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 LaCuTeO (Materials Project id mp-546790)

       137       41       47        0        0        0  
        41      137       47        0        0        0  
        47       47       78        0        0        0  
         0        0        0       13        0        0  
         0        0        0        0       13        0  
         0        0        0        0        0       36  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 69.111 GPaEV = 71.354 GPaGV = 26.867 GPaνV = 0.32792
ReussKR = 64.836 GPaER = 55.153 GPaGR = 20.303 GPaνR = 0.35822
HillKH = 66.973 GPaEH = 63.322 GPaGH = 23.585 GPaνH = 0.34242

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
13 GPa 13 GPa 36 GPa 44.825 GPa 96 GPa 211.17 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 40.619 GPa 107.2 GPa 3.2749 TPa–1 8.8739 TPa–1 13 GPa 48 GPa0.106330.64592Value
Anisotropy 2.639 2.7097 3.692 6.0748Anisotropy
Axis -0.4448
0.4449
-0.7773
1.0000
0.0000
0.0000
0.5000
0.8660
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.7071
0.7071
0.0000
-0.9204
0.0000
0.3909
0.8500
0.0002
0.5268
Axis
0.1735
0.9848
-0.0000
-0.7071
0.7071
0.0000
-0.0000
-1.0000
-0.0000
0.5268
0.0001
-0.8500
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