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 Fe (Materials Project id mp-136)

       538      170      153        0        0        0  
       170      538      153        0        0        0  
       153      153      622        0        0        0  
         0        0        0      168        0        0  
         0        0        0        0      168        0  
         0        0        0        0        0      184

Average properties

Averaging scheme	Bulk modulus	Young's modulus	Shear modulus	Poisson's ratio
Voigt	K_V = 294.44 GPa	E_V = 459.85 GPa	G_V = 185.47 GPa	ν_V = 0.23971
Reuss	K_R = 293.7 GPa	E_R = 455.4 GPa	G_R = 183.4 GPa	ν_R = 0.24157
Hill	K_H = 294.07 GPa	E_H = 457.63 GPa	G_H = 184.43 GPa	ν_H = 0.24064

Eigenvalues of the stiffness matrix

λ₁	λ₂	λ₃	λ₄	λ₅	λ₆
168 GPa	168 GPa	184 GPa	368 GPa	444.39 GPa	885.61 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	433.72 GPa	555.87 GPa	1.0215 TPa^–1	1.1917 TPa^–1	168 GPa	211.62 GPa	0.18091	0.30643	Value
Anisotropy	1.282		1.1667		1.26		1.6938		Anisotropy
Axis	0.6858 0.4150 0.5978	0.0000 0.0000 1.0000	0.0000 0.0000 1.0000	0.5000 0.8660 0.0000	0.0000 0.0000 1.0000	0.5644 0.4260 0.7071	0.4550 0.8905 0.0000	0.6611 0.0001 -0.7503	Axis
					-0.7660 -0.6428 0.0000	0.5646 0.4258 -0.7071	0.0000 0.0000 -1.0000	-0.7503 -0.0001 -0.6611	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