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 AcOF (Materials Project id mp-36526)

       181       71       71        0        0        0  
        71      181       71        0        0        0  
        71       71      181        0        0        0  
         0        0        0       42        0        0  
         0        0        0        0       42        0  
         0        0        0        0        0       42  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 107.67 GPaEV = 123.55 GPaGV = 47.2 GPaνV = 0.30875
ReussKR = 107.67 GPaER = 121.68 GPaGR = 46.386 GPaνR = 0.31164
HillKH = 107.67 GPaEH = 122.62 GPaGH = 46.793 GPaνH = 0.31019

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
42 GPa 42 GPa 42 GPa 110 GPa 110 GPa 323 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 111.5 GPa 140.99 GPa 3.096 TPa–1 3.096 TPa–1 42 GPa 55 GPa0.235110.40064Value
Anisotropy 1.264 1.0000 1.31 1.7041Anisotropy
Axis 0.5774
0.5773
-0.5774
1.0000
0.0000
0.0000
0.7934
0.0000
0.6088
0.3314
0.8001
0.5000
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
0.7071
-0.0005
0.7071
0.7071
-0.0000
-0.7071
Axis
-0.7660
-0.6428
0.0000
-0.7071
-0.0002
-0.7071
0.0004
1.0000
0.0003
-0.7071
0.0002
-0.7071
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