ELATE: Elastic tensor analysis

Welcome to ELATE, the online tool for analysis of elastic tensors, developed by Romain Gaillac and François-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 KY2Ti2S2O5 (Materials Project id mp-6847)

       165       45       30        0        0        0  
        45      165       30        0        0        0  
        30       30      133        0        0        0  
         0        0        0       11        0        0  
         0        0        0        0       11        0  
         0        0        0        0        0       56

Average properties

Averaging scheme	Bulk modulus	Young's modulus	Shear modulus	Poisson's ratio
Voigt	K_V = 74.778 GPa	E_V = 100.69 GPa	G_V = 39.467 GPa	ν_V = 0.27559
Reuss	K_R = 73.399 GPa	E_R = 58.544 GPa	G_R = 21.412 GPa	ν_R = 0.36707
Hill	K_H = 74.088 GPa	E_H = 80.318 GPa	G_H = 30.439 GPa	ν_H = 0.31932

Eigenvalues of the stiffness matrix

λ₁	λ₂	λ₃	λ₄	λ₅	λ₆
11 GPa	11 GPa	56 GPa	114.21 GPa	120 GPa	228.79 GPa

Variations of the elastic moduli

	Young's modulus		Linear compressibility		Shear modulus		Poisson's ratio
	E_min	E_max	β_min	β_max	G_min	G_max	ν_min	ν_max
Value	38.583 GPa	149 GPa	3.9418 TPa^–1	5.7405 TPa^–1	11 GPa	58.67 GPa	0.052862	0.75961	Value
Anisotropy	3.862		1.4563		5.334		14.3695		Anisotropy
Axis	0.4965 0.4965 0.7120	1.0000 0.0000 0.0000	1.0000 0.0000 0.0000	0.0000 0.0000 1.0000	0.0000 0.0000 1.0000	0.7071 0.0001 -0.7071	0.6560 0.0003 -0.7547	0.7269 -0.0006 0.6868	Axis
					-0.7880 0.6157 -0.0000	-0.7071 -0.0002 -0.7071	-0.0005 1.0000 -0.0000	0.6868 -0.0006 -0.7269	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