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 TiFe (Materials Project id mp-305)

       386       98       98        0        0        0  
        98      386       98        0        0        0  
        98       98      386        0        0        0  
         0        0        0       74        0        0  
         0        0        0        0       74        0  
         0        0        0        0        0       74  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 194 GPaEV = 260.37 GPaGV = 102 GPaνV = 0.27632
ReussKR = 194 GPaER = 238.02 GPaGR = 91.862 GPaνR = 0.29552
HillKH = 194 GPaEH = 249.28 GPaGH = 96.931 GPaνH = 0.28584

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
74 GPa 74 GPa 74 GPa 288 GPa 288 GPa 582 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 196.96 GPa 346.31 GPa 1.7182 TPa–1 1.7182 TPa–1 74 GPa 144 GPa0.129070.49162Value
Anisotropy 1.758 1.0000 1.946 3.8089Anisotropy
Axis 0.5774
0.5773
-0.5774
0.0000
0.0000
1.0000
0.6088
0.0000
0.7934
-0.3044
0.3967
0.8660
-0.0000
-0.0000
1.0000
0.7071
0.0001
-0.7071
0.7071
-0.0000
0.7071
0.7071
-0.0000
-0.7071
Axis
-0.7648
0.6443
0.0000
-0.7071
-0.0002
-0.7071
0.0000
1.0000
0.0000
-0.7071
0.0002
-0.7071
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