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 ZrCu (Materials Project id mp-2210)

       141      105      105        0        0        0  
       105      141      105        0        0        0  
       105      105      141        0        0        0  
         0        0        0       43        0        0  
         0        0        0        0       43        0  
         0        0        0        0        0       43  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 117 GPaEV = 90.492 GPaGV = 33 GPaνV = 0.37109
ReussKR = 117 GPaER = 76.874 GPaGR = 27.643 GPaνR = 0.39049
HillKH = 117 GPaEH = 83.731 GPaGH = 30.321 GPaνH = 0.38072

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
36 GPa 36 GPa 43 GPa 43 GPa 43 GPa 351 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 51.366 GPa 114.92 GPa 2.849 TPa–1 2.849 TPa–1 18 GPa 43 GPa0.0205960.72934Value
Anisotropy 2.237 1.0000 2.389 35.4113Anisotropy
Axis 0.0000
0.0000
1.0000
0.5774
0.5774
0.5773
0.3536
0.8536
0.3827
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
-0.0000
0.0000
1.0000
0.7071
-0.0002
0.7071
0.0000
0.7071
0.7071
Axis
0.7071
-0.0005
-0.7071
-0.7660
0.6428
-0.0000
0.7071
-0.0006
-0.7071
-1.0000
0.0000
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