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 ErNi2B2C (Materials Project id mp-6098)

       248      115      115        0        0        0  
       115      248      115        0        0        0  
       115      115      274        0        0        0  
         0        0        0       58        0        0  
         0        0        0        0       58        0  
         0        0        0        0        0      138  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 162.22 GPaEV = 204.2 GPaGV = 79.133 GPaνV = 0.29021
ReussKR = 161.89 GPaER = 186.58 GPaGR = 71.329 GPaνR = 0.30791
HillKH = 162.06 GPaEH = 195.45 GPaGH = 75.231 GPaνH = 0.29899

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
58 GPa 58 GPa 133 GPa 138 GPa 149.89 GPa 487.11 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 161.13 GPa 271.15 GPa 1.8216 TPa–1 2.1777 TPa–1 58 GPa 138 GPa-0.0175730.52332Value
Anisotropy 1.683 1.1955 2.379Anisotropy
Axis 0.7716
0.0000
-0.6361
0.7071
0.7071
0.0000
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
1.0000
-0.0002
-0.0000
-0.7071
0.7071
0.0000
0.5611
0.5611
0.6085
Axis
1.0000
0.0000
-0.0000
0.0002
1.0000
-0.0000
-0.7071
-0.7071
-0.0000
0.4302
0.4303
-0.7936
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