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 NaLa3 (Materials Project id mp-975994)

        26       25       25        0        0        0  
        25       26       25        0        0        0  
        25       25       26        0        0        0  
         0        0        0       15        0        0  
         0        0        0        0       15        0  
         0        0        0        0        0       15  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 25.333 GPaEV = 24.62 GPaGV = 9.2 GPaνV = 0.33803
ReussKR = 25.333 GPaER = 3.5163 GPaGR = 1.1905 GPaνR = 0.47687
HillKH = 25.333 GPaEH = 14.588 GPaGH = 5.1952 GPaνH = 0.40402

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
1 GPa 1 GPa 15 GPa 15 GPa 15 GPa 76 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 1.4902 GPa 37.582 GPa 13.158 TPa–1 13.158 TPa–1 0.5 GPa 15 GPa-0.822431.9122Value
Anisotropy 25.22 1.0000 30Anisotropy
Axis 1.0000
0.0000
0.0000
-0.5774
0.5774
-0.5773
0.0000
0.0000
1.0000
0.1294
0.9830
0.1305
0.7071
-0.0003
0.7071
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
-0.6516
0.6517
0.3881
Axis
0.7071
-0.0005
-0.7071
0.7660
0.6428
-0.0000
-0.7071
-0.0002
-0.7071
-0.2748
0.2741
-0.9216
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