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 CaBr2 (Materials Project id mp-22888)

        20       17       15        0        0        0  
        17       32       19        0        0        0  
        15       19       45        0        0        0  
         0        0        0       10        0        0  
         0        0        0        0        9        0  
         0        0        0        0        0       22  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 22.111 GPaEV = 28.893 GPaGV = 11.267 GPaνV = 0.28222
ReussKR = 19.045 GPaER = 21.753 GPaGR = 8.3051 GPaνR = 0.30963
HillKH = 20.578 GPaEH = 25.341 GPaGH = 9.7859 GPaνH = 0.29476

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
7.895 GPa 9 GPa 10 GPa 20.399 GPa 22 GPa 68.706 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 10.255 GPa 36.186 GPa 6.2359 TPa–1 39.946 TPa–1 4.077 GPa 22 GPa-0.226790.71373Value
Anisotropy 3.529 6.4058 5.396Anisotropy
Axis 1.0000
0.0000
0.0000
0.6393
0.7690
-0.0000
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
-0.7071
0.7071
-0.0000
1.0000
0.0000
0.0000
-0.6951
0.7190
-0.0000
0.0000
0.9377
0.3475
Axis
-0.7071
-0.7071
0.0000
-0.0000
1.0000
-0.0000
-0.7190
-0.6951
0.0000
-1.0000
0.0000
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