Zr9Sc9(Re4P)2

High-Entropy Materials HEA

MP-ID: mp-3294522 · Space group: P3m1 (#156)

Materials Project API

Basic Information

Formula

Zr9Sc9(Re4P)2

MP-ID

mp-3294522

Elements

Sites

Density

8.2781

g/cm³

Volume

557.10

Å³

Cell a

8.6584

Cell b

8.6584

Cell c

8.5806

α Angle

90.00

β Angle

90.00

γ Angle

120.00

Space Group

P3m1

Point Group

Crystal System

Trigonal

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
10.31	8.5806	1.9	(0,0,0,1)
11.80	7.4984	100.0	(1,0,-1,0)
11.80	7.4984	50.0	(1,-1,0,0)
20.52	4.3292	2.5	(2,-1,-1,0)
20.70	4.2903	1.3	(0,0,0,2)
23.90	3.7239	3.3	(1,0,-1,2)
25.93	3.4356	11.8	(2,0,-2,1)
31.57	2.8341	2.9	(2,1,-3,0)
31.57	2.8341	2.9	(3,-1,-2,0)
33.29	2.6912	5.8	(3,-1,-2,1)
33.53	2.6724	7.3	(1,0,-1,3)
35.93	2.4995	4.3	(3,0,-3,0)
35.93	2.4995	2.2	(3,-3,0,0)
37.48	2.3997	48.4	(3,0,-3,1)
38.05	2.3648	84.3	(3,-1,-2,2)
39.63	2.2740	30.8	(2,0,-2,3)
41.73	2.1646	3.7	(2,2,-4,0)
41.73	2.1646	7.3	(4,-2,-2,0)
41.83	2.1597	5.6	(3,0,-3,2)
41.83	2.1597	2.8	(3,-3,0,2)
42.12	2.1452	15.3	(0,0,0,4)
43.90	2.0624	13.7	(1,0,-1,4)
44.84	2.0212	12.1	(4,-1,-3,1)
44.84	2.0212	2.4	(4,-3,-1,1)

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Energy Properties

Formation Energy/atom

-0.48876

eV/atom

Energy/atom

-27.08246

eV/atom

Energy above Hull

0.0000

eV/atom

Uncorrected Energy

-27.0825

eV/atom

Volume/atom

19.90

Å³

c/a Ratio

0.9910

Electronic Properties

Metallic

Metal

Band Gap

Direct Gap

CBM

N/A

Magnetic Properties

Magnetic

Total Mag. Moment

0.2587

μB

Mag. Ordering

Mag. Sites

Magnetization/Volume

0.000460

μB/Å³

Elastic Properties

Elastic data not available

Feature Analysis

Composition Overview

Element Composition (atomic fraction)

Composition Info

Major / Matrix Element

Zr · 0.321

Element Family

4d-TM

Solute Fraction

0.679

Interstitial Fraction

0.071

High-Entropy Alloy Features

Composite Radar (normalized)

Element-Class Share

Mix Entropy ΔS/R

1.2761

HEA criterion (>1.0 = high entropy)

Mix Entropy ΔS

10.6092

J/mol·K

Ω Parameter

0.6780

Ω > 1.1 favors solid solution

Atomic Size Mismatch δr

10.310%

δr < 6.6% favors single-phase solid solution

Electronegativity Diff Δχ

0.3020

smaller = more stable mixing

VEC

4.607

valence electron concentration, affects phase stability

Mix Enthalpy ΔH_mix

-35.646

kJ/mol; negative = exothermic mixing

Entropy Norm

0.9205

SS Former

Phase Tendency

Related Tasks

Related computation task IDs (1)

aaahflok

Citation & References

Materials Project Page

https://materialsproject.org/materials/mp-3294522

Reference Citation

The crystal structure and related material properties of Zr9Sc9(Re4P)2 were obtained from the Materials Project database (MP-ID: mp-3294522, 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

Loading 3D structure…

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Raw CIF Data

# generated using pymatgen
data_Zr9Sc9(Re4P)2
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   8.65844464
_cell_length_b   8.65844500
_cell_length_c   8.58063253
_cell_angle_alpha   90.00000000
_cell_angle_beta   90.00000000
_cell_angle_gamma   119.99999481
_symmetry_Int_Tables_number   1
_chemical_formula_structural   Zr9Sc9(Re4P)2
_chemical_formula_sum   'Zr9 Sc9 Re8 P2'
_cell_volume   557.09562143
_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
  Zr  Zr0  1  0.80481870  0.19518130  0.54621450  1.0
  Zr  Zr1  1  0.80481870  0.60963740  0.54621450  1.0
  Zr  Zr2  1  0.39036260  0.19518130  0.54621450  1.0
  Zr  Zr3  1  0.80377074  0.19622926  0.95389233  1.0
  Zr  Zr4  1  0.80377074  0.60754148  0.95389233  1.0
  Zr  Zr5  1  0.39245852  0.19622926  0.95389233  1.0
  Zr  Zr6  1  0.19582493  0.80417507  0.04645434  1.0
  Zr  Zr7  1  0.19582493  0.39165086  0.04645434  1.0
  Zr  Zr8  1  0.60834914  0.80417507  0.04645434  1.0
  Sc  Sc9  1  0.19688025  0.80311975  0.45340090  1.0
  Sc  Sc10  1  0.19688025  0.39376050  0.45340090  1.0
  Sc  Sc11  1  0.60623950  0.80311975  0.45340090  1.0
  Sc  Sc12  1  0.53992413  0.46007587  0.25170193  1.0
  Sc  Sc13  1  0.53992413  0.07984827  0.25170193  1.0
  Sc  Sc14  1  0.92015173  0.46007587  0.25170193  1.0
  Sc  Sc15  1  0.46015516  0.53984484  0.75049308  1.0
  Sc  Sc16  1  0.46015516  0.92030932  0.75049308  1.0
  Sc  Sc17  1  0.07969068  0.53984484  0.75049308  1.0
  Re  Re18  1  0.89238529  0.10761471  0.24916155  1.0
  Re  Re19  1  0.89238529  0.78477058  0.24916155  1.0
  Re  Re20  1  0.21522942  0.10761471  0.24916155  1.0
  Re  Re21  1  0.10718715  0.89281285  0.75041539  1.0
  Re  Re22  1  0.10718715  0.21437530  0.75041539  1.0
  Re  Re23  1  0.78562470  0.89281285  0.75041539  1.0
  Re  Re24  1  0.00000000  0.00000000  0.49689598  1.0
  Re  Re25  1  0.00000000  0.00000000  0.99938149  1.0
  P  P26  1  0.33333300  0.66666700  0.24986893  1.0
  P  P27  1  0.66666700  0.33333300  0.74864758  1.0

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