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 BaCO3 (Materials Project id mp-675324)

        96       23       46        0        0        0  
        23      100       25        0        0        0  
        46       25       71        0        0        0  
         0        0        0        6        0        0  
         0        0        0        0       21        0  
         0        0        0        0        0        6  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 50.556 GPaEV = 48.59 GPaGV = 18.133 GPaνV = 0.33981
ReussKR = 49.771 GPaER = 30.227 GPaGR = 10.805 GPaνR = 0.39878
HillKH = 50.163 GPaEH = 39.6 GPaGH = 14.469 GPaνH = 0.36843

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
6 GPa 6 GPa 21 GPa 35.179 GPa 79.243 GPa 152.58 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 20.666 GPa 90.498 GPa 4.6245 TPa–1 8.7083 TPa–1 6 GPa 35.033 GPa0.0745950.7601Value
Anisotropy 4.379 1.8831 5.839 10.1897Anisotropy
Axis -0.0000
0.6781
0.7349
0.0000
1.0000
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.8474
0.0000
-0.5309
-0.7071
0.7071
-0.0001
-1.0000
-0.0000
0.0001
0.5185
0.7449
0.4198
Axis
-0.0000
1.0000
0.0000
-0.7071
-0.7071
-0.0001
0.0000
-1.0000
0.0000
-0.5780
0.6671
-0.4699
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