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 TiSe (Materials Project id mp-10027)

       128       32       72        0        0        0  
        32      128       72        0        0        0  
        72       72      190        0        0        0  
         0        0        0       64        0        0  
         0        0        0        0       64        0  
         0        0        0        0        0       48  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 88.667 GPaEV = 133 GPaGV = 53.2 GPaνV = 0.25
ReussKR = 79.492 GPaER = 124.54 GPaGR = 50.264 GPaνR = 0.23888
HillKH = 84.079 GPaEH = 128.78 GPaGH = 51.732 GPaνH = 0.24472

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
48 GPa 64 GPa 64 GPa 72.078 GPa 96 GPa 277.92 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 100.49 GPa 154.03 GPa 0.79872 TPa–1 5.8906 TPa–1 39.799 GPa 64 GPa0.0468230.45Value
Anisotropy 1.533 7.3750 1.608 9.6107Anisotropy
Axis 0.9659
0.2588
0.0000
-0.2319
0.5856
0.7767
0.0000
0.0000
1.0000
0.6088
0.7934
0.0000
0.6705
0.2246
0.7071
0.0000
0.0000
1.0000
0.7863
0.6178
0.0000
0.0000
0.0000
-1.0000
Axis
0.6706
0.2244
-0.7071
0.7660
0.6428
-0.0000
-0.6178
0.7863
0.0000
0.5000
0.8660
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