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 CrO3 (Materials Project id mp-510421)

        77        6        2        0        0        0  
         6        7        2        0        0        0  
         2        2        9        0        0        0  
         0        0        0        1        0        0  
         0        0        0        0        3        0  
         0        0        0        0        0        7  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 12.556 GPaEV = 19.248 GPaGV = 7.7333 GPaνV = 0.24449
ReussKR = 4.9119 GPaER = 6.6079 GPaGR = 2.5897 GPaνR = 0.27579
HillKH = 8.7337 GPaEH = 12.936 GPaGH = 5.1615 GPaνH = 0.25314

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
1 GPa 3 GPa 5.5169 GPa 7 GPa 9.9043 GPa 77.579 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 3.2864 GPa 71.847 GPa 1.6513 TPa–1 117.24 TPa–1 1 GPa 7.4894 GPa-0.242280.79592Value
Anisotropy 21.86 71.0000 7.489Anisotropy
Axis 0.0000
0.7305
-0.6829
1.0000
0.0000
0.0000
1.0000
0.0000
0.0000
0.0000
1.0000
0.0000
-0.0003
-0.0000
1.0000
0.7071
0.0001
-0.7071
0.8477
0.4732
-0.2399
0.8475
0.3783
0.3723
Axis
0.0000
1.0000
0.0000
-0.7071
-0.0002
-0.7071
-0.5222
0.6643
-0.5348
0.0708
0.6146
-0.7857
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