ELATE: Elastic tensor analysis

Welcome to ELATE, the online tool for analysis of elastic tensors, developed by Romain Gaillac and François-Xavier Coudert at CNRS / Chimie ParisTech.
If you use the software in published results (paper, conference, etc.), please cite the corresponding paper (J. Phys. Condens. Matter, 2016, 28, 275201) and give the website URL.

ELATE is open source software. Any queries or comments are welcome at

Summary of the properties

Input: stiffness matrix (coefficients in GPa) of TbScO3 (Materials Project id mp-31119)

       320      116      119        0        0        0  
       116      216      107        0        0        0  
       119      107      283        0        0        0  
         0        0        0       78        0        0  
         0        0        0        0       78        0  
         0        0        0        0        0       98  

Average properties

Averaging scheme	Bulk modulus	Young's modulus	Shear modulus	Poisson's ratio
Voigt	KV = 167 GPa	EV = 212.73 GPa	GV = 82.6 GPa	νV = 0.2877
Reuss	KR = 161.74 GPa	ER = 207.3 GPa	GR = 80.577 GPa	νR = 0.28638
Hill	KH = 164.37 GPa	EH = 210.02 GPa	GH = 81.588 GPa	νH = 0.28705

Eigenvalues of the stiffness matrix

λ1	λ2	λ3	λ4	λ5	λ6
78 GPa	78 GPa	98 GPa	130.11 GPa	181.56 GPa	507.33 GPa

Variations of the elastic moduli

	Young's modulus		Linear compressibility		Shear modulus		Poisson's ratio
	Emin	Emax	βmin	βmax	Gmin	Gmax	νmin	νmax
Value	156.87 GPa	249.75 GPa	1.3594 TPa–1	2.9929 TPa–1	68.271 GPa	98 GPa	0.17056	0.4045	Value
Anisotropy	1.592		2.2016		1.435		2.3715		Anisotropy
Axis	0.0000 1.0000 0.0000	0.8966 0.4429 -0.0000	1.0000 0.0000 0.0000	0.0000 1.0000 0.0000	0.4162 0.7071 0.5716	1.0000 0.0000 -0.0000	0.6185 0.7444 0.2515	1.0000 -0.0000 0.0000	Axis
					-0.4162 0.7071 -0.5716	-0.0000 1.0000 0.0000	-0.7139 0.6661 -0.2161	0.0000 1.0000 -0.0001	Second axis

Spatial dependence of Young's modulus

[[320.0, 116.0, 119.0, 0.0, 0.0, 0.0], [116.0, 216.0, 107.0, 0.0, 0.0, 0.0], [119.0, 107.0, 283.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 78.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 78.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 98.0]] TbScO3 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-31119" target="_blank">mp-31119</a>) young

Spatial dependence of linear compressibility

[[320.0, 116.0, 119.0, 0.0, 0.0, 0.0], [116.0, 216.0, 107.0, 0.0, 0.0, 0.0], [119.0, 107.0, 283.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 78.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 78.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 98.0]] TbScO3 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-31119" target="_blank">mp-31119</a>) lc

Spatial dependence of shear modulus

[[320.0, 116.0, 119.0, 0.0, 0.0, 0.0], [116.0, 216.0, 107.0, 0.0, 0.0, 0.0], [119.0, 107.0, 283.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 78.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 78.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 98.0]] TbScO3 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-31119" target="_blank">mp-31119</a>) shear

Spatial dependence of Poisson's ratio

[[320.0, 116.0, 119.0, 0.0, 0.0, 0.0], [116.0, 216.0, 107.0, 0.0, 0.0, 0.0], [119.0, 107.0, 283.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 78.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 78.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 98.0]] TbScO3 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-31119" target="_blank">mp-31119</a>) poisson

Code version: 2023.01.19 (running on Python 3.10.6)