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 TmCu4Ag (Materials Project id mp-1025116)

       146       91       91        0        0        0  
        91      146       91        0        0        0  
        91       91      146        0        0        0  
         0        0        0       30        0        0  
         0        0        0        0       30        0  
         0        0        0        0        0       30  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 109.33 GPaEV = 79.933 GPaGV = 29 GPaνV = 0.37815
ReussKR = 109.33 GPaER = 79.799 GPaGR = 28.947 GPaνR = 0.37835
HillKH = 109.33 GPaEH = 79.866 GPaGH = 28.974 GPaνH = 0.37825

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
30 GPa 30 GPa 30 GPa 55 GPa 55 GPa 328 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 76.118 GPa 82.458 GPa 3.0488 TPa–1 3.0488 TPa–1 27.5 GPa 30 GPa0.346270.40746Value
Anisotropy 1.083 1.0000 1.091 1.1767Anisotropy
Axis 0.0000
0.0000
1.0000
0.5774
0.5774
0.5773
0.9659
0.0000
0.2588
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
0.0000
0.0000
1.0000
0.7071
-0.0002
0.7071
0.7071
-0.0001
0.7071
Axis
0.7071
-0.0005
-0.7071
0.7660
0.6428
-0.0000
0.7071
-0.0005
-0.7071
0.0001
1.0000
0.0001
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