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 C (Materials Project id mp-569567)

      1160       97       47        7        0        0  
        97     1160       47       -7        0        0  
        47       47     1218        0        0        0  
         7       -7        0      483        0        0  
         0        0        0        0      483        7  
         0        0        0        0        7      531  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 435.56 GPaEV = 1119.8 GPaGV = 522.53 GPaνV = 0.071507
ReussKR = 435.55 GPaER = 1115.6 GPaGR = 519.81 GPaνR = 0.0731
HillKH = 435.55 GPaEH = 1117.7 GPaGH = 521.17 GPaνH = 0.072303

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
482 GPa 482.83 GPa 532 GPa 1063.2 GPa 1168.2 GPa 1306.8 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 1069.4 GPa 1214.5 GPa 0.76182 TPa–1 0.76706 TPa–1 482 GPa 570.2 GPa0.0355180.11992Value
Anisotropy 1.136 1.0069 1.183 3.3763Anisotropy
Axis 0.6637
0.3865
-0.6404
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
-0.8819
0.4714
0.0000
0.0000
-0.1414
0.9900
0.0017
0.6917
-0.7221
0.0000
0.2165
-0.9763
0.0003
0.6847
-0.7288
Axis
1.0000
0.0000
-0.0000
-0.0013
-0.7221
-0.6917
-1.0000
0.0000
-0.0000
0.0000
-0.7288
-0.6847
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