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 CaPdF4 (Materials Project id mp-8161)

        94       59       56        0        0        0  
        59       94       56        0        0        0  
        56       56      142        0        0        0  
         0        0        0       34        0        0  
         0        0        0        0       34        0  
         0        0        0        0        0       36  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 74.667 GPaEV = 82.619 GPaGV = 31.4 GPaνV = 0.31558
ReussKR = 72.554 GPaER = 76.646 GPaGR = 28.946 GPaνR = 0.32393
HillKH = 73.61 GPaEH = 79.638 GPaGH = 30.173 GPaνH = 0.31969

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
34 GPa 34 GPa 35 GPa 36 GPa 68.113 GPa 226.89 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 52.966 GPa 101.01 GPa 2.653 TPa–1 5.5649 TPa–1 17.5 GPa 36 GPa0.148460.53201Value
Anisotropy 1.907 2.0976 2.057 3.5835Anisotropy
Axis 1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
-0.7071
0.7071
-0.0000
1.0000
-0.0000
-0.0000
0.7863
0.0002
0.6178
-0.8266
0.0000
0.5627
Axis
-0.7071
-0.7071
-0.0000
0.0000
1.0000
-0.0000
0.6178
0.0004
-0.7863
0.0000
-1.0000
0.0000
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