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 Si (Materials Project id mp-10649)

       117       64       77        0        0        0  
        64      117       77        0        0        0  
        77       77      101        0        0        0  
         0        0        0       62        0        0  
         0        0        0        0       62        0  
         0        0        0        0        0       26  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 85.667 GPaEV = 98.86 GPaGV = 37.8 GPaνV = 0.30767
ReussKR = 85.64 GPaER = 72.136 GPaGR = 26.528 GPaνR = 0.35961
HillKH = 85.653 GPaEH = 85.758 GPaGH = 32.164 GPaνH = 0.33313

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
24.991 GPa 26 GPa 53 GPa 62 GPa 62 GPa 257.01 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 35.486 GPa 112.97 GPa 3.7366 TPa–1 4.2036 TPa–1 14.361 GPa 62 GPa-0.147930.73079Value
Anisotropy 3.183 1.1250 4.317Anisotropy
Axis 0.0000
0.0000
1.0000
0.7759
0.0000
0.6308
0.3827
0.9239
0.0000
0.0000
0.0000
1.0000
-0.5000
0.5000
-0.7071
-0.0000
0.0000
1.0000
0.5064
0.5064
-0.6979
-0.4843
0.4843
-0.7286
Axis
0.5000
-0.5000
-0.7071
-1.0000
0.0000
-0.0000
0.4935
0.4935
0.7162
-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