Synchrotron powder X-ray diffraction of a refractory high entropy alloy, Mo_0.20Nb_0.21Ta_0.19V_0.20W_0.20

Powder X-ray diffraction data collected at the Advanced Photon Source 16-BM–D, confirms that the alloy with composition Mo_0.20Nb_0.21Ta_0.19V_0.20W_0.20 crystallizes in a simple body-centered cubic (bcc) structure with all five elements distributed over a single crystallographic site (Wyckoff position 2a of space group Im3m).

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Structure description

High-entropy alloys (HEAs) have attracted considerable attention because of their remarkable physical properties and simple crystal structures. Refractory HEAs remain relatively unexplored but are of particular inter­est for their high melting points and mechanical strength. The title compound, a near equiatomic solid solution with composition Mo_0.20Nb_0.21Ta_0.19V_0.20W_0.20, combines these attributes and has potential for extreme pressure/temperature applications owing to its high shear strength and melting temperature. We report here its crystal structure along with the first publicly available crystallographic information file (CIF) of a refractory HEA (to the best of our knowledge).

Much like the well known Cantor alloy (Cantor et al., 2004), the Mo_0.20Nb_0.21Ta_0.19V_0.20W_0.20 solid solution adopts a simple bcc structure (space group Imm), just like the constituent elements themselves. The refined lattice parameter is a = 3.19634 (3) Å, with all constituent elements sharing a single Wyckoff position 2a (0, 0, 0) (Fig. 1). The shortest M—M distance and some angles are listed in Table 1. Using the following lattice parameters for individual elements, Mo = 3.147 Å (Ross & Hume-Rothery, 1963), Nb = 3.3004 Å (Straumanis & Zyszczynski, 1970), Ta = 3.38 Å (Srivastava et al., 2011), V = 3.0241 Å (James & Straumanis, 1960), and W = 3.16475 Å (Deshpande & Pawar, 1962), we find that the average elemental lattice parameter is <a>= 3.20325 Å and therefore the difference relative to the title compound is 0.22%. With such a small difference from the mean we report that Vegard's law holds for this solid solution (Denton & Ashcroft, 1991). The elemental and high-entropy alloy lattice parameters along with the arithmetic mean of the constituent elements are shown in Fig. 2.

Table 1
Selected geometric parameters (Å, °)

Mo3—Mo3^i	2.7681 (3)
Mo3^i—Nb2—Mo3^ii	70.529	Mo3^i—Nb2—Mo3^iii	109.471
Symmetry codes: (i) ; (ii) ; (iii) .

Figure 1 The first nearest neighbors coordination formed around the 2a site with coordination number 8; the different colors represent the fractional occupancies.

Figure 2 The elemental and high-entropy alloy lattice parameters along with the arithmetic mean of the constituent elements as a dashed line.

Synthesis and crystallization

Elemental powders of Mo, Nb, Ta, V, and W (nominal purity >99.9%) were weighed in equiatomic proportions and mixed thoroughly to achieve homogeneity. The mixture was pressed into a pellet and placed into the chamber of a MAM-1 vacuum arc-melter (Edmund Bühler GmbH, Bodelshausen, Germany). The chamber was evacuated and then pumped with argon to ensure an inert atmosphere. The pellet was then melted at approximately 3500 K and cooled rapidly on a water-cooled copper hearth yielding a dense, single-phase ingot. The ingot was then powdered in a mortar and pestle until particle size was below 5 microns.

Refinement

Crystal data, data collection, and structure refinement details can be found in Table 2. Synchrotron powder X-ray diffraction data were processed using DIOPTAS (Prescher & Prakapenka, 2015) and analyzed via Rietveld refinement in GSAS-II (Toby & von Dreele, 2013). A single crystallographic site was used for all five elements; their fractional occupancies were constrained to sum to unity during refinement, as determined by energy dispersive spectroscopy, using a Quanta 650 FEG scanning electron microscope (see supplementary figure). Isotropic displacement parameters for all elements were held fixed at the default GSAS-II value and not refined. Since there are five different atoms on a single Wyckoff site, refining this lead to unphysical values. It should be noted that the rather high reliability factors of the Rietveld refinement (Fig. 3) probably are due to the standard uncertainties being overestimated (Toby, 2006).

Table 2
Experimental details

Crystal data
Chemical formula	Mo0.20Nb0.21Ta0.19V0.20W0.20
Mr	120.04
Crystal system, space group	Cubic, Imm
Temperature (K)	300
a (Å)	3.19634 (3)
V (Å^3)	32.66 (1)
Z	2
Radiation type	Synchrotron, Advanced Photon Source, 16-BM-D, λ = 0.42460 Å
μ (mm^−1)	28.17
Specimen shape, size (mm)	Irregular, 0.0015 × 0.0015
Data collection
Diffractometer	Local diffractometer set-up
Specimen mounting	Ambient sample holder on Kapton tape
Data collection mode	Transmission
Scan method	Step
2θ values (°)	2θmin = 2.737 2θmax = 33.372 2θstep = 0.020
Refinement
R factors and goodness of fit	Rp = 0.266, Rwp = 0.388, Rexp = 0.563, R(F^2) = 0.27811, χ^2 = 0.476
No. of parameters	1
Computer programs: EPICS (Mooney et al., 1996), GSAS-II (Toby & Von Dreele, 2013), DIOPTAS (Prescher & Prakapenka, 2015) and VESTA (Momma & Izumi, 2008), publCIF (Westrip, 2010).

Figure 3 Rietveld difference plot for the single-phase refinement of Mo0.20Nb0.21Ta0.19V0.20W0.20. The blue crosses show the observed data, the red line the calculated data and the gray line the difference plot. Calculated Bragg reflection positions are indicated by green tick marks.

Structural data

Computing details

Molybdenum niobium tantalum vanadium tungsten

Crystal data

Mo0.20Nb0.21Ta0.19V0.20W0.20	Dx = 12.208 Mg m^−3
Mr = 120.04	Synchrotron, Advanced Photon Source, 16-BM-D radiation, λ = 0.42460 Å
Cubic, Im3m	µ = 28.17 mm^−1
Hall symbol: -I423	T = 300 K
a = 3.19634 (3) Å	gray metallic
V = 32.66 (1) Å^3	irregular, 0.002 × 0.002 mm
Z = 2	Specimen preparation: Prepared at 3500 K

Data collection

Local diffractometer set-up	Scan method: step
Specimen mounting: Ambient sample holder on Kapton tape	2θmin = 2.737°, 2θmax = 33.372°, 2θstep = 0.020°
Data collection mode: transmission

Refinement

Least-squares matrix: full	1 parameters
Rp = 0.266	0 restraints
Rwp = 0.388	0 constraints
Rexp = 0.563	Weighting scheme based on measured s.u.'s
R(F^2) = 0.27811	(Δ/σ)max < 0.001
1505 data points	Background function: Background function: "chebyschev-1" function with 3 terms: 0.059, 0.001, 0.094,
Profile function: Finger-Cox-Jephcoat function parameters U, V, W, X, Y, SH/L: peak variance(Gauss) = Utan(Th)^2+Vtan(Th)+W: peak HW(Lorentz) = X/cos(Th)+Ytan(Th); SH/L = S/L+H/L U, V, W in (centideg)^2, X & Y in centideg 1.163, -0.126, 50.000, 0.000, 6.864, 0.002,	Preferred orientation correction: March-Dollase correction coef. = 1.000 axis = [0, 0, 1]

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
Mo3	0.00000	0.00000	0.00000	0.0250*	0.2000
Nb2	0.00000	0.00000	0.00000	0.0250*	0.2100
Ta1	0.00000	0.00000	0.00000	0.0250*	0.1900
V1	0.00000	0.00000	0.00000	0.0250*	0.2000
W4	0.00000	0.00000	0.00000	0.0250*	0.2000

Geometric parameters (Å, º)

Mo3—Mo3^i	2.7681 (3)
Mo3^i—Nb2—Mo3^ii	70.529	Mo3^i—Nb2—Mo3^iii	109.471

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