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 TiRu3 (Materials Project id mp-998947)

       319      210      210        0        0        0  
       210      319      210        0        0        0  
       210      210      319        0        0        0  
         0        0        0      132        0        0  
         0        0        0        0      132        0  
         0        0        0        0        0      132  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 246.33 GPaEV = 266.57 GPaGV = 101 GPaνV = 0.31964
ReussKR = 246.33 GPaER = 226.62 GPaGR = 84.14 GPaνR = 0.34667
HillKH = 246.33 GPaEH = 246.8 GPaGH = 92.57 GPaνH = 0.33302

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
109 GPa 109 GPa 132 GPa 132 GPa 132 GPa 739 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 152.27 GPa 335.99 GPa 1.3532 TPa–1 1.3532 TPa–1 54.5 GPa 132 GPa-0.0222430.67295Value
Anisotropy 2.207 1.0000 2.422Anisotropy
Axis 0.0000
0.0000
1.0000
-0.5774
0.5774
0.5773
0.6036
0.7866
0.1305
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
-0.0000
0.7071
-0.7071
Axis
0.7071
-0.0005
-0.7071
1.0000
0.0000
-0.0000
0.7071
-0.0005
-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