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 TiAlFeCo (Materials Project id mp-998980)

       355       85       85        0        0        0  
        85      355       85        0        0        0  
        85       85      355        0        0        0  
         0        0        0      122        0        0  
         0        0        0        0      122        0  
         0        0        0        0        0      122  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 175 GPaEV = 307.18 GPaGV = 127.2 GPaνV = 0.20745
ReussKR = 175 GPaER = 306.57 GPaGR = 126.89 GPaνR = 0.20803
HillKH = 175 GPaEH = 306.87 GPaGH = 127.04 GPaνH = 0.20774

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
122 GPa 122 GPa 122 GPa 270 GPa 270 GPa 525 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 296.99 GPa 322.16 GPa 1.9048 TPa–1 1.9048 TPa–1 122 GPa 135 GPa0.181640.24141Value
Anisotropy 1.085 1.0000 1.107 1.3291Anisotropy
Axis -0.5774
0.5774
-0.5773
0.0000
0.0000
1.0000
0.2500
0.9330
0.2588
0.0000
0.0000
1.0000
-0.0000
-0.0000
1.0000
0.7071
-0.0003
0.7071
-0.7071
-0.0000
0.7071
0.7071
-0.0002
0.7071
Axis
1.0000
0.0002
0.0000
0.7071
-0.0005
-0.7071
0.0000
-1.0000
-0.0000
0.7071
-0.0006
-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