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 PrTm3 (Materials Project id mp-975651)

        71       22       25        0        0        0  
        22       71       25        0        0        0  
        25       25       82        0        0        0  
         0        0        0       23        0        0  
         0        0        0        0       23        0  
         0        0        0        0        0       25  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 40.889 GPaEV = 60.916 GPaGV = 24.333 GPaνV = 0.2517
ReussKR = 40.611 GPaER = 60.658 GPaGR = 24.242 GPaνR = 0.25107
HillKH = 40.75 GPaEH = 60.787 GPaGH = 24.288 GPaνH = 0.25138

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
23 GPa 23 GPa 25 GPa 49 GPa 51.719 GPa 123.28 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 58.991 GPa 68.559 GPa 6.744 TPa–1 8.9398 TPa–1 23 GPa 25.735 GPa0.216310.30611Value
Anisotropy 1.162 1.3256 1.119 1.4151Anisotropy
Axis 0.8555
0.0000
0.5177
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.4997
0.5003
0.7071
-0.6616
0.6616
0.3530
-0.4538
0.4538
0.7669
Axis
0.1734
0.9849
-0.0000
0.5002
0.4998
-0.7071
-0.7071
-0.7071
0.0000
0.5423
-0.5422
0.6418
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