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 LaN (Materials Project id mp-567290)

       127       93       75        0        0        0  
        93      127       75        0        0        0  
        75       75       83        0        0        0  
         0        0        0       36        0        0  
         0        0        0        0       36        0  
         0        0        0        0        0       17  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 91.444 GPaEV = 66.377 GPaGV = 24.067 GPaνV = 0.37902
ReussKR = 81.512 GPaER = 55.164 GPaGR = 19.883 GPaνR = 0.38721
HillKH = 86.478 GPaEH = 60.776 GPaGH = 21.975 GPaνH = 0.38287

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
17 GPa 25.237 GPa 34 GPa 36 GPa 36 GPa 277.76 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 31.864 GPa 71.616 GPa 1.1412 TPa–1 9.9857 TPa–1 13.623 GPa 36 GPa-0.0486330.68366Value
Anisotropy 2.248 8.7500 2.643Anisotropy
Axis 0.0000
0.0000
1.0000
0.7159
0.3246
0.6182
0.1305
0.9914
0.0000
0.0000
0.0000
1.0000
0.3283
0.6263
-0.7071
0.0000
0.0000
1.0000
-0.6896
0.1729
-0.7032
-0.7247
0.2490
0.6425
Axis
-0.3282
-0.6263
-0.7071
0.4962
0.8682
-0.0000
0.6821
-0.1710
-0.7110
-0.3249
-0.9458
0.0000
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