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 LiFeO2 (Materials Project id mp-19419)

       295       84       43      -20        0        0  
        84      295       43       20        0        0  
        43       43      196        0        0        0  
       -20       20        0       49        0        0  
         0        0        0        0       49      -20  
         0        0        0        0      -20      106  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 125.11 GPaEV = 201.62 GPaGV = 81.867 GPaνV = 0.23141
ReussKR = 117.84 GPaER = 167.59 GPaGR = 66.348 GPaνR = 0.26297
HillKH = 121.48 GPaEH = 184.75 GPaGH = 74.107 GPaνH = 0.24652

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
42.683 GPa 44.204 GPa 112.32 GPa 177.64 GPa 215.8 GPa 397.36 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 116.09 GPa 275.63 GPa 2.1676 TPa–1 4.151 TPa–1 42.648 GPa 112.32 GPa-0.0282120.53858Value
Anisotropy 2.374 1.9150 2.634Anisotropy
Axis 0.0000
0.7244
-0.6894
0.8544
0.4974
-0.1505
0.9914
0.1305
0.0000
0.0000
0.0000
1.0000
-0.2620
0.1516
-0.9531
-0.0000
0.9536
-0.3012
0.5310
0.3071
-0.7898
-0.6025
0.3491
-0.7178
Axis
-0.5001
-0.8660
-0.0002
-1.0000
-0.0000
-0.0000
-0.5004
0.8658
0.0003
0.6211
-0.3598
-0.6963
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