Difference In Lattice Parameters Research Articles

A black pigment that shows strong near-infrared reflectivity for solar heat control

Solar thermal energy regulation is important for sustainable development, comfortable housing, and living. Black compounds are usually considered as an absorber of solar heat. This work reports a series of black near-infrared reflective pigments, Ca2-yMgyMn(1)1-xMn(2)xO4 (x = 0–1, y = 0–0.5), which show strong near-infrared (NIR) reflectivity. Comprehensive analyses were carried out to characterize the obtained pigments including X-ray diffraction, scanning electron microscopy, Raman spectroscopy, and UV–Vis–NIR spectrophotometry. Through the substitution of MnO2 with Mn2O3, NIR solar reflectance of the black pigment can be enhanced by 13%, which might be mainly attributed to differences in particle size and lattice parameters. Meanwhile, through Mg doping, the obtained pigment Ca1.8Mg0.2MnO4 shows excellent color performances (L* = 43, a* = 0.36, b* = −0.37) and NIR solar reflectance (R*, ∼60%). EnergyPlus simulation results show that for a warm city (Haikou), using the Ca1.8Mg0.2MnO4 coating (L* = 25, R* = 51%) can reduce annual cooling energy consumption by 21%.

Strain accumulation and relaxation on crack formation in epitaxial AlN film on Si (111) substrate

The formation of cracks is often observed in the epitaxial growth of ultrawide-bandgap aluminum nitride (AlN) semiconductor films on economical and versatile silicon (Si) substrates due to the significant differences in in-plane lattice parameters and thermal expansion coefficients between the film and the substrate, which hampers the development of template, buffer layer, and device structure with a relatively thick AlN layer for devices. The present study aims to elucidate the conditions of crack formation through a simple but comprehensive estimation of strain energy accumulation and relaxation by lattice strain, misfit dislocation density, and crack formation. Strain energy in the epitaxial film from lattice and thermal mismatches is evaluated by an elastic strain equation tailored to the epitaxy of the hexagonal crystal structure. The effects of temperature, thickness, and dislocation density on the lattice and dislocation strain energies of the film are also considered. Finally, the comparison in the changes in the total strain energy and cleavage energy with decreasing temperature shows that cleavage energy is higher than strain energy if the film is thinner than 400 nm but becomes lower than the strain energy if the film is thicker than 400 nm during cooldown, suggesting the crack formation, which matches well with experimental observations.

Synthesis and characterization of b-site controlled la-based high entropy perovskite oxides

High entropy perovskite oxide materials are a highly promising class of materials with a wide range of potential applications. They offer a unique combination of perovskite oxides and high entropy oxides, making them suitable for various fields, particularly in electrochemical energy storage systems and hydrogen production. Given the growing demand for clean energy and efficient energy storage solutions, the development of high entropy materials holds great significance. In this study, a cost-effective and rapid fabrication method was employed to produce several single-phase high entropy perovskite oxides by altering the B-site cations. The results demonstrated that these high entropy perovskite oxides could be synthesized with the same crystal structure, despite having significantly different elemental compositions. These variations in elemental composition led to differences in lattice parameters, metal-oxygen bond strengths, and oxygen vacancy content within the materials. Understanding and manipulating these factors can have important implications for the design of high entropy materials for energy storage and other applications.

Features of the crystal structure of 2D honeycomb frustrated magnet Li<sub>2</sub>Ni<sub>2</sub>TeO<sub>6</sub>

Using neutron powder diffraction at a temperature of 35 K, slightly above the Neel temperature, the features of the crystal structure of two samples of layered honeycomb oxides of the same stoichiometric composition Li2Ni2TeO6 synthesized from precursors, Na2Ni2TeO6 and K2Ni2TeO6, were determined. They have a similar crystal structure, hexagonal space group P63/mcm, structure type P2, but there is a significant difference in the distances between the layers. Both Li2Ni2TeO6 samples crystallize into the orthorhombic space group Cmca, with minor differences in the unit lattice parameters. If Li2Ni2TeO6 from the potassium precursor is single-phase, then the compound from the sodium precursor contains 16 wt % of an additional phase with the same Li2Ni2TeO6 stoichiometry, but more deformed with monoclinic distortions described by the С2/m space group.

The effect of chemical element on hardness in high-entropy transition metal diboride ceramics

The relationship between the chemical elements of high-entropy boride (HEB) ceramics and their hardness is important for the prediction of high-hardness HEB ceramics. In this work, by designing four HEB ceramics with different chemical elements, the effect of lattice parameter difference factor (δ, represents the difference-degree in lattice parameters among the five individual constitute diborides) on phase composition and lattice-distortion, and the effect of rule of mixture (ROM) average hardness and lattice-distortion on HEB ceramics hardness were studied. The results indicated that, as δ value increases, more severe lattice-distortion occurs inside the HEB ceramics, and a single solid-solution is difficult to be formed. Furthermore, lattice-distortion and the ROM average hardness codetermine the HEB ceramics hardness. The greater lattice-distortion brings about significantly higher hardness for HEB ceramics than their ROM average hardness. Among the four HEBs, (Hf0.2Zr0.2Ta0.2V0.2Nb0.2)B2 exhibits the high hardness of 26 GPa measured using a load of 9.8 N.

Effects of lattice and mass mismatch on primary radiation damage in W-Ta and W-Mo binary alloys

The fundamental mechanisms of radiation damage in metal alloys of equiatomic composition are of great research interest due to the possibility to use them as new materials for radiation-hard environments. With W-Ta and W-Mo alloys as examples, this study investigates the effect of two factors, namely the difference in lattice parameters and the difference in masses of the constituent elements, on primary radiation damage by means of atomistic simulations. We compare the trends obtained with the available embedded atom method (EAM) interatomic potential and the tabulated Gaussian approximation potential (tabGAP). We observe a similar trend in the number of surviving defects as a function of alloy composition in W-Mo for both potentials, while the absolute numbers are fairly different. The tabGAP predicts higher resistance to irradiation, i.e. fewer surviving defects after the cascades. On the contrary, the trends of the dependence of surviving defects on alloy composition in W-Ta alloys are very different in the two potentials. We explain this difference by analyzing the threshold displacement energies (TDE) and melting temperatures in these alloys. The mass difference in W-Mo alloys results in Mo atoms with higher TDE in W-Mo alloys. The effect of the lattice parameter mismatch in W-Ta alloys is visible in the change of the number of surviving defects with increase of the W content in W-Ta alloys.

Effect of microsegregation and heat treatment on localised γ and γ’ compositions in single crystal Ni-based superalloys

The present work investigates the impact of residual segregation on the underlying microstructure of a 3rd generation single crystal, nickel-based superalloy to understand potential variation in mechanical behaviour between dendrite cores and interdendritic regions. Despite the applied heat-treatments, chemical variation between dendrite cores and interdendritic regions persisted particularly for elements Re, Nb and Ta. Atom probe tomography (APT) was utilized for its nanoscale capability to map site-specific chemical changes in the γ matrix, γ’ precipitates and across the γ/γ’ interface. Greater interfacial segregation of Re, matched by a corresponding depletion of Ni were observed within dendrite cores, with the extent found to increase following heat treatment. Differences in lattice parameters between dendrite cores and interdendritic regions were identified, with larger lattice misfits associated with interdendritic regions.

Dynamic Structural Transformations in a Series of Zero-Strain Lithium-Ion Battery Materials: Almost Simultaneous Operando X-ray Diffraction and X-ray Absorption Spectroscopy on Li2ZnTi3O8 and Related Compounds

A series of Li4/3-2x/3ZnxTi5/3-x/3O4 (LZTO) with 0 ≤ x ≤ 0.5 have received considerable interest as a negative electrode material for long-cycle-life lithium-ion batteries. However, their dynamic structural transformations under operating conditions have remained unknown, making an in-depth understanding essential for further improving the electrochemical performance. We, thus, performed almost simultaneous operando X-ray diffraction (XRD) and X-ray absorption spectroscopy (XAS) studies on x = 0.125, 0.375, and 0.5. The x = 0.5 sample, Li2ZnTi3O8, indicated differences in the cubic lattice parameter between the discharge and charge reactions (δacs), corresponding to the reversible movement of Zn2+ ions between the tetrahedral and octahedral sites. δac was also observed for x = 0.125 and 0.375, although the capacity region exhibiting δac decreased with a decrease in x. For all of the samples, there is no significant difference in the nearest-neighbor distance of the Ti-O bond (dTi-O) between the discharge and charge reactions. We also demonstrated different structural transformations between the micro- (XRD) and atomic (XAS) scales. In the case for x = 0.5, for instance, the maximum microscale change in ac was within +0.29(3)%, whereas at the atomic scale, dTi-O changed by up to +4.8(3)%. Combined with our previous results for ex situ XRD and operando XRD/XAS measurements on other x compositions, the whole structural nature of LZTO, such as correspondence between ac and dTi-O, origins for voltage hysteresis, and zero-strain reaction mechanisms, has been unveiled.

Processing-dependent stabilization of a dissimilar rare-earth boride in high-entropy (Ti0.2Zr0.2Hf0.2Ta0.2Er0.2)B2 with enhanced hardness and grain boundary segregation

This study demonstrates that 20% of a rare-earth (RE) diboride (ErB2) can be stabilized in a high-entropy transition metal (TM) diboride, despite the dissimilar chemical properties of RE and TM elements and large differences in lattice parameters of ErB2 and typical TMB2. However, the phase formation depends on the fabrication route, which is a noteworthy observation. Specifically, single-phase (Ti0.2Zr0.2Hf0.2Ta0.2Er0.2)B2 is synthesized via reactive spark plasma sintering (SPS) using elemental boron and metal elements. In contract, a specimen made by borocarbothermal reduction of binary oxides and SPS possess significant amounts of two Er-rich secondary phases. Notably, the RE addition in high-entropy TM diboride leads to improved hardness. Aberration-corrected scanning transmission electron microscopy (AC STEM) and energy-dispersive X-ray spectroscopy (EDS) elemental analyses further reveal significant Er segregation at grain boundaries. This work suggests that high-entropy ceramics can have significant solubilities of dissimilar components that may enable new, tunable, and improved properties.

Photo-resistor applications of Bi:ZnSe nano-composition deposited on micro-glass

Bi:ZnSe films at different concentrations (0, 5, 10, and 15%) were made by the laser deposition technique. The scanning electron microscopy and Uv–visible spectroscopy were used to investigate the surface topography and optical properties of the prepared films, respectively. The calculated energy gap was (3.0, 2.6, 3.2, and 3.1 eV) due to differences in lattice parameters. Moreover, the electrical characteristics reveal enhanced dark current with all samples probably due to the essential property of p-type doped ZnSe Nano-composition. The density, refractive index, permittivity, and reflection loss were also studied versus Bi-dopant. The structural characteristics of the coated films have been tested by an X-ray diffractometer. In addition, the interstitial or substitutional Zn ion by Bi ion in the lattice was also explained in this paper.

Characterization of carbide particle-reinforced 316L stainless steel fabricated by selective laser melting

In this study, we have fabricated a TiC particle strengthened 316L stainless steel metal matrix composite using selective laser melting and characterized the microstructure with a particular focus on the TiC carbides in terms of their crystallography and orientation relationship with the austenitic matrix. Two families of TiC carbides are found to form in the SLM fabricated microstructure – firstly, the carbides that form along the high angle grain boundaries and secondly, those that form in the grain interior. The latter is primarily nano-crystalline TiC that are believed to precipitate out from the melt pool following a cube-on-cube orientation relationship with the f.c.c. austenitic matrix. Under this crystal registry, due to the differences in lattice parameters, a lattice mismatch between two phases occurs. The formation of TiC carbides and their morphology and distribution have been explained on the basis of melting of the powder bed under laser beam and strong melt pool dynamics during SLM process. Finally, the contribution of coherent nano-sized TiC precipitates on the overall strength of SLMed 316L-TiC metal matrix composite has been discussed wherein the TiC precipitates were found to contribute to ~50% of the strength increment in comparison to SLMed pure 316L. • Selective laser melting of 316L-TiC nanocomposite was conducted. • Nanoprecipitation of TiC was observed homogeneously within the sample. • The TiC nanoprepitates showed a cube-on-cube orientation relationship with austensite. • The formation of cuboidal TiC described by SLM meltpool dynamics. • The contribution of TiC precipitates to overall strength increment was discussed.

A coarse-grained – Atomistic multi-scale method to study the mechanical behavior of heterogeneous FCC nano-materials

In this paper, a multi-scale method is developed to couple the atomistic domain with the coarse-grained system to model the mechanical properties of materials with defects and heterogeneity. The material properties are determined in the nano-scale level by Molecular Dynamics analysis, in which the interatomic potential is used to determine the interaction between the particles. The main issue with the Molecular Dynamics method is its high computational cost. Hence, the coarse-grained method is employed, where a number of atoms are assumed as a bigger bid, and the interatomic potential is modified in terms of the position of the grains. This method reduces the computational cost as the degrees of freedom decreases. Moreover, it has the advantage of using the same interatomic potential as molecular dynamics method comparing to the continuum-based approaches. One issue with the coarse-grained method is that phenomena with small wavelengths cannot be captured comparing to the all-atoms system. To this end, a multi-scale method is presented to couple the atomistic domain with the coarse-grained system. In this method, the regions near to the cracks, defects, or heterogeneity are modeled by the conventional MD scheme and farther regions by the coarse-grained method. In order to illustrate the capability of the proposed computational model, the evolution of misfit dislocation is investigated at the interface of Ni3Aland Ni, which is formed by their subtle difference in lattice parameter. Obviously, dislocations play a crucial role in determining the mechanical behavior of superalloys even though a considerable number of atoms are located in perfect lattice-structures, and dislocations comprise a small region of the domain. Thus, it is rational to apply the proposed CG–MD multi-scale method to study the mechanical behavior of such materials. Finally, the effect of loading and temperature is investigated on dislocation density of the Ni-based superalloys using the CG–MD multi-scale method; it is shown that dislocation density increases as the temperature or strain increases.

Electrochemical mechanism and effects of Fe doping and grinding process on the microstructural and electrochemical properties of Na2Co1-xFexSiO4 cathode material for sodium-ion batteries

Sodium-based orthosilicates are considered promising candidates as positive electrode materials for rechargeable sodium-ion batteries (SIBs). Na2Co1-xFexSiO4 (NCFS), with x = 0.1 and 0.2 cathode materials have been synthesized by low cost method (improved solid-state). The effects of Fe substitution and grinding process on the structural, morphological, and electrochemical properties of Na2Co0.9Fe0.1SiO4 (NCFS1) and Na2Co0.8Fe0.2SiO4 (NCFS2) are deeply investigated. The prepared Na2Co1-xFexSiO4 cathodes are indexed based on the orthorhombic system with Pca21 space group with a slight difference in lattice parameters. The morphological properties are strongly determined by the suspension formalism, which has an impact on the electrochemical performances. The ball-milling process leads to enhanced electrochemical performance and higher reversible capacity although with capacity fading after 100 cycles. Na2Co0.8Fe0.2SiO4 demonstrated an initial discharge capacity at C/50 of 131.4 mAh.g−1 (1C= 272.7 mA.g−1) that is two times higher than that of the Na2Co0.9Fe0.1SiO4 (54.6 mAh.g−1 (1C= 272.27 mA.g−1)). All the above features and insights make the new materials highly promising for use as potential cathode material for SIBs.

Low-temperature synthesis of single-phase refractory metal compound carbides

The compound carbide of refractory metal had great potential applications in ultra-high temperature, biomedical and nuclear fields. In the present study, a novel method composed of vacuum carbothermal reduction followed by calcium treatment was proposed to synthesize single-phase compound carbide. It was found that the required temperature for the formation of single-phase Ta4HfC5 solid solution in liquid calcium was above 1573 K. Meanwhile, the single-phase binary carbides (NbTaC2), ternary carbides (TiNbTaC3, ZrNbTaC3), quaternary carbides (TiHfNbTaC4, ZrHfNbTaC4), pentanary carbides (TiZrHfNbTaC5) and hexanary carbides (TiZrHfVNbTaC6) were also synthesized by the current method. The formation mechanism of the single-phase compound carbide was discussed and two parameters TSS (based on the mixing enthalpy change and mixing entropy change) and δa (based on the difference of lattice parameter) were proposed for predicting the formation ability of solid solution. It was found that the necessary conditions for formation of solid solution by current method were TSS < 1800 K and δa < 3.2%. In addition, when the value of TSS was lower than 5.5 × 103·ln(1/δa)-19 × 103, the single-phase compound carbides could be easily synthesized.

Molecular alignment descriptor to search for the most stable adsorption sites of saturated cyclic compounds on metal surfaces

We propose a new descriptor, called degree of molecular alignment (DMA), which can facilitate identification of the most stable adsorption configurations of saturated cyclic compounds. It exploits the binding phenomenon by lower axial CH bond activation on a metal surface. To validate this descriptor, seven saturated cyclic compounds were chosen to be adsorbed on Pd(111) and Pt(111) surfaces and confirmed that DMA was linearly related to adsorption energy. Isosurfaces of the charge density difference for the most stable adsorption configuration appeared perpendicularly, which means that good molecular alignment (parallel ring to surface) is important for the binding interaction. Moreover, origin of the differences in adsorption behaviors between Pd(111) and Pt(111) such as sensitivity towards values of DMA is studied by calculating bonding and deformation energies. The results revealed that differences in lattice parameters of catalyst induce adsorbates to have unique degree of deformation leading to different variation of bonding energy and adsorption energy with respect to values of DMA. Our result will provide a useful guideline to search for the most stable adsorption configurations of saturated cyclic compounds on metal surfaces.

(La&lt;sub&gt;1–&lt;i&gt;x&lt;/i&gt;&lt;/sub&gt;Sr&lt;sub&gt;&lt;i&gt;x&lt;/i&gt;&lt;/sub&gt;)(Zn&lt;sub&gt;1–&lt;i&gt;x&lt;/i&gt;&lt;/sub&gt;Mn&lt;sub&gt;&lt;i&gt;x&lt;/i&gt;&lt;/sub&gt;)SbO: A novel 1111-type diluted magnetic semiconductor

Diluted magnetic semiconductor (DMS) that combines the properties of spin and charge degrees of freedom, which has potential applications in the field of spintronic devices. In the 1990s, due to the breakthrough of low-temperature molecular beam epitaxy technology, scientists successfully synthesized III-V DMS (Ga, Mn)As, and developed some spintronics devices accordingly. However, the maximum Curie temperature of (Ga, Mn)As is only 200 K, which is still below room temperature that is required for practical applications. Searching for diluted magnetic semiconductors with higher Curie temperature and the exploring of their magnetism is still one of the focuses at present. In recent years, developed from iron-based superconductors, a series of novel magnetic semiconductors have been reported. These new DMSs have the advantages of decoupled charge and spin doping, and each concentration can be precisely controlled. In this paper, novel bulk diluted magnetic semiconductors (La&lt;sub&gt;1–&lt;i&gt;x&lt;/i&gt;&lt;/sub&gt;Sr&lt;sub&gt;&lt;i&gt;x&lt;/i&gt;&lt;/sub&gt;)(Zn&lt;sub&gt;1–&lt;i&gt;x&lt;/i&gt;&lt;/sub&gt;Mn&lt;sub&gt;&lt;i&gt;x&lt;/i&gt;&lt;/sub&gt;)SbO (&lt;i&gt;x&lt;/i&gt; = 0.025, 0.050,0.075, 0.10) are successfully synthesized, with the highest &lt;i&gt;T&lt;/i&gt;&lt;sub&gt;c&lt;/sub&gt; ~ 27.1 K for the doping level of &lt;i&gt;x&lt;/i&gt; = 0.10. We dope Sr&lt;sup&gt;2+&lt;/sup&gt; and Mn&lt;sup&gt;2+&lt;/sup&gt; into the parent semiconductor material LaZnSbO to introduce holes and moments, respectively. The ferromagnetic ordered phase transition can be observed in the samples with various doping concentrations. A relatively large coercive field is observed to be ~ 5000 Oe from the iso-thermal magnetization measurement at 2 K. The (La&lt;sub&gt;1–&lt;i&gt;x&lt;/i&gt;&lt;/sub&gt;Sr&lt;sub&gt;&lt;i&gt;x&lt;/i&gt;&lt;/sub&gt;)(Zn&lt;sub&gt;1–&lt;i&gt;x&lt;/i&gt;&lt;/sub&gt;Mn&lt;sub&gt;&lt;i&gt;x&lt;/i&gt;&lt;/sub&gt;)SbO has the same crystal structure as the “1111-type” iron-based superconductor LaFeAsO, and the lattice parameter difference is very small. It provides a possible material choice for preparing the multifunctional heterojunction devices.

O-Band Emitting InAs Quantum Dots Grown By MOCVD On A 300 mm Ge-Buffered Si (001) Substrate.

The epitaxy of III-V semiconductors on silicon substrates remains challenging because of lattice parameter and material polarity differences. In this work, we report on the Metal Organic Chemical Vapor Deposition (MOCVD) and characterization of InAs/GaAs Quantum Dots (QDs) epitaxially grown on quasi-nominal 300 mm Ge/Si(001) and GaAs(001) substrates. QD properties were studied by Atomic Force Microscopy (AFM) and Photoluminescence (PL) spectroscopy. A wafer level µPL mapping of the entire 300 mm Ge/Si substrate shows the homogeneity of the three-stacked InAs QDs emitting at 1.30 ± 0.04 µm at room temperature. The correlation between PL spectroscopy and numerical modeling revealed, in accordance with transmission electron microscopy images, that buried QDs had a truncated pyramidal shape with base sides and heights around 29 and 4 nm, respectively. InAs QDs on Ge/Si substrate had the same shape as QDs on GaAs substrates, with a slightly increased size and reduced luminescence intensity. Our results suggest that 1.3 μm emitting InAs QDs quantum dots can be successfully grown on CMOS compatible Ge/Si substrates.

Intrinsic nanostructures on the (001) surface of strontium titanate at low temperatures

Atomically smooth (001) surfaces of SrTiO3 cut from the high-quality single crystals at two different miscut angles 0.9 and 7.0 deg between the real flat surfaces and crystallographic planes (001) were analyzed by means of the reflection high energy electron diffraction (RHEED) method from the room down to liquid helium temperatures. The diffraction patterns typical of the RHEED geometry close to ideal for a small miscut angle and those exhibiting distinct features of the specific periodicity associated with regular steps, which form due to the larger miscut angle, are presented. The surface symmetry and energetics were shown to impose differences in lattice parameters in parallel to a surface with respect to the bulk. This effect results in weak incommensurability between lattice parameters in surface layers and the bulk values relaxed due to step edges and misfit dislocations. The special surface nanostructures formed on the etched surfaces treated in chemically active solvents are also analyzed. The intrinsic nanostructures on single crystal surfaces open new prospects for applications when the ordered and controlled nanoscale architecture is required.

Evaluation of Thermal Expansion Coefficient in Ge1-x Sn x Nanowire Using Reciprocal Space Mapping

Ge1-x Sn x is expected to be a new material for next-generation electronic and thermoelectric device because it has higher carrier mobilities and lower thermal conductivity than pure Si and Ge. Here, strain is an important factor for designing electric and thermoelectric devices. It has been reported that there is a correlation between strain and thermal conductivity for group IV semiconductors [1]. In plane compressive strain is induced in epitaxially grown GeSn thin film on a Ge substrate due to the difference in lattice parameter. Anisotropic strain relaxation has been occurred in the GeSn nanowires. Anisotropic strain may cause anisotropic thermal expansion and thermal conductivity. In this study, we evaluated the thermal expansion of Ge1-x Sn x nanowire fabricated on Ge substrate using reciprocal space mapping (RSM) by synchrotron radiation X-ray diffraction (XRD) measurement.The Ge1-x Sn x thin films were epitaxially grown on Ge (001) substrate for 34 and 45 nm by home-made metal organic chemical vapor deposition [2]. Sn concentrations (x) is 3.2% as confirmed by Rutherford backscattering spectrometry. Then, the nanowires were fabricated by electron beam lithography and dry etching as shown in Fig. 1. The major axis length (L) parallel to [110] were fixed at 10 µm while the minor axis width (W) parallel to [-110] were 200 or 500 nm. For the measurement of RSM, multi-axis diffractometer in BL19B2 of SPring-8 was used. The photon energy was 10 keV, which is just under the K-edge of Ge at 11 keV. We fabricated many nanowires to obtain sufficiently strong X-ray diffraction. The sample temperature was controlled using a heating stage (Anton Paar DHS1100).Figure 2 shows the relationship between temperature and the lattice parameters in Ge0.968Sn0.032 nanowire with W=500 nm. Thermal expansion for the sample with W=200 nm showed an isotropic change. However, it was revealed that the thermal expansion between the in-plane minor axis [-110] and the out-of-plane [001] directions were different for the sample with W=500 nm. In the previous study, we have confirmed the uniaxial strain relaxation (minor axis direction [-110]) has been occurred with decreasing W for Ge1-x Sn x nanowire [3]. Thus, it is considered that the thermal expansion become isotropic as the nanowire width gets shorter. References Xu et al., J. Appl. Phys. 106, 114302 (2009).Suda et al., ECS Trans. 64 (6). 697 (2014).K. Yoshioka et al., Thin Solid Films 697, 137797 (2020). Figure 1

Efficacious symmetry-adapted atomic displacement method for lattice dynamical studies

Small displacement methods have been successfully used to calculate the lattice dynamical properties of crystals. It involves displacing atoms by a small amount in order to calculate the induced forces on all atoms in a supercell for the computation of force constants. Even though these methods are widely in use, to our knowledge, there is no systematic discussion of optimal displacement directions from the crystal’s symmetry point of view nor a rigorous error analysis of such methods. Based on the group theory and point group symmetry of a crystal, we propose displacement directions, with an equivalent concept of the group of k, deduced directly in the Cartesian coordinates rather than the usual fractional coordinates, that maintain the theoretical maximum for the triple product V spanned by the three displacements to avoid possible severe roundoff errors. The proposed displacement directions are generated from a minimal set of irreducible atomic displacements that keep the required independent force calculations to a minimum. We find the error in the calculated force constants explicitly depends on the inverse of V and inaccuracy of the forces. Test systems such as Si, graphene, and orthorhombic Sb2S3 are used to illustrate the method. Our symmetry-adapted atomic displacement method is shown to be very robust in treating low-symmetry cells with a large ‘aspect ratio’ due to huge differences in lattice parameters, use of a large vacuum height, or a very oblique unit cell due to unconventional choice of primitive lattice vectors. It is expected that our atomic displacement strategy can be used to address higher-order interatomic interactions to achieve good accuracy and efficiency.