Na2Ti3Cr(PO4)6

High-Entropy Materials HEA

MP-ID: mp-772553 · Space group: R3 (#146)

Materials Project API

Basic Information

Formula

Na2Ti3Cr(PO4)6

MP-ID

mp-772553

Elements

Sites

Density

2.8854

g/cm³

Volume

466.96

Å³

Cell a

8.9115

Cell b

8.9115

Cell c

8.9115

α Angle

57.10

β Angle

57.10

γ Angle

57.10

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
14.40	6.1517	17.4	(1,1,0)
19.97	4.4471	24.8	(2,1,1)
20.86	4.2589	34.9	(1,0,-1)
23.95	3.7159	2.6	(2,2,2)
24.08	3.6952	100.0	(2,1,0)
25.44	3.5016	3.3	(2,0,0)
29.03	3.0759	25.5	(2,2,0)
31.96	2.8000	51.1	(3,2,1)
32.36	2.7666	14.4	(2,0,-1)
33.12	2.7048	2.0	(2,1,-1)
36.02	2.4936	2.8	(3,1,0)
36.54	2.4589	15.9	(2,-1,-1)
38.57	2.3344	3.1	(2,2,-1)
40.57	2.2235	2.5	(4,2,2)
42.20	2.1414	6.1	(4,3,2)
43.12	2.0979	2.6	(4,2,1)
44.17	2.0506	3.6	(3,3,0)
44.25	2.0471	2.6	(3,1,-1)
46.05	1.9711	12.5	(4,3,1)
47.33	1.9206	2.7	(3,2,-1)
47.66	1.9080	1.9	(4,4,2)
49.03	1.8579	3.3	(4,4,4)
49.32	1.8476	16.9	(4,2,0)
50.14	1.8194	2.6	(2,2,-2)

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Energy Properties

Formation Energy/atom

-2.86963

eV/atom

Energy/atom

-8.07148

eV/atom

Energy above Hull

0.0168

eV/atom

Uncorrected Energy

-7.5580

eV/atom

Volume/atom

12.97

Å³

c/a Ratio

1.0000

Electronic Properties

Metallic

Metal

Band Gap

Direct Gap

CBM

N/A

Magnetic Properties

Magnetic

Yes

Total Mag. Moment

2.0009

μB

Mag. Ordering

Mag. Sites

Magnetization/Volume

0.004280

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

0.0570

Ω > 1.1 favors solid solution

Atomic Size Mismatch δr

45.218%

δr < 6.6% favors single-phase solid solution

Electronegativity Diff Δχ

0.8310

smaller = more stable mixing

VEC

4.056

valence electron concentration, affects phase stability

Mix Enthalpy ΔH_mix

-50.240

kJ/mol; negative = exothermic mixing

Entropy Norm

0.6438

SS Former

Phase Tendency

Related Tasks

Related computation task IDs (2)

aaabzikc aaadzltj

Citation & References

Materials Project Page

https://materialsproject.org/materials/mp-772553

Reference Citation

The crystal structure and related material properties of Na2Ti3Cr(PO4)6 were obtained from the Materials Project database (MP-ID: mp-772553, 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_Na2Ti3Cr(PO4)6
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   8.91152987
_cell_length_b   8.91152987
_cell_length_c   8.91152986
_cell_angle_alpha   57.09796295
_cell_angle_beta   57.09796295
_cell_angle_gamma   57.09796094
_symmetry_Int_Tables_number   1
_chemical_formula_structural   Na2Ti3Cr(PO4)6
_chemical_formula_sum   'Na2 Ti3 Cr1 P6 O24'
_cell_volume   466.95871237
_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
  Na  Na0  1  0.99873600  0.99873600  0.99873600  1.0
  Na  Na1  1  0.49983000  0.49983000  0.49983000  1.0
  Ti  Ti2  1  0.64713000  0.64713000  0.64713000  1.0
  Ti  Ti3  1  0.35299700  0.35299700  0.35299700  1.0
  Ti  Ti4  1  0.14398400  0.14398400  0.14398400  1.0
  Cr  Cr5  1  0.85574300  0.85574300  0.85574300  1.0
  P  P6  1  0.96538500  0.24623100  0.53820600  1.0
  P  P7  1  0.46325300  0.03536000  0.75102200  1.0
  P  P8  1  0.75102200  0.46325300  0.03536000  1.0
  P  P9  1  0.24623100  0.53820600  0.96538500  1.0
  P  P10  1  0.53820600  0.96538500  0.24623100  1.0
  P  P11  1  0.03536000  0.75102200  0.46325300  1.0
  O  O12  1  0.00040700  0.19836500  0.37726000  1.0
  O  O13  1  0.90916100  0.09497700  0.73648300  1.0
  O  O14  1  0.90411700  0.26624200  0.09317100  1.0
  O  O15  1  0.51140900  0.14928900  0.25175500  1.0
  O  O16  1  0.79883500  0.44024400  0.53641800  1.0
  O  O17  1  0.46692000  0.19952200  0.55484500  1.0
  O  O18  1  0.74616000  0.48846300  0.85141200  1.0
  O  O19  1  0.00849100  0.79787600  0.62030000  1.0
  O  O20  1  0.79787600  0.62030000  0.00849100  1.0
  O  O21  1  0.26624200  0.09317100  0.90411700  1.0
  O  O22  1  0.85141200  0.74616000  0.48846300  1.0
  O  O23  1  0.55484500  0.46692000  0.19952200  1.0
  O  O24  1  0.44024400  0.53641800  0.79883500  1.0
  O  O25  1  0.14928900  0.25175500  0.51140900  1.0
  O  O26  1  0.73648300  0.90916100  0.09497700  1.0
  O  O27  1  0.19836500  0.37726000  0.00040700  1.0
  O  O28  1  0.25175500  0.51140900  0.14928900  1.0
  O  O29  1  0.53641800  0.79883500  0.44024400  1.0
  O  O30  1  0.19952200  0.55484500  0.46692000  1.0
  O  O31  1  0.48846300  0.85141200  0.74616000  1.0
  O  O32  1  0.62030000  0.00849100  0.79787600  1.0
  O  O33  1  0.37726000  0.00040700  0.19836500  1.0
  O  O34  1  0.09497700  0.73648300  0.90916100  1.0
  O  O35  1  0.09317100  0.90411700  0.26624200  1.0

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