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 ZrBi (Materials Project id mp-30933)

       157       40       55        0        0        0  
        40      162       72        0        0        0  
        55       72      109        0        0        0  
         0        0        0       64        0        0  
         0        0        0        0       65        0  
         0        0        0        0        0       32  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 84.667 GPaEV = 124.49 GPaGV = 49.6 GPaνV = 0.25494
ReussKR = 83.339 GPaER = 109.62 GPaGR = 42.796 GPaνR = 0.28077
HillKH = 84.003 GPaEH = 117.12 GPaGH = 46.198 GPaνH = 0.26762

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
32 GPa 52.496 GPa 64 GPa 65 GPa 120.17 GPa 255.33 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 67.583 GPa 154.09 GPa 2.8458 TPa–1 5.4012 TPa–1 27.465 GPa 65 GPa-0.0570420.64622Value
Anisotropy 2.28 1.8979 2.367Anisotropy
Axis 0.0000
0.0000
1.0000
-0.0000
0.8108
0.5853
0.0000
1.0000
0.0000
0.0000
0.0000
1.0000
0.4067
0.5784
-0.7071
0.0000
0.0000
1.0000
0.5551
0.4433
-0.7038
0.0000
1.0000
-0.0000
Axis
-0.4071
-0.5782
-0.7071
1.0000
0.0000
-0.0000
0.5480
0.4416
0.7104
0.0001
-0.0000
-1.0000
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