Three new crystal structures in the Na–Pb system: solving structures without additional experimental input

The structures of three Na–Pb compounds, γ, δ and δ′, have remained incompletely solved for nearly 60 years. The space group, lattice parameters and positions of the Pb atoms of these three structures have been determined, but the positions of the Na atoms are still unknown. In this work, the First-Principles Assisted Structure Solution (FPASS) method [Meredig & Wolverton (2013). Nat. Mater. 12, 123–127] has been used to complete the description of these three structures using only experimental information available from the literature as input. The paper also discusses the relative advantages of constrained crystal structure prediction tools, like FPASS, in comparison to conventional crystal structure prediction methods in reference to their abilities to complete the solution of other unsolved structures.

Computing details

Figures

(delta-prime)

Crystal data

Na9Pb4	V = ? Å^3
Mr = ?	Z = 2
Hexagonal, ?	? radiation, λ = ? Å
a = 5.4700 Å	× × mm
c = 30.4100 Å

Data collection

h = ?→?	l = ?→?
k = ?→?

Refinement

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Biso*/Beq
Pb1	0.0000	0.0000	0.0500
Pb2	0.3333	0.6667	0.3000
Na1	0.3333	0.6667	0.7500
Na2	0.3333	0.6667	0.6357
Na3	0.0000	0.0000	0.3166
Na4	0.3333	0.6667	0.4087
Na5	0.3333	0.6667	0.5198

(delta)

Crystal data

Na5Pb2	V = ? Å^3
Mr = ?	Z = 3
Hexagonal, ?	? radiation, λ = ? Å
a = 5.5400 Å	× × mm
c = 23.1500 Å

Data collection

h = ?→?	l = ?→?
k = ?→?

Refinement

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Biso*/Beq
Pb1	0.0000	0.0000	0.0700
Na1	0.3333	0.6667	0.3097
Na2	0.0000	0.0000	0.2150
Na3	0.0000	0.0000	0.5000

(gamma)

Crystal data

Na13Pb5	V = ? Å^3
Mr = ?	Z = 2
Hexagonal, ?	? radiation, λ = ? Å
a = 5.5100 Å	× × mm
c = 40.3900 Å

Data collection

h = ?→?	l = ?→?
k = ?→?

Refinement

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Biso*/Beq
Pb1	0.0000	0.0000	0.2500
Pb2	0.3333	0.6667	0.4500
Pb3	0.3333	0.6667	0.3700
Na1	0.0000	0.0000	0.0000
Na2	0.3333	0.6667	0.2883
Na3	0.0000	0.0000	0.4167
Na4	0.3333	0.6667	0.8826
Na5	0.0000	0.0000	0.1666
Na6	0.3333	0.6667	0.7897
Na7	0.3333	0.6667	0.5316