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 ZrBeSi (Materials Project id mp-10200)

       299       68       71        0        0        0  
        68      299       71        0        0        0  
        71       71      234        0        0        0  
         0        0        0      132        0        0  
         0        0        0        0      132        0  
         0        0        0        0        0      116  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 139.11 GPaEV = 275 GPaGV = 117.47 GPaνV = 0.17053
ReussKR = 137.56 GPaER = 269.99 GPaGR = 115.1 GPaνR = 0.17289
HillKH = 138.34 GPaEH = 272.49 GPaGH = 116.28 GPaνH = 0.1717

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
116 GPa 132 GPa 132 GPa 180.07 GPa 231 GPa 420.93 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 206.53 GPa 290.22 GPa 2.1505 TPa–1 2.9685 TPa–1 95.937 GPa 132 GPa0.0629530.25325Value
Anisotropy 1.405 1.3804 1.376 4.0228Anisotropy
Axis 0.0000
0.0000
1.0000
-0.5922
0.5922
-0.5465
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
0.0000
0.0000
1.0000
0.6976
-0.0002
0.7165
0.7071
0.7071
0.0000
Axis
0.7071
-0.0005
-0.7071
1.0000
0.0000
-0.0000
0.7165
-0.0004
-0.6976
0.0001
-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