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 Li3PO4 (Materials Project id mp-13725)

       132       50       34        0        0        0  
        50      123       38        0        0        0  
        34       38      134        0        0        0  
         0        0        0       47        0        0  
         0        0        0        0       37        0  
         0        0        0        0        0       42  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 70.333 GPaEV = 107.16 GPaGV = 43 GPaνV = 0.24606
ReussKR = 70.277 GPaER = 105.86 GPaGR = 42.381 GPaνR = 0.24894
HillKH = 70.305 GPaEH = 106.51 GPaGH = 42.69 GPaνH = 0.2475

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
37 GPa 42 GPa 47 GPa 76.484 GPa 101.37 GPa 211.15 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 95.44 GPa 119.18 GPa 4.4886 TPa–1 4.9712 TPa–1 37 GPa 49.104 GPa0.166130.35962Value
Anisotropy 1.249 1.1075 1.327 2.1647Anisotropy
Axis 0.7481
0.0000
0.6636
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.7071
0.0002
-0.7071
0.0000
0.0000
1.0000
1.0000
0.0002
0.0000
Axis
1.0000
0.0000
-0.0000
-0.7071
-0.0002
-0.7071
-1.0000
0.0000
0.0000
-0.0002
1.0000
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