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 Pr3(CuSn)4 (Materials Project id mp-975640)

       125       31       59        0        0        0  
        31      141       40        0        0        0  
        59       40      146        0        0        0  
         0        0        0       50        0        0  
         0        0        0        0       59        0  
         0        0        0        0        0       39  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 74.667 GPaEV = 119.4 GPaGV = 48.4 GPaνV = 0.23348
ReussKR = 73.805 GPaER = 115.8 GPaGR = 46.749 GPaνR = 0.23851
HillKH = 74.236 GPaEH = 117.6 GPaGH = 47.574 GPaνH = 0.23597

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
39 GPa 50 GPa 59 GPa 75.489 GPa 110.86 GPa 225.65 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 94.938 GPa 142 GPa 3.3964 TPa–1 5.1582 TPa–1 37.914 GPa 59 GPa0.114080.42481Value
Anisotropy 1.496 1.5187 1.556 3.7236Anisotropy
Axis 0.8391
0.5440
0.0000
0.6593
0.0000
0.7518
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.7071
-0.0003
0.7071
0.0000
0.0000
1.0000
-1.0000
0.0000
-0.0000
0.0000
0.0000
1.0000
Axis
0.7071
-0.0005
-0.7071
-1.0000
0.0000
0.0000
-0.0000
-1.0000
-0.0000
1.0000
0.0000
-0.0000
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