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 Mn5O8 (Materials Project id mp-18922)

       225       74       84        0      -15        0  
        74      257       96        0        1        0  
        84       96      256        0      -13        0  
         0        0        0       79        0        8  
       -15        1      -13        0       29        0  
         0        0        0        8        0       29  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 138.44 GPaEV = 156.52 GPaGV = 59.667 GPaνV = 0.31158
ReussKR = 134.15 GPaER = 122.23 GPaGR = 45.333 GPaνR = 0.34815
HillKH = 136.3 GPaEH = 139.58 GPaGH = 52.5 GPaνH = 0.32932

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
27.203 GPa 27.751 GPa 80.249 GPa 153.92 GPa 167.87 GPa 418 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 76.623 GPa 211.04 GPa 1.3172 TPa–1 3.9662 TPa–1 27.426 GPa 84.429 GPa0.0403650.78313Value
Anisotropy 2.754 3.0112 3.078 19.4013Anisotropy
Axis 0.7214
0.0000
0.6925
-0.0624
0.9290
-0.3649
-0.5810
-0.0000
0.8139
0.8139
-0.0000
0.5811
0.0139
0.0000
0.9999
0.6986
0.7071
-0.1092
0.7688
0.5555
0.3167
-0.6849
-0.0001
0.7287
Axis
0.9999
0.0000
-0.0139
-0.6986
0.7071
0.1092
-0.0513
0.5473
-0.8354
-0.7287
0.0001
-0.6849
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