MnCr3(PO4)6

High-Entropy Materials HEA

MP-ID: mp-774419 · Space group: R3 (#146)

Materials Project API

Basic Information

Formula

MnCr3(PO4)6

MP-ID

mp-774419

Elements

Sites

Density

2.8528

g/cm³

Volume

454.46

Å³

Cell a

8.7447

Cell b

8.7447

Cell c

8.7447

α Angle

58.30

β Angle

58.30

γ Angle

58.30

Space Group

Point Group

Crystal System

Trigonal

Bravais Lattice

Stability

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
14.52	6.1002	42.0	(1,1,0)
20.32	4.3694	56.4	(2,1,1)
20.85	4.2597	26.8	(1,0,-1)
24.25	3.6701	100.0	(2,1,0)
24.63	3.6151	4.6	(2,2,2)
29.28	3.0501	46.8	(2,2,0)
32.37	2.7658	15.4	(2,0,-1)
32.48	2.7563	31.4	(3,2,1)
36.22	2.4799	5.9	(3,1,0)
36.22	2.4799	3.0	(3,0,1)
36.54	2.4593	12.7	(2,-1,-1)
43.13	2.0976	5.9	(4,3,2)
43.67	2.0728	2.2	(4,2,1)
44.34	2.0430	3.7	(3,1,-1)
44.56	2.0334	1.5	(4,1,1)
45.09	2.0108	2.5	(3,0,-1)
46.73	1.9440	11.3	(4,3,1)
47.49	1.9145	7.7	(3,2,-1)
48.70	1.8698	3.5	(4,4,2)
49.68	1.8350	3.9	(2,0,4)
49.68	1.8350	7.8	(4,2,0)
50.17	1.8184	1.6	(2,2,-2)
50.17	1.8184	3.2	(2,-2,2)
50.49	1.8076	1.9	(4,4,4)

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Energy Properties

Formation Energy/atom

-2.28883

eV/atom

Energy/atom

-7.85839

eV/atom

Energy above Hull

0.0617

eV/atom

Uncorrected Energy

-7.1480

eV/atom

Volume/atom

13.37

Å³

c/a Ratio

1.0000

Electronic Properties

Metallic

Metal

Band Gap

Direct Gap

CBM

N/A

Magnetic Properties

Magnetic

Yes

Total Mag. Moment

6.9991

μB

Mag. Ordering

Mag. Sites

Magnetization/Volume

0.015400

μB/Å³

Elastic Properties

Elastic data not available

Feature Analysis

Composition Overview

Element Composition (atomic fraction)

Composition Info

Major / Matrix Element

O · 0.706

Element Family

Metalloid-Nonmetal

Solute Fraction

0.294

Interstitial Fraction

0.176

High-Entropy Alloy Features

Composite Radar (normalized)

Element-Class Share

Mix Entropy ΔS/R

0.8699

HEA criterion (>1.0 = high entropy)

Mix Entropy ΔS

7.2323

J/mol·K

Ω Parameter

3.9000

Ω > 1.1 favors solid solution

Atomic Size Mismatch δr

34.432%

δr < 6.6% favors single-phase solid solution

Electronegativity Diff Δχ

0.6875

smaller = more stable mixing

VEC

4.441

valence electron concentration, affects phase stability

Mix Enthalpy ΔH_mix

-0.615

kJ/mol; negative = exothermic mixing

Entropy Norm

0.6275

SS Former

Phase Tendency

Related Tasks

Related computation task IDs (2)

aaabzixe aaadzoqi

Citation & References

Materials Project Page

https://materialsproject.org/materials/mp-774419

Reference Citation

The crystal structure and related material properties of MnCr3(PO4)6 were obtained from the Materials Project database (MP-ID: mp-774419, 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_MnCr3(PO4)6
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   8.74469218
_cell_length_b   8.74469218
_cell_length_c   8.74469277
_cell_angle_alpha   58.30199064
_cell_angle_beta   58.30199064
_cell_angle_gamma   58.30198818
_symmetry_Int_Tables_number   1
_chemical_formula_structural   MnCr3(PO4)6
_chemical_formula_sum   'Mn1 Cr3 P6 O24'
_cell_volume   454.45761419
_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
  Mn  Mn0  1  0.85567000  0.85567000  0.85567000  1.0
  Cr  Cr1  1  0.14282800  0.14282800  0.14282800  1.0
  Cr  Cr2  1  0.35708300  0.35708300  0.35708300  1.0
  Cr  Cr3  1  0.64213600  0.64213600  0.64213600  1.0
  P  P4  1  0.03287500  0.46784400  0.75019400  1.0
  P  P5  1  0.46784400  0.75019400  0.03287500  1.0
  P  P6  1  0.75019400  0.03287500  0.46784400  1.0
  P  P7  1  0.24713800  0.96569600  0.53603600  1.0
  P  P8  1  0.53603600  0.24713800  0.96569600  1.0
  P  P9  1  0.96569600  0.53603600  0.24713800  1.0
  O  O10  1  0.13631400  0.50888800  0.27899000  1.0
  O  O11  1  0.27899000  0.13631400  0.50888800  1.0
  O  O12  1  0.06174500  0.28223600  0.92346300  1.0
  O  O13  1  0.50888800  0.27899000  0.13631400  1.0
  O  O14  1  0.21771700  0.43754500  0.57743700  1.0
  O  O15  1  0.01139600  0.64055400  0.77479600  1.0
  O  O16  1  0.28223600  0.92346300  0.06174500  1.0
  O  O17  1  0.43754500  0.57743700  0.21771700  1.0
  O  O18  1  0.57743700  0.21771700  0.43754500  1.0
  O  O19  1  0.21950500  0.99100800  0.36371600  1.0
  O  O20  1  0.07303700  0.94080200  0.72053400  1.0
  O  O21  1  0.36371600  0.21950500  0.99100800  1.0
  O  O22  1  0.64055400  0.77479600  0.01139600  1.0
  O  O23  1  0.92346300  0.06174500  0.28223600  1.0
  O  O24  1  0.77479600  0.01139600  0.64055400  1.0
  O  O25  1  0.42231000  0.78180400  0.56304800  1.0
  O  O26  1  0.56304800  0.42231000  0.78180400  1.0
  O  O27  1  0.72053400  0.07303700  0.94080200  1.0
  O  O28  1  0.99100800  0.36371600  0.21950500  1.0
  O  O29  1  0.78180400  0.56304800  0.42231000  1.0
  O  O30  1  0.49224900  0.72168600  0.86172000  1.0
  O  O31  1  0.94080200  0.72053400  0.07303700  1.0
  O  O32  1  0.72168600  0.86172000  0.49224900  1.0
  O  O33  1  0.86172000  0.49224900  0.72168600  1.0

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