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 MnP (Materials Project id mp-999516)

       180       60      104        0        0        0  
        60      180      104        0        0        0  
       104      104      231        0        0        0  
         0        0        0      139        0        0  
         0        0        0        0      139        0  
         0        0        0        0        0       60  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 125.22 GPaEV = 216.12 GPaGV = 89.133 GPaνV = 0.21235
ReussKR = 118.21 GPaER = 178.48 GPaGR = 71.484 GPaνR = 0.24836
HillKH = 121.72 GPaEH = 197.49 GPaGH = 80.309 GPaνH = 0.22957

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
60 GPa 88.353 GPa 120 GPa 139 GPa 139 GPa 382.65 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 131.87 GPa 254.67 GPa 0.94652 TPa–1 3.7565 TPa–1 47.998 GPa 139 GPa-0.0849290.54416Value
Anisotropy 1.931 3.9688 2.896Anisotropy
Axis 0.8660
0.5000
0.0000
0.2667
0.6412
0.7195
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.7071
0.0002
0.7071
0.0000
0.0000
1.0000
0.3362
0.6210
-0.7081
0.5706
0.0003
0.8212
Axis
0.7071
-0.0001
-0.7071
1.0000
0.0000
-0.0000
0.3371
0.6227
0.7061
-0.0006
1.0000
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