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 Li2SiO3 (Materials Project id mp-5012)

       130       43       45        0        0        0  
        43      151       43        0        0        0  
        45       43      140        0        0        0  
         0        0        0       53        0        0  
         0        0        0        0       70        0  
         0        0        0        0        0       39  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 75.889 GPaEV = 126.46 GPaGV = 51.733 GPaνV = 0.22226
ReussKR = 75.681 GPaER = 122.46 GPaGR = 49.768 GPaνR = 0.23031
HillKH = 75.785 GPaEH = 124.47 GPaGH = 50.751 GPaνH = 0.22627

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
39 GPa 53 GPa 70 GPa 89.193 GPa 103.68 GPa 228.13 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 102.51 GPa 147.57 GPa 3.9984 TPa–1 4.8635 TPa–1 39 GPa 70 GPa0.0509220.36919Value
Anisotropy 1.44 1.2164 1.795 7.2501Anisotropy
Axis -0.8056
0.5924
0.0000
0.6746
0.0000
0.7382
0.0000
1.0000
0.0000
1.0000
0.0000
0.0000
1.0000
-0.0008
0.0000
-0.0000
0.0000
1.0000
0.6868
0.1786
-0.7046
-0.5332
0.6536
-0.5372
Axis
0.0008
1.0000
0.0000
-1.0000
0.0000
-0.0000
-0.6853
-0.1640
-0.7096
-0.6429
-0.7258
-0.2449
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