ElATools: A tool for analyzing anisotropic elastic properties of the 2D and 3D materials

We introduce a computational method and a user-friendly code with a terminalbased graphical user interface (GUI), named ElATools, developed to analyze mechanical and anisotropic elastic properties. ElATools enables facile analysis of the second-order elastic stiffness tensor of two-dimensional (2D) and three-dimensional (3D) crystal systems. It computes and displays the main mechanical properties including the bulk modulus, Young’s modulus, shear modulus, hardness, p-wave modulus, universal anisotropy index, Chung-Buessem anisotropy index, log-Euclidean anisotropy parameter, Cauchy pressures, Poisson’s ratio, and Pugh’s ratio, using three averaging schemes of Voigt, Reuss, and Hill. It includes an online and offline database from the Materials Project with more than 13,000 elastic stiffness constants for 3D materials. The program supports output files of the well-known computational codes IRelast, IRelast2D, ElaStic, and AELAS. Four types of plotting and visualization tools are integrated to conveniently interface with GNUPLOT, XMGRACE, view3dscene and plotly libraries, offering immediate post-processing of the results. ElATools provides reliable means to investigate the mechanical stability based on the calculation of six (three) eigenvalues of the elastic tensor in 3D (2D) materials. It can efficiently identify anomalous mechanical properties, such as negative linear compressibility, negative Poisson’s ratio, and highly-anisotropic elastic modulus in 2D and 3D materials, which are central properties to design and develop highperformance nanoscale electromechanical devices. Moreover, ElATools can predict the behavior of the sound velocities and their anisotropic properties, such as acoustic phase/group velocities and power flow angles in materials, by solving the Christoffel equation. Six case studies on selected material systems, namely, ZnAu2(CN)4, CrB2, δ-phosphorene, Pd2O6Se2 monolayer, and GaAs, and a hypothetical set of systems with cubic symmetry are presented to demonstrate the descriptive and predictive capabilities of ElATools.

[1]  Georg Kresse,et al.  Performance of the Vienna ab initio simulation package (VASP) in chemical applications , 2003 .

[2]  David M. Teter,et al.  Computational Alchemy: The Search for New Superhard Materials , 1998 .

[3]  John D. Hunter,et al.  Matplotlib: A 2D Graphics Environment , 2007, Computing in Science & Engineering.

[4]  M. Peng,et al.  Insight into anisotropies in mechanical and thermal properties of AGdS2 (A = alkali metals) ternary gadolinium sulfides , 2021 .

[5]  Carlos G. Levi,et al.  MATERIALS DESIGN FOR THE NEXT GENERATION THERMAL BARRIER COATINGS , 2003 .

[6]  Baughman,et al.  Materials with negative compressibilities in one or more dimensions , 1998, Science.

[7]  L. Auger.  The Journal of the Acoustical Society of America , 1949 .

[8]  M. Bilal,et al.  IR-elastic package , 2017 .

[9]  Bo Xu,et al.  Microscopic theory of hardness and design of novel superhard crystals , 2012 .

[10]  A. Reuss,et al.  Berechnung der Fließgrenze von Mischkristallen auf Grund der Plastizitätsbedingung für Einkristalle . , 1929 .

[11]  R. Orlando,et al.  CRYSTAL14: A program for the ab initio investigation of crystalline solids , 2014 .

[12]  R. Lakes.  Foam Structures with a Negative Poisson's Ratio , 1987, Science.

[13]  X. Chong,et al.  Elastic properties and electronic structures of CrxBy as superhard compounds , 2014 .

[14]  Ting Zhu,et al.  Atomistic mechanisms governing elastic limit and incipient plasticity in crystals , 2002, Nature.

[15]  P. Alam.  ‘A’ , 2021, Composites Engineering: An A–Z Guide.

[16]  Claudia Ambrosch-Draxl,et al.  ElaStic: A tool for calculating second-order elastic constants from first principles , 2013, Comput. Phys. Commun..

[17]  P. Alam.  ‘G’ , 2021, Composites Engineering: An A–Z Guide.

[18]  Elsevier Sdol,et al.  International Journal of Refractory Metals and Hard Materials , 2009 .

[19]  Tanmoy Das,et al.  Superconductivity and topological Fermi surface transitions in electron-doped cuprates near optimal doping , 2007, 0711.1504.

[20]  P. Hohenberg,et al.  Inhomogeneous Electron Gas , 1964 .

[21]  Bane Sullivan,et al.  PyVista: 3D plotting and mesh analysis through a streamlined interface for the Visualization Toolkit (VTK) , 2019, J. Open Source Softw..

[22]  R. Baughman,et al.  Negative Poisson's ratios as a common feature of cubic metals , 1998, Nature.

[23]  Enlai Gao,et al.  Elastic anisotropy measure for two-dimensional crystals , 2020 .

[24]  Kristin A. Persson,et al.  Commentary: The Materials Project: A materials genome approach to accelerating materials innovation , 2013 .

[25]  P. Saeidi,et al.  The investigation of structural, electronic, elastic and thermodynamic properties of Gd1−Y AuPb alloys: A first principle study , 2019, Physics Letters A.

[26]  A. L. Ivanovskii,et al.  Hardness of hexagonal AlB2-like diborides of s, p and d metals from semi-empirical estimations , 2013 .

[27]  Chun Lu,et al.  Effect of elastic anisotropy on the elastic fields and vertical alignment of quantum dots , 2003 .

[28]  G. Fitzgerald,et al.  'I. , 2019, Australian journal of primary health.

[29]  Martin Ostoja-Starzewski,et al.  Universal elastic anisotropy index. , 2008, Physical review letters.

[30]  Paolo Ruggerone,et al.  Computational Materials Science X , 2002 .

[31]  A. Vaez,et al.  Ab-initio thermodynamic and elastic properties of AlNi and AlNi3 intermetallic compounds , 2018 .

[32]  Aldo H. Romero,et al.  MechElastic: A Python library for analysis of mechanical and elastic properties of bulk and 2D materials , 2020, Comput. Phys. Commun..

[33]  D. Raabe,et al.  Design of Mg alloys: The effects of Li concentration on the structure and elastic properties in the Mg–Li binary system by first principles calculations , 2017 .

[34]  P. Alam.  ‘S’ , 2021, Composites Engineering: An A–Z Guide.

[35]  H. J. Mcskimin.  Ultrasonic Measurement Techniques Applicable to Small Solid Specimens , 1950 .

[36]  François-Xavier Coudert,et al.  Anisotropic elastic properties of flexible metal-organic frameworks: how soft are soft porous crystals? , 2012, Physical review letters.

[37]  A. Goodwin,et al.  Negative linear compressibility. , 2015, Physical chemistry chemical physics : PCCP.

[38]  K. Evans.  Auxetic polymers: a new range of materials , 1991 .

[39]  A. Boochani,et al.  Ti2VGe Heuslerene: theoretical prediction of a novel 2D material , 2019, Journal of Materials Chemistry C.

[40]  S. Pugh.  XCII. Relations between the elastic moduli and the plastic properties of polycrystalline pure metals , 1954 .

[41]  W. Kohn,et al.  Self-Consistent Equations Including Exchange and Correlation Effects , 1965 .

[42]  Longke Bao,et al.  Structural, electronic, and elastic properties of orthorhombic, hexagonal, and cubic Cu3Sn intermetallic compounds in Sn–Cu lead-free solder , 2020 .

[43]  H. Ledbetter,et al.  Elastic Properties of Metals and Alloys, I. Iron, Nickel, and Iron-Nickel Alloys , 1973 .

[44]  Zachary Cope,et al.  The London , 1963 .

[45]  Kevin S. Knight,et al.  Negative Linear Compressibility and Massive Anisotropic Thermal Expansion in Methanol Monohydrate , 2011, Science.

[46]  W. Hume-rothery.  Elasticity and Anelasticity of Metals , 1949, Nature.

[47]  P. W. Bridgman.  The Compressibility of Metals at High Pressures. , 1922, Proceedings of the National Academy of Sciences of the United States of America.

[48]  Leonard Kleinman,et al.  Deformation Potentials in Silicon. I. Uniaxial Strain , 1962 .

[49]  B. Auld,et al.  Acoustic fields and waves in solids , 1973 .

[50]  δ-Phosphorene: a two dimensional material with a highly negative Poisson's ratio. , 2017, Nanoscale.

[51]  Qian Wang,et al.  TiC2: a new two-dimensional sheet beyond MXenes. , 2016, Nanoscale.

[52]  Carson Sievert.  Interactive Web-Based Data Visualization with R, plotly, and shiny , 2020 .

[53]  Jijun Zhao,et al.  Correlation between hardness and elastic moduli of the covalent crystals , 2011 .

[54]  O. Anderson,et al.  A simplified method for calculating the debye temperature from elastic constants , 1963 .

[55]  R. Vacher,et al.  Brillouin Scattering: A Tool for the Measurement of Elastic and Photoelastic Constants , 1972 .

[56]  K. Schwarz,et al.  WIEN2k: An APW+lo program for calculating the properties of solids. , 2020, The Journal of chemical physics.

[57]  Proceedings of the Physical Society , 1948, Nature.

[58]  J. Hutchinson,et al.  Microcracking in Ceramics Induced by Thermal Expansion or Elastic Anisotropy , 1988 .

[59]  Z. Li,et al.  The single-crystal elastic constants of cubic (3C) SiC to 1000° C , 1987 .

[60]  Kenneth E. Evans,et al.  ElAM: A computer program for the analysis and representation of anisotropic elastic properties , 2010, Comput. Phys. Commun..

[61]  S. Woods,et al.  The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science. S. 211-215 , 2005 .

[62]  Christopher M. Kube,et al.  Elastic anisotropy of crystals , 2016 .

[63]  B. M. Fulk.  MATH , 1992 .

[64]  R. F. Zhang,et al.  AELAS: Automatic ELAStic property derivations via high-throughput first-principles computation , 2017, Comput. Phys. Commun..

[65]  Philipp K. Janert,et al.  Gnuplot in Action: Understanding Data with Graphs , 2009 .

[66]  Tsuyoshi Murata,et al.  {m , 1934, ACML.

[67]  J. Nye.  Physical Properties of Crystals: Their Representation by Tensors and Matrices , 1957 .

[68]  D. G. Pettifor,et al.  Theoretical predictions of structure and related properties of intermetallics , 1992 .

[69]  E. B. Wilson.  PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES. , 1919, Science.

[70]  P. Dobson,et al.  Physical Properties of Crystals – Their Representation by Tensors and Matrices , 1985 .

[71]  Andrew N. Norris,et al.  Poisson's ratio in cubic materials , 2006, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[72]  Jakoah Brgoch,et al.  Hard and superhard materials: A computational perspective , 2019, Journal of Solid State Chemistry.

[73]  K. Jacobsen,et al.  The Computational 2D Materials Database: high-throughput modeling and discovery of atomically thin crystals , 2018, 2D Materials.

[74]  Watson,et al.  Lower limit to the thermal conductivity of disordered crystals. , 1992, Physical review. B, Condensed matter.

[75]  H. Altenbach,et al.  Visualising elastic anisotropy: theoretical background and computational implementation , 2018, Continuum Mechanics and Thermodynamics.

[76]  James G. Berryman,et al.  Long-wave elastic anisotropy in transversely isotropic media , 1979 .

[77]  P. Saeidi,et al.  The structural and elastic properties of InSb1-xBix alloys , 2019, Computational Condensed Matter.

[78]  A. Ramazani,et al.  Insight into the topological phase and elastic properties of halide perovskites CsSnX3 (X = l, Br, Cl) under hydrostatic pressures , 2020 .

[79]  W. Marsden.  I and J , 2012 .

[80]  S C Cowin,et al.  The fabric dependence of the orthotropic elastic constants of cancellous bone. , 1990, Journal of biomechanics.

[81]  R. Hill.  The Elastic Behaviour of a Crystalline Aggregate , 1952 .