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 TiAlNi2 (Materials Project id mp-7187)

       202      142      142        0        0        0  
       142      202      142        0        0        0  
       142      142      202        0        0        0  
         0        0        0       93        0        0  
         0        0        0        0       93        0  
         0        0        0        0        0       93  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 162 GPaEV = 178.5 GPaGV = 67.8 GPaνV = 0.31636
ReussKR = 162 GPaER = 137.35 GPaGR = 50.543 GPaνR = 0.3587
HillKH = 162 GPaEH = 158.25 GPaGH = 59.172 GPaνH = 0.33719

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
60 GPa 60 GPa 93 GPa 93 GPa 93 GPa 486 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 84.767 GPa 234.19 GPa 2.0576 TPa–1 2.0576 TPa–1 30 GPa 93 GPa-0.126060.79158Value
Anisotropy 2.763 1.0000 3.1Anisotropy
Axis 0.0000
0.0000
1.0000
0.5774
0.5773
-0.5774
0.9239
0.0000
0.3827
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
0.0000
0.7071
0.7071
Axis
-0.7071
-0.0002
-0.7071
0.7660
0.6428
-0.0000
-0.7071
-0.0002
-0.7071
-1.0000
0.0000
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