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 Ca5Si3 (Materials Project id mp-793)

        81       22       26        0        0        0  
        22       81       26        0        0        0  
        26       26       59        0        0        0  
         0        0        0       29        0        0  
         0        0        0        0       29        0  
         0        0        0        0        0       40  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 41 GPaEV = 71.185 GPaGV = 29.4 GPaνV = 0.21063
ReussKR = 40.385 GPaER = 67.813 GPaGR = 27.789 GPaνR = 0.22014
HillKH = 40.692 GPaEH = 69.503 GPaGH = 28.594 GPaνH = 0.21533

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
29 GPa 29 GPa 38.151 GPa 40 GPa 59 GPa 123.85 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 45.874 GPa 80.381 GPa 6.9841 TPa–1 10.794 TPa–1 21.043 GPa 40 GPa0.000529380.44044Value
Anisotropy 1.752 1.5455 1.901831.9962Anisotropy
Axis 0.0000
0.0000
1.0000
0.6820
0.6820
0.2642
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
1.0000
-0.0003
-0.0000
0.7071
0.7071
-0.0000
0.7071
0.7071
0.0000
Axis
0.7071
-0.0005
-0.7071
0.0003
1.0000
0.0000
-0.7071
0.7071
0.0000
-0.0000
-0.0001
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