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 Zr2Rh (Materials Project id mp-571664)

       155       93       93        0        0        0  
        93      158      155        0        0        0  
        93      155      158        0        0        0  
         0        0        0       15        0        0  
         0        0        0        0        6        0  
         0        0        0        0        0        6  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 128.11 GPaEV = 40.71 GPaGV = 14.067 GPaνV = 0.44704
ReussKR = 124.37 GPaER = 13.578 GPaGR = 4.5817 GPaνR = 0.4818
HillKH = 126.24 GPaEH = 27.3 GPaGH = 9.3242 GPaνH = 0.46396

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
3 GPa 6 GPa 6 GPa 15 GPa 80.576 GPa 387.42 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 5.9119 GPa 99.735 GPa 1.9861 TPa–1 4.0683 TPa–1 1.5 GPa 28.462 GPa-0.0210190.98653Value
Anisotropy 16.87 2.0484 18.97Anisotropy
Axis 0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
-0.0000
0.7071
0.7071
0.7071
0.5000
-0.5000
0.7673
-0.0006
0.6413
-0.6197
0.7848
-0.0000
Axis
0.0001
0.7071
-0.7071
-0.7071
0.5000
-0.5000
0.6413
-0.0010
-0.7673
0.0000
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