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 Ca3Mn2O7 (Materials Project id mp-19124)

       272       58       86        0        0        0  
        58      272       86        0        0        0  
        86       86      279        0        0        0  
         0        0        0       77        0        0  
         0        0        0        0       77        0  
         0        0        0        0        0       84  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 142.56 GPaEV = 217.16 GPaGV = 87.133 GPaνV = 0.24611
ReussKR = 142.06 GPaER = 214.21 GPaGR = 85.774 GPaνR = 0.24868
HillKH = 142.31 GPaEH = 215.68 GPaGH = 86.454 GPaνH = 0.24739

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
77 GPa 77 GPa 84 GPa 180.23 GPa 214 GPa 428.77 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 200.34 GPa 241.45 GPa 2.0446 TPa–1 2.4975 TPa–1 77 GPa 107 GPa0.128280.35478Value
Anisotropy 1.205 1.2215 1.39 2.7657Anisotropy
Axis -0.5699
0.5698
0.5920
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.7071
0.7071
-0.0000
1.0000
-0.0000
-0.0000
0.7176
-0.0002
0.6964
Axis
0.1734
0.9849
-0.0000
-0.7071
0.7071
0.0000
0.0000
1.0000
0.0000
0.6964
-0.0005
-0.7176
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