Ti3Cr2Co(PO4)6

High-Entropy Materials HEA

MP-ID: mp-775780 · Space group: R3 (#146)

Materials Project API

Basic Information

Formula

Ti3Cr2Co(PO4)6

MP-ID

mp-775780

Elements

Sites

Density

3.1879

g/cm³

Volume

456.48

Å³

Cell a

8.6468

Cell b

8.6468

Cell c

8.6468

α Angle

59.94

β Angle

59.94

γ Angle

59.94

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
20.54	4.3234	7.7	(2,1,1)
20.56	4.3192	67.9	(1,0,-1)
24.15	3.6849	100.0	(2,1,0)
25.25	3.5272	13.7	(2,0,0)
29.23	3.0556	9.3	(2,2,0)
31.93	2.8027	15.5	(2,0,-1)
32.76	2.7341	43.6	(3,1,2)
32.76	2.7341	21.8	(3,2,1)
32.78	2.7320	1.6	(2,-1,1)
32.78	2.7320	3.2	(2,1,-1)
36.00	2.4945	1.2	(3,1,0)
36.02	2.4937	29.9	(2,-1,-1)
41.79	2.1617	6.1	(4,2,2)
43.79	2.0673	1.7	(3,2,4)
43.79	2.0673	3.4	(4,3,2)
43.81	2.0664	1.7	(4,2,1)
43.84	2.0652	3.0	(3,1,-1)
44.47	2.0371	4.7	(3,3,0)
47.01	1.9331	24.9	(4,3,1)
48.87	1.8635	3.7	(4,1,0)
49.47	1.8425	16.0	(4,0,2)
49.47	1.8425	8.0	(4,2,0)
49.49	1.8418	1.3	(2,-2,2)
51.77	1.7659	4.5	(4,4,4)

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Energy Properties

Formation Energy/atom

-2.72073

eV/atom

Energy/atom

-8.31434

eV/atom

Energy above Hull

0.0826

eV/atom

Uncorrected Energy

-7.6998

eV/atom

Volume/atom

12.68

Å³

c/a Ratio

1.0000

Electronic Properties

Metallic

Metal

Band Gap

Direct Gap

CBM

N/A

Magnetic Properties

Magnetic

Yes

Total Mag. Moment

11.3063

μB

Mag. Ordering

Mag. Sites

Magnetization/Volume

0.024770

μB/Å³

Elastic Properties

Elastic data not available

Feature Analysis

Composition Overview

Element Composition (atomic fraction)

Composition Info

Major / Matrix Element

O · 0.667

Element Family

Metalloid-Nonmetal

Solute Fraction

0.333

Interstitial Fraction

0.167

High-Entropy Alloy Features

Composite Radar (normalized)

Element-Class Share

Mix Entropy ΔS/R

1.0361

HEA criterion (>1.0 = high entropy)

Mix Entropy ΔS

8.6144

J/mol·K

Ω Parameter

0.0772

Ω > 1.1 favors solid solution

Atomic Size Mismatch δr

38.443%

δr < 6.6% favors single-phase solid solution

Electronegativity Diff Δχ

0.7389

smaller = more stable mixing

VEC

4.417

valence electron concentration, affects phase stability

Mix Enthalpy ΔH_mix

-46.996

kJ/mol; negative = exothermic mixing

Entropy Norm

0.6438

SS Former

Phase Tendency

Related Tasks

Related computation task IDs (1)

aaaczgng

Citation & References

Materials Project Page

https://materialsproject.org/materials/mp-775780

Reference Citation

The crystal structure and related material properties of Ti3Cr2Co(PO4)6 were obtained from the Materials Project database (MP-ID: mp-775780, 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_Ti3Cr2Co(PO4)6
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   8.64684145
_cell_length_b   8.64684145
_cell_length_c   8.64684170
_cell_angle_alpha   59.93554135
_cell_angle_beta   59.93554135
_cell_angle_gamma   59.93554490
_symmetry_Int_Tables_number   1
_chemical_formula_structural   Ti3Cr2Co(PO4)6
_chemical_formula_sum   'Ti3 Cr2 Co1 P6 O24'
_cell_volume   456.48036100
_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
  Ti  Ti0  1  0.14433900  0.14433900  0.14433900  1.0
  Ti  Ti1  1  0.35487100  0.35487100  0.35487100  1.0
  Ti  Ti2  1  0.64595400  0.64595400  0.64595400  1.0
  Cr  Cr3  1  0.99714500  0.99714500  0.99714500  1.0
  Cr  Cr4  1  0.49945200  0.49945200  0.49945200  1.0
  Co  Co5  1  0.85511800  0.85511800  0.85511800  1.0
  P  P6  1  0.45789700  0.75159200  0.04331600  1.0
  P  P7  1  0.75159200  0.04331600  0.45789700  1.0
  P  P8  1  0.95727500  0.54346700  0.25026100  1.0
  P  P9  1  0.25026100  0.95727500  0.54346700  1.0
  P  P10  1  0.54346700  0.25026100  0.95727500  1.0
  P  P11  1  0.04331600  0.45789700  0.75159200  1.0
  O  O12  1  0.49373400  0.31287800  0.12016300  1.0
  O  O13  1  0.12016300  0.49373400  0.31287800  1.0
  O  O14  1  0.26072900  0.91498500  0.05801800  1.0
  O  O15  1  0.31287800  0.12016300  0.49373400  1.0
  O  O16  1  0.61274300  0.80659800  0.01282500  1.0
  O  O17  1  0.43428200  0.58378800  0.23500300  1.0
  O  O18  1  0.91498500  0.05801800  0.26072900  1.0
  O  O19  1  0.58378800  0.23500300  0.43428200  1.0
  O  O20  1  0.00023500  0.37764800  0.19421000  1.0
  O  O21  1  0.23500300  0.43428200  0.58378800  1.0
  O  O22  1  0.94685600  0.73435100  0.08908900  1.0
  O  O23  1  0.19421000  0.00023500  0.37764800  1.0
  O  O24  1  0.80659800  0.01282500  0.61274300  1.0
  O  O25  1  0.05801800  0.26072900  0.91498500  1.0
  O  O26  1  0.76623500  0.55466300  0.41817700  1.0
  O  O27  1  0.01282500  0.61274300  0.80659800  1.0
  O  O28  1  0.41817700  0.76623500  0.55466300  1.0
  O  O29  1  0.08908900  0.94685600  0.73435100  1.0
  O  O30  1  0.55466300  0.41817700  0.76623500  1.0
  O  O31  1  0.37764800  0.19421000  0.00023500  1.0
  O  O32  1  0.69477300  0.87758300  0.49974900  1.0
  O  O33  1  0.73435100  0.08908900  0.94685600  1.0
  O  O34  1  0.87758300  0.49974900  0.69477300  1.0
  O  O35  1  0.49974900  0.69477300  0.87758300  1.0

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