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 BaRh2 (Materials Project id mp-568430)

       132       76       76        0        0        0  
        76      132       76        0        0        0  
        76       76      132        0        0        0  
         0        0        0       32        0        0  
         0        0        0        0       32        0  
         0        0        0        0        0       32  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 94.667 GPaEV = 82.382 GPaGV = 30.4 GPaνV = 0.35496
ReussKR = 94.667 GPaER = 82.064 GPaGR = 30.27 GPaνR = 0.35552
HillKH = 94.667 GPaEH = 82.223 GPaGH = 30.335 GPaνH = 0.35524

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
32 GPa 32 GPa 32 GPa 56 GPa 56 GPa 284 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 76.462 GPa 86.278 GPa 3.5211 TPa–1 3.5211 TPa–1 28 GPa 32 GPa0.306180.39947Value
Anisotropy 1.128 1.0000 1.143 1.3047Anisotropy
Axis 1.0000
0.0000
0.0000
0.5774
0.5774
0.5773
0.0000
0.0000
1.0000
0.9239
0.0000
0.3827
0.7071
0.0001
-0.7071
0.0000
0.0000
1.0000
0.7071
-0.0002
0.7071
0.7071
-0.0001
0.7071
Axis
-0.7071
-0.0002
-0.7071
0.7660
0.6428
-0.0000
0.7071
-0.0006
-0.7071
0.0001
1.0000
0.0001
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