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 YbCuGe (Materials Project id mp-13306)

       107       43       43        0        0        0  
        43      107       43        0        0        0  
        43       43      107        0        0        0  
         0        0        0        1        0        0  
         0        0        0        0        1        0  
         0        0        0        0        0        1  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 64.333 GPaEV = 37.59 GPaGV = 13.4 GPaνV = 0.40262
ReussKR = 64.333 GPaER = 4.8569 GPaGR = 1.6327 GPaνR = 0.48742
HillKH = 64.333 GPaEH = 21.704 GPaGH = 7.5163 GPaνH = 0.44377

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
1 GPa 1 GPa 1 GPa 64 GPa 64 GPa 193 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 2.9845 GPa 82.347 GPa 5.1813 TPa–1 5.1813 TPa–1 1 GPa 32 GPa0.0136880.96594Value
Anisotropy 27.59 1.0000 32 70.5698Anisotropy
Axis 0.5774
0.5774
0.5773
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.4330
0.7500
0.5000
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
-0.7071
-0.0000
0.7071
0.7071
0.0000
-0.7071
Axis
1.0000
0.0000
-0.0000
-0.7071
-0.0002
-0.7071
-0.0000
-1.0000
-0.0000
-0.7071
0.0001
-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