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 Ti2C (Materials Project id mp-10721)

       199      109      109        0        0        0  
       109      199      109        0        0        0  
       109      109      199        0        0        0  
         0        0        0      113        0        0  
         0        0        0        0      113        0  
         0        0        0        0        0      113  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 139 GPaEV = 213.48 GPaGV = 85.8 GPaνV = 0.24403
ReussKR = 139 GPaER = 180.76 GPaGR = 70.429 GPaνR = 0.28326
HillKH = 139 GPaEH = 197.37 GPaGH = 78.115 GPaνH = 0.26334

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
90 GPa 90 GPa 113 GPa 113 GPa 113 GPa 417 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 121.85 GPa 266.72 GPa 2.3981 TPa–1 2.3981 TPa–1 45 GPa 113 GPa-0.0902260.59716Value
Anisotropy 2.189 1.0000 2.511Anisotropy
Axis 0.0000
0.0000
1.0000
0.5774
0.5774
0.5773
0.0000
0.0000
1.0000
0.4830
0.6294
0.6088
0.7071
-0.0003
0.7071
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
0.0000
0.7071
0.7071
Axis
0.7071
-0.0005
-0.7071
0.5000
0.8660
-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