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 Na3P (Materials Project id mp-1598)

        49       21        8        0        0        0  
        21       49        8        0        0        0  
         8        8       60        0        0        0  
         0        0        0       10        0        0  
         0        0        0        0       10        0  
         0        0        0        0        0       14  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 25.778 GPaEV = 37.409 GPaGV = 14.867 GPaνV = 0.25813
ReussKR = 25.772 GPaER = 33.669 GPaGR = 13.129 GPaνR = 0.28226
HillKH = 25.775 GPaEH = 35.557 GPaGH = 13.998 GPaνH = 0.27008

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
10 GPa 10 GPa 14 GPa 28 GPa 52.631 GPa 77.369 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 28.635 GPa 58.171 GPa 12.77 TPa–1 13.261 TPa–1 10 GPa 21.578 GPa0.114290.44734Value
Anisotropy 2.031 1.0385 2.158 3.9142Anisotropy
Axis 0.7499
0.1117
0.6520
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.5291
0.4691
-0.7071
0.0000
0.0000
1.0000
0.3427
0.5674
0.7487
Axis
-0.7660
0.6428
-0.0000
-0.5291
-0.4692
-0.7071
0.7660
0.6428
-0.0000
-0.3871
-0.6409
0.6629
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