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 LiIr3 (Materials Project id mp-30738)

       409      159      148        0        0        0  
       159      399      125        0        0        0  
       148      125      520        0        0        0  
         0        0        0       82        0        0  
         0        0        0        0      126        0  
         0        0        0        0        0       79  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 243.56 GPaEV = 302.85 GPaGV = 117.13 GPaνV = 0.29276
ReussKR = 241.52 GPaER = 279.87 GPaGR = 107.08 GPaνR = 0.30687
HillKH = 242.54 GPaEH = 291.41 GPaGH = 112.1 GPaνH = 0.29974

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
79 GPa 82 GPa 126 GPa 243.82 GPa 348.01 GPa 736.17 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 235.21 GPa 452.95 GPa 1.1389 TPa–1 1.5849 TPa–1 79 GPa 162.73 GPa0.124180.51335Value
Anisotropy 1.926 1.3917 2.06 4.1339Anisotropy
Axis -0.5247
0.7087
0.4716
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.0000
1.0000
0.0000
1.0000
-0.0000
0.0000
-0.0000
0.7071
0.7071
-0.5789
0.8154
0.0001
0.7056
0.7086
-0.0000
Axis
0.0000
1.0000
-0.0000
0.0001
0.7071
-0.7071
0.0001
-0.0000
1.0000
-0.7086
0.7056
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