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 BaEr2F8 (Materials Project id mp-12803)

       173       40       48        0       -8        0  
        40      161       59        0      -11        0  
        48       59      158        0       -9        0  
         0        0        0       32        0       -5  
        -8      -11       -9        0       38        0  
         0        0        0       -5        0       17  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 87.333 GPaEV = 105.01 GPaGV = 40.4 GPaνV = 0.2996
ReussKR = 85.018 GPaER = 84.976 GPaGR = 31.864 GPaνR = 0.33341
HillKH = 86.176 GPaEH = 95.104 GPaGH = 36.132 GPaνH = 0.31606

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
15.486 GPa 33.514 GPa 36.779 GPa 99.496 GPa 130.54 GPa 263.19 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 50.856 GPa 155.56 GPa 2.4098 TPa–1 5.3083 TPa–1 15.486 GPa 63.094 GPa0.064270.71664Value
Anisotropy 3.059 2.2028 4.074 11.1504Anisotropy
Axis -0.6591
0.6997
-0.2758
0.9979
0.0000
-0.0646
-0.6902
0.0000
0.7236
0.7236
-0.0000
0.6902
0.9571
-0.0000
0.2897
0.7063
0.7071
0.0341
-0.1240
0.5153
-0.8480
-0.7459
0.5978
0.2937
Axis
0.0000
1.0000
0.0000
-0.7063
0.7071
-0.0341
-0.8742
0.3476
0.3390
-0.6543
-0.7401
-0.1554
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