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 TmBi2BrO4 (Materials Project id mp-546350)

       162       86       27        0        0        0  
        86      162       27        0        0        0  
        27       27       76        0        0        0  
         0        0        0       21        0        0  
         0        0        0        0       21        0  
         0        0        0        0        0       83  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 75.556 GPaEV = 107.01 GPaGV = 42.333 GPaνV = 0.26394
ReussKR = 59.555 GPaER = 79.933 GPaGR = 31.314 GPaνR = 0.2763
HillKH = 67.555 GPaEH = 93.486 GPaGH = 36.824 GPaνH = 0.26936

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
21 GPa 21 GPa 67.904 GPa 76 GPa 83 GPa 256.1 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 58.017 GPa 192.41 GPa 2.8177 TPa–1 11.156 TPa–1 21 GPa 83 GPa0.0743690.51713Value
Anisotropy 3.316 3.9592 3.952 6.9535Anisotropy
Axis 0.6100
-0.0000
0.7924
0.7071
0.7071
0.0000
0.2588
0.9659
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
1.0000
-0.0003
-0.0000
0.5069
0.5069
0.6972
-0.5889
0.5890
0.5534
Axis
-0.7660
-0.6428
0.0000
0.0003
1.0000
0.0000
-0.7071
0.7071
0.0000
-0.3915
0.3912
-0.8329
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