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 CsMgBr3 (Materials Project id mp-29750)

        18        6        3        0        0        0  
         6       18        3        0        0        0  
         3        3       36        0        0        0  
         0        0        0        1        0        0  
         0        0        0        0        1        0  
         0        0        0        0        0        6  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 10.667 GPaEV = 14.298 GPaGV = 5.6 GPaνV = 0.2766
ReussKR = 10.071 GPaER = 5.8264 GPaGR = 2.0756 GPaνR = 0.40358
HillKH = 10.369 GPaEH = 10.249 GPaGH = 3.8378 GPaνH = 0.33526

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
1 GPa 1 GPa 6 GPa 12 GPa 22.652 GPa 37.348 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 3.6848 GPa 35.25 GPa 21.277 TPa–1 39.007 TPa–1 1 GPa 10.162 GPa0.0375750.85056Value
Anisotropy 9.566 1.8333 10.16 22.6365Anisotropy
Axis 0.6966
0.1843
0.6934
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
-0.1699
0.6864
-0.7071
-0.3125
0.4159
0.8540
0.3093
0.5433
-0.7805
Axis
1.0000
0.0000
-0.0000
0.1700
-0.6864
-0.7071
-0.7995
-0.6006
-0.0000
-0.3862
-0.6782
-0.6252
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