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 MnO (Materials Project id mp-999539)

       129       87       54        0        0        0  
        87      129       54        0        0        0  
        54       54      136        0        0        0  
         0        0        0       36        0        0  
         0        0        0        0       36        0  
         0        0        0        0        0       21  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 87.111 GPaEV = 85.21 GPaGV = 31.867 GPaνV = 0.33697
ReussKR = 86.559 GPaER = 78.024 GPaGR = 28.903 GPaνR = 0.34977
HillKH = 86.835 GPaEH = 81.633 GPaGH = 30.385 GPaνH = 0.34332

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
21 GPa 36 GPa 36 GPa 42 GPa 89.791 GPa 262.21 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 67.6 GPa 109 GPa 3.4828 TPa–1 4.5872 TPa–1 21 GPa 36 GPa0.155050.60952Value
Anisotropy 1.612 1.3171 1.714 3.9312Anisotropy
Axis 0.8660
0.5000
0.0000
0.0000
0.0000
1.0000
0.9239
0.3827
0.0000
0.0000
0.0000
1.0000
0.9573
0.2890
0.0000
0.0000
0.0000
1.0000
-0.6725
0.7401
-0.0000
-0.1878
0.9822
-0.0000
Axis
-0.2890
0.9573
-0.0000
0.4962
0.8682
-0.0000
-0.0000
0.0000
1.0000
-0.9822
-0.1878
0.0000
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