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 Ca(MnBi)2 (Materials Project id mp-29615)

        47       18       28       -7        0        0  
        18       47       28        7        0        0  
        28       28       56        0        0        0  
        -7        7        0       18        0        0  
         0        0        0        0       18       -7  
         0        0        0        0       -7       14  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 33.111 GPaEV = 39.247 GPaGV = 15.067 GPaνV = 0.30245
ReussKR = 31.877 GPaER = 32.672 GPaGR = 12.29 GPaνR = 0.32917
HillKH = 32.494 GPaEH = 35.986 GPaGH = 13.679 GPaνH = 0.31542

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
8.7199 GPa 12.175 GPa 20.647 GPa 23.28 GPa 34.825 GPa 100.35 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 23.763 GPa 56.556 GPa 4.3436 TPa–1 13.514 TPa–1 8.7199 GPa 23.419 GPa0.053650.62624Value
Anisotropy 2.38 3.1111 2.686 11.6726Anisotropy
Axis -0.8036
0.4803
0.3515
-0.0000
0.7967
0.6044
0.0000
0.0000
1.0000
-0.7934
0.6088
0.0000
-1.0000
0.0000
-0.0000
0.5286
0.3088
0.7907
-1.0000
0.0000
-0.0000
-0.4138
0.2346
0.8796
Axis
-0.0000
-0.7983
-0.6022
-0.5045
0.8634
0.0001
0.0000
-0.8159
-0.5782
-0.5126
-0.8585
-0.0122
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