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 Cu2O3 (Materials Project id mp-760432)

       219       67       62        0        0        0  
        67      220       96        0        0        0  
        62       96       81        0        0        0  
         0        0        0       70        0        0  
         0        0        0        0       31        0  
         0        0        0        0        0       73  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 107.78 GPaEV = 139.84 GPaGV = 54.467 GPaνV = 0.28375
ReussKR = 77.162 GPaER = 91.968 GPaGR = 35.336 GPaνR = 0.30135
HillKH = 92.47 GPaEH = 115.94 GPaGH = 44.901 GPaνH = 0.29103

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
28.126 GPa 31 GPa 70 GPa 73 GPa 155.77 GPa 336.1 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 33.704 GPa 182.63 GPa -1.6638 TPa–1 13.319 TPa–1 16.124 GPa 76.611 GPa-0.0802281.2141Value
Anisotropy 5.419 4.751Anisotropy
Axis 0.0000
0.0000
1.0000
0.0000
0.8438
-0.5367
0.0000
1.0000
0.0000
0.0000
0.0000
1.0000
-0.0004
0.7071
0.7071
-0.7072
0.6410
-0.2984
0.8086
0.5883
0.0000
0.0000
1.0000
-0.0000
Axis
0.0003
0.7071
-0.7071
-0.7071
-0.6411
0.2983
-0.5883
0.8086
0.0000
-0.0004
-0.0000
-1.0000
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