Low-symmetry Structures Research Articles

Adsorption-Free Growth of Ultra-Thin Molybdenum Membranes with a Low-Symmetry Rectangular Lattice Structure.

Although low-symmetry lattice structure of 2D transition metals is highly anticipated for both fundamental research and potentially distinctive application, it still has not been experimentally realized, which greatly hinders the exploration of the unique properties. Here, ultra-thin body-centered-cubic (bcc) phase molybdenum (Mo) membranes are successfully synthesized with a low-symmetry rectangular (110) crystal face via an adsorption-free reaction. Through experimental and density functional theory studies, no foreign atoms being adsorbed is shown to be a key factor for the successful preparation of the bcc phase 2D transition metal with (110) faces. The realization of 2D Mo(110) with a low-symmetric rectangular lattice structure extends the scope of 2D structures and is also beneficial for the exploration and development of low-symmetry rectangular lattice-structured materials with unique properties.

Exploring phononic properties of two-dimensional materials using machine learning interatomic potentials

Phononic properties are commonly studied by calculating force constants using the density functional theory (DFT) simulations. Although DFT simulations offer accurate estimations of phonon dispersion relations or thermal properties, but for low-symmetry and nanoporous structures the computational cost quickly becomes very demanding. Moreover, the computational setups may yield nonphysical imaginary frequencies in the phonon dispersion curves, impeding the assessment of phononic properties and the dynamical stability of the considered system. Here, we compute phonon dispersion relations and examine the dynamical stability of a large ensemble of novel materials and compositions. We propose a fast and convenient alternative to DFT simulations which derived from machine-learning interatomic potentials passively trained over computationally efficient ab-initio molecular dynamics trajectories. Our results for diverse two-dimensional (2D) nanomaterials confirm that the proposed computational strategy can reproduce fundamental thermal properties in close agreement with those obtained via the DFT approach. The presented method offers a stable, efficient, and convenient solution for the examination of dynamical stability and exploring the phononic properties of low-symmetry and porous 2D materials.

Accessing Catalytically Active Ordered Intermetallics Compounds Via Electrochemically Driven Phase Transformations

The conversion of O2 to H2O is an important fuel cell reaction for the recovery of renewable electricity from chemical fuels. Alloys of Pt-group metals (PGMs) with transition metals have emerged as catalysts with enhanced activity and durability for the oxygen reduction reaction (ORR). To date, most studies focus exclusively on alloys that adopt a Face-centered cubic (FCC) or Face-centered tetragonal (FCT) crystal lattice. Under ORR operating conditions, these materials evolve from alloys to Pt core-alloy shell materials, in this case both the alloy core and Pt shell retains the CCP type crystal structure; indicating that materials can dynamically change during catalysis.Here we present the synthesis of Pd-Bi based ordered intermetallics by partial dealloying of a Bi rich alloy. We found that under ORR operation conditions, ß-PdBi2 which adopts a tetragonal lattice, transforms to Pd3B orthorhombic crystal structure; this transformation is mediated by oxidative Bi corrosion under potential cycling, and reconstruction of the atoms in the bulk. To the best of our knowledge, this is the first report of a material that exhibits an electrochemically driven, non-congruent phase transition among materials with different crystal structures. The resulting phase-converted Pd3Bi is stable and exhibits high performance for ORR. Phase-converted Pd3Bi outperform Pt and Pd metal, reaching mass activities of 2.6 A/mgPd, which is nearly 10X higher than Pt/C (~0.3 A/mgPt) and Pd/C (~0.2 A/mg) at 0.9 V vs the Real Hydrogen Electrode (RHE). The mass activity of Pd3Bi decreases by ~38% after 10,000 cycles, indicating that it is stable. Activation energy (Ea) determined by temperature dependent electro-kinetic measurements indicates that the activity enhancement on phase-converted Pd3Bi originates from anion-poisoning resistant behavior. These results establish that PGMs-based ordered intermetallics with low-symmetry crystal structures can be highly active and durable electrocatalysts.

Defect-induced Dzyaloshinskii–Moriya interaction in a nanocrystalline two-phase alloy

The Dzyaloshinskii–Moriya interaction (DMI) is believed to be operative in low-symmetry crystal structures lacking space-inversion symmetry. However, already in 1963, Arrott pointed out that even in a high-symmetry lattice, where the DMI would normally vanish, this interaction is present in the vicinity of any lattice defect. Based on these considerations and recent theoretical work, first experimental studies of the impact of the DMI on the spin-polarized magnetic small-angle neutron scattering (SANS) of polycrystalline magnets exhibiting a large density of microstructural defects have been performed. They demonstrated that an asymmetry in the difference between the two polarized SANS cross sections is induced by the DMI in nanocrystalline terbium and holmium as well as in mechanically-deformed microcrystalline cobalt. Here, we present a more complicated case, the nanocrystalline magnetically-textured soft magnet Vitroperm (Fe73Si16B7Nb3Cu1), where the interface between the FeSi nanoparticles and the amorphous magnetic matrix serves as the defect. The SANS cross section exhibits the polarization-dependent asymmetric term originating from the DMI. The effect has a magnetic field dependence and is less pronounced at higher fields until it eventually vanishes at full saturation. The result supports the generic relevance of the DMI for the magnetic structure of defect-rich ferromagnets. Furthermore, it shows that polarized SANS is a particularly powerful tool for investigating defect-induced DMI, which is a consequence of the unique dependence of the SANS cross section on the chiral interactions.

Quantitative theory of triplet pairing in the unconventional superconductor LaNiGa2

The exceptionally low-symmetry crystal structures of the time-reversal symmetry breaking superconductors LaNiC$_2$ and LaNiGa$_2$ lead to an internally-antisymmetric non-unitary triplet (INT) state as the only possibility compatible with experiments. We argue that this state has a distinct signature: a double-peak structure in the Density of States (DOS) which resolves in the spin channel in a particular way. We construct a detailed model of LaNiGa$_2$ capturing its electronic band structure and magnetic properties ab initio. The pairing mechanism is described via a single adjustable parameter. The latter is fixed by the critical temperature $T_c$ allowing parameter-free predictions. We compute the electronic specific heat and find excellent agreement with experiment. The size of the ordered moment in the superconducting state is compatible with zero-field muon spin relaxation experiments and the predicted spin-resolved DOS suggests the spin-splitting is within the reach of present experimental technology.

Infrared active phonons in monoclinic lutetium oxyorthosilicate

A combined generalized spectroscopic ellipsometry measurement and density functional theory calculation analysis is performed to obtain the complete set of infrared active phonon modes in Lu2SiO5 with a monoclinic crystal structure. Two different crystals, each cut perpendicular to a different crystal axis, are investigated. Ellipsometry measurements from 40to1200cm−1 are used to determine the frequency dependent dielectric function tensor elements. The eigendielectric displacement vector summation approach and the eigendielectric displacement loss vector summation approach, both augmented with anharmonic lattice broadening parameters proposed recently for low-symmetry crystal structures [Mock et al., Phys. Rev. B 95, 165202 (2017)], are applied for our ellipsometry data analysis. All measured and model calculated dielectric function tensor and inverse dielectric function tensor elements match excellently. 23 Au symmetry and 22 Bu symmetry infrared active transverse and longitudinal optical modes are found. We also determine the directional limiting modes and the order of the phonon modes within the monoclinic plane. Results from density functional theory and ellipsometry measurements are compared and nearly perfect agreement is observed. We further compare our results to those obtained recently for the monoclinic crystal Y2SiO5, which is isostructural to Lu2SiO5 [Mock et al., Phys. Rev. B 97, 165203 (2018)]. We find that the lattice mode behavior of monoclinic Lu2SiO5 is qualitatively identical with Y2SiO5 and differs only quantitatively. We anticipate that members of the isostructural group of monoclinic symmetry oxyorthosilicates such as Dy2SiO5 or Yb2SiO5 will likely behave very similar in their phonon mode properties as reported here for Lu2SiO5.

Predicting deformation behavior of α-uranium during tension, compression, load reversal, rolling, and sheet forming using elasto-plastic, multi-level crystal plasticity coupled with finite elements

An elasto-plastic self-consistent (EPSC) polycrystal plasticity formulation is adapted to model deformation of wrought α-uranium (α-U) accommodated by a combination of elasticity, dislocation glide, and deformation twinning. The EPSC model incorporates a strain-path, strain rate, and temperature sensitive dislocation density-based hardening law for the evolution of resistance to slip, twinning, and de-twinning and a slip system-level kinematic back-stress law to influence the driving force for activation. The model is used to interpret the complex deformation behavior of α-U as a function of strain-path and temperature. Samples of α-U with different initial orientation distributions are experimentally evaluated in simple compression, tension, and load reversal at room temperature and in compression and rolling at 573 K under a quasi-static deformation rate. Evolution of texture and twinning is characterized using electron backscattered diffraction and in-situ and ex-situ neutron diffraction during deformation. It is observed that the behavior of the material is highly anisotropic owing to its low-symmetry orthorhombic crystal structure and different activation stresses for crystallographic deformation modes. The model is calibrated and validated under these deformation conditions and predicts the stress-strain responses, amount of twinning, texture evolution, and lattice strains with one set of parameters for the hardening and back-stress evolution laws. Subsequently, the developed model is used as a constitutive law in the implicit finite element (FE) framework to simulate drawing of a hemispherical part from a rolled sheet of α-U. Here, the FE-EPSC model is a two-level homogenization scheme with EPSC relating the grain-level to the polycrystalline aggregate-level response, while the FE framework scales the polycrystalline to the part-level response. The simulation results and insights from the calculations, such as location dependent texture evolution is in good agreement with experiments.

Porous structured BaCo0.8Nb0.1Sc0.1O3-δ perovskite synthesized by template method as high performance cathode for intermediate-temperature solid oxide fuel cells

BaCoO3-δ is a potential cathode material because of its mixed ionic and electronic conducting. Unfortunately, the low symmetry structure and oxygen reduction activity of BaCoO3-δ has limited its application on solid oxide fuel cells. Porous structured BaCo0.8Nb0.1Sc0.1O3-δ cubic perovskite is synthesized by template method. The area specific resistance (ASR) of porous BaCo0.8Nb0.1Sc0.1O3–δ is 0.0257 Ω‧cm2 at 700 °C and the activation energy was only 126.8 kJ‧mol−1. The further study shows that the charge transfer process and adsorption-desorption of oxygen process jointly determine the rate-determining-step of porous BaCo0.8Nb0.1Sc0.1O3–δ.

First-principles phonon-based model and theory of martensitic phase transformation in NiTi shape memory alloy

Remarkable shape memory property of Nitinol (NiTi) originates from a diffusion-free reversible phase transition it exhibits upon cooling from the cubic austenite to a low-symmetry martensite structure. Atomistic mechanisms of this martensitic transformation (MT) and consequent emergence of its various low-symmetry structures are not understood yet. Starting with first-principles density functional theoretical calculations, we present here a phonon-based model and its statistical mechanical analysis to obtain atomistic insights into martensitic phases and transformation in NiTi. We uncover seven order parameters that are relevant to the MT in NiTi. From Monte Carlo simulations of an effective model Hamiltonian derived to capture its low energy landscape, we determine its soft phonons and establish the cell-doubling M5′ mode as the primary order parameter. Using Landau theoretical analysis, we show that relative strengths of its third-order coupling with secondary order parameters (e.g. strain) determine the symmetry of low-T structures emerging at its MT. These couplings can be used as the descriptors of stability of martensitic phases that will guide the strategies to improve the shape memory of NiTi through substitutional alloying.

Role of electronic and magnetic interactions in defect formation and anomalous diffusion in δ-Pu

Previous experimental work has shown self-irradiation in Pu solids produces point defect populations that correlate with increases in local disorder, long-range structural changes, induced magnetic moments, and other thermo-physical property changes. Thermally activated kinetic processes drive these defects to diffuse and interact toward either damage evolution or lattice recovery. Using DFT and cNEB, as implemented in VASP, barriers for mono-vacancy and split-interstitial diffusion and Frenkel pair recombination were calculated in fcc δ-Pu. The results indicate the migration barrier of a monoclinic mono-vacancy is lower when compared to the migration barrier of a tetragonal split-interstitial in δ-Pu, contrary to typical fcc metal point defect migration. This fundamentally different diffusion mechanism is a result of local symmetry breaking induced by electronic and magnetic interactions leading to the development of Pu–Pu short bonds (<3.0 Å) within a many-atom complex defect forming and migrating. The migration of the monoclinic mono-vacancy maintains short bonds with anti-parallel spins throughout the transition; whereas, during the migration transition state for the tetragonal split-interstitial, formation of short bonds with parallel spins and a spin-flip of the migrating Pu interstitial occurs. The associated energy cost is reflected in an increase in the migration barrier energy. Frenkel pair recombination is not spontaneous at 0K, but correlates with magnetic moment interactions, leading to an energy barrier for recombination. From these results, it is concluded that migration of defects in unalloyed δ-Pu are highly dependent on the electronic and magnetic interactions that induce associated low-symmetry structures and consequently influence the diffusional properties. Typical fcc defect diffusion mechanisms do not apply to the monoclinic mono-vacancy and tetragonal split-interstitial in the complex 5f δ-Pu system suggesting that the experimental observation of radiation damage induced localized magnetic moments and anomalous diffusion properties measured in δ-Pu could be understood in terms of defect kinetics and interactions.

Circular dichroism in non-chiral metal halide perovskites.

We demonstrate theoretically that non-chiral perovskite layers can exhibit circular dichroism (CD) in the absence of a magnetic field and without chiral activation by chiral molecules. The effect is shown to be due to splitting of helical excitonic states which can form in structures of orthorhombic or lower symmetry that exhibit Rashba spin effects. The selective coupling of these helical exciton states to helical light is shown to give rise to circular dichroism. Polarization dependent absorption is shown to occur due to the combined effect of Rashba splitting, in-plane symmetry breaking, and the effect of the exciton momentum on its fine structure, which takes the form of Zeeman splitting in an effective magnetic field. This phenomenon, which can be considered as a manifestation of extrinsic chirality, results in significant CD with an anisotropy factor of up to 30% in orthorhombic perovskite layers under off-normal, top illumination conditions, raising the possibility of its observation in non-chiral perovskite structures.

Deeply Exploring Anisotropic Evolution toward Large-Scale Growth of Monolayer ReS2.

Among large numbers of transition metal dichalcogenides (TMDCs), monolayer rhenium disulfide (ReS2) is of particular interest due to its unique structural anisotropy, which opens up unprecedented opportunities in dichroic atomical electronics. Understanding the domain structure and controlling the anisotropic evolution of ReS2 during the growth is considered critical for increasing the domain size toward a large-scale growth of monolayer ReS2. Herein, by employing angle-resolved Raman spectroscopy, we reveal that the hexagonal ReS2 domain is constructed by six well-defined subdomains with each b-axis parallel to the diagonal of the hexagon. By further combining the first-principles calculations and the transmission electron microscopy (TEM) characterization, a dislocation-involved anisotropic evolution is proposed to explain the formation of the domain structures and understand the limitation of the domain size. Based on these findings, growth rates of different crystal planes are well controlled to enlarge the domain size, and moreover, single-crystal domains with a triangle shape are obtained. With the improved domain size, large-scale uniform, strictly monolayer ReS2 films are grown further. Scalable field-effect transistor (FET) arrays are constructed, which show good electrical performances comparable or even superior to that of the single domains reported at room temperature. This work not only sheds light on comprehending the novel growth mechanism of ReS2 but also offers a robust and controllable strategy for the synthesis of large-area and high-quality two-dimensional materials with low structural symmetry.

A comparative study on the high and low symmetric structures of (LaMnO3)n/(LaNiO3)n superlattices by first-principles calculations

We have employed the + U extension of Generalized Gradient Approximation (GGA) of the Density Functional Theory (DFT) to study the (LaMnO3)n/(LaNiO3)n oriented (0 0 1) superlattices. We built superlattices for both high (cubic) and low (rhombohedral) symmetry structures. Structural, electronic, and interfacial energy calculations reveal charge transfer from Mn to Ni interfacial atoms in both structures inducing magnetic moment at the Ni atom. Magnetic calculations show that the Mn and Ni atoms are ferromagnetically coupled. Our results indicate that the amount of charge transfer and magnetic moment are largest in the (LaMnO3)1/(LaNiO3)1 than (LaMnO3)2/(LaNiO3)2, and in the low symmetry (rhombohedral) than the high symmetry (cubic) superlattices, because of the Transition Metal-Oxygen (TMO) bonds created, and suggest the low symmetric structure for more efficient magnetic moment in the (LaMnO3)/(LaNiO3) superlattices.

Boosting phosphorescence efficiency by crystal anisotropy in SrAl2O4:Eu,Dy textured ceramic layers

Among persistent luminescence materials, one of the most studied systems is SrO-Al2O3 due to its chemical stability and the longest green-afterglow duration. This research is focused on the synthesis of SrAl2O4:Eu,Dy textured layers by the screen-printing. The novelty of the approach is the employment of molten salt to promote crystal growth. The reactive ink, composed by the mixture of precursors in adequate proportions (SrCO3, Eu2O3, Dy2O3, and NaCl-KCl) and an organic-based vehicle, was printed onto the Al2O3 substrates in a single step, obtaining epitaxial films. Control experiments showed that both heat treatment and substrate nature were vital ones for the improvement of the PL. Highly oriented layers demonstrated a twofold enhancement of the luminescence as compared with unoriented films. These results evidence, for the first time, that the crystal anisotropy plays a key role in the luminescence of the low symmetry structures such as the monoclinic SrAl2O4 material. The results give the possibility of the cost-efficient production of layers by an easily scalable process.

Cerium induced Raman spectra of (Ba0.5Sr0.5)(Fe1-xCex)O3-δ (x = 0 - 1)

The effect of cerium insertion in sol-gel derived (Ba0.5Sr0.5)(Fe1-xCex)O3-δ (x = 0 – 1) powders has been investigated by Raman spectroscopy and findings correlated with crystalline phases present. A perovskite-type (ABO3) cubic phase of composition (x = 0) displays no Raman band but cerium substitution of iron is shown to induce distortion via BO6 octahedra tilt and to displace B-ion from its centro-symmetrical location besides expansion (due to its large ionic radius) with formation of an orthorhombic structure of lower symmetry (space group Pmnb or D4h16), characterized by several Raman bands including ~ 342 and 350 cm−1, 467 cm−1, and ~599 cm−1 associated with symmetric stretching of oxygen ions around B-ion, occupation of some cerium at A-site and/or F2g mode of CeO2, and occurrence of oxygen vacancies, respectively. The creation of anion vacancies makes the compounds useful for industrial application, viz., for obtaining pure oxygen from air.

Probing the low-symmetry structure determined anisotropic elastic properties of rhenium disulphide by first-principle calculations

As a distinct member of layered structure transition metal dichalcogenides, the anisotropic response of rhenium disulphide (ReS2) is important for the potential applications in flexible devices, while the atomic bonding structure determined mechanical properties underlying the distorted low symmetry remains to be well understood. The objective of the present work is to disentangle the atomic-scale structure determined anisotropic mechanical properties of ReS2. The elastic constants of ReS2 are studied by first-principles calculations. Based on the calculated elastic constants, the mechanical properties, such as bulk modulus, shear modulus, Young’s modulus, and Poisson’s ratio are obtained via Hill’s approximations. While having a higher in-plane elastic modulus C22 and C33 values, the layered structure has a low-strength shearing elastic constants C55 and C66, making ReS2 more flexible than most studied common transition metal dichalcogenides such as MoS2. Projected phonon density of states (PDOS) along different directions, the electronic density charge distribution as well as the Mulliken charge population are calculated underlying the anisotropic atomic bonding mechanism of this low symmetry structure, which provides an interpretation of the anisotropic mechanical properties.

Hidden structural transition in epitaxial Ca0.5Sr0.5IrO3/SrTiO3 thin film

A structural transition in an ABO$_{3}$ perovskite thin film involving the change of the BO$_{6}$ octahedral rotation pattern can be hidden under the global lattice symmetry imposed by the substrate and often easily overlooked. We carried out high-resolution x-ray diffraction experiments to investigate the structures of epitaxial Ca$_{0.5}$Sr$_{0.5}$IrO$_{3}$ (CSIO) perovskite iridate films grown on the SrTiO$_{3}$ (STO) and GdScO$_{3}$ (GSO) substrates in detail. Although the CSIO/STO film layer displays a global tetragonal lattice symmetry evidenced by the reciprocal space mapping, synchrotron x-ray data indicates that its room temperature structure is monoclinic due to Glazer's a$^{+}$a$^{-}$c$^{-}$-type rotation of the IrO$_{6}$ octahedra. In order to accommodate the lower-symmetry structure under the global tetragonal symmetry, the film breaks into four twinned domains, resulting in the splitting of the (half-integer, 0, integer) superlattice reflections. Surprisingly, the splitting of these superlattice reflections decrease with increasing temperature, eventually disappearing at T$_{S}$ = 510(5) K, which signals a structural transition to an orthorhombic phase with a$^{+}$a$^{-}$c$^{0}$ octahedral rotation. In contrast, the CSIO/GSO film displays a stable monoclinic symmetry with a$^{+}$b$^{-}$c$^{-}$ octahedral rotation, showing no structural instability caused by the substrate up to 520 K. Our study illustrates the importance of the symmetry in addition to the lattice mismatch of the substrate in determining the structure of epitaxial thin films.

Magnetism and Optical Anisotropy in van der Waals Antiferromagnetic Insulator CrOCl.

van der Waals (vdW) magnetic insulators are of significance in both fundamental research and technological application, but most two-dimensional (2D) vdW magnetic systems are unstable and of high lattice symmetry. Stable 2D vdW magnetic insulators with anisotropic structure are needed to modulate the properties and unlock potential applications. Here we present a stable vdW antiferromagnetic material, CrOCl, with low-symmetry orthorhombic structure, and investigate systematically its magnetism, phase transition behavior, and optical anisotropy. Spin-phonon coupling effects are uncovered by the abnormal frequency shifts of Raman-active modes, suggesting the formation of a magnetic superstructure. The sizable abnormal change of interplanar spacing indicates the presence of a structural transition at around 27 K. Further in-plane vibrational, reflectional, and absorptional anisotropic properties are explored both experimentally and theoretically, revealing a highly polarization sensitive characteristic and linear dichroism in 2D CrOCl. Meanwhile, the particularly high polarization dependency of the second-harmonic generation and the nonlinear susceptibility of ∼2.24 × 10-11 m/V make it suitable in the field of polarization-dependent nonlinear optics. The findings on the intricate properties of 2D CrOCl lay foundations for future applications of low-symmetry vdW magnets in spin-dependent electronic and optoelectronic devices.

Understanding of fission products transport in SiC layer of TRISO fuels by nanoscale characterization and modeling

This paper details recent advances in the understanding of both intergranular and intragranular fission product transport in the silicon carbide (SiC) layer of neutron-irradiated tristructural isotropic (TRISO) coated-fuel particles from Advanced Gas Reactor (AGR)-1 and AGR-2 experiments. The SiC layer is the primary barrier responsible for retaining metallic fission products in the fuel particle. Chemical reactions between the SiC layer and fission products have been observed. Previously, intragranular precipitates rich in fission product Pd were identified as nanosized nodular and columnar features, distributed through the irradiated SiC grains. More recent studies reported hexagonal-shaped Pd silicide at Frank loops and stacking faults, where α-SiC (amid the bulk β-SiC) acts as a precursor for Pd silicide formation. While the Pd silicide precipitates were identified as having L12-Pd3Si stoichiometry from electron diffraction study, ab initio phonon calculations performed in this study suggest that the L12-Pd3Si structure remains dynamically unstable from zero pressure up to at least 100 GPa and will spontaneously transform into other lower-symmetry structures via different unstable phonon modes. Apart from the nanoscale hexagonal morphology of the Pd3Si precipitate, a new form of elongated Pd silicide, confined between a pair of stacking faults, has been observed in a high 110mAg-retention TRISO-coated particle. The peculiar discontinuity of such precipitates along the stacking faults raises questions regarding the necessity of α-SiC precursors for their nucleation, as well as the nature of the intragranular-transport pathway of Pd along the radial direction of SiC. The large-scale fission product precipitates in the inner-pyrolytic carbon (IPyC) and grain boundaries of SiC layers were characterized, and different chemically segregated regions were observed within single fission product precipitates.

The stabilities and geometries of Re-encapsulated Sin(n=16, 20, 24, 28, 32, 36, and 40) clusters: A computational investigation

Abstract Geometry optimization of the mixed SinRe (n=12, 16, 20, 24, 28, 32, 36, and 40) cages with doublet, quartet, and sextet spin configurations is carried out systematically at the UHF/LanL2DZ level. Equilibrium structures, total energies, and stabilities of Re@Sin cages are presented and discussed. The calculated results show that all Re@Sin cages of highest symmetry undergo slight distortion into much more stable structures of lower symmetry. The Re atom in the Re@Sin (n=12, 16, 20, 24, 28, 32, 36, and 40) cages deviates from the cage center site of Sin fullerenes. Charge-transfer between Re and Si atoms makes a contribution to the stability of the Sin fullerenes; In addition, the relative stability is discussed, the most stable geometry is assigned.