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 AlCuO2 (Materials Project id mp-3098)

       294       90      103        0        0        0  
        90      294      103        0        0        0  
       103      103      509        0        0        0  
         0        0        0       39        0        0  
         0        0        0        0       39        0  
         0        0        0        0        0      102  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 187.67 GPaEV = 231.45 GPaGV = 89.4 GPaνV = 0.29445
ReussKR = 176 GPaER = 172.77 GPaGR = 64.639 GPaνR = 0.33639
HillKH = 181.83 GPaEH = 202.47 GPaGH = 77.02 GPaνH = 0.31442

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
39 GPa 39 GPa 102 GPa 204 GPa 287.99 GPa 605.01 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 130.15 GPa 453.74 GPa 1.0216 TPa–1 2.3301 TPa–1 39 GPa 137.03 GPa0.102580.68504Value
Anisotropy 3.486 2.2809 3.514 6.6782Anisotropy
Axis 0.6821
0.2850
0.6734
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
-0.1305
0.9914
0.0000
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
0.4911
0.4464
-0.7480
0.5916
0.2208
0.7754
Axis
0.9397
0.3420
-0.0000
-0.7071
-0.0002
-0.7071
-0.6727
0.7399
-0.0000
-0.7265
-0.2711
0.6315
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