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 Co (Materials Project id mp-54)

       358      165      114        0        0        0  
       165      358      114        0        0        0  
       114      114      409        0        0        0  
         0        0        0       95        0        0  
         0        0        0        0       95        0  
         0        0        0        0        0       96  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 212.33 GPaEV = 272.63 GPaGV = 106 GPaνV = 0.286
ReussKR = 212.33 GPaER = 265.67 GPaGR = 102.86 GPaνR = 0.29147
HillKH = 212.33 GPaEH = 269.16 GPaGH = 104.43 GPaνH = 0.28873

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
95 GPa 95 GPa 96 GPa 193 GPa 295 GPa 637 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 248.76 GPa 359.3 GPa 1.5699 TPa–1 1.5699 TPa–1 95 GPa 130.29 GPa0.16430.41055Value
Anisotropy 1.444 1.0000 1.371 2.4988Anisotropy
Axis 0.5745
0.5746
0.5829
0.0000
0.0000
1.0000
0.7934
0.0000
0.6088
-0.1294
0.9830
-0.1305
-0.0000
-0.0000
1.0000
0.7071
-0.0003
0.7071
-0.7071
0.7071
-0.0000
0.7071
0.7071
-0.0000
Axis
0.1738
0.9848
0.0000
0.7071
-0.0005
-0.7071
-0.0000
-0.0000
1.0000
-0.7071
0.7071
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