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 Zr3Ga2 (Materials Project id mp-30684)

       156       82       82        0        0        0  
        82      203       59        0        0        0  
        82       59      203        0        0        0  
         0        0        0       69        0        0  
         0        0        0        0       81        0  
         0        0        0        0        0       81  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 112 GPaEV = 171.32 GPaGV = 68.8 GPaνV = 0.24506
ReussKR = 111.48 GPaER = 162.11 GPaGR = 64.452 GPaνR = 0.25763
HillKH = 111.74 GPaEH = 166.74 GPaGH = 66.626 GPaνH = 0.2513

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
69 GPa 81 GPa 81 GPa 81.497 GPa 144 GPa 336.5 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 104.67 GPa 189.28 GPa 2.6984 TPa–1 3.5735 TPa–1 45.452 GPa 81 GPa0.0994230.47338Value
Anisotropy 1.808 1.3243 1.782 4.7613Anisotropy
Axis 1.0000
0.0000
0.0000
-0.5742
0.0000
0.8187
0.0000
0.9659
0.2588
1.0000
0.0000
0.0000
-0.7071
0.5000
-0.5000
0.0000
0.0000
1.0000
-0.0000
-0.0000
1.0000
0.0000
0.0000
1.0000
Axis
-0.7071
-0.5000
0.5000
-1.0000
0.0000
0.0000
-0.0000
-1.0000
-0.0000
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