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 Li3PS4 (Materials Project id mp-985583)

        34       16       11        0        0        0  
        16       50       17        0        0        0  
        11       17       31        0        0        0  
         0        0        0       10        0        0  
         0        0        0        0       12        0  
         0        0        0        0        0       12  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 22.556 GPaEV = 29.561 GPaGV = 11.533 GPaνV = 0.28157
ReussKR = 21.007 GPaER = 28.685 GPaGR = 11.272 GPaνR = 0.27242
HillKH = 21.781 GPaEH = 29.125 GPaGH = 11.403 GPaνH = 0.27714

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
10 GPa 12 GPa 12 GPa 20.536 GPa 24.15 GPa 70.314 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 24.15 GPa 37.376 GPa 6.3661 TPa–1 21.909 TPa–1 10 GPa 12.401 GPa0.149260.43087Value
Anisotropy 1.548 3.4414 1.24 2.8866Anisotropy
Axis 0.0000
0.0000
1.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.0000
0.0000
0.0000
1.0000
-0.0003
-0.0000
1.0000
0.7071
0.7071
0.0001
0.6743
-0.0001
0.7384
0.0000
1.0000
-0.0000
Axis
0.0000
1.0000
0.0000
-0.7071
0.7071
-0.0000
0.7384
-0.0001
-0.6743
-0.0000
0.0000
1.0000
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