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 CaNi4B (Materials Project id mp-8307)

       204       90       88        0        0        0  
        90      204       88        0        0        0  
        88       88      265        0        0        0  
         0        0        0       58        0        0  
         0        0        0        0       58        0  
         0        0        0        0        0       57  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 133.89 GPaEV = 160.53 GPaGV = 61.733 GPaνV = 0.30017
ReussKR = 132.25 GPaER = 157.82 GPaGR = 60.65 GPaνR = 0.3011
HillKH = 133.07 GPaEH = 159.18 GPaGH = 61.192 GPaνH = 0.30063

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
57 GPa 58 GPa 58 GPa 114 GPa 154.21 GPa 404.79 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 150.09 GPa 212.32 GPa 1.8904 TPa–1 2.8355 TPa–1 57 GPa 71.235 GPa0.21660.35242Value
Anisotropy 1.415 1.5000 1.25 1.6271Anisotropy
Axis 0.8127
0.3469
-0.4682
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
1.0000
-0.0008
-0.0000
0.4650
0.5327
0.7071
0.5266
0.8501
0.0000
0.5505
0.2102
0.8079
Axis
0.0008
1.0000
-0.0000
0.4650
0.5327
-0.7071
-0.0000
0.0000
1.0000
0.7547
0.2883
-0.5893
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