New insights on the GeSe_xTe_1−x phase diagram from theory and experiment

The high-pressure and low-temperature behaviour of the GeSe_xTe_1−x system (x = 0, 0.2, 0.5, 0.75, 1) was studied using a combination of powder diffraction measurements and first-principles calculations. Compounds in the stability field of the GeTe structure type (x = 0, 0.2, 0.5) follow the high-pressure transition pathway: GeTe-I (R3m) → GeTe-II (f.c.c.) → GeTe-III (Pnma). The newly determined GeTe-III structure is isostructural to β-GeSe, a high-pressure and high-temperature polymorph of GeSe. Pressure-dependent formation enthalpies and stability regimes of the GeSe_xTe_1−x polymorphs were studied by DFT calculations. Hexagonal Ge₄Se₃Te is stable up to at least 25 GPa. Significant differences in the high-pressure and low-temperature behaviour of the GeTe-type structures and the hexagonal phase are highlighted. The role of Ge...Ge interactions is elucidated using the crystal orbital Hamilton population method. Finally, a sketch of the high-pressure phase diagram of the system is provided.

Computing details

Data collection: software available at beamline; cell refinement: Crysalis; data reduction: Crysalis and Jana2006; program(s) used to solve structure: Sir2014; program(s) used to refine structure: Jana2006; molecular graphics: Vesta.

(I)

Crystal data

GeTe	F(000) = 336
Mr = 200.2	High Pressure data: 18.8 GPa
Orthorhombic, Pnma	Dx = 8.068 Mg m^−3
Hall symbol: -P -2xa bc;-2yb;-2zac	Synchrotron radiation, λ = 0.2905 Å
a = 7.3690 (18) Å	Cell parameters from 94 reflections
b = 3.9249 (10) Å	θ = 2.6–13.7°
c = 5.698 (9) Å	µ = 10.39 mm^−1
V = 164.8 (3) Å^3	T = 293 K
Z = 4	, black

Data collection

Extreme Conditions Beamline 02.2, PETRA III diffractometer	Rint = 0.040
Graphite monochromator	θmax = 13.9°, θmin = 2.6°
ω scan	h = −1→3
135 measured reflections	k = −6→6
86 independent reflections	l = −9→8
84 reflections with I > 3σ(I)

Refinement

Refinement on F	0 restraints
R[F^2 > 2σ(F^2)] = 0.047	0 constraints
wR(F^2) = 0.054	Weighting scheme based on measured s.u.'s w = 1/(σ^2(F) + 0.0001F^2)
S = 2.39	(Δ/σ)max = 0.001
86 reflections	Δρmax = 2.11 e Å^−3
13 parameters	Δρmin = −1.60 e Å^−3

Special details

Refinement. High pressure data (18.8 GPa)

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

	x	y	z	Uiso*/Ueq
Ge1	0.0703 (13)	0.25	0.8267 (4)	0.025 (8)
Te1	0.1716 (5)	0.25	0.37428 (19)	0.019 (3)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Ge1	0.04 (3)	0.0167 (9)	0.0194 (17)	0	0.005 (2)	0
Te1	0.035 (10)	0.0093 (6)	0.0117 (9)	0	−0.0009 (7)	0

Geometric parameters (Å, º)

Ge1—Ge1^i	3.925 (2)	Ge1—Te1^v	3.396 (10)
Ge1—Ge1^ii	3.925 (2)	Te1—Te1^i	3.925 (2)
Ge1—Ge1^iii	2.971 (7)	Te1—Te1^ii	3.925 (2)
Ge1—Ge1^iv	2.971 (7)	Te1—Te1^xii	3.647 (7)
Ge1—Ge1^v	3.787 (14)	Te1—Te1^viii	3.647 (7)
Ge1—Ge1^vi	3.787 (14)	Te1—Te1^xiii	3.647 (7)
Ge1—Te1	2.684 (9)	Te1—Te1^ix	3.647 (7)
Ge1—Te1^vii	3.208 (10)	Te1—Te1^x	3.507 (5)
Ge1—Te1^viii	2.746 (7)	Te1—Te1^xi	3.507 (5)
Ge1—Te1^ix	2.746 (7)	Te1—Te1^xiv	3.947 (6)
Ge1—Te1^x	2.888 (7)	Te1—Te1^xv	3.947 (6)
Ge1—Te1^xi	2.888 (7)
Ge1^iii—Ge1—Ge1^iv	82.69 (17)	Te1^viii—Ge1—Te1^x	88.91 (8)
Ge1^iii—Ge1—Te1	137.36 (7)	Te1^viii—Ge1—Te1^xi	162.22 (14)
Ge1^iii—Ge1—Te1^viii	72.78 (17)	Te1^ix—Ge1—Te1^x	162.22 (14)
Ge1^iii—Ge1—Te1^ix	130.4 (2)	Te1^ix—Ge1—Te1^xi	88.91 (8)
Ge1^iii—Ge1—Te1^x	66.38 (18)	Te1^x—Ge1—Te1^xi	85.6 (2)
Ge1^iii—Ge1—Te1^xi	119.8 (4)	Ge1—Te1—Ge1^xii	106.70 (15)
Ge1^iv—Ge1—Te1	137.36 (7)	Ge1—Te1—Ge1^xiii	106.70 (15)
Ge1^iv—Ge1—Te1^viii	130.4 (2)	Ge1—Te1—Ge1^x	102.1 (2)
Ge1^iv—Ge1—Te1^ix	72.78 (17)	Ge1—Te1—Ge1^xi	102.1 (2)
Ge1^iv—Ge1—Te1^x	119.8 (4)	Ge1^xii—Te1—Ge1^xiii	91.2 (2)
Ge1^iv—Ge1—Te1^xi	66.38 (18)	Ge1^xii—Te1—Ge1^x	84.4 (2)
Te1—Ge1—Te1^viii	84.4 (2)	Ge1^xii—Te1—Ge1^xi	150.92 (11)
Te1—Ge1—Te1^ix	84.4 (2)	Ge1^xiii—Te1—Ge1^x	150.92 (11)
Te1—Ge1—Te1^x	77.93 (12)	Ge1^xiii—Te1—Ge1^xi	84.4 (2)
Te1—Ge1—Te1^xi	77.93 (12)	Ge1^x—Te1—Ge1^xi	85.60 (19)
Te1^viii—Ge1—Te1^ix	91.2 (3)

Symmetry codes: (i) x, y−1, z; (ii) x, y+1, z; (iii) −x, y−1/2, −z+2; (iv) −x, y+1/2, −z+2; (v) x−1/2, −y+1/2, −z+3/2; (vi) x+1/2, −y+1/2, −z+3/2; (vii) x, y, z+1; (viii) −x+1/2, −y, z+1/2; (ix) −x+1/2, −y+1, z+1/2; (x) −x, y−1/2, −z+1; (xi) −x, y+1/2, −z+1; (xii) −x+1/2, −y, z−1/2; (xiii) −x+1/2, −y+1, z−1/2; (xiv) x−1/2, −y+1/2, −z+1/2; (xv) x+1/2, −y+1/2, −z+1/2.