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 Ca(AgGe)2 (Materials Project id mp-7878)

       100        8       37        0        0        0  
         8      100       37        0        0        0  
        37       37      102        0        0        0  
         0        0        0       28        0        0  
         0        0        0        0       28        0  
         0        0        0        0        0       18  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 51.778 GPaEV = 74.304 GPaGV = 29.467 GPaνV = 0.26082
ReussKR = 50.476 GPaER = 68.408 GPaGR = 26.845 GPaνR = 0.27412
HillKH = 51.127 GPaEH = 71.367 GPaGH = 28.156 GPaνH = 0.26735

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
18 GPa 28 GPa 28 GPa 52.588 GPa 92 GPa 157.41 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 49.876 GPa 86.239 GPa 4.1073 TPa–1 7.8521 TPa–1 18 GPa 46 GPa-0.0626190.40848Value
Anisotropy 1.729 1.9118 2.556Anisotropy
Axis 0.7071
0.7071
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.8660
0.5000
0.0000
1.0000
-0.0002
-0.0000
0.7071
0.7071
-0.0000
1.0000
0.0007
-0.0000
-0.5371
0.5371
-0.6504
Axis
0.0002
1.0000
-0.0001
-0.7071
0.7071
-0.0000
-0.0007
1.0000
0.0001
-0.7071
-0.7071
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