Pr4HoP12Ru19
High-Entropy Materials HEAMP-ID: mp-3293413 · Space group: P-6 (#174)
Basic Information
Formula
Pr4HoP12Ru19
MP-ID
mp-3293413
Elements
4
Sites
36
Density
9.1813
g/cm³
Volume
546.31
ų
Cell a
12.5481
Å
Cell b
12.5481
Å
Cell c
4.0063
Å
α Angle
90.00
°
β Angle
90.00
°
γ Angle
120.00
°
Space Group
P-6
Point Group
-6
Crystal System
Hexagonal
Bravais Lattice
hP
Stability
No
Packing Fraction
0.7405
X-ray Diffraction
Diffraction Pattern
X-axis: 2θ (°); Y-axis: relative intensity; Cu Kα ; λ=1.5418 Å
Diffraction Peaks (Top 24)
| 2θ | d (Å) | I | hkl |
|---|---|---|---|
| 8.14 | 10.8670 | 1.2 | (1,0,-1,0) |
| 23.67 | 3.7590 | 2.0 | (1,0,-1,1) |
| 26.40 | 3.3766 | 5.1 | (2,-1,-1,1) |
| 28.45 | 3.1370 | 16.6 | (4,-2,-2,0) |
| 29.64 | 3.0140 | 1.8 | (4,-1,-3,0) |
| 31.19 | 2.8680 | 6.6 | (3,-1,-2,1) |
| 33.35 | 2.6869 | 4.7 | (3,0,-3,1) |
| 36.03 | 2.4931 | 5.4 | (5,-2,-3,0) |
| 36.37 | 2.4699 | 100.0 | (4,-2,-2,1) |
| 37.34 | 2.4085 | 26.4 | (4,-1,-3,1) |
| 37.94 | 2.3714 | 11.5 | (5,-1,-4,0) |
| 40.10 | 2.2485 | 1.6 | (4,0,-4,1) |
| 41.55 | 2.1734 | 6.5 | (5,0,-5,0) |
| 43.26 | 2.0914 | 3.7 | (6,-3,-3,0) |
| 44.10 | 2.0537 | 4.1 | (6,-2,-4,0) |
| 44.39 | 2.0407 | 4.9 | (5,-1,-4,1) |
| 45.27 | 2.0032 | 24.1 | (0,0,0,2) |
| 46.53 | 1.9518 | 9.2 | (6,-1,-5,0) |
| 47.60 | 1.9104 | 8.3 | (5,0,-5,1) |
| 49.14 | 1.8540 | 3.3 | (6,-3,-3,1) |
| 50.38 | 1.8112 | 13.3 | (6,0,-6,0) |
| 51.13 | 1.7865 | 4.2 | (7,-3,-4,0) |
| 52.13 | 1.7546 | 1.7 | (6,-1,-5,1) |
| 54.34 | 1.6883 | 5.7 | (4,-2,-2,2) |
Energy Properties
Formation Energy/atom
-0.88856
eV/atom
Energy/atom
-21.48823
eV/atom
Energy above Hull
0.0003
eV/atom
Uncorrected Energy
-21.4882
eV/atom
Volume/atom
15.18
ų
c/a Ratio
0.3193
Electronic Properties
Metallic
Metal
Band Gap
0
eV
Direct Gap
No
CBM
N/A
eV
Magnetic Properties
Magnetic
No
Total Mag. Moment
0.0100
μB
Mag. Ordering
NM
Mag. Sites
0
Magnetization/Volume
0.000020
μB/ų
Elastic Properties
Elastic data not available
Feature Analysis
Composition Overview
Element Composition (atomic fraction)
Composition Info
Major / Matrix Element
Ru · 0.528
Element Family
4d-TM
Solute Fraction
0.472
Interstitial Fraction
0.333
High-Entropy Alloy Features
Composite Radar (normalized)
Element-Class Share
Mix Entropy ΔS/R
1.0472
HEA criterion (>1.0 = high entropy)
Mix Entropy ΔS
8.7062
J/mol·K
Ω Parameter
0.9958
Ω > 1.1 favors solid solution
Atomic Size Mismatch δr
17.274%
δr < 6.6% favors single-phase solid solution
Electronegativity Diff Δχ
0.3621
smaller = more stable mixing
VEC
6.528
valence electron concentration, affects phase stability
Mix Enthalpy ΔH_mix
14.548
kJ/mol; negative = exothermic mixing
Entropy Norm
0.7554
SS Former
0
Phase Tendency
IM
Related Tasks
Related computation task IDs (1)
Citation & References
Materials Project Page
https://materialsproject.org/materials/mp-3293413
Reference Citation
The crystal structure and related material properties of Pr4HoP12Ru19 were obtained from the Materials Project database (MP-ID: mp-3293413, 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_Pr4HoP12Ru19
_symmetry_space_group_name_H-M 'P 1'
_cell_length_a 12.54813521
_cell_length_b 12.54813517
_cell_length_c 4.00632548
_cell_angle_alpha 90.00000000
_cell_angle_beta 90.00000000
_cell_angle_gamma 120.00000008
_symmetry_Int_Tables_number 1
_chemical_formula_structural Pr4HoP12Ru19
_chemical_formula_sum 'Pr4 Ho1 P12 Ru19'
_cell_volume 546.30507885
_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
Pr Pr0 1 0.99896673 0.18356695 0.50000000 1.0
Pr Pr1 1 0.81643305 0.81539978 0.50000000 1.0
Pr Pr2 1 0.18460022 0.00103327 0.50000000 1.0
Pr Pr3 1 0.66666700 0.33333300 0.00000000 1.0
Ho Ho4 1 0.33333300 0.66666700 0.00000000 1.0
P P5 1 0.00232358 0.81208882 0.00000000 1.0
P P6 1 0.18791118 0.19023577 0.00000000 1.0
P P7 1 0.80976423 0.99767642 0.00000000 1.0
P P8 1 0.69496388 0.16958494 0.50000000 1.0
P P9 1 0.83041506 0.52537894 0.50000000 1.0
P P10 1 0.47462106 0.30503612 0.50000000 1.0
P P11 1 0.17623001 0.69723821 0.50000000 1.0
P P12 1 0.52100920 0.82376999 0.50000000 1.0
P P13 1 0.30276179 0.47899080 0.50000000 1.0
P P14 1 0.99884554 0.37482656 0.00000000 1.0
P P15 1 0.62517344 0.62401898 0.00000000 1.0
P P16 1 0.37598102 0.00115446 0.00000000 1.0
Ru Ru17 1 0.00000609 0.55433179 0.00000000 1.0
Ru Ru18 1 0.44566821 0.44567430 0.00000000 1.0
Ru Ru19 1 0.55432570 0.99999391 0.00000000 1.0
Ru Ru20 1 0.00293415 0.71488536 0.50000000 1.0
Ru Ru21 1 0.28511464 0.28804879 0.50000000 1.0
Ru Ru22 1 0.71195121 0.99706585 0.50000000 1.0
Ru Ru23 1 0.80463929 0.18296264 0.00000000 1.0
Ru Ru24 1 0.81703736 0.62167664 0.00000000 1.0
Ru Ru25 1 0.37832336 0.19536071 0.00000000 1.0
Ru Ru26 1 0.18766743 0.80508600 0.00000000 1.0
Ru Ru27 1 0.61741857 0.81233257 0.00000000 1.0
Ru Ru28 1 0.19491400 0.38258143 0.00000000 1.0
Ru Ru29 1 0.87612401 0.36695875 0.50000000 1.0
Ru Ru30 1 0.63304125 0.50916526 0.50000000 1.0
Ru Ru31 1 0.49083474 0.12387599 0.50000000 1.0
Ru Ru32 1 0.36973518 0.87369013 0.50000000 1.0
Ru Ru33 1 0.50395495 0.63026482 0.50000000 1.0
Ru Ru34 1 0.12630987 0.49604505 0.50000000 1.0
Ru Ru35 1 0.00000000 0.00000000 0.00000000 1.0
