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 TmNi2B2C (Materials Project id mp-6754)

       296      176      136        0        0        0  
       176      296      136        0        0        0  
       136      136      271        0        0        0  
         0        0        0       57        0        0  
         0        0        0        0       57        0  
         0        0        0        0        0      140  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 195.44 GPaEV = 207.62 GPaGV = 78.467 GPaνV = 0.32295
ReussKR = 193.45 GPaER = 186.54 GPaGR = 69.643 GPaνR = 0.33928
HillKH = 194.45 GPaEH = 197.14 GPaGH = 74.055 GPaνH = 0.33103

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
57 GPa 57 GPa 120 GPa 140 GPa 154.49 GPa 588.51 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 157.11 GPa 305.25 GPa 1.4848 TPa–1 2.1997 TPa–1 57 GPa 140 GPa0.0901680.54095Value
Anisotropy 1.943 1.4815 2.456 5.9993Anisotropy
Axis 0.0000
0.7503
0.6611
0.7071
0.7071
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
1.0000
-0.0002
-0.0000
-0.7071
0.7071
-0.0000
-0.5854
0.5855
0.5608
Axis
1.0000
0.0002
-0.0000
0.0002
1.0000
-0.0000
-0.7071
-0.7071
-0.0000
-0.3967
0.3964
-0.8279
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