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 Li3VO4 (Materials Project id mp-19219)

       111       46       40        0        0        0  
        46      111       39        0        0        0  
        40       39       96        0        0        0  
         0        0        0       37        0        0  
         0        0        0        0       32        0  
         0        0        0        0        0       32  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 63.111 GPaEV = 84.451 GPaGV = 33.067 GPaνV = 0.27698
ReussKR = 62.572 GPaER = 83.976 GPaGR = 32.898 GPaνR = 0.27632
HillKH = 62.842 GPaEH = 84.214 GPaGH = 32.982 GPaνH = 0.27665

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
32 GPa 32 GPa 37 GPa 62.694 GPa 65.159 GPa 190.15 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 76.117 GPa 89.105 GPa 4.6771 TPa–1 6.527 TPa–1 31.535 GPa 37 GPa0.189720.32968Value
Anisotropy 1.171 1.3955 1.173 1.7377Anisotropy
Axis 0.0000
0.0000
1.0000
-0.0000
0.8228
0.5683
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
0.0001
-0.0001
1.0000
0.0000
0.6772
0.7358
0.6108
0.6847
0.3976
Axis
0.7071
-0.0005
-0.7071
-0.0000
-1.0000
-0.0001
-0.0000
0.7358
-0.6772
-0.7916
0.5172
0.3253
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