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 ZrCo2 (Materials Project id mp-929)

       256      118      118        0        0        0  
       118      256      118        0        0        0  
       118      118      256        0        0        0  
         0        0        0       81        0        0  
         0        0        0        0       81        0  
         0        0        0        0        0       81  

Average properties

Averaging scheme	Bulk modulus	Young's modulus	Shear modulus	Poisson's ratio
Voigt	KV = 164 GPa	EV = 197.94 GPa	GV = 76.2 GPa	νV = 0.29884
Reuss	KR = 164 GPa	ER = 196.89 GPa	GR = 75.732 GPa	νR = 0.29991
Hill	KH = 164 GPa	EH = 197.42 GPa	GH = 75.966 GPa	νH = 0.29937

Eigenvalues of the stiffness matrix

λ1	λ2	λ3	λ4	λ5	λ6
81 GPa	81 GPa	81 GPa	138 GPa	138 GPa	492 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	181.54 GPa	208.65 GPa	2.0325 TPa–1	2.0325 TPa–1	69 GPa	81 GPa	0.24161	0.34957	Value
Anisotropy	1.149		1.0000		1.174		1.4469		Anisotropy
Axis	1.0000 0.0000 0.0000	0.5774 0.5774 0.5773	0.0000 0.0000 1.0000	0.7934 0.0000 0.6088	0.7071 -0.0003 0.7071	-0.0000 0.0000 1.0000	0.7071 -0.0000 -0.7071	0.7071 -0.0005 0.7071	Axis
					0.7071 -0.0005 -0.7071	-0.9397 0.3420 -0.0000	-0.7071 0.0002 -0.7071	0.0003 1.0000 0.0004	Second axis

Spatial dependence of Young's modulus

[[256.0, 118.0, 118.0, 0.0, 0.0, 0.0], [118.0, 256.0, 118.0, 0.0, 0.0, 0.0], [118.0, 118.0, 256.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 81.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 81.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 81.0]] ZrCo2 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-929" target="_blank">mp-929</a>) young

Spatial dependence of linear compressibility

[[256.0, 118.0, 118.0, 0.0, 0.0, 0.0], [118.0, 256.0, 118.0, 0.0, 0.0, 0.0], [118.0, 118.0, 256.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 81.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 81.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 81.0]] ZrCo2 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-929" target="_blank">mp-929</a>) lc

Spatial dependence of shear modulus

[[256.0, 118.0, 118.0, 0.0, 0.0, 0.0], [118.0, 256.0, 118.0, 0.0, 0.0, 0.0], [118.0, 118.0, 256.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 81.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 81.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 81.0]] ZrCo2 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-929" target="_blank">mp-929</a>) shear

Spatial dependence of Poisson's ratio

[[256.0, 118.0, 118.0, 0.0, 0.0, 0.0], [118.0, 256.0, 118.0, 0.0, 0.0, 0.0], [118.0, 118.0, 256.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 81.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 81.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 81.0]] ZrCo2 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-929" target="_blank">mp-929</a>) poisson

Code version: 2020.07.26 (running on Python 3.7.2)