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(BeGe)2 (Materials Project id mp-31209)

       113       49       22        0        0        0  
        49      113       22        0        0        0  
        22       22      163        0        0        0  
         0        0        0       60        0        0  
         0        0        0        0       60        0  
         0        0        0        0        0       66  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 63.889 GPaEV = 131.68 GPaGV = 56.933 GPaνV = 0.15648
ReussKR = 63.595 GPaER = 123.95 GPaGR = 52.74 GPaνR = 0.17514
HillKH = 63.742 GPaEH = 127.85 GPaGH = 54.837 GPaνH = 0.16571

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
60 GPa 60 GPa 64 GPa 66 GPa 131.38 GPa 193.62 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 90.774 GPa 157.02 GPa 4.6387 TPa–1 5.5429 TPa–1 32 GPa 66 GPa0.0310260.41834Value
Anisotropy 1.73 1.1949 2.062 13.4837Anisotropy
Axis 0.0000
1.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.3826
0.9239
0.0000
-0.7071
0.7071
-0.0000
1.0000
0.0000
0.0000
0.7282
-0.0003
0.6853
1.0000
-0.0007
0.0000
Axis
-0.7071
-0.7071
0.0000
-0.0000
1.0000
0.0000
0.6853
-0.0006
-0.7282
0.0007
1.0000
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