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 BiIO (Materials Project id mp-22987)

        87       31        3        0        0        0  
        31       87        3        0        0        0  
         3        3        6        0        0        0  
         0        0        0        2        0        0  
         0        0        0        0        2        0  
         0        0        0        0        0       35  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 28.222 GPaEV = 43.163 GPaGV = 17.333 GPaνV = 0.2451
ReussKR = 5.8475 GPaER = 9.406 GPaGR = 3.8177 GPaνR = 0.23191
HillKH = 17.035 GPaEH = 26.287 GPaGH = 10.576 GPaνH = 0.24281

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
2 GPa 2 GPa 5.8395 GPa 35 GPa 56 GPa 118.16 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 5.2865 GPa 87.027 GPa 4.3478 TPa–1 162.32 TPa–1 2 GPa 35 GPa0.0254240.58489Value
Anisotropy 16.46 37.3333 17.5 23.0057Anisotropy
Axis 0.4931
0.0000
0.8700
0.7071
0.7071
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
1.0000
0.0007
0.0000
0.0000
0.0000
1.0000
-0.6572
0.6573
0.3688
Axis
1.0000
0.0000
-0.0000
-0.0007
1.0000
0.0000
0.1736
0.9848
-0.0000
-0.2608
0.2608
-0.9295
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