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 CePRuO (Materials Project id mp-21372)

       275      100       72        0        0        0  
       100      275       72        0        0        0  
        72       72      142        0        0        0  
         0        0        0       47        0        0  
         0        0        0        0       47        0  
         0        0        0        0        0      120  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 131.11 GPaEV = 184.01 GPaGV = 72.667 GPaνV = 0.26609
ReussKR = 115.58 GPaER = 157.76 GPaGR = 61.989 GPaνR = 0.27252
HillKH = 123.35 GPaEH = 170.89 GPaGH = 67.328 GPaνH = 0.26909

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
47 GPa 47 GPa 103.77 GPa 120 GPa 175 GPa 413.23 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 114.22 GPa 267.45 GPa 1.6324 TPa–1 5.3869 TPa–1 47 GPa 120 GPa0.114370.45856Value
Anisotropy 2.341 3.3000 2.553 4.0095Anisotropy
Axis 0.2144
-0.0000
0.9767
0.7071
0.7071
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
1.0000
-0.0003
-0.0000
0.7071
0.7071
0.0000
0.6672
0.6670
0.3316
Axis
0.4998
0.8662
-0.0000
0.0003
1.0000
0.0000
-0.7071
0.7071
0.0000
0.2343
0.2346
-0.9434
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