Structural phase transitions of HfV₂ at low temperatures

We report a high-resolution synchrotron X-ray powder diffraction study on HfV₂, hafnium divanadium, at low temperatures. In this work we show, for the first time, a complete sequence of structural phase transitions of HfV₂ from cubic (Fd3m) to tetragonal (I4₁/amd) to orthorhombic (Imma) in succession as temperature decreases. Peak splitting and extra diffraction peaks owing to lattice distortion can be clearly distinguished for the low-symmetry phases. The atomic positions and lattice parameters were obtained by Rietveld refinement. The bond lengths and angles of the HfV₂ crystal structure at the low-symmetry phases were correctly determined from the structure refinement. The face-centered cubic (Fd3m) unit cell (Z = 24) transforms to a body-centered tetragonal (I4₁/amd) phase with a 45° rotation relative to the cubic cell and with a reduced number of atoms (Z = 12) in the unit cell at a temperature of T = 112 K. The orthorhombic phase occurs at T = 102 K and it keeps the body-centered symmetry (Imma) and Z = 12 in the unit cell. The refinement results indicate that there may be a small amount of untransformed cubic phase left over in the lower symmetry phases. The abnormal thermal contraction of both tetragonal phase and orthorhombic phase marks the significance of structural change in HfV₂.

Computing details

For all compounds, program(s) used to refine structure: GSAS.

(125K)

Crystal data

Cubic, Fd3m

a = 7.37515 (3) Å

Data collection

2θmin = 8.002°, 2θmax = 48.574°, 2θstep = 0.006°

Refinement

Rp = 0.202	6763 data points
Rwp = 0.274	9 parameters
Rexp = 0.075	(Δ/σ)max = 0.20

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

	x	y	z	Uiso*/Ueq
V	0.0	0.0	0.0	0.0127 (9)*
Hf	0.375	0.375	0.375	0.005*

Bond lengths (Å)

V—V^i	2.6075 (1)	Hf—Hf^iii	3.1935 (1)
V—Hf^ii	3.0576 (1)

Symmetry codes: (i) x+1/4, y+1/4, −z; (ii) −z+1/4, x−1/2, −y+3/4; (iii) x+1/4, y+1/4, −z+1.

(108K)

Crystal data

Tetragonal, I41/amd	c = 7.40141 (12) Å
a = 5.20713 (5) Å

Data collection

2θmin = 8.002°, 2θmax = 60.094°, 2θstep = 0.006°

Refinement

Rp = 0.207	8683 data points
Rwp = 0.266	11 parameters
Rexp = 0.072	(Δ/σ)max = 0.05

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

	x	y	z	Uiso*/Ueq
V	0.0	0.0	0.0	0.0097 (7)*
Hf	0.0	0.25	0.375	0.005*

Bond lengths (Å)

V—V^i	2.6102 (2)	V—Hf^iii	3.0544 (3)
V—V^ii	2.6036 (3)	Hf—Hf^iv	3.1941 (3)
V—Hf	3.0657 (4)

Symmetry codes: (i) −y+1/4, x−1/4, z+1/4; (ii) −x, −y−1/2, z; (iii) y+1/4, −x+1/4, z−1/4; (iv) −y+1/4, −x−1/4, z+1/4.

(IMMA_90K_publ)

Crystal data

Orthorhombic, Imma	b = 5.21235 (9) Å
a = 5.19096 (8) Å	c = 7.41751 (10) Å

Data collection

2θmin = 8.002°, 2θmax = 51.802°, 2θstep = 0.006°

Refinement

Rp = 0.206	7301 data points
Rwp = 0.270	14 parameters
Rexp = 0.064	(Δ/σ)max = 2.32

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

	x	y	z	Uiso*/Ueq
V1	0.0	0.0	0.0	0.0114 (18)*
V2	0.25	0.75	0.25	0.021 (2)*
Hf	0.0	0.25	0.3753 (4)	0.005*

Bond lengths (Å)

V1—V1^i	2.6062 (5)	V1—Hf^iv	3.0481 (9)
V1—V2^ii	2.6117 (2)	V1—Hf	3.0560 (9)
V1—V2^i	2.6117 (2)	V1—Hf^v	3.068 (3)
V1—V2^iii	2.5955 (4)	Hf—Hf^v	3.196 (4)
V1—Hf	3.073 (3)	Hf—Hf^iv	3.192 (4)

Symmetry codes: (i) x, −y+1/2, z; (ii) x, y−1, z; (iii) −x, y, z; (iv) −x+1/2, −y+1/2, −z+1/2; (v) −x, −y+1, −z+1.

(20K)

Crystal data

Orthorhombic, Imma	b = 5.22109 (12) Å
a = 5.17349 (10) Å	c = 7.43197 (15) Å

Data collection

2θmin = 8.002°, 2θmax = 56.992°, 2θstep = 0.006°

Refinement

Rp = 0.218	8166 data points
Rwp = 0.293	14 parameters
Rexp = 0.072	(Δ/σ)max = 0.77

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

	x	y	z	Uiso*/Ueq
V1	0.0	0.0	0.0	0.0109 (14)*
V2	0.25	0.75	0.25	0.0189 (15)*
Hf	0.0	0.25	0.3747 (3)	0.005*

Bond lengths (Å)

V1—V1^i	2.6105 (6)	V1—Hf^iv	3.0433 (7)
V1—V2^ii	2.6132 (3)	V1—Hf	3.0573 (7)
V1—V2^i	2.6132 (3)	V1—Hf^v	3.074 (2)
V1—V2^iii	2.5867 (5)	Hf—Hf^v	3.206 (3)
V1—Hf	3.076 (2)	Hf—Hf^iv	3.183 (3)

Symmetry codes: (i) x, −y+1/2, z; (ii) x, y−1, z; (iii) −x, y, z; (iv) −x+1/2, −y+1/2, −z+1/2; (v) −x, −y+1, −z+1.