imposed constraints. In this work, we focus on the assembly of equilibrium networks. These networks can be seen as disordered, porous monolayers and can be of interest for instance in nano-filtration and optical applications. We investigate the formation and properties of two dimensional networks from shape anisotropic colloids functionalized with four patches. We characterize the connectivity properties, the typical local bonding motives, as well as the geometric features of the emerging networks for a large variety of different systems. Our results show that networks of shape anisotropic colloids assemble into highly versatile network topologies, that may be utilized for applications at the nanoscale.

Data-driven texture design for reducing elastic and plastic anisotropy in titanium alloys

Polycrystalline titanium alloys exhibit anisotropic elastic and plastic properties, which hinder their extensive application as structural components. Overcoming this anisotropy via texture control is challenging due to the anisotropy intrinsic to the titanium single crystal. We propose a theoretical framework to derive textures that minimize anisotropy while maximizing Young’s modulus or flow stress. The workflow integrates data-driven methods, convex optimization theory, and computational crystal plasticity, using measured elastic constants and the alloy’s three slip modes. Optimization constraints are applied to predict textures that satisfy an anisotropy-reducing texture-property relationship. Examples include minimizing both elastic and plastic anisotropy while maximizing stiffness or flow stress, maximizing both stiffness and flow stress, and minimizing the number of distinct orientations. Deformation crystal plasticity simulations of 3D polycrystal microstructure realizations of the example textures demonstrate the achievement of target properties. We show that uniformly distributed (or no) textures or textures designed to purely reduce elastic anisotropy are accompanied by reduced moduli. Counterintuitively, the analysis reveals that appropriate fractions of a relatively small number of select orientations can reduce elastic or plastic anisotropy. Moreover, we derive anisotropy-reducing textures constrained to achieve similarity to those from common metal forming processes like rolling. Finally, we show that anisotropy-reducing textures from this framework can be effectively used for minimizing anisotropy in other Ti alloys, without the need to repeat the data-collection and optimization processes. This study offers new insights into the link between microstructure texture and structural properties, providing a novel approach to designing materials of anisotropic hexagonal close-packed crystals.

Non-crystallographic helices in polymers and close-packed metallic crystals determined by the four-dimensional counterpart of the icosahedron

Non-crystallographic fractional screw axes are inherent to the constructions of n-dimensional crystallography, where 3 < n ≤ 8. This fact allows one to consider experimentally obtained helices as periodic approximants of helices from the four-dimensional {3, 3, 5} polytope and its derivative constructions. For the tetrahedral Coxeter–Boerdijk helix (tetrahelix) with a 30/11 axis from the {3, 3, 5} polytope, approximants with 11/4 and 8/3 axes in three-dimensional Euclidean space {\bb E}^{3} are considered. These determine the structure of rods composed of deformed tetrahedra in close-packed crystals of α-Mn and β-Mn. In the {3, 3, 5} polytope, highlighted here for the first time, is a 40-vertex helix with a 20/9 axis composed of seven-vertex quadruples of tetrahedra (tetrablocks), whose 7/3 approximants determine in a crystal of an α-Mn rod of deformed tetrablocks with the same period as the 11/4 approximant of the tetrahelix. In the spaces of the three-dimensional sphere and {\bb E}^{3}, the parameters of 20/9, 40/9 and 40/11 helices, as well as of their 20- and 40-vertex approximants, are calculated. The parameters of the approximant of the 40/11 helix in {\bb E}^{3} correspond to experimentally determined parameters of the α-helix, which allows us to explain the versatility of the α-helix in proteins by the symmetry of the polytope. The set of fractional axes of all periodic approximants of helices with 30/11, 20/9, 40/9, 40/11 axes, as well as the powers of these axes, are combined into a tetrahedral-polytope class of 50 basic axes. The basic axes as well as composite (defined as a combination of basic ones) fractional axes of this class cover all fractional axes known to us according to literature data for polymers, biopolymers and close-packed metals.

An assessment of polarized light microscopy as a characterization method for crystal plasticity simulations

Polarized light microscopy is a large-area, high-resolution, high-throughput microstructural characterization method for polycrystalline materials comprised of hexagonal close-packed crystals. Due to the fact that polarized light microscopy only determines the orientation of a crystal’s c axis, it is necessary to assess the applicability of this new characterization modality for use in integrated computational materials engineering workflows for simulating the deformation response of polycrystalline materials. We present a computational study in which the effect of this orientation ambiguity on the predictions of crystal plasticity finite element simulations is quantified. We focus on an idealized polycrystalline sample with random texture, from which a number of c axis-similar samples are generated, each with random rotations about each constituent crystal’s c axis. We scrutinize the differences in stress field predictions between the reference sample and the randomly altered samples during monotonic tensile tests, as well as the spatial differences in predictions. Our findings indicate that differences are lowest in the elastic regime, and increase dramatically during the macroscopic elastic–plastic transition. We further find that results do not exhibit a strong spatial dependence, indicating that orientation and neighborhood are the primary causes of differences in stress field predictions.

Low-temperature anomalies in solid 4He (Review article)

The thermodynamic and mechanic anomalies within the region 0.1–0.5 K experimentally observed in hexagonal close-packed solid 4He crystal are discussed and interpreted on the basis of a polytypic HCP structure (close-packed stack of 2D crystalline planes on the triangular lattice). It elucidated the principal role of the stacking faults and Shockley’s partial dislocations in the quite unexpected low-temperature behavior of the solid 4He.

Densest-known packings and phase behavior of hard spherical capsids.

By mostly using Monte Carlo numerical simulation, this work investigates the densest-known packings and phase behavior of hard spherical capsids, i.e., hard infinitesimally thin spherical caps with a subtended angle larger than the straight angle. The infinitely degenerate densest-known packings are all characterized by hard spherical capsids that interlock and can be subdivided into three families. The first family includes crystalline packings that are constructed by suitably rotating and stacking layers of hexagonally arranged and suitably tilted hard spherical capsids; depending on the successive rotations, the crystalline packings of this family can become the face-centered cubic crystal, the hexagonal close-packed crystal, and their infinitely degenerate variants in the hard-sphere limit. The second family includes crystalline packings that are characterized by rhombic motifs; they all become the face-centered cubic crystal in the hard-sphere limit. The third family includes crystalline packings that are constructed by suitably shifting and stacking layers in which hard spherical capsids are arranged in tightly packed, straight or zigzag, columns; depending on the successive shifts, the crystalline packings of this family can become the face-centered cubic crystal, the hexagonal close-packed crystal, and their infinitely degenerate variants in the hard-sphere limit. In the plane number density vs subtended angle, the phase diagram of hard spherical capsids features a hexagonal columnar liquid-crystalline phase, toward the hard-hemispherical-cap limit, and a plastic-crystalline phase, toward the hard-sphere limit, in addition to the isotropic fluid phase and crystalline phases. On departing from the hard-sphere limit, the increasing propensity of hard spherical capsids to interlock progressively disfavors the plastic-crystalline phase while favoring auto-assemblage into mostly dimeric interlocks in the denser isotropic fluid phase so that a purely entropic isotropic-fluid-plastic-crystal-isotropic-fluid re-entrant sequence of phase transitions is observed in systems of hard spherical capsids with a subtended angle intermediate between the straight angle and the complete angle.

Modeling Thermoelasticity of HCP single crystals using a nonlocal discrete approach

This paper presents full-field modeling Thermoelasticity of hexagonal close-packed (HCP) single crystals using reformulations of conventional continuum theories based on a novel nonlocal lattice particle method (LPM). In LPM, grain domain is modeled as an assembly of regularly packed material particles according to the atomic lattice. The interaction between material particles is nonlocal, e.g., for mechanical problems, a material particle interacts with neighboring material particles up to certain distance via bonds and the interaction between two material particles depends on the deformation states of not only the two material particles but also all their neighbors. To determine the nonlocal interaction between material particles, a top-down approach based on the classical continuum theories is developed. Equivalency assumptions of energy, heat transfer rate and thermal strain between LPM and its continuum counterpart are made to consistently determine the material particle interaction for mechanical, thermal, and thermal–mechanical coupling problems, respectively. To capture the crystallographic orientation, a lattice rotation scheme that is equivalent to the coordinate transformation used in the classical continuum theories is adopted. Numerical studies regarding validity of the proposed nonlocal discrete reformulation and accuracy of the model prediction are conducted for all three types of analysis. Good agreements are observed between the results from the developed reformulations and the conventional continuum theories.

A New Anti-Alias Model of Ab Initio Calculations of the Generalized Stacking Fault Energy in Face-Centered Cubic Crystals

The anti-alias model is an effective method to calculate the generalized stacking fault energy of the hexagonal close-packed crystals, but it has not been applied to the face-centered cubic crystals due to two different stacking faults occurring in the supercell during the sliding process. Based on the symmetry of these two stacking faults and the existing single analytic formula of the generalized stacking fault energy, we successfully extend the anti-alias model to compute the generalized stacking fault energy of face-centered cubic crystals, and the common fcc metals Al, Ni, Ag and Cu are taken as specific examples to illustrate the computational details. Finally, the validity of the proposed model is verified by data comparison and analysis. It is suggested that the anti-alias model is a good choice for the researchers to obtain more accurate generalized stacking fault energy of face-centered cubic metals.

Gold Nanoparticle–Polyelectrolyte Complexes with Tunable Structure Probed by Synchrotron Small-Angle X-ray Scattering: Implications for the Production of Colloidal Crystals-Based Nanophotonic Materials

Close-packed colloidal crystals of gold nanoparticles (AuNPs) are of great interest in the field of nanophotonics due to their lattice-pattern-dependent optical properties. One challenge resides in producing such crystalline assemblies by a scalable approach involving polydisperse AuNPs obtained by standard synthesis routes and structuring natural molecules in water at room temperature. Electrostatic complexation between functionalized AuNPs and oppositely charged polyelectrolytes (PELs) is a very simple way to create AuNP self-assemblies of different morphologies and compactness. Our work investigates, using synchrotron small-angle X-ray scattering, their structure as a function of concentration, PEL persistence length and ionic strength. By decreasing the radius, R, of the positively charged gold nanoparticles to a few nm (R ≤ 3 nm) and increasing the polyelectrolyte persistence length, LT, substituting flexible sodium polystyrenesulfonate for natural semiflexible hyaluronan, we tuned the characteristic ratio LT/R up to values of ≥1.85. Such ratios allow the successful formation of a new AuNPs arrangement with a high degree of short-range order at low ionic strength and of crystalline order when interactions are screened by addition of salt. This approach involving commercially available natural water-soluble semiflexible PELs, opens a low-cost and promising way for the one-step production of gold colloidal crystals, which can be of ubiquitous utility in nanophotonics.

Thermal plasma sintering of forsterite ceramics

To date, new synthesis methods of forsterite (Mg2SiO4) ceramics are being searched for refractory industry. The limiting factor of Mg2SiO4 synthesis is its high melting point of 1890 °C, which makes it difficult to conduct experimental studies.The paper proposes a new method of forsterite synthesis based on thermal plasma. The plasma source is an effective medium for heating and melting refractory materials. For the Mg2SiO4synthesis, such initial materials are used as natural and sub-standard raw materials (silica sand sifting, microsilica, magnesite). The degree of crystallinity varies from 10 to 98 %, which allows studying the formation of the phase composition at different parameters.According to powder X-ray diffraction patterns, at a MgO/SiO2stoichiometric ratio of 1.34, the obtained melting products consist up to 90 % Mg2SiO4and the X-ray amorphous phase content varies from 5 to 12 %. After isothermal exposure, the amorphous phase is represented by silicon dioxide in the polymorphic modification of cristobalite. According to scanning electron microscopy observations, the formation of hexagonal close-packed crystals occurs on the surface of the ceramic sample, with the size ranging from 180 to 250 µm. The elemental composition of the crystal consists of ~ 38.60 wt. % O, ~ 28.54 wt. % Mg, ~ 26.92 wt. % Si, which matches the theoretical composition of Mg2SiO4. A detailed analysis of a single crystal shows that the surface structure consists of acicular microcrystals arranged symmetrically, but at the same time overlapping each other, thereby forming a lattice structure. The growth angle between the cubic microcrystals tends to ~87–94 degrees.

Resolving local microstructure variations in Zr-2.5Nb CANDU pressure tubes using high spatial resolution electron backscatter diffraction and imaging

The alloy Zr-2.5Nb is used for manufacturing the pressure tubes installed in the core of Canada Deuterium Uranium (CANDU) nuclear reactors. This alloy consists of α-zirconium with hexagonal close-packed (HCP) crystals and a minor β-zirconium phase with body centered cubic (BCC) crystals that are mainly located in between the α-grains. Due to the significant elastic and plastic anisotropy of HCP crystals as well as the development of strong textures during manufacturing, these tubes exhibit significant mechanical anisotropy. However, both local microstructure and texture can change, affecting the local patterning of stress fields and the subsequent hydrogen embrittlement rate. Resolving the local microstructure variation of Zr-2.5Nb is challenging due to the development of nano-sized grains during manufacturing. This paper focuses on developing a procedure for the consistent characterization of such local variations using high spatial resolution electron backscatter diffraction (EBSD) and imaging. Microstructure variations along the radial and transverse directions of the transverse-radial plane, as well as along the axial direction of the transverse-axial and radial-axial planes are studied. It is shown that microstructure variations are non-negligible. For the locations that the transverse-radial planes are studied, pole figures rotate, and Kearns factors decrease along the radial direction. In addition, the morphologies of both α- and β-crystals change significantly along the radial direction. With the procedure used for characterization, some β-crystals are indexed and their orientation relationship with their neighboring α-grains are examined.

Local and Global Order in Dense Packings of Semi-Flexible Polymers of Hard Spheres.

The local and global order in dense packings of linear, semi-flexible polymers of tangent hard spheres are studied by employing extensive Monte Carlo simulations at increasing volume fractions. The chain stiffness is controlled by a tunable harmonic potential for the bending angle, whose intensity dictates the rigidity of the polymer backbone as a function of the bending constant and equilibrium angle. The studied angles range between acute and obtuse ones, reaching the limit of rod-like polymers. We analyze how the packing density and chain stiffness affect the chains' ability to self-organize at the local and global levels. The former corresponds to crystallinity, as quantified by the Characteristic Crystallographic Element (CCE) norm descriptor, while the latter is computed through the scalar orientational order parameter. In all cases, we identify the critical volume fraction for the phase transition and gauge the established crystal morphologies, developing a complete phase diagram as a function of packing density and equilibrium bending angle. A plethora of structures are obtained, ranging between random hexagonal closed packed morphologies of mixed character and almost perfect face centered cubic (FCC) and hexagonal close-packed (HCP) crystals at the level of monomers, and nematic mesophases, with prolate and oblate mesogens at the level of chains. For rod-like chains, a delay is observed between the establishment of the long-range nematic order and crystallization as a function of the packing density, while for right-angle chains, both transitions are synchronized. A comparison is also provided against the analogous packings of monomeric and fully flexible chains of hard spheres.

Colloidal Photonic Crystal-Enhanced Fluorescence of Gold Nanoclusters: A Highly Sensitive Solid-state Fluorescent Probe for Creatinine.

Gold nanoclusters (AuNCs) are an intensely pursued class of fluorophores with excellent biocompatibility, high water solubility, and ease of further conjugation. However, their low quantum yield limits their applications, such as ultra-sensitive chemical or molecular sensing. To address this problem, various strategies have been adopted for augmenting their fluorescence intensity. Herein, we report a facile and scalable approach for the fluorescence enhancement of bovine serum albumin (BSA) capped AuNCs (BSA-AuNCs) using periodic, close-packed polystyrene colloidal photonic crystals (CPCs). The slow photon effect at the bandgap edges is utilized for the increased light-matter interactions and thereby enhancing the fluorescence intensity of the BSA-AuNCs. Compared to the planar polystyrene control sample, the CPC film yielded a 14-fold enhancement in fluorescence intensity. Further, we demonstrated the as-prepared BSA-AuNCs-CPC as a solid-state platform for the highly sensitive and selective fluorescence turn-off detection of creatinine at nanomolar level.

Single-orientation colloidal crystals from capillary-action-induced shear.

We study the crystallization of colloidal dispersions under capillary-action-induced shear as the dispersion is drawn into flat walled capillaries. Using confocal microscopy and small angle x-ray scattering, we find that the shear near the capillary walls influences the crystallization to result in large random hexagonal close-packed (RHCP) crystals with long-range orientational order over tens of thousands of colloidal particles. We investigate the crystallization mechanism and find partial crystallization under shear, initiating with hexagonal planes at the capillary walls, where shear is highest, followed by epitaxial crystal growth from these hexagonal layers after the shear is stopped. We then characterize the three-dimensional crystal structure finding that the shear-induced crystallization leads to larger particle separations parallel to the shear and vorticity directions as compared to the equilibrium RHCP structure. Confocal microscopy reveals that competing shear directions, where the capillary walls meet at a corner, create differently oriented hexagonal planes of particles. The single-orientation RHCP colloidal crystals remain stable after formation and are produced without the need of complex shear cell arrangements.

A model of porous plastic single crystals based on fractal slip lines distribution

The ductile failure of crystalline materials is strongly linked to the growth of intragranular voids. The estimation of the overall yield criterion thus requires to take into account the anisotropic plastic behavior of the single crystal. In the framework of the kinematic limit-analysis approach, this problem has been considered up to now with Gurson-type isotropic trial velocity fields. In the present work, a different class of piecewise constant velocity fields is proposed based on a detailed analysis of FFT numerical results on the strain localization in porous single crystals with periodic distributions of voids. This original approach is implemented for the model 2D problem of a square or hexagonal array of cylindrical voids in a hexagonal close-packed single crystal with in-plane prismatic slip systems. For equibiaxial loadings, the assumption of discontinuous velocity field provides a good approximation of the smooth jumps observed in the numerical results. Consistently, this new proposal leads to a significant improvement on the macroscopic yield stress with respect to the estimate based on an isotropic velocity field. Our theoretical estimate almost coincides with the FFT numerical results for all the unit-cells and crystalline orientations considered.

Nucleation and growth of [formula omitted] compression twin in Mg single crystals

The {101¯1} compression twin is more commonly observed under a-axis tension rather than c-axis compression in hexagonal close-packed (hcp) Mg single crystals both in experiments and atomistic simulations. In this work, molecular dynamics simulations are applied to investigate the nucleation and growth of {101¯1} twin in Mg single crystal, which is crucial for a comprehensive understanding of the plasticity of hcp metals. A {101¯1} twin embryo with 4-layer height is found to be naturally nucleated at the free surface via 〈a〉 dislocation slip in Mg single crystal. The nucleation of the {101¯1} twin embryo involves the cross-slip of the nucleated prismatic 〈a〉 dislocation onto pyramidal {101¯1} plane, which is achieved by slip of 〈a〉 dislocation and shear along the 〈101¯2〉 direction. Basal stacking faults (SFs) forms in twin embryo and grows with the migration of {101¯1} twin boundary. The formation of basal SFs in {101¯1} twin embryo can greatly reduce the required atomic shuffling in 〈12¯10〉 direction, thus facilitate the development of a {101¯1} twin embryo. The basal SFs inside {101¯1} twin are anomalous SFs without dislocation activities involved, thus the {101¯1} twinning shear is not influenced by the existence of basal SFs, which is consistent with the irrational shear of 2-layer twinning dislocation.