ELATE: Elastic tensor analysis

Welcome to ELATE, the online tool for analysis of elastic tensors, developed by Romain Gaillac and Fran├žois-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 Li2FeO3 (Materials Project id mp-774155)

       186       32       37        0        1        0  
        32      222       63        0       15        0  
        37       63      226        0      -15        0  
         0        0        0       79        0       16  
         1       15      -15        0       51        0  
         0        0        0       16        0       42  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 99.778 GPaEV = 165.97 GPaGV = 67.867 GPaνV = 0.22277
ReussKR = 97.848 GPaER = 146.78 GPaGR = 58.714 GPaνR = 0.24998
HillKH = 98.813 GPaEH = 156.47 GPaGH = 63.29 GPaνH = 0.23609

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
36.041 GPa 47.032 GPa 84.959 GPa 163.17 GPa 168.01 GPa 306.79 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 101.13 GPa 212.46 GPa 2.8492 TPa–1 4.2823 TPa–1 36.041 GPa 86.955 GPa-0.031090.51928Value
Anisotropy 2.101 1.5030 2.413Anisotropy
Axis 0.6631
0.6718
-0.3303
-0.1914
-0.0000
0.9815
0.0535
-0.0000
0.9986
0.9986
0.0000
-0.0535
-0.9371
0.0000
0.3490
0.2994
0.7071
-0.6406
0.0394
0.4927
-0.8693
0.7463
0.5866
0.3145
Axis
-0.0000
-1.0000
0.0000
-0.2995
0.7072
0.6405
-0.8102
-0.4934
-0.3164
-0.6651
0.6759
0.3175
Second axis

Spatial dependence of Young's modulus



Young's modulus in (xy) plane

Young's modulus in (xz) plane

Young's modulus in (yz) plane

Spatial dependence of linear compressibility



linear compressibility in (xy) plane

linear compressibility in (xz) plane

linear compressibility in (yz) plane

Spatial dependence of shear modulus



Shear modulus in (xy) plane

Shear modulus in (xz) plane

Shear modulus in (yz) plane

Spatial dependence of Poisson's ratio



Poisson's ratio in (xy) plane

Poisson's ratio in (xz) plane

Poisson's ratio in (yz) plane