Ba4Zr(RuO4)3

High-Entropy Materials HEA

MP-ID: mp-6716 · Space group: R-3m (#166)

Materials Project API

Basic Information

Formula

Ba4Zr(RuO4)3

MP-ID

mp-6716

Elements

Sites

Density

6.4512

g/cm³

Volume

292.34

Å³

Cell a

10.3208

Cell b

10.3208

Cell c

10.3208

α Angle

33.13

β Angle

33.13

γ Angle

33.13

Space Group

R-3m

Point Group

-3m

Crystal System

Trigonal

Bravais Lattice

Stability

Yes

Packing Fraction

X-ray Diffraction

Diffraction Pattern

Target / Radiation

X-axis: 2θ (°); Y-axis: relative intensity; Cu Kα ; λ=1.5418 Å

Diffraction Peaks (Top 24)

2θ	d (Å)	I	hkl
17.66	5.0212	6.7	(1,0,0)
18.44	4.8128	5.3	(1,1,0)
23.15	3.8421	11.0	(2,2,1)
27.46	3.2485	1.5	(3,3,3)
27.61	3.2305	84.8	(3,2,2)
30.09	2.9700	12.9	(3,2,3)
30.09	2.9700	6.5	(3,3,2)
30.37	2.9427	100.0	(1,0,-1)
30.37	2.9427	50.0	(1,-1,0)
35.39	2.5360	7.8	(3,3,4)
35.39	2.5360	15.6	(4,3,3)
36.89	2.4364	3.6	(4,4,4)
38.19	2.3567	5.0	(4,3,4)
38.19	2.3567	2.5	(4,4,3)
38.54	2.3362	5.3	(1,1,3)
38.54	2.3362	10.7	(3,1,1)
41.40	2.1809	3.6	(4,3,2)
41.51	2.1755	50.9	(3,3,1)
43.28	2.0904	3.3	(2,2,4)
43.28	2.0904	6.6	(4,2,2)
44.01	2.0576	2.0	(4,4,5)
44.01	2.0576	4.0	(5,4,4)
47.02	1.9324	17.5	(5,5,4)
47.32	1.9211	17.5	(4,4,2)

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Energy Properties

Formation Energy/atom

-2.56019

eV/atom

Energy/atom

-7.73131

eV/atom

Energy above Hull

0.0000

eV/atom

Uncorrected Energy

-7.3191

eV/atom

Volume/atom

14.62

Å³

c/a Ratio

1.0000

Electronic Properties

Metallic

Metal

Band Gap

Direct Gap

CBM

N/A

Magnetic Properties

Magnetic

Yes

Total Mag. Moment

3.9801

μB

Mag. Ordering

Mag. Sites

Magnetization/Volume

0.013610

μB/Å³

Elastic Properties

Elastic data not available

Feature Analysis

Composition Overview

Element Composition (atomic fraction)

Composition Info

Major / Matrix Element

O · 0.600

Element Family

Metalloid-Nonmetal

Solute Fraction

0.400

Interstitial Fraction

0.000

High-Entropy Alloy Features

Composite Radar (normalized)

Element-Class Share

Mix Entropy ΔS/R

1.0627

HEA criterion (>1.0 = high entropy)

Mix Entropy ΔS

8.8356

J/mol·K

Ω Parameter

4.3101

Ω > 1.1 favors solid solution

Atomic Size Mismatch δr

58.370%

δr < 6.6% favors single-phase solid solution

Electronegativity Diff Δχ

1.0542

smaller = more stable mixing

VEC

4.200

valence electron concentration, affects phase stability

Mix Enthalpy ΔH_mix

-1.497

kJ/mol; negative = exothermic mixing

Entropy Norm

0.7666

SS Former

Phase Tendency

Related Tasks

Related computation task IDs (5)

aaadnnsy aaadtfys aaadzcut aaaetopv aaafygzi

Citation & References

Materials Project Page

https://materialsproject.org/materials/mp-6716

Reference Citation

The crystal structure and related material properties of Ba4Zr(RuO4)3 were obtained from the Materials Project database (MP-ID: mp-6716, database version v2026.04.13).

Literature Citation

Horton, M.K., Huck, P., Yang, R.X. et al. Accelerated data-driven materials science with the Materials Project. Nat. Mater. 24, 1522–1532 (2025). https://doi.org/10.1038/s41563-025-02272-0

3D Crystal Structure Rendering

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Raw CIF Data

# generated using pymatgen
data_Ba4Zr(RuO4)3
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   10.32082214
_cell_length_b   10.32082214
_cell_length_c   10.32082279
_cell_angle_alpha   33.13238573
_cell_angle_beta   33.13238573
_cell_angle_gamma   33.13238154
_symmetry_Int_Tables_number   1
_chemical_formula_structural   Ba4Zr(RuO4)3
_chemical_formula_sum   'Ba4 Zr1 Ru3 O12'
_cell_volume   292.33729540
_cell_formula_units_Z   1
loop_
 _symmetry_equiv_pos_site_id
 _symmetry_equiv_pos_as_xyz
  1  'x, y, z'
loop_
 _atom_site_type_symbol
 _atom_site_label
 _atom_site_symmetry_multiplicity
 _atom_site_fract_x
 _atom_site_fract_y
 _atom_site_fract_z
 _atom_site_occupancy
  Ba  Ba0  1  0.71335900  0.71335900  0.71335900  1.0
  Ba  Ba1  1  0.28664100  0.28664100  0.28664100  1.0
  Ba  Ba2  1  0.87152600  0.87152600  0.87152600  1.0
  Ba  Ba3  1  0.12847400  0.12847400  0.12847400  1.0
  Zr  Zr4  1  0.00000000  0.00000000  0.00000000  1.0
  Ru  Ru5  1  0.41258200  0.41258200  0.41258200  1.0
  Ru  Ru6  1  0.50000000  0.50000000  0.50000000  1.0
  Ru  Ru7  1  0.58741800  0.58741800  0.58741800  1.0
  O  O8  1  0.21104900  0.21104900  0.70098700  1.0
  O  O9  1  0.70098700  0.21104900  0.21104900  1.0
  O  O10  1  0.21104900  0.70098700  0.21104900  1.0
  O  O11  1  0.78895100  0.29901300  0.78895100  1.0
  O  O12  1  0.78895100  0.78895100  0.29901300  1.0
  O  O13  1  0.29901300  0.78895100  0.78895100  1.0
  O  O14  1  0.38807100  0.38807100  0.85451300  1.0
  O  O15  1  0.85451300  0.38807100  0.38807100  1.0
  O  O16  1  0.14548700  0.61192900  0.61192900  1.0
  O  O17  1  0.61192900  0.61192900  0.14548700  1.0
  O  O18  1  0.61192900  0.14548700  0.61192900  1.0
  O  O19  1  0.38807100  0.85451300  0.38807100  1.0

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