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 CaC2 (Materials Project id mp-684668)

       138       24       48        0        0        0  
        24      113       17        0        0        0  
        48       17      103        0        0        0  
         0        0        0       25        0        0  
         0        0        0        0       11        0  
         0        0        0        0        0       15  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 59.111 GPaEV = 72.247 GPaGV = 27.867 GPaνV = 0.2963
ReussKR = 57.03 GPaER = 54.615 GPaGR = 20.373 GPaνR = 0.34039
HillKH = 58.07 GPaEH = 63.559 GPaGH = 24.12 GPaνH = 0.31758

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
11 GPa 15 GPa 25 GPa 69.409 GPa 100.78 GPa 183.81 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 38.556 GPa 113.29 GPa 3.6382 TPa–1 7.0463 TPa–1 11 GPa 48.389 GPa0.0419410.75774Value
Anisotropy 2.938 1.9367 4.399 18.0666Anisotropy
Axis 0.6908
-0.0000
-0.7230
1.0000
0.0000
0.0000
1.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
0.0000
-1.0000
-0.7071
0.7071
0.0000
-0.6394
-0.0000
0.7689
0.7558
-0.0000
0.6547
Axis
-1.0000
0.0000
-0.0000
-0.7071
-0.7071
-0.0000
0.0000
-1.0000
-0.0000
0.6547
-0.0000
-0.7558
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