Zr2Sc3HgPb3

High-Entropy Materials HEA

MP-ID: mp-3296723 · Space group: P6_3/mcm (#193)

Materials Project API

Basic Information

Formula

Zr2Sc3HgPb3

MP-ID

mp-3296723

Elements

Sites

Density

9.1123

g/cm³

Volume

415.30

Å³

Cell a

8.9140

Cell b

8.9140

Cell c

6.0352

α Angle

90.00

β Angle

90.00

γ Angle

120.00

Space Group

P6_3/mcm

Point Group

6/mmm

Crystal System

Hexagonal

Bravais Lattice

Stability

Yes

Packing Fraction

0.7405

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
11.46	7.7198	2.5	(1,0,-1,0)
23.04	3.8599	20.8	(2,0,-2,0)
24.83	3.5853	68.5	(2,-1,-1,1)
29.60	3.0176	6.7	(0,0,0,2)
30.64	2.9178	2.0	(3,-1,-2,0)
31.84	2.8105	7.1	(1,0,-1,2)
34.13	2.6269	29.5	(3,-1,-2,1)
34.87	2.5733	96.3	(3,0,-3,0)
35.94	2.4988	100.0	(2,-1,-1,2)
40.48	2.2285	1.1	(4,-2,-2,0)
43.13	2.0976	1.3	(2,-3,1,2)
43.13	2.0976	2.5	(3,-1,-2,2)
43.28	2.0905	12.6	(4,-2,-2,1)
44.92	2.0179	13.4	(4,-3,-1,1)
44.92	2.0179	6.7	(4,-1,-3,1)
46.37	1.9580	3.9	(3,0,-3,2)
49.72	1.8336	11.6	(2,-1,-1,3)
50.94	1.7926	28.1	(4,-2,-2,2)
51.61	1.7710	5.5	(5,-3,-2,0)
51.61	1.7710	2.8	(5,-2,-3,0)
52.40	1.7462	9.6	(4,-1,-3,2)
53.96	1.6994	2.3	(5,-3,-2,1)
55.48	1.6562	2.4	(2,-3,1,3)
55.48	1.6562	4.9	(3,-1,-2,3)

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Energy Properties

Formation Energy/atom

-0.48574

eV/atom

Energy/atom

-33.58777

eV/atom

Energy above Hull

0.0000

eV/atom

Uncorrected Energy

-33.5878

eV/atom

Volume/atom

23.07

Å³

c/a Ratio

0.6770

Electronic Properties

Metallic

Metal

Band Gap

Direct Gap

CBM

N/A

Magnetic Properties

Magnetic

Total Mag. Moment

0.5559

μB

Mag. Ordering

Mag. Sites

Magnetization/Volume

0.001340

μB/Å³

Elastic Properties

Elastic data not available

Feature Analysis

Composition Overview

Element Composition (atomic fraction)

Composition Info

Major / Matrix Element

Sc · 0.333

Element Family

3d-TM

Solute Fraction

0.667

Interstitial Fraction

0.000

High-Entropy Alloy Features

Composite Radar (normalized)

Element-Class Share

Mix Entropy ΔS/R

1.3108

HEA criterion (>1.0 = high entropy)

Mix Entropy ΔS

10.8979

J/mol·K

Ω Parameter

0.5821

Ω > 1.1 favors solid solution

Atomic Size Mismatch δr

4.841%

δr < 6.6% favors single-phase solid solution

Electronegativity Diff Δχ

0.4571

smaller = more stable mixing

VEC

4.556

valence electron concentration, affects phase stability

Mix Enthalpy ΔH_mix

-24.409

kJ/mol; negative = exothermic mixing

Entropy Norm

0.9455

SS Former

Phase Tendency

Related Tasks

Related computation task IDs (1)

aaahfovb

Citation & References

Materials Project Page

https://materialsproject.org/materials/mp-3296723

Reference Citation

The crystal structure and related material properties of Zr2Sc3HgPb3 were obtained from the Materials Project database (MP-ID: mp-3296723, 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_Zr2Sc3HgPb3
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   8.91401160
_cell_length_b   8.91401270
_cell_length_c   6.03517151
_cell_angle_alpha   90.00000000
_cell_angle_beta   90.00000000
_cell_angle_gamma   120.00000330
_symmetry_Int_Tables_number   1
_chemical_formula_structural   Zr2Sc3HgPb3
_chemical_formula_sum   'Zr4 Sc6 Hg2 Pb6'
_cell_volume   415.30453842
_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
  Zr  Zr0  1  0.66666700  0.33333300  0.00000000  1.0
  Zr  Zr1  1  0.33333300  0.66666700  0.00000000  1.0
  Zr  Zr2  1  0.33333300  0.66666700  0.50000000  1.0
  Zr  Zr3  1  0.66666700  0.33333300  0.50000000  1.0
  Sc  Sc4  1  0.71374036  0.71374036  0.75000000  1.0
  Sc  Sc5  1  0.28625964  0.00000000  0.75000000  1.0
  Sc  Sc6  1  1.00000000  0.28625964  0.75000000  1.0
  Sc  Sc7  1  0.28625964  0.28625964  0.25000000  1.0
  Sc  Sc8  1  0.71374036  1.00000000  0.25000000  1.0
  Sc  Sc9  1  0.00000000  0.71374036  0.25000000  1.0
  Hg  Hg10  1  0.00000000  0.00000000  0.00000000  1.0
  Hg  Hg11  1  0.00000000  0.00000000  0.50000000  1.0
  Pb  Pb12  1  0.37519231  0.37519231  0.75000000  1.0
  Pb  Pb13  1  0.62480769  0.00000000  0.75000000  1.0
  Pb  Pb14  1  1.00000000  0.62480769  0.75000000  1.0
  Pb  Pb15  1  0.62480769  0.62480769  0.25000000  1.0
  Pb  Pb16  1  0.37519231  1.00000000  0.25000000  1.0
  Pb  Pb17  1  0.00000000  0.37519231  0.25000000  1.0

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