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 Li2LaTa2O7 (Materials Project id mp-15901)

       308       83       65        0        0        0  
        83      308       65        0        0        0  
        65       65      107        0        0        0  
         0        0        0       67        0        0  
         0        0        0        0       67        0  
         0        0        0        0        0       63  

Average properties

Averaging scheme	Bulk modulus	Young's modulus	Shear modulus	Poisson's ratio
Voigt	KV = 127.67 GPa	EV = 184.79 GPa	GV = 73.4 GPa	νV = 0.25876
Reuss	KR = 96.774 GPa	ER = 158.26 GPa	GR = 64.47 GPa	νR = 0.22743
Hill	KH = 112.22 GPa	EH = 171.66 GPa	GH = 68.935 GPa	νH = 0.24506

Eigenvalues of the stiffness matrix

λ1	λ2	λ3	λ4	λ5	λ6
63 GPa	67 GPa	67 GPa	79.843 GPa	225 GPa	418.16 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	85.389 GPa	261.46 GPa	1.258 TPa–1	7.8174 TPa–1	47.224 GPa	112.5 GPa	0.053647	0.50903	Value
Anisotropy	3.062		6.2143		2.382		9.4885		Anisotropy
Axis	0.0000 0.0000 1.0000	0.0000 1.0000 0.0000	0.2549 0.9670 0.0000	0.0000 0.0000 1.0000	0.5001 0.5000 -0.7071	0.7071 0.7071 -0.0000	0.4859 0.4859 0.7265	1.0000 0.0002 0.0000	Axis
					-0.5000 -0.5000 -0.7071	-0.7071 0.7071 -0.0000	0.5137 0.5137 -0.6871	0.0000 0.0003 -1.0000	Second axis

Spatial dependence of Young's modulus

[[308.0, 83.0, 65.0, 0.0, 0.0, 0.0], [83.0, 308.0, 65.0, 0.0, 0.0, 0.0], [65.0, 65.0, 107.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 67.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 67.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 63.0]] Li2LaTa2O7 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-15901" target="_blank">mp-15901</a>) young

Spatial dependence of linear compressibility

[[308.0, 83.0, 65.0, 0.0, 0.0, 0.0], [83.0, 308.0, 65.0, 0.0, 0.0, 0.0], [65.0, 65.0, 107.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 67.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 67.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 63.0]] Li2LaTa2O7 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-15901" target="_blank">mp-15901</a>) lc

Spatial dependence of shear modulus

[[308.0, 83.0, 65.0, 0.0, 0.0, 0.0], [83.0, 308.0, 65.0, 0.0, 0.0, 0.0], [65.0, 65.0, 107.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 67.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 67.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 63.0]] Li2LaTa2O7 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-15901" target="_blank">mp-15901</a>) shear

Spatial dependence of Poisson's ratio

[[308.0, 83.0, 65.0, 0.0, 0.0, 0.0], [83.0, 308.0, 65.0, 0.0, 0.0, 0.0], [65.0, 65.0, 107.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 67.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 67.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 63.0]] Li2LaTa2O7 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-15901" target="_blank">mp-15901</a>) poisson

Code version: 2023.01.19 (running on Python 3.10.6)