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 CsAgSe4 (Materials Project id mp-18105)

        12        5        3        0        0        0  
         5       16        4        0        0        0  
         3        4       31        0        0        0  
         0        0        0        5        0        0  
         0        0        0        0        6        0  
         0        0        0        0        0        3  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 9.2222 GPaEV = 14.657 GPaGV = 5.9333 GPaνV = 0.23512
ReussKR = 8.2409 GPaER = 12.21 GPaGR = 4.872 GPaνR = 0.25306
HillKH = 8.7315 GPaEH = 13.437 GPaGH = 5.4027 GPaνH = 0.24352

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
3 GPa 5 GPa 6 GPa 8.6119 GPa 17.534 GPa 32.854 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 8.8718 GPa 29.707 GPa 21.367 TPa–1 62.286 TPa–1 3 GPa 8.3238 GPa0.0531450.50205Value
Anisotropy 3.348 2.9151 2.775 9.4468Anisotropy
Axis -0.7820
0.6233
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
1.0000
-0.0001
-0.0000
-0.0001
0.7071
0.7071
-0.8373
0.5467
0.0000
0.6226
0.7826
0.0000
Axis
0.0001
1.0000
0.0000
0.0001
0.7071
-0.7071
-0.0001
-0.0002
-1.0000
-0.7826
0.6226
-0.0000
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