TiCr2Ni3(PO4)6

High-Entropy Materials HEA

MP-ID: mp-776057 · Space group: R3 (#146)

Materials Project API

Basic Information

Formula

TiCr2Ni3(PO4)6

MP-ID

mp-776057

Elements

Sites

Density

3.4113

g/cm³

Volume

437.02

Å³

Cell a

8.4004

Cell b

8.4004

Cell c

8.4004

α Angle

61.90

β Angle

61.90

γ Angle

61.90

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
14.71	6.0206	2.4	(1,1,0)
20.56	4.3204	28.2	(1,-1,0)
20.56	4.3204	56.4	(1,0,-1)
21.17	4.1967	13.4	(2,1,1)
24.45	3.6402	100.0	(2,1,0)
25.37	3.5102	14.3	(2,0,0)
29.68	3.0103	7.6	(2,2,0)
31.95	2.8013	13.6	(2,0,-1)
32.88	2.7244	2.1	(2,-1,1)
32.88	2.7244	1.0	(2,1,-1)
33.67	2.6618	65.5	(3,2,1)
36.01	2.4944	28.5	(2,-1,-1)
36.01	2.4944	14.2	(1,1,-2)
36.37	2.4699	7.9	(3,1,0)
38.82	2.3198	1.9	(3,0,2)
41.82	2.1602	1.7	(2,0,-2)
43.11	2.0984	10.0	(4,2,2)
44.01	2.0577	1.9	(3,1,-1)
45.18	2.0069	4.7	(3,0,3)
45.40	1.9976	1.3	(3,2,4)
45.40	1.9976	2.6	(4,3,2)
46.40	1.9570	1.3	(4,3,3)
48.21	1.8875	20.2	(4,1,3)
48.21	1.8875	10.1	(4,3,1)

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Energy Properties

Formation Energy/atom

-2.36068

eV/atom

Energy/atom

-7.79918

eV/atom

Energy above Hull

0.0902

eV/atom

Uncorrected Energy

-7.0184

eV/atom

Volume/atom

12.14

Å³

c/a Ratio

1.0000

Electronic Properties

Metallic

Metal

Band Gap

Direct Gap

CBM

N/A

Magnetic Properties

Magnetic

Yes

Total Mag. Moment

13.9998

μB

Mag. Ordering

Mag. Sites

Magnetization/Volume

0.032030

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

0.1991

Ω > 1.1 favors solid solution

Atomic Size Mismatch δr

36.089%

δr < 6.6% favors single-phase solid solution

Electronegativity Diff Δχ

0.7029

smaller = more stable mixing

VEC

4.778

valence electron concentration, affects phase stability

Mix Enthalpy ΔH_mix

-17.673

kJ/mol; negative = exothermic mixing

Entropy Norm

0.6438

SS Former

Phase Tendency

Related Tasks

Related computation task IDs (2)

aaabzkev aaadzjue

Citation & References

Materials Project Page

https://materialsproject.org/materials/mp-776057

Reference Citation

The crystal structure and related material properties of TiCr2Ni3(PO4)6 were obtained from the Materials Project database (MP-ID: mp-776057, 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_TiCr2Ni3(PO4)6
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   8.40034748
_cell_length_b   8.40034748
_cell_length_c   8.40034773
_cell_angle_alpha   61.90362888
_cell_angle_beta   61.90362888
_cell_angle_gamma   61.90363418
_symmetry_Int_Tables_number   1
_chemical_formula_structural   TiCr2Ni3(PO4)6
_chemical_formula_sum   'Ti1 Cr2 Ni3 P6 O24'
_cell_volume   437.01701131
_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  0.85313700  0.85313700  0.85313700  1.0
  Cr  Cr1  1  0.00083500  0.00083500  0.00083500  1.0
  Cr  Cr2  1  0.50188600  0.50188600  0.50188600  1.0
  Ni  Ni3  1  0.14463100  0.14463100  0.14463100  1.0
  Ni  Ni4  1  0.35871200  0.35871200  0.35871200  1.0
  Ni  Ni5  1  0.64311400  0.64311400  0.64311400  1.0
  P  P6  1  0.94877100  0.54852600  0.25160500  1.0
  P  P7  1  0.25160500  0.94877100  0.54852600  1.0
  P  P8  1  0.54852600  0.25160500  0.94877100  1.0
  P  P9  1  0.44894300  0.74754200  0.05021000  1.0
  P  P10  1  0.74754200  0.05021000  0.44894300  1.0
  P  P11  1  0.05021000  0.44894300  0.74754200  1.0
  O  O12  1  0.51310700  0.32502500  0.10214900  1.0
  O  O13  1  0.10214900  0.51310700  0.32502500  1.0
  O  O14  1  0.24969000  0.90413700  0.06065700  1.0
  O  O15  1  0.32502500  0.10214900  0.51310700  1.0
  O  O16  1  0.61131600  0.82695200  0.98854500  1.0
  O  O17  1  0.44342000  0.60103600  0.25237200  1.0
  O  O18  1  0.90413700  0.06065700  0.24969000  1.0
  O  O19  1  0.60103600  0.25237200  0.44342000  1.0
  O  O20  1  0.99686300  0.39765400  0.17387300  1.0
  O  O21  1  0.25237200  0.44342000  0.60103600  1.0
  O  O22  1  0.93440400  0.75433200  0.09250700  1.0
  O  O23  1  0.17387300  0.99686300  0.39765400  1.0
  O  O24  1  0.82695200  0.98854500  0.61131600  1.0
  O  O25  1  0.06065700  0.24969000  0.90413700  1.0
  O  O26  1  0.74540000  0.56830100  0.40083500  1.0
  O  O27  1  0.98854500  0.61131600  0.82695200  1.0
  O  O28  1  0.40083500  0.74540000  0.56830100  1.0
  O  O29  1  0.09250700  0.93440400  0.75433200  1.0
  O  O30  1  0.56830100  0.40083500  0.74540000  1.0
  O  O31  1  0.39765400  0.17387300  0.99686300  1.0
  O  O32  1  0.66548200  0.90250000  0.49153300  1.0
  O  O33  1  0.75433200  0.09250700  0.93440400  1.0
  O  O34  1  0.90250000  0.49153300  0.66548200  1.0
  O  O35  1  0.49153300  0.66548200  0.90250000  1.0

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