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 K (Materials Project id mp-972981)

         8        2        3        0        0        0  
         2        7        3        0        0        0  
         3        3        6        0        0        0  
         0        0        0        1        0        0  
         0        0        0        0        1        0  
         0        0        0        0        0        1  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 4.1111 GPaEV = 3.9324 GPaGV = 1.4667 GPaνV = 0.34058
ReussKR = 4.0962 GPaER = 3.4026 GPaGR = 1.2495 GPaνR = 0.36155
HillKH = 4.1036 GPaEH = 3.6695 GPaGH = 1.3581 GPaνH = 0.35097

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
1 GPa 1 GPa 1 GPa 3.1278 GPa 5.5077 GPa 12.365 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 2.7736 GPa 6.4545 GPa 70.423 TPa–1 89.202 TPa–1 1 GPa 2.7308 GPa0.0909090.60207Value
Anisotropy 2.327 1.2667 2.731 6.6228Anisotropy
Axis 0.5655
0.5774
0.5890
1.0000
0.0000
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.7071
0.7071
0.0000
-1.0000
-0.0000
-0.0001
0.8042
0.0001
0.5944
Axis
1.0000
0.0000
-0.0000
-0.7071
0.7071
-0.0000
0.0000
-1.0000
-0.0000
0.5944
0.0003
-0.8042
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