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 MnSe (Materials Project id mp-604910)

        87       73        4        0        0        0  
        73       87        4        0        0        0  
         4        4       10        0        0        0  
         0        0        0        2        0        0  
         0        0        0        0        2        0  
         0        0        0        0        0       72  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 38.444 GPaEV = 55.568 GPaGV = 22.067 GPaνV = 0.2591
ReussKR = 9.561 GPaER = 10.148 GPaGR = 3.8348 GPaνR = 0.32311
HillKH = 24.003 GPaEH = 32.93 GPaGH = 12.951 GPaνH = 0.27135

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
2 GPa 2 GPa 9.787 GPa 14 GPa 72 GPa 160.21 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 6.1814 GPa 150.13 GPa 3.8265 TPa–1 96.939 TPa–1 2 GPa 71.999 GPa0.0250.73769Value
Anisotropy 24.29 25.3333 36 29.5076Anisotropy
Axis 0.6409
0.0000
-0.7676
0.7071
0.7071
0.0000
0.1305
0.9914
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
1.0000
0.0007
-0.0000
0.0000
0.0000
1.0000
-0.6509
0.6509
0.3908
Axis
1.0000
0.0000
-0.0000
-0.0007
1.0000
-0.0000
0.1736
0.9848
-0.0000
0.2763
-0.2763
0.9205
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