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 SnBiO4 (Materials Project id mp-754839)

       204       66       92        0        0        0  
        66      204       92        0        0        0  
        92       92      161        0        0        0  
         0        0        0       23        0        0  
         0        0        0        0       23        0  
         0        0        0        0        0       25  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 118.78 GPaEV = 96.768 GPaGV = 35.467 GPaνV = 0.36422
ReussKR = 118.49 GPaER = 82.252 GPaGR = 29.709 GPaνR = 0.38431
HillKH = 118.63 GPaEH = 89.563 GPaGH = 32.588 GPaνH = 0.37418

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
23 GPa 23 GPa 25 GPa 74.439 GPa 138 GPa 356.56 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 66.264 GPa 150.24 GPa 2.5997 TPa–1 3.2401 TPa–1 23 GPa 69 GPa0.0886790.64277Value
Anisotropy 2.267 1.2464 3 7.2482Anisotropy
Axis 0.5510
0.5510
0.6267
1.0000
0.0000
0.0000
0.1305
0.9914
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.7071
0.7071
-0.0000
1.0000
-0.0000
-0.0000
0.8127
0.0001
0.5827
Axis
0.1734
0.9849
-0.0000
-0.7071
0.7071
-0.0000
0.0000
1.0000
-0.0000
0.5827
0.0003
-0.8127
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