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 VF4 (Materials Project id mp-554799)

         9        3        3        0       -1        0  
         3       41       24        0       -0        0  
         3       24       66        0        2        0  
         0        0        0       59        0       -2  
        -1       -0        2        0        4        0  
         0        0        0       -2        0        9  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 19.556 GPaEV = 44.968 GPaGV = 20.133 GPaνV = 0.11675
ReussKR = 7.9308 GPaER = 17.503 GPaGR = 7.73 GPaνR = 0.13217
HillKH = 13.743 GPaEH = 31.239 GPaGH = 13.932 GPaνH = 0.12116

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
3.6976 GPa 8.9197 GPa 8.9201 GPa 26.551 GPa 59.08 GPa 80.832 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 7.3387 GPa 92.668 GPa 2.993 TPa–1 109.2 TPa–1 3.6094 GPa 59.08 GPa-0.443530.89685Value
Anisotropy 12.63 36.4836 16.37Anisotropy
Axis 0.9196
0.0000
0.3929
-0.0158
0.6265
-0.7793
-0.1171
-0.0000
0.9931
-0.9931
-0.0000
-0.1171
-0.9878
0.0000
0.1558
-0.0399
-0.0000
0.9992
0.1502
0.7004
-0.6977
-0.1878
0.6409
0.7443
Axis
-0.1558
-0.0001
-0.9878
0.0000
-1.0000
-0.0000
-0.4121
0.6859
0.5998
-0.8916
0.2066
-0.4029
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