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 TiB (Materials Project id mp-7857)

       418      109       60        0        0        0  
       109      418       88        0        0        0  
        60       88      519        0        0        0  
         0        0        0      220        0        0  
         0        0        0        0      195        0  
         0        0        0        0        0      176  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 207.67 GPaEV = 439.25 GPaGV = 191.4 GPaνV = 0.14747
ReussKR = 206.79 GPaER = 432.79 GPaGR = 187.98 GPaνR = 0.15118
HillKH = 207.23 GPaEH = 436.03 GPaGH = 189.69 GPaνH = 0.14932

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
176 GPa 195 GPa 220 GPa 306.59 GPa 420.09 GPa 628.32 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 379.32 GPa 500.7 GPa 1.4472 TPa–1 1.7599 TPa–1 154.11 GPa 220 GPa0.0740350.24518Value
Anisotropy 1.32 1.2161 1.428 3.3117Anisotropy
Axis 0.0000
1.0000
0.0000
-0.0000
0.3649
0.9310
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
-0.7071
0.7071
0.0000
0.0001
0.0002
1.0000
1.0000
-0.0004
0.0000
1.0000
-0.0007
-0.0000
Axis
-0.7071
-0.7071
0.0000
-0.0000
1.0000
-0.0002
0.0000
-0.0003
-1.0000
0.0007
1.0000
0.0000
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