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 Na2LiAlP2 (Materials Project id mp-9719)

        78       21       27        0        0        0  
        21       73       22        0        0        0  
        27       22       73        0        0        0  
         0        0        0       24        0        0  
         0        0        0        0       43        0  
         0        0        0        0        0       23  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 40.444 GPaEV = 68.777 GPaGV = 28.267 GPaνV = 0.21658
ReussKR = 40.342 GPaER = 65.764 GPaGR = 26.77 GPaνR = 0.22831
HillKH = 40.393 GPaEH = 67.277 GPaGH = 27.518 GPaνH = 0.22241

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
23 GPa 24 GPa 43 GPa 47.851 GPa 54.563 GPa 121.59 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 58.406 GPa 87.975 GPa 7.5508 TPa–1 9.0629 TPa–1 23 GPa 43 GPa0.0209160.35819Value
Anisotropy 1.506 1.2003 1.87 17.1251Anisotropy
Axis 0.6867
0.7269
-0.0000
0.7318
-0.0000
0.6815
1.0000
0.0000
0.0000
0.0000
1.0000
0.0000
1.0000
-0.0000
0.0000
-0.0000
0.0000
1.0000
0.7066
-0.0003
0.7077
0.5570
0.6028
0.5713
Axis
0.0000
1.0000
0.0000
-1.0000
0.0000
-0.0000
0.7077
-0.0005
-0.7066
-0.4675
0.7961
-0.3843
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