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 ErBi2IO4 (Materials Project id mp-551250)

       156       77       29        0        0        0  
        77      156       29        0        0        0  
        29       29       77        0        0        0  
         0        0        0       23        0        0  
         0        0        0        0       23        0  
         0        0        0        0        0       77  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 73.222 GPaEV = 104.79 GPaGV = 41.533 GPaνV = 0.26149
ReussKR = 59.996 GPaER = 83.305 GPaGR = 32.834 GPaνR = 0.26858
HillKH = 66.609 GPaEH = 94.05 GPaGH = 37.184 GPaνH = 0.26467

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
23 GPa 23 GPa 66.875 GPa 77 GPa 79 GPa 243.12 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 61.711 GPa 178.1 GPa 2.9522 TPa–1 10.763 TPa–1 23 GPa 77 GPa0.0888010.48111Value
Anisotropy 2.886 3.6458 3.348 5.4179Anisotropy
Axis 0.5772
0.0000
0.8166
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
0.5181
0.5181
0.6805
-0.5925
0.5927
0.5455
Axis
0.1734
0.9849
-0.0000
-0.0007
1.0000
0.0000
-0.7071
0.7071
-0.0000
-0.3859
0.3856
-0.8381
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