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 Li3PrBi2 (Materials Project id mp-1018770)

        81       15       18       14        0        0  
        15       81       18      -14        0        0  
        18       18       73        0        0        0  
        14      -14        0       28        0        0  
         0        0        0        0       28       14  
         0        0        0        0       14       33  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 37.444 GPaEV = 71.155 GPaGV = 30.067 GPaνV = 0.18329
ReussKR = 37.412 GPaER = 60.617 GPaGR = 24.642 GPaνR = 0.22996
HillKH = 37.428 GPaEH = 65.987 GPaGH = 27.354 GPaνH = 0.20616

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
16.279 GPa 19.559 GPa 44.721 GPa 56.567 GPa 74.441 GPa 112.43 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 42.766 GPa 94.25 GPa 8.6478 TPa–1 9.434 TPa–1 16.279 GPa 44.721 GPa-0.114320.53336Value
Anisotropy 2.204 1.0909 2.747Anisotropy
Axis 0.7209
0.4162
-0.5542
-0.7836
0.4524
0.4258
0.9659
0.2588
0.0000
0.0000
0.0000
1.0000
-0.0000
0.6419
-0.7668
0.6640
0.3834
-0.6420
-0.6131
0.3540
0.7063
-0.5000
0.8660
0.0000
Axis
-1.0000
0.0000
0.0000
-0.5001
0.8660
-0.0001
-0.5000
-0.8660
-0.0000
-0.6446
-0.3722
0.6678
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