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 Mn(ReO4)2 (Materials Project id mp-31907)

        58       20       13        3        0        0  
        20       58       13       -3        0        0  
        13       13       17        0        0        0  
         3       -3        0        8        0        0  
         0        0        0        0        8        3  
         0        0        0        0        3       19  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 25 GPaEV = 32.802 GPaGV = 12.8 GPaνV = 0.28132
ReussKR = 16.467 GPaER = 23.785 GPaGR = 9.4439 GPaνR = 0.25926
HillKH = 20.733 GPaEH = 28.305 GPaGH = 11.122 GPaνH = 0.27247

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
7.235 GPa 7.4115 GPa 11.888 GPa 19.765 GPa 38.588 GPa 83.112 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 12.667 GPa 47.789 GPa 4.0486 TPa–1 52.632 TPa–1 7.0849 GPa 19.765 GPa0.0834720.69939Value
Anisotropy 3.773 13.0000 2.79 8.3788Anisotropy
Axis 0.0000
0.0000
1.0000
0.0000
0.9881
-0.1536
-0.1305
0.9914
0.0000
0.0000
0.0000
1.0000
0.0000
0.3279
0.9447
0.8392
0.4845
-0.2471
0.6764
0.3905
0.6245
0.5000
0.8660
0.0000
Axis
-0.0000
0.9447
-0.3279
-0.5000
0.8660
-0.0000
-0.5000
0.8660
0.0000
-0.3894
0.2249
-0.8932
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