Pr3Cu4(P2O)2

High-Entropy Materials HEA

MP-ID: mp-3293946 · Space group: I4/mmm (#139)

Materials Project API

Basic Information

Formula

Pr3Cu4(P2O)2

MP-ID

mp-3293946

Elements

Sites

Density

6.4466

g/cm³

Volume

214.52

Å³

Cell a

4.0168

Cell b

4.0168

Cell c

13.5954

α Angle

98.50

β Angle

98.50

γ Angle

90.00

Space Group

I4/mmm

Point Group

4/mmm

Crystal System

Tetragonal

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
6.65	13.2954	2.8	(0,0,1)
13.32	6.6477	5.7	(0,0,2)
20.04	4.4318	3.0	(0,0,3)
22.38	3.9717	2.5	(1,0,-1)
24.33	3.6586	80.6	(1,0,-2)
27.83	3.2053	28.0	(1,0,-3)
31.50	2.8403	17.8	(1,-1,0)
32.23	2.7776	7.1	(1,-1,1)
32.23	2.7776	2.4	(1,1,0)
32.44	2.7600	66.5	(1,0,-4)
32.44	2.7600	66.5	(1,0,3)
33.71	2.6591	38.6	(0,0,5)
34.33	2.6119	77.7	(1,1,-3)
37.61	2.3913	100.0	(1,1,-4)
43.70	2.0712	2.3	(1,0,-6)
43.70	2.0712	2.3	(1,0,5)
45.14	2.0084	84.6	(2,0,-1)
46.80	1.9412	1.1	(1,1,-6)
46.80	1.9412	1.1	(1,-1,-5)
47.89	1.8993	1.9	(0,0,7)
50.04	1.8227	12.2	(1,0,-7)
50.04	1.8227	12.2	(1,0,6)
51.94	1.7606	2.8	(2,-1,-2)
51.94	1.7606	19.4	(1,-2,2)

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Energy Properties

Formation Energy/atom

-1.49055

eV/atom

Energy/atom

-15.30227

eV/atom

Energy above Hull

0.0000

eV/atom

Uncorrected Energy

-15.3023

eV/atom

Volume/atom

16.50

Å³

c/a Ratio

3.3846

Electronic Properties

Metallic

Metal

Band Gap

Direct Gap

CBM

N/A

Magnetic Properties

Magnetic

Total Mag. Moment

0.0001

μB

Mag. Ordering

Mag. Sites

Magnetization/Volume

0.000000

μB/Å³

Elastic Properties

Elastic data not available

Feature Analysis

Composition Overview

Element Composition (atomic fraction)

Composition Info

Major / Matrix Element

Cu · 0.308

Element Family

3d-TM

Solute Fraction

0.692

Interstitial Fraction

0.308

High-Entropy Alloy Features

Composite Radar (normalized)

Element-Class Share

Mix Entropy ΔS/R

1.3517

HEA criterion (>1.0 = high entropy)

Mix Entropy ΔS

11.2379

J/mol·K

Ω Parameter

1.7014

Ω > 1.1 favors solid solution

Atomic Size Mismatch δr

31.485%

δr < 6.6% favors single-phase solid solution

Electronegativity Diff Δχ

0.7110

smaller = more stable mixing

VEC

6.231

valence electron concentration, affects phase stability

Mix Enthalpy ΔH_mix

-5.302

kJ/mol; negative = exothermic mixing

Entropy Norm

0.9750

SS Former

Phase Tendency

Related Tasks

Related computation task IDs (1)

aaahfksg

Citation & References

Materials Project Page

https://materialsproject.org/materials/mp-3293946

Reference Citation

The crystal structure and related material properties of Pr3Cu4(P2O)2 were obtained from the Materials Project database (MP-ID: mp-3293946, 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_Pr3Cu4(P2O)2
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   4.01679639
_cell_length_b   4.01679634
_cell_length_c   13.59535767
_cell_angle_alpha   98.49522092
_cell_angle_beta   98.49522035
_cell_angle_gamma   90.00000527
_symmetry_Int_Tables_number   1
_chemical_formula_structural   Pr3Cu4(P2O)2
_chemical_formula_sum   'Pr3 Cu4 P4 O2'
_cell_volume   214.51590500
_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  0.00000000  0.00000000  0.00000000  1.0
  Pr  Pr1  1  0.70419672  0.70419672  0.40839244  1.0
  Pr  Pr2  1  0.29580328  0.29580328  0.59160756  1.0
  Cu  Cu3  1  0.59359981  0.09359981  0.18719861  1.0
  Cu  Cu4  1  0.09359981  0.59359981  0.18719861  1.0
  Cu  Cu5  1  0.90640119  0.40640019  0.81280139  1.0
  Cu  Cu6  1  0.40640019  0.90640119  0.81280139  1.0
  P  P7  1  0.54193499  0.54193499  0.08386797  1.0
  P  P8  1  0.13807205  0.13807205  0.27614409  1.0
  P  P9  1  0.86192895  0.86192895  0.72385491  1.0
  P  P10  1  0.45806601  0.45806601  0.91613303  1.0
  O  O11  1  0.75000100  0.25000000  0.50000000  1.0
  O  O12  1  0.25000000  0.75000100  0.50000000  1.0

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