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 Ti3Sb (Materials Project id mp-569837)

       198       54       54        0        0        0  
        54      214       76        0        0        0  
        54       76      214        0        0        0  
         0        0        0       75        0        0  
         0        0        0        0       37        0  
         0        0        0        0        0       37  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 110.44 GPaEV = 150.82 GPaGV = 59.267 GPaνV = 0.2724
ReussKR = 109.76 GPaER = 136.48 GPaGR = 52.784 GPaνR = 0.29277
HillKH = 110.1 GPaEH = 143.7 GPaGH = 56.025 GPaνH = 0.28247

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
37 GPa 37 GPa 75 GPa 138 GPa 154.85 GPa 333.15 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 110.81 GPa 190.39 GPa 2.7913 TPa–1 3.528 TPa–1 37 GPa 77.117 GPa0.13490.50972Value
Anisotropy 1.718 1.2639 2.084 3.7786Anisotropy
Axis 0.7091
0.0000
0.7051
0.0000
0.7071
0.7071
0.0000
0.9239
0.3827
1.0000
0.0000
0.0000
0.0000
0.0000
-1.0000
0.7071
0.5000
-0.5000
0.7810
0.4416
0.4416
-0.6974
0.5068
0.5068
Axis
-1.0000
-0.0000
-0.0000
-0.7071
0.5000
-0.5000
-0.0000
0.7071
-0.7071
-0.7167
-0.4931
-0.4931
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