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 Zr(CuP)2 (Materials Project id mp-8219)

       231       80       79      -16        0        0  
        80      231       79       16        0        0  
        79       79      220        0        0        0  
       -16       16        0       48        0        0  
         0        0        0        0       48      -16  
         0        0        0        0      -16       76  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 128.67 GPaEV = 164.69 GPaGV = 64 GPaνV = 0.28667
ReussKR = 128.59 GPaER = 150.02 GPaGR = 57.454 GPaνR = 0.30556
HillKH = 128.63 GPaEH = 157.41 GPaGH = 60.727 GPaνH = 0.29604

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
40.74 GPa 43.248 GPa 83.26 GPa 144.87 GPa 155.75 GPa 386.13 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 111.37 GPa 202.53 GPa 2.5206 TPa–1 2.7352 TPa–1 40.675 GPa 83.26 GPa0.0472480.55386Value
Anisotropy 1.818 1.0851 2.047 11.7225Anisotropy
Axis -0.0000
0.7750
-0.6320
0.8400
0.4893
-0.2347
1.0000
-0.0001
0.0000
0.0000
0.0000
1.0000
0.3602
0.2087
-0.9092
1.0000
-0.0006
-0.0006
0.5791
0.3357
-0.7429
0.5507
0.3198
-0.7710
Axis
-0.5006
0.8657
0.0004
0.0003
0.9106
-0.4132
-0.5011
0.8654
0.0004
-0.6673
-0.3862
-0.6368
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