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 CdAuO2 (Materials Project id mp-997037)

       170       87       62        0        0        0  
        87      222      106        0        0        0  
        62      106      189        0        0        0  
         0        0        0       36        0        0  
         0        0        0        0       15        0  
         0        0        0        0        0       23  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 121.22 GPaEV = 99.595 GPaGV = 36.533 GPaνV = 0.36307
ReussKR = 116.3 GPaER = 78.86 GPaGR = 28.428 GPaνR = 0.38699
HillKH = 118.76 GPaEH = 89.301 GPaGH = 32.481 GPaνH = 0.37468

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
15 GPa 23 GPa 36 GPa 94.421 GPa 116.98 GPa 369.6 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 50.405 GPa 144.32 GPa 1.4181 TPa–1 3.995 TPa–1 15 GPa 58.339 GPa0.150540.68016Value
Anisotropy 2.863 2.8172 3.889 4.5181Anisotropy
Axis 0.7081
-0.0000
0.7061
0.0000
1.0000
0.0000
0.0000
1.0000
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.7071
-0.0000
-0.7071
0.0000
0.0000
1.0000
0.7051
0.0002
-0.7091
Axis
1.0000
0.0000
-0.0000
-0.7071
0.0002
-0.7071
-1.0000
0.0000
0.0000
-0.7091
-0.0002
-0.7051
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