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 MnCuO2 (Materials Project id mp-510589)

       355       97       78        0       -4        0  
        97      202       50        0       -1        0  
        78       50      122        0       -1        0  
         0        0        0       44        0        1  
        -4       -1       -1        0       19        0  
         0        0        0        1        0       27  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 125.44 GPaEV = 128.34 GPaGV = 48.267 GPaνV = 0.32949
ReussKR = 98.021 GPaER = 92.719 GPaGR = 34.536 GPaνR = 0.34235
HillKH = 111.73 GPaEH = 110.55 GPaGH = 41.401 GPaνH = 0.3351

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
18.952 GPa 26.941 GPa 44.059 GPa 92.709 GPa 156.7 GPa 429.63 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 61.457 GPa 281.96 GPa 0.52048 TPa–1 6.6201 TPa–1 18.952 GPa 82.96 GPa0.0916440.72767Value
Anisotropy 4.588 12.7193 4.377 7.9402Anisotropy
Axis -0.6469
0.0000
-0.7625
0.9999
0.0000
-0.0139
0.9987
-0.0000
-0.0510
0.0510
-0.0000
0.9987
0.0072
0.0000
1.0000
0.7070
0.7071
-0.0103
-0.6873
0.0000
-0.7264
-0.8504
0.0000
0.5261
Axis
1.0000
-0.0000
-0.0072
-0.7070
0.7071
0.0104
-0.0000
-1.0000
-0.0000
-0.5261
-0.0001
-0.8504
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