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 NbCrGe (Materials Project id mp-21440)

       309      141      149        0        0        0  
       141      309      149        0        0        0  
       149      149      269        0        0        0  
         0        0        0      130        0        0  
         0        0        0        0      130        0  
         0        0        0        0        0       84  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 196.11 GPaEV = 253.49 GPaGV = 98.667 GPaνV = 0.28457
ReussKR = 195.53 GPaER = 237.83 GPaGR = 91.666 GPaνR = 0.29728
HillKH = 195.82 GPaEH = 245.7 GPaGH = 95.166 GPaνH = 0.29088

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
84 GPa 130 GPa 130 GPa 130.17 GPa 168 GPa 588.83 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 170.33 GPa 281.39 GPa 1.5656 TPa–1 1.9831 TPa–1 69.014 GPa 130 GPa0.0678390.44056Value
Anisotropy 1.652 1.2667 1.884 6.4943Anisotropy
Axis 0.0000
0.0000
1.0000
0.7052
0.2943
0.6451
0.5000
0.8660
0.0000
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
0.0000
0.0000
1.0000
0.5192
0.4736
-0.7114
0.3703
0.5710
0.7327
Axis
0.7071
-0.0005
-0.7071
0.7660
0.6428
-0.0000
-0.5255
-0.4795
-0.7028
-0.8390
0.5441
-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