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 TmAgPb (Materials Project id mp-20522)

       104       43       55        0        0        0  
        43      104       55        0        0        0  
        55       55      103        0        0        0  
         0        0        0       38        0        0  
         0        0        0        0       38        0  
         0        0        0        0        0       30  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 68.556 GPaEV = 82.475 GPaGV = 31.733 GPaνV = 0.29949
ReussKR = 68.353 GPaER = 79.626 GPaGR = 30.488 GPaνR = 0.30585
HillKH = 68.454 GPaEH = 81.053 GPaGH = 31.111 GPaνH = 0.30266

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
30 GPa 38 GPa 38 GPa 44.167 GPa 61 GPa 205.83 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 61.844 GPa 91.094 GPa 4.07 TPa–1 5.2799 TPa–1 23.659 GPa 38 GPa0.185540.43645Value
Anisotropy 1.473 1.2973 1.606 2.3523Anisotropy
Axis 0.0000
0.0000
1.0000
0.7570
0.0001
0.6535
0.0000
0.0000
1.0000
0.4943
0.8693
0.0000
-0.5000
0.5000
0.7071
0.0000
0.0000
1.0000
-0.4922
0.4922
0.7180
1.0000
-0.0004
-0.0000
Axis
-0.5000
0.5000
-0.7071
-0.7660
0.6428
-0.0000
0.5077
-0.5077
0.6960
-0.0000
-0.0003
-1.0000
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