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 NdCrGe3 (Materials Project id mp-13008)

       185       63       42        0        0        0  
        63      185       42        0        0        0  
        42       42      147        0        0        0  
         0        0        0       61        0        0  
         0        0        0        0       61        0  
         0        0        0        0        0       61  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 90.111 GPaEV = 149.84 GPaGV = 61.267 GPaνV = 0.22286
ReussKR = 88.043 GPaER = 148.63 GPaGR = 60.98 GPaνR = 0.21865
HillKH = 89.077 GPaEH = 149.24 GPaGH = 61.124 GPaνH = 0.22077

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
61 GPa 61 GPa 61 GPa 119.54 GPa 122 GPa 275.46 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 132.77 GPa 157.97 GPa 3.1888 TPa–1 4.9806 TPa–1 60.927 GPa 61 GPa0.169350.2948Value
Anisotropy 1.19 1.5619 1.001 1.7407Anisotropy
Axis 0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.3907
0.9205
-0.0000
Axis
0.7071
-0.0005
-0.7071
0.7660
0.6428
-0.0000
0.1736
0.9848
-0.0000
-0.9205
0.3907
-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