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 Al(CrB)2 (Materials Project id mp-7692)

       447      114      117        0        0        0  
       114      421      101        0        0        0  
       117      101      518        0        0        0  
         0        0        0      160        0        0  
         0        0        0        0      211        0  
         0        0        0        0        0      158  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 227.78 GPaEV = 419.99 GPaGV = 176.07 GPaνV = 0.19269
ReussKR = 226.27 GPaER = 414.4 GPaGR = 173.42 GPaνR = 0.19476
HillKH = 227.02 GPaEH = 417.19 GPaGH = 174.74 GPaνH = 0.19372

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
158 GPa 160 GPa 211 GPa 319.19 GPa 378.12 GPa 688.68 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 378.72 GPa 485.39 GPa 1.2709 TPa–1 1.67 TPa–1 158 GPa 211 GPa0.122690.2532Value
Anisotropy 1.282 1.3140 1.335 2.0637Anisotropy
Axis -0.0000
0.9162
0.4006
0.4971
0.0000
0.8677
0.0000
0.0000
1.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.0000
0.0000
0.0000
-1.0000
0.7317
-0.0003
0.6817
0.5986
0.5854
0.5468
Axis
-1.0000
0.0000
0.0000
-1.0000
0.0000
-0.0000
0.6817
-0.0007
-0.7317
-0.3878
0.8091
-0.4416
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