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 Zr4Al3 (Materials Project id mp-12752)

       218       43       61        0        0        0  
        43      218       61        0        0        0  
        61       61      208        0        0        0  
         0        0        0       70        0        0  
         0        0        0        0       70        0  
         0        0        0        0        0       87  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 108.22 GPaEV = 187.37 GPaGV = 77.333 GPaνV = 0.21144
ReussKR = 108.19 GPaER = 185.73 GPaGR = 76.505 GPaνR = 0.21387
HillKH = 108.21 GPaEH = 186.55 GPaGH = 76.919 GPaνH = 0.21266

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
70 GPa 70 GPa 87 GPa 144.25 GPa 175 GPa 324.75 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 177.22 GPa 196.96 GPa 2.9672 TPa–1 3.1379 TPa–1 70 GPa 87.5 GPa0.125480.28066Value
Anisotropy 1.111 1.0576 1.25 2.2367Anisotropy
Axis 0.3640
0.3639
-0.8574
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.3793
0.9253
-0.0000
0.0000
0.0000
1.0000
0.7071
0.7071
0.0000
1.0000
-0.0001
-0.0000
0.7703
-0.0002
-0.6377
Axis
-0.9397
0.3420
0.0000
-0.7071
0.7071
-0.0000
0.0001
1.0000
0.0000
-0.6377
-0.0001
-0.7703
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