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 C (Materials Project id mp-1008374)

       494       27       14        0        0        0  
        27     1102      170        0        0        0  
        14      170     1134        0        0        0  
         0        0        0      500        0        0  
         0        0        0        0      117        0  
         0        0        0        0        0       55  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 350.22 GPaEV = 704.33 GPaGV = 302.33 GPaνV = 0.16482
ReussKR = 289.62 GPaER = 375.92 GPaGR = 146.42 GPaνR = 0.28367
HillKH = 319.92 GPaEH = 545.59 GPaGH = 224.38 GPaνH = 0.21577

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
55 GPa 117 GPa 492.73 GPa 500 GPa 947.49 GPa 1289.8 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 189.35 GPa 1127.2 GPa 0.74427 TPa–1 1.9625 TPa–1 55 GPa 500 GPa-0.173740.75425Value
Anisotropy 5.953 2.6368 9.091Anisotropy
Axis 0.7323
0.6810
0.0000
-0.0000
0.6142
0.7891
0.0000
1.0000
0.0000
1.0000
0.0000
0.0000
1.0000
-0.0002
-0.0001
-0.0000
0.0000
1.0000
0.2142
0.6068
0.7655
-0.5376
0.6603
0.5244
Axis
0.0002
1.0000
-0.0000
-0.0000
-1.0000
0.0000
0.5685
0.5598
-0.6029
-0.7976
-0.5999
-0.0625
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