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 HoRh (Materials Project id mp-2163)

       190       86       86        0        0        0  
        86      190       86        0        0        0  
        86       86      190        0        0        0  
         0        0        0       38        0        0  
         0        0        0        0       38        0  
         0        0        0        0        0       38  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 120.67 GPaEV = 116.74 GPaGV = 43.6 GPaνV = 0.33876
ReussKR = 120.67 GPaER = 114.31 GPaGR = 42.586 GPaνR = 0.34211
HillKH = 120.67 GPaEH = 115.53 GPaGH = 43.093 GPaνH = 0.34043

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
38 GPa 38 GPa 38 GPa 104 GPa 104 GPa 362 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 103.17 GPa 136.41 GPa 2.7624 TPa–1 2.7624 TPa–1 38 GPa 52 GPa0.250960.44555Value
Anisotropy 1.322 1.0000 1.368 1.7754Anisotropy
Axis -0.5774
0.5774
-0.5773
0.0000
0.0000
1.0000
0.5880
0.7663
0.2588
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
0.7071
-0.0001
0.7071
0.7071
-0.0000
-0.7071
Axis
1.0000
0.0000
-0.0000
0.7071
-0.0005
-0.7071
0.0001
1.0000
0.0000
-0.7071
0.0002
-0.7071
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