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 Li5NCl2 (Materials Project id mp-29151)

        85       25       14       -2        0        0  
        25       85       14        2        0        0  
        14       14       65        0        0        0  
        -2        2        0       24        0        0  
         0        0        0        0       24       -2  
         0        0        0        0       -2       30  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 37.889 GPaEV = 66.882 GPaGV = 27.733 GPaνV = 0.2058
ReussKR = 36.728 GPaER = 65.258 GPaGR = 27.104 GPaνR = 0.20387
HillKH = 37.309 GPaEH = 66.07 GPaGH = 27.418 GPaνH = 0.20485

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
23.394 GPa 23.779 GPa 30.606 GPa 57.529 GPa 60.221 GPa 117.47 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 56.884 GPa 76.787 GPa 7.5466 TPa–1 12.134 TPa–1 23.394 GPa 30.606 GPa0.107520.29158Value
Anisotropy 1.35 1.6078 1.308 2.7120Anisotropy
Axis 0.5541
0.3199
0.7686
0.0001
0.9931
0.1175
0.9914
0.1305
0.0000
0.0000
0.0000
1.0000
0.0000
0.2898
0.9571
-0.0000
0.9571
-0.2898
0.3366
0.1943
-0.9214
1.0000
-0.0008
-0.0002
Axis
-1.0000
-0.0000
0.0000
-1.0000
-0.0000
-0.0000
-0.5000
0.8660
-0.0000
0.0006
0.9305
-0.3663
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