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 CsTiCl3 (Materials Project id mp-28283)

        23        9       10        0        0        0  
         9       23       10        0        0        0  
        10       10       48        0        0        0  
         0        0        0        8        0        0  
         0        0        0        0        8        0  
         0        0        0        0        0        7  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 16.889 GPaEV = 22.783 GPaGV = 8.9333 GPaνV = 0.27517
ReussKR = 15.182 GPaER = 20.795 GPaGR = 8.1758 GPaνR = 0.27172
HillKH = 16.035 GPaEH = 21.789 GPaGH = 8.5546 GPaνH = 0.27353

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
7 GPa 8 GPa 8 GPa 14 GPa 23.752 GPa 56.248 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 18.61 GPa 41.75 GPa 8.982 TPa–1 28.443 TPa–1 7 GPa 10.799 GPa0.139440.36206Value
Anisotropy 2.243 3.1667 1.543 2.5965Anisotropy
Axis 0.9082
0.3660
0.2031
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.6088
0.7934
0.0000
0.6375
0.7705
-0.0000
-0.4023
0.5815
-0.7071
0.9482
0.3177
-0.0000
0.4896
0.0001
-0.8720
Axis
-0.7705
0.6375
0.0000
0.4024
-0.5815
-0.7071
0.0001
-0.0002
-1.0000
-0.8720
-0.0001
-0.4896
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