Ba4Cu3PbO9

High-Entropy Materials HEA Elasticity Data ELA

MP-ID: mp-1023127 · Space group: Pm-3n (#223)

Materials Project API

Basic Information

Formula

Ba4Cu3PbO9

MP-ID

mp-1023127

Elements

Sites

Density

6.5896

g/cm³

Volume

549.93

Å³

Cell a

8.1929

Cell b

8.1929

Cell c

8.1929

α Angle

90.00

β Angle

90.00

γ Angle

90.00

Space Group

Pm-3n

Point Group

m-3m

Crystal System

Cubic

Bravais Lattice

Stability

Packing Fraction

0.5236

X-ray Diffraction

Diffraction Pattern

Target / Radiation

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

Diffraction Peaks (Top 19)

2θ	d (Å)	I	hkl
15.29	5.7932	13.1	(1,1,0)
26.65	3.3447	4.2	(2,1,1)
30.87	2.8966	100.0	(2,2,0)
34.62	2.5908	4.8	(3,1,0)
38.05	2.3651	3.1	(2,2,2)
41.23	2.1896	3.9	(3,2,1)
44.22	2.0482	26.8	(4,0,0)
47.06	1.9311	2.8	(4,1,1)
52.38	1.7467	1.3	(3,3,2)
54.90	1.6724	39.1	(4,2,2)
57.34	1.6068	3.0	(5,1,0)
64.32	1.4483	16.5	(4,4,0)
66.55	1.4051	1.5	(5,3,0)
70.91	1.3291	1.2	(5,3,2)
73.04	1.2954	17.3	(6,2,0)
81.37	1.1825	5.6	(4,4,4)
83.42	1.1586	1.3	(7,1,0)
87.49	1.1149	1.2	(7,2,1)
89.52	1.0948	21.2	(6,4,2)

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Energy Properties

Formation Energy/atom

-1.99421

eV/atom

Energy/atom

-6.00702

eV/atom

Energy above Hull

0.0367

eV/atom

Uncorrected Energy

-5.6433

eV/atom

Volume/atom

16.17

Å³

c/a Ratio

1.0000

Electronic Properties

Metallic

Metal

Band Gap

Direct Gap

CBM

N/A

Magnetic Properties

Magnetic

Total Mag. Moment

0.0042

μB

Mag. Ordering

Mag. Sites

Magnetization/Volume

0.000010

μB/Å³

Elastic Properties

K_VRH

97.683

GPa

G_VRH

44.106

GPa

Young's Modulus E

115.008

GPa

Poisson Ratio ν

0.304

Pugh Ratio K/G

2.215

Vickers Hardness Est.

4.228

GPa

Ductility

Brittle

Anisotropy

0.274

Lame λ

68.279

GPa

Feature Analysis

Composition Overview

Element Composition (atomic fraction)

Composition Info

Major / Matrix Element

O · 0.529

Element Family

Metalloid-Nonmetal

Solute Fraction

0.471

Interstitial Fraction

0.000

High-Entropy Alloy Features

Composite Radar (normalized)

Element-Class Share

Mix Entropy ΔS/R

1.1499

HEA criterion (>1.0 = high entropy)

Mix Entropy ΔS

9.5604

J/mol·K

Ω Parameter

20.6946

Ω > 1.1 favors solid solution

Atomic Size Mismatch δr

56.212%

δr < 6.6% favors single-phase solid solution

Electronegativity Diff Δχ

1.0691

smaller = more stable mixing

VEC

4.765

valence electron concentration, affects phase stability

Mix Enthalpy ΔH_mix

0.249

kJ/mol; negative = exothermic mixing

Entropy Norm

0.8295

SS Former

Phase Tendency

Elasticity Features

Elastic Modulus Comparison (GPa)

Elastic Features

Elastic Anisotropy A^U

0.2740

Homogeneous Poisson ν

0.3040

Debye Temperature

476.3

Sound Velocity

2,891.2

m/s

Homogeneity

0.3040

Related Tasks

Related computation task IDs (3)

aaacggrh aaadrycj aaaefnxo

Citation & References

Materials Project Page

https://materialsproject.org/materials/mp-1023127

Reference Citation

The crystal structure and related material properties of Ba4Cu3PbO9 were obtained from the Materials Project database (MP-ID: mp-1023127, 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_Ba4Cu3PbO9
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   8.19284500
_cell_length_b   8.19284500
_cell_length_c   8.19284500
_cell_angle_alpha   90.00000000
_cell_angle_beta   90.00000000
_cell_angle_gamma   90.00000000
_symmetry_Int_Tables_number   1
_chemical_formula_structural   Ba4Cu3PbO9
_chemical_formula_sum   'Ba8 Cu6 Pb2 O18'
_cell_volume   549.92595241
_cell_formula_units_Z   2
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  0.25000000  0.25000000  0.25000000  1.0
  Ba  Ba1  1  0.75000000  0.75000000  0.25000000  1.0
  Ba  Ba2  1  0.75000000  0.25000000  0.75000000  1.0
  Ba  Ba3  1  0.25000000  0.75000000  0.75000000  1.0
  Ba  Ba4  1  0.25000000  0.75000000  0.25000000  1.0
  Ba  Ba5  1  0.75000000  0.25000000  0.25000000  1.0
  Ba  Ba6  1  0.25000000  0.25000000  0.75000000  1.0
  Ba  Ba7  1  0.75000000  0.75000000  0.75000000  1.0
  Cu  Cu8  1  0.50000000  0.00000000  0.50000000  1.0
  Cu  Cu9  1  0.50000000  0.00000000  0.00000000  1.0
  Cu  Cu10  1  0.00000000  0.50000000  0.00000000  1.0
  Cu  Cu11  1  0.00000000  0.00000000  0.50000000  1.0
  Cu  Cu12  1  0.50000000  0.50000000  0.00000000  1.0
  Cu  Cu13  1  0.00000000  0.50000000  0.50000000  1.0
  Pb  Pb14  1  0.50000000  0.50000000  0.50000000  1.0
  Pb  Pb15  1  0.00000000  0.00000000  0.00000000  1.0
  O  O16  1  0.00000000  0.50000000  0.25000000  1.0
  O  O17  1  0.50000000  0.50000000  0.22867200  1.0
  O  O18  1  0.22867200  0.50000000  0.50000000  1.0
  O  O19  1  0.50000000  0.75000000  0.00000000  1.0
  O  O20  1  0.25000000  0.00000000  0.50000000  1.0
  O  O21  1  0.75000000  0.00000000  0.50000000  1.0
  O  O22  1  0.50000000  0.25000000  0.00000000  1.0
  O  O23  1  0.00000000  0.00000000  0.27132800  1.0
  O  O24  1  0.00000000  0.00000000  0.72867200  1.0
  O  O25  1  0.00000000  0.27132800  0.00000000  1.0
  O  O26  1  0.50000000  0.77132800  0.50000000  1.0
  O  O27  1  0.27132800  0.00000000  0.00000000  1.0
  O  O28  1  0.72867200  0.00000000  0.00000000  1.0
  O  O29  1  0.50000000  0.22867200  0.50000000  1.0
  O  O30  1  0.00000000  0.50000000  0.75000000  1.0
  O  O31  1  0.50000000  0.50000000  0.77132800  1.0
  O  O32  1  0.77132800  0.50000000  0.50000000  1.0
  O  O33  1  0.00000000  0.72867200  0.00000000  1.0

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