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 LiCu3 (Materials Project id mp-862658)

       109       83       77        0        0        0  
        83      109       77        0        0        0  
        77       77      121        0        0        0  
         0        0        0       61        0        0  
         0        0        0        0       61        0  
         0        0        0        0        0       59  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 90.333 GPaEV = 111.33 GPaGV = 43 GPaνV = 0.29459
ReussKR = 90.27 GPaER = 77.811 GPaGR = 28.684 GPaνR = 0.35634
HillKH = 90.302 GPaEH = 94.962 GPaGH = 35.842 GPaνH = 0.32473

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
26 GPa 41.965 GPa 59 GPa 61 GPa 61 GPa 271.03 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 40.733 GPa 148.06 GPa 3.341 TPa–1 3.8685 TPa–1 13 GPa 61 GPa-0.261490.93403Value
Anisotropy 3.635 1.1579 4.692Anisotropy
Axis 1.0000
0.0000
0.0000
0.5724
0.5724
0.5871
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
-0.7071
0.7071
0.0000
0.0000
0.0000
1.0000
0.6924
0.0001
-0.7216
0.0000
0.7069
-0.7073
Axis
-0.7071
-0.7071
-0.0000
0.7660
0.6428
-0.0000
-0.7216
-0.0002
-0.6924
-1.0000
-0.0000
-0.0000
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