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 CrBO3 (Materials Project id mp-19299)

       405      132      104       34        0        0  
       132      405      104      -34        0        0  
       104      104      220        0        0        0  
        34      -34        0      104        0        0  
         0        0        0        0      104       34  
         0        0        0        0       34      137  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 190 GPaEV = 287.08 GPaGV = 115 GPaνV = 0.24818
ReussKR = 172.03 GPaER = 257.06 GPaGR = 102.75 GPaνR = 0.25095
HillKH = 181.01 GPaEH = 272.07 GPaGH = 108.87 GPaνH = 0.24949

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
82.708 GPa 91.277 GPa 158.29 GPa 162.27 GPa 285.72 GPa 594.73 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 179.72 GPa 379.6 GPa 1.202 TPa–1 3.409 TPa–1 82.602 GPa 158.29 GPa0.0864040.51926Value
Anisotropy 2.112 2.8362 1.916 6.0097Anisotropy
Axis -0.0000
-0.0000
1.0000
0.8175
0.4736
0.3277
0.9914
0.1305
0.0000
0.0000
0.0000
1.0000
-0.4607
0.2673
0.8463
1.0000
0.0004
-0.0003
0.5870
0.3399
0.7347
-1.0000
0.0000
0.0000
Axis
-0.4997
-0.8662
0.0016
-0.0002
0.8475
0.5307
-0.5004
0.8658
-0.0008
-0.0000
-0.6446
-0.7646
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