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 Co2CuGe2 (Materials Project id mp-19955)

       281       99      100        0        0        0  
        99      290      107        0        0        0  
       100      107      268        0        0        0  
         0        0        0       79        0        0  
         0        0        0        0       89        0  
         0        0        0        0        0       38  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 161.22 GPaEV = 198.68 GPaGV = 76.733 GPaνV = 0.29461
ReussKR = 161.07 GPaER = 180.42 GPaGR = 68.689 GPaνR = 0.31331
HillKH = 161.15 GPaEH = 189.61 GPaGH = 72.711 GPaνH = 0.30389

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
38 GPa 79 GPa 89 GPa 168.58 GPa 186.5 GPa 483.93 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 121.64 GPa 232.96 GPa 1.9264 TPa–1 2.1766 TPa–1 38 GPa 93.199 GPa0.0667740.60613Value
Anisotropy 1.915 1.1299 2.453 9.0774Anisotropy
Axis -0.7086
0.7057
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.0000
0.0000
0.0000
1.0000
1.0000
-0.0001
-0.0000
0.7071
0.7071
-0.0000
0.5365
0.4970
-0.6820
0.6470
0.6608
0.3803
Axis
0.0001
1.0000
0.0000
-0.7071
0.7071
-0.0000
0.5111
0.4518
0.7313
-0.7027
0.7104
-0.0389
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