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 TaRu (Materials Project id mp-1601)

       393      206      208        0        0        0  
       206      393      208        0        0        0  
       208      208      350        0        0        0  
         0        0        0       51        0        0  
         0        0        0        0       51        0  
         0        0        0        0        0       61  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 264.44 GPaEV = 185.01 GPaGV = 66.867 GPaνV = 0.3834
ReussKR = 263.64 GPaER = 175.41 GPaGR = 63.138 GPaνR = 0.38911
HillKH = 264.04 GPaEH = 180.22 GPaGH = 65.002 GPaνH = 0.38624

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
51 GPa 51 GPa 61 GPa 155.08 GPa 187 GPa 793.92 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 149.88 GPa 244.19 GPa 1.1533 TPa–1 1.4863 TPa–1 51 GPa 93.5 GPa0.232010.55913Value
Anisotropy 1.629 1.2887 1.833 2.4100Anisotropy
Axis 0.5272
0.5273
0.6663
1.0000
0.0000
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.7071
0.7071
-0.0000
0.7593
-0.0004
-0.6507
0.7531
-0.0004
0.6579
Axis
-0.7660
0.6428
-0.0000
-0.7071
0.7071
0.0000
0.0004
1.0000
-0.0002
0.6579
-0.0010
-0.7531
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