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 Mn2SiO4 (Materials Project id mp-18928)

       190       82       84        0        0        0  
        82      154       77        0        0        0  
        84       77      231        0        0        0  
         0        0        0       52        0        0  
         0        0        0        0       51        0  
         0        0        0        0        0       41  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 117.89 GPaEV = 133.56 GPaGV = 50.933 GPaνV = 0.31117
ReussKR = 114.7 GPaER = 129.46 GPaGR = 49.34 GPaνR = 0.31189
HillKH = 116.3 GPaEH = 131.51 GPaGH = 50.137 GPaνH = 0.31153

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
41 GPa 51 GPa 52 GPa 87.242 GPa 129.8 GPa 357.96 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 110.04 GPa 179.86 GPa 2.0161 TPa–1 4.0997 TPa–1 41 GPa 61.955 GPa0.204060.4238Value
Anisotropy 1.635 2.0335 1.511 2.0769Anisotropy
Axis -0.1292
0.9916
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.0000
1.0000
0.0000
1.0000
-0.0001
-0.0000
0.7071
0.0001
-0.7071
0.6211
0.7837
0.0001
-0.9249
0.3801
0.0000
Axis
0.0001
1.0000
-0.0000
-0.7071
-0.0002
-0.7071
-0.0003
0.0003
-1.0000
-0.3801
-0.9249
-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