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 Ba2Cd (Materials Project id mp-8093)

        28        9        9        0        0        0  
         9       28        9        0        0        0  
         9        9       21        0        0        0  
         0        0        0        9        0        0  
         0        0        0        0        9        0  
         0        0        0        0        0       11  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 14.556 GPaEV = 22.66 GPaGV = 9.1333 GPaνV = 0.24053
ReussKR = 14.302 GPaER = 22.159 GPaGR = 8.9222 GPaνR = 0.24178
HillKH = 14.429 GPaEH = 22.41 GPaGH = 9.0278 GPaνH = 0.24115

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
9 GPa 9 GPa 11 GPa 13.967 GPa 19 GPa 44.033 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 16.622 GPa 25.125 GPa 19.512 TPa–1 30.894 TPa–1 7.529 GPa 11 GPa0.142060.36769Value
Anisotropy 1.512 1.5833 1.461 2.5882Anisotropy
Axis 0.0000
0.0000
1.0000
0.7071
0.7071
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
1.0000
-0.0000
-0.0000
0.7071
0.7071
-0.0001
0.7071
0.7071
-0.0000
Axis
0.7071
-0.0005
-0.7071
0.0000
1.0000
0.0000
-0.7071
0.7071
-0.0001
0.0000
-0.0000
-1.0000
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