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 PdF3 (Materials Project id mp-13679)

        54        4       34      -17        0        0  
         4       54       34       17        0        0  
        34       34       81        0        0        0  
       -17       17        0       28        0        0  
         0        0        0        0       28      -17  
         0        0        0        0      -17       25  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 37 GPaEV = 59.2 GPaGV = 24 GPaνV = 0.23333
ReussKR = 28.405 GPaER = 36.619 GPaGR = 14.247 GPaνR = 0.28514
HillKH = 32.702 GPaEH = 48.012 GPaGH = 19.124 GPaνH = 0.25531

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
9.434 GPa 12.561 GPa 20.061 GPa 43.566 GPa 65.439 GPa 118.94 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 23.851 GPa 85.24 GPa -4.1911 TPa–1 19.698 TPa–1 9.434 GPa 43.566 GPa-0.417380.79221Value
Anisotropy 3.574 4.618Anisotropy
Axis 0.8129
0.4693
0.3449
-0.0000
0.7762
0.6305
0.0000
0.0000
1.0000
0.2430
0.9700
0.0000
-0.6387
0.3688
-0.6753
-0.5849
0.3377
0.7375
-0.7221
0.4169
-0.5521
0.3145
0.1816
0.9317
Axis
-0.5000
-0.8660
-0.0000
-0.5000
-0.8660
-0.0000
-0.5000
-0.8660
-0.0000
-0.5000
0.8660
-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