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 AlZnIr2 (Materials Project id mp-862705)

       341      161      161        0        0        0  
       161      341      161        0        0        0  
       161      161      341        0        0        0  
         0        0        0      123        0        0  
         0        0        0        0      123        0  
         0        0        0        0        0      123  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 221 GPaEV = 282.6 GPaGV = 109.8 GPaνV = 0.28688
ReussKR = 221 GPaER = 276.99 GPaGR = 107.27 GPaνR = 0.29111
HillKH = 221 GPaEH = 279.8 GPaGH = 108.53 GPaνH = 0.28899

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
123 GPa 123 GPa 123 GPa 180 GPa 180 GPa 663 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 237.73 GPa 311.26 GPa 1.5083 TPa–1 1.5083 TPa–1 90 GPa 123 GPa0.174460.38977Value
Anisotropy 1.309 1.0000 1.367 2.2342Anisotropy
Axis 0.0000
0.0000
1.0000
0.5774
0.5774
0.5773
0.0000
0.0000
1.0000
0.4320
0.7511
0.4993
0.7071
0.0001
-0.7071
0.0000
0.0000
1.0000
0.7071
-0.0002
0.7071
0.7071
-0.0005
0.7071
Axis
-0.7071
-0.0002
-0.7071
0.7660
0.6428
-0.0000
0.7071
-0.0006
-0.7071
0.0004
1.0000
0.0004
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