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 Ce2MgSi2 (Materials Project id mp-505296)

       110       41       41        0        0        0  
        41       83       27        0        0        0  
        41       27       83        0        0        0  
         0        0        0       59        0        0  
         0        0        0        0       77        0  
         0        0        0        0        0       77  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 54.889 GPaEV = 121.54 GPaGV = 53.733 GPaνV = 0.13095
ReussKR = 52.639 GPaER = 101.36 GPaGR = 42.982 GPaνR = 0.17907
HillKH = 53.764 GPaEH = 111.61 GPaGH = 48.358 GPaνH = 0.15401

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
52.017 GPa 56 GPa 59 GPa 77 GPa 77 GPa 167.98 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 65.69 GPa 150.91 GPa 3.2044 TPa–1 7.8965 TPa–1 26.885 GPa 77 GPa-0.195320.49644Value
Anisotropy 2.297 2.4643 2.864Anisotropy
Axis 0.0000
0.0000
1.0000
0.6688
0.5257
0.5257
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.7071
-0.0002
0.7071
-0.0000
0.0000
1.0000
0.0004
0.7071
-0.7071
0.8000
0.0005
0.6000
Axis
0.7071
-0.0006
-0.7071
-1.0000
0.0000
-0.0000
0.0002
-0.7071
-0.7071
-0.0001
1.0000
-0.0006
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