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 P2O5 (Materials Project id mp-990076)

       797       70       31       -0        0        0  
        70      344      142       -0        0        0  
        31      142      531       -1        0        0  
        -0       -0       -1       43        0        0  
         0        0        0        0      251       -0  
         0        0        0        0       -0      158  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 239.78 GPaEV = 442.73 GPaGV = 185.67 GPaνV = 0.19227
ReussKR = 225.12 GPaER = 291.6 GPaGR = 113.54 GPaνR = 0.28411
HillKH = 232.45 GPaEH = 369.53 GPaGH = 149.6 GPaνH = 0.23504

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
42.998 GPa 158 GPa 251 GPa 263.27 GPa 590.37 GPa 818.35 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 147.68 GPa 782.75 GPa 1.0142 TPa–1 2.1895 TPa–1 42.997 GPa 293.61 GPa-0.245350.79568Value
Anisotropy 5.3 2.1588 6.829Anisotropy
Axis -0.0000
0.7316
0.6818
1.0000
0.0000
0.0000
1.0000
0.0000
0.0000
-0.0000
0.9999
0.0151
-0.0000
-0.0022
1.0000
0.7071
-0.0017
0.7071
-0.8143
0.3587
0.4563
0.6324
0.4845
-0.6044
Axis
0.0000
1.0000
0.0022
0.7071
0.0022
-0.7071
-0.5798
-0.5400
-0.6102
0.0426
0.7574
0.6516
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