Structural homogeneity and mass density of bulk metallic glasses revealed by their rough surfaces and ultra-small angle neutron scattering (USANS)

The ultra-small angle neutron scattering (USANS) measures the microscale structure of heterogeneity and the scattering from rough surfaces with small scattering volumes can be neglected. But this is not true in amorphous alloys. The small angle scattering from such surfaces is not negligible, regardless of scattering volume. However, we demonstrate that the unwanted rough surfaces can be utilized to determine the homogeneity and mass density of amorphous metallic glasses using the USANS and surface neutron contrast matching technique. The power law scattering of the homogeneous Cu50Zr50 amorphous alloy disappeared under the surface contrast-matched environment, a mixture of hydrogenated/deuterated ethanol having low surface tension against the metallic alloys, indicating that the scattering originated not from its internal structure but from the rough surface. This confirms the structural homogeneity not only at the atomic level but also on a larger scale of micrometer. On the other hand, the crystallized Cu50Zr50 alloy showed strong power-law scattering under the matching environment due to the structural heterogeneity inside the alloy. This technique can apply to the bulk samples when the transmission is high enough not causing multiple scattering that is easily detected with USANS and when the surface roughness is dominant source of scattering.

Metallic alloys with robust glass forming ability, also known as metallic glasses, consist of amorphous structure that is free of heterogeneities like crystalline phase, grain boundaries, and dislocations. The structural homogeneity of metallic glasses is widely investigated at an atomic level using X-ray diffraction and transmission electron microscopy. In only a few cases, the small angle x-ray scatterings (SAXS) and small angle neutron scatterings (SANS) have been used to measure the heterogeneities at a nanometer level [1][2][3][4][5][6][7][8][9][10] .
In addition to the well-known homogeneous nature of the amorphous metallic structure in the nanometer scale, spontaneous decomposition in larger scale, also known as phase separation, was also reported 11,12 . The molecular dynamics simulation showed density fluctuation (i.e., local structural fluctuation) on the atomic length scale in the quenched Cu 57 Zr 43 alloy 13 . However, only limited information on the phase uniformity of metallic glasses is available in a wide range of length scales. In this context, we have questioned whether the homogeneity of metallic glasses confirmed at the atomic and nanometer levels can be sustained at a much larger scale, at least up to the micrometer scale. Ultra-small angle neutron scattering (USANS) enables us to measure the homogeneity and heterogeneity up to tens of micrometers. Due to the strong penetration power of neutrons into most alloys with the interaction of a neutron to nucleus, USANS and SANS are excellent tools to investigate the structure of thick samples over hundreds of micrometers or even thicker samples when the transmission is high enough not to cause multiple scattering, while SAXS may require the specimen to be thinned down to a few microns in materials with high atomic number due to the shallow penetration capability caused by the interaction of the electromagnetic waves with electrons that have a higher number density than nucleus.
Bulk metallic ribbons have inherent rough surface of which surface topology has been known to affect properties such as corrosion, friction, wear, and plastic deformation 14,15 . For bulk samples in most alloys, the surface roughness can be less important in USANS and SANS measurements due to the smaller surface-to-volume ratio than SAXS 16 . However, in amorphous materials like BMGs, scattering from the surface cannot be neglected even though the scattering volume is considerably less than that of bulk samples, since the internal homogeneous (i.e., no density and composition fluctuation) phase must not have any structures that cause scattering. In fact, Roth demonstrated that the Porod scattering (i.e., the scattering intensity decreases with a power of −4 against Q, representing a sharp interface of a structure) from SANS originated from the surface irregularities and oxide layers of pure polycrystalline metals 17 . Rodmacq et al. showed the influence of surface conditions on the SANS profile of Pd 80 Si 20 alloys by measuring specimens under different surface treatments: quenched, polished, and chemically etched 18,19 . Therefore, it is likely that the rough surface causes the non-trivial surface scatterings which could lead to misinterpretation of SANS and USANS data as the homogeneous amorphous alloys have inner heterogeneity.
Thus, the surface roughness hinders us from determining the structural homogeneity of metallic glass structure. In addition, the evaluation of the mass density of an amorphous metallic glasses with the rough surface is another challenging task. For example, in the well-known Archimedes method, entrapped air bubbles can cause lower density when high surface tension liquids are used 20,21 , or by the closed pores that liquids cannot be accessible. Also, if any internal heterogeneities are present, the measured density can be misunderstood as the density of the sample in a pure homogeneous state, unless homogeneities or heterogeneities are confirmed with other density measurement methods. In this study, however, we will show how the rough surface, which is not desired in most characterization methods, can be applied to determine the microscale homogeneity and the mass density of BMG alloys simultaneously using the unique contrast-matched USANS technique. For this purpose, USANS is more useful than SANS because only USANS can properly evaluate the typical micron-sized roughness. Also, USANS is less sensitive to incoherent backgrounds than SANS.

Surface neutron contract-matching (SNCM) method
Expected small angle scatterings from an amorphous alloy can be schematically shown in Fig. 1. Small angle scattering is registered on the detector when scattering materials have a contrast (ΔSLD) 2 defined as the squared difference of the coherent scattering length densities (SLD) 22,23 and/or volume fraction φ(1 − φ) between domains (or elements), i and j: where the macroscopic scattering cross-section (cross section per unit volume, cm −1 ), dΣ(Q)/dQ, is a function of the scattering vector, Q = (4π/λ)sin(θ), defined with the neutron wavelength λ and the scattering angle 2θ. P(Q) and S(Q) is a form factor that represents a shape of scattering object (i.e., scatterer) and a structure factor that does an inter-correlation distance, respectively. For the homogeneous phase (i.e., single phase) as shown in Fig. 1(a), no small angle scattering must be observed since Eq. (1) becomes equal to zero since there are no scatterers (i.e., φ(1 − φ) = 0) due to internal homogeneity and smooth surface even with a difference in SLD between surface and air (see also Table 1). Unlike our expectation, the preliminary USANS and SANS results of Cu 50 Zr 50 (see Fig. S1 of supplementary information) and literature 5,[17][18][19] show strong power-law scattering under air environment, which may indicate significant heterogeneities in the metallic glasses. However, since the homogeneous BMG alloys have no scattering regardless of scattering volume (i.e, thin or bulk samples), the rough surface ( Fig. 1(b)) could be a reason for the power law or fractal-like scattering. In this case, the origin of the power law scattering may be due to the contrast (SLD surface − SLD air ) 2 between the rough surface SLD surface and the air environment SLD air (as shown in Fig. 1(ii)), even with the inner homogeneity of the metallic glass. When the rough surface is contrast-matched (CM) to the neutron SLD of the homogeneous phase to make SLD inside = SLD surface = SLD CM (i.e., the air environment is replaced with a surface neutron contrast-matched (SNCM) environment by filling the surface furrows with a matching liquid which masks the rough surface from neutrons ( Fig. 1(c)), the scattering from the rough surface should not be observed because of no contrast as shown schematically in Fig. 1(iii). It is shown that the scattering from the rough surface or open networked-pores can be suppressed by the neutron contrast-matching technique 19,22,24 .
When the sample has heterogeneities, such as polycrystals with boundaries ( Fig. 1(d)) and dispersion of particles or voids ( Fig. 1(e)) in a matrix, USANS and SANS scatterings from such heterogeneities occur due to a contrast mismatching, i.e., ≠ (SLD  SLD ) hetero CM , with the CM liquid matched to the homogeneous phase ( Fig. 1(iv)). In this case, the surface contrast may be selectively matched to only one of the phases in a system comprising multi heterogeneous domains ( Fig. 1(d) and (e)), which may enable us to measure the other phases or pores.
In the process of finding the optimum liquid composition that matches the SLD of a constituent phase, the mass density of the constituent phase could be estimated. The procedure for density estimation will be presented in detail in the later part of this paper. Overall, the schematics in Fig. 1 will be demonstrated and used to determine the microscale homogeneity and the mass density of BMG alloys.

Results and Discussion
Homogeneity in atomic level. Before determining the homogeneity and the mass density using USANS, the structure of Cu 50 Zr 50 metallic glass samples in the form of ribbons was checked by DSC thermal analysis and X-ray diffraction (Fig. 2). The DSC thermal scan was carried out twice to confirm the complete crystallization after the first scan up to 550 °C; upon cooling and reheating of the same specimen for the second run, the heat flow curve (dotted green line in Fig. 2(A)) was almost constant suggesting complete crystallization of the amorphous phase during the first heating (orange solid line). For the XRD spectra (shown in Fig. 2(B)), the two broad amorphous halos and full width at half maxima (FWHM) of both the as-cast and sub-T g annealed samples were identical within a lab-scale XRD error range indicating the same atomic number density and no noticeable change in correlation distances between atoms (i.e., identical amorphous structures in both the as-cast and sub-T g annealed Cu 50 Zr 50 ). Results of the X-ray and DSC analyses confirm that Cu and Zr elements in the as-cast and sub-T g annealed Cu 50 Zr 50 are homogeneously mixed and do not form any crystallite at the atomic level (in the available range of lab-scale XRD). The USANS measurements were undertaken to investigate whether the homogeneity in the amorphous phase is limited at the atomic level or is extended to larger scale, i.e., micrometers.

Determination of homogeneity and heterogeneity in the micron scale with SNCM technique.
Before investigating the homogeneity at the micrometer level, the USANS profiles of the Cu 50 Zr 50 ribbons without surface polishing (open orange triangle) and with polishing (open green circle) by means of the sandpapers (600, 1000, and finally 2000 grade in order) were compared with air scattering (closed circle) in Fig. 3(a).
Scatterings from both samples are stronger than the window scattering from the empty sample container, indicating the presence of effective scatterers (i.e., heterogeneity in the structure) which must not be observed crystallized (i.e., heterogeneous) BMGs with rough surface, and (e) BMGs with precipitates, pores, and/or rough surface. Corresponding SLD profiles with path length (i.e., sample thickness) are displayed in (i-iv). SLD hetero indicates heterogeneity from precipitates, rough surfaces, or/and voids. The symbol Δ represents the difference between the SLDs. No scatterings are expected in (a)-(i) condition because there are no scatterers (i.e. φ(1−φ) = 0) even with a difference in SLD between surface and air and in (c)-(iii) condition because of no contrast (i.e., Δ = 0). Sample thickness and roughness are not scaled. The samples have two surfaces that contribute to the forward scatterings, but for clarity, note that the schematics show only one-sided surfaces. k i → and → k s are the incident and scattered wave vectors, respectively. → Q is the scattering vector. in the homogeneous BMG as shown in Fig. 1(a) and Table 1 Fig. 3], suggesting that the surface scratches (i.e. rough surface) could be the origin of the USANS scattering. However, in the case of metallic glass ribbons having both macro-heterogeneity and rough surface, it would not be clear whether the power law scattering results from the large heterogeneity (i.e., much larger than atomic scale) inside the sample or from the rough surface [ Fig. 1(d) and (e)]. To identify the origin of the scattering and to determine the homogeneity in much larger size scale than atomic level, the USANS measurements were performed at different sample environments corresponding to each schematic diagrams of Fig. 1 for the homogeneous Cu 50 Zr 50 alloy.
The sample immersed in the 100% hydrogenated ethanol-h ( Fig. 4(a)), shows strong scattering due to the large contrast, while the same specimen immersed in the 100% deuterated ethanol-d shows weak scattering ( Fig. 4(d)). In the mixture of ethanol-h/ethanol-d, 20.8/79.2 vol./vol. ratio (Fig. 4(c)), the scattering (open circles) from the sample almost superimposes to the scattering (closed circles) from the buffer liquid of 79.2% ethanol-d, confirming that the SLD of the buffer liquid is close to that of the homogeneous Cu 50 Zr 50 alloy. The estimated density of Cu 50 Zr 50 alloy from this ratio is approximately 8.23 g/cm 3 that is about 11-14% higher than the known densities, 7.23 ~ 7.41 g/cm 3 , in the literature [25][26][27][28] . The exact matching ratio and density determination will be shown from a SLD matching plot later in the section of mass density estimation. Figure 4(c) indicates that the USANS scattering of the BMG is not from the internal heterogeneous structure but mostly from the rough surface (i.e., no scattering from the inside as shown in Fig. 1(c) and 1(iii)).
The USANS scattering phenomena measured with the ethanol-h/ethanol-d mixtures with low surface tension were cross-checked with the H 2 O and D 2 O mixtures with high surface tension in the same manner as that of the ethanol mixture. Figure 5  Mass density estimation. The rough surface can be further applied to determine the mass density of homogeneous metallic glasses together with the SNCM technique. Two methods were used in this study: the invariant method and the zero-angle scattering method. The invariant, Q inv , defined as: is used 23 . In Eq. (2), the Q inv depends only on the contrast term, (ΔSLD) 2 , in a two-phase system that can be controlled by tuning the sample environment as shown in the CM experiments, since the volume fraction (φ) of the empty space in the rough surface and the rest, (1 − φ), composed of the Cu 50 Zr 50 materials are constant. Q inv is obtained from the area of the invariant plot, Σ Ω ⋅ d Q d Q ( ( )/ ) 2 vs.Q, in the desmeared scattering profile:  the Appendix]. If the system is a two-phase alloy (i.e., consisting of the homogeneous phase of metallic glass and the empty space in rough surface), the data must align linearly and the exact surface neutron CM ratio is determined from the x-intercept that represents ΔSLD = 0.   Since the SLD of Cu 50 Zr 50 must be the same as that of the matched mixture at the SNCM condition (i.e., SLD Cu50Zr50 = SLD CM ), the mass density of homogeneous BMG is determined using the following relation: are the molecular weight and the scattering length of BMG consisting of atomic species i with the number (n i ) of atoms i, atomic weight (M i ) and scattering length (b i ), and N A is Avogadro number. The mass density of Cu 50 Zr 50 using Eq. (4) and the values listed in Tables 2 and 3 is estimated as ρ Cu50Zr50 = 7.3(1) ± 0.2(4) g/cm 3 . The mass density, from the rough surface and the USANS surface neutron contrast-matched) method agrees with the density of the literature, 7.25 25 , 7.2 3 26 , 7.39 27 , and 7.41 g/cm 3 28 . This invariant method was further cross-checked with a plot of the squared root of the zero-angle scattering ( Fig. 6(b)), since the macroscopic scattering cross-section is also proportional to the contrast term (see Eq. (1)) like the invariant 29 . The vertical error bar in Fig. 6(b) is expressed in Eq. (A12). The USANS resolution limit, Q = 2 × 10 −5 Å −1 , was used as the zero-angle, dΣ(Q → 0)/dΩ, for convenience since the scattering cross-section at Q = 0 cannot be determined in the power law scattering. It should also be noted that other low Q limits can be used and it does not affect the match point. The squared root zero-angle scattering method shows a mass density of approximately ρ Cu50Zr50 = 7.2(4) ± 0.2(3) g/cm 3 , which is identical with the invariant method with an approximately 1% difference.

Conclusion
The results demonstrate that the rough surface of amorphous metallic materials, which is a result of manufacturing process or intended purpose, can be used to determine the homogeneity and mass density of the bulk metallic glasses when the surfaces are sufficiently rough. The power-law scattering of amorphous Cu 50 Zr 50 melt-spun ribbons with rough surface in the USANS measurements disappeared at the SNCM (surface neutron contrast-matched) condition which can be optimized by finding a proper composition of ethanol-h/ethanol-d mixture as well as H 2 O/D 2 O mixture within the experimental error. However, the crystallized ribbons showed strong power-law scattering with the matching mixture suggesting that the inside of the alloy is heterogeneous. This confirms that the small angle scattering originates from the rough surface and that, at the same time, the Mw(g/mole) density (g/cm 3 ) SLD × 10 −10 (cm −2 ) a ΔSLD 2 × 10 −20 (cm −4 ) b  Table 3. Density and SLD of Cu50Zr50, water, ethanol, and contrast matched ratio at 25 °C. a Read the numbers in the column as −0.55993 × 10 10 , 6.3988 × 10 10 and so on. b Read the numbers in the column as 23.0508 × 10 20 , 17.9878 × 10 20 and so on. c Estimated from this study using the squared invariant. Also, from the squared zeroangle scattering method, we obtained the density of ρ Cu50Zr50 = 7.2(4) ± 0.2(3) (see main text for details) d from the matching ratio, 70.9(9) vol. % of ethanol-d from SNCM plot of squared root invariants BMG consists of the homogeneous single phase. The compositional homogeneity of the amorphous metals down to the atomic level turned out to hold over an even a wider range of scale: nanometer to micrometer, over 4 orders. It was also demonstrated that the rough surface can be used to determine the mass density of a homogeneous amorphous metallic ribbon, Cu 50 Zr 50 .
Therefore, by utilizing USANS, which has much higher Q resolution and is less sensitive in incoherent scattering than the typical SANS, the SNCM technique can be an alternative characterization method for determining homogeneity of BMG in a larger scale (i.e., micron level) than the atomic level and can be used for estimating the mass density of homogeneous BMG with a rough surface. Our method can also be applied to much thicker BMG alloys due to their high transparency to neutrons

Methods
Sample preparation. Cu 50 Zr 50 ribbons of ~80 μm in thickness and ~75 mm in width were produced by the melt-spinning method at Eco-FM Company, Incheon, Korea. The ribbons were isothermally annealed under a vacuum environment at a temperature of 400 °C for 1 hour to homogenize the as-cast structure by equilibrating at a temperature slightly under the glass transition point (T g ~ 404 °C). The metallic glass ribbons were also crystallized at 500 °C above a crystallization temperature (T x1 = 456 °C, see Fig. 2(A)) under a vacuum environment. To remove oxide layers that can evolve on the sample surface during heat treatment, the samples were polished using 600, 1000, and 2000 grade sandpapers.
Thermal Analysis and X-ray Diffraction. Thermal analysis was carried out using a differential scanning calorimeter (Perkin Elmer Diamond DSC) with a heating rate of 10 °C/min under flowing nitrogen condition. The wide-angle X-ray diffraction (WAXD) (model: PAN analytical, EMPYREAN) was measured with a Cu Kα radiation generated at 40 kV and 45 mA.

Ultra-small angle scattering (USANS) measurement.
Pieces about 20 × 20 mm 2 in size cut from the Cu 50 Zr 50 ribbons (approximately, 80μm thickness), stacked in three layers to increase the scattering intensity, were attached on a Gadolinium (Gd) diaphragm with a 5/8 inch aperture. The metallic glass ribbons were placed in a SNCM environment, i.e., degassed hydrogenated ethanol (C 2 H 5 OH)/deuterated ethanol (C 2 D 5 OD) mixtures, in the 1 mm path length quartz cell for SNCM experiments. Ethanol was selected due to the low surface tension on the Cu 50 Zr 50 . The H 2 O/D 2 O mixtures with high surface tension were also used to cross-check the results from the ethanol mixtures. The entrapped air bubbles were removed under vacuum.
Ultra-small angle neutron scattering (USANS) was measured with the recently commissioned KIST-USANS at the HANARO cold neutron guide, CG4B, Daejeon, Korea. The KIST-USANS instrument uses a pair of modified Bonse-Hart-Agamalian channel-cut crystals 10,31 as a monochromator and an analyzer, with a wavelength of 4 Å. The minimum Q-resolution can reach down to ~2 × 10 −5 Å −1 . The transmission of Cu 50 Zr 50 was more than 92%, which assures no multiple scatterings from the metallic samples. Details of multiple scattering is described in the next section. The data reduction was performed with the NIST data reduction package 32 modified for the KIST-USANS instrument. The USANS intensities are expressed in intensity, I(Q), (unit: counts/sec/ Monx10 6 ) corrected only with instrumental parameters for the comparison of the scatterings from the sample with a sample environment, or expressed in smeared macroscopic nuclear scattering cross-section, dΣ sm (Q)/dQ, (unit: cm −1 sr −1 ) in absolute unit with additional corrections for sample thickness, transmission, and background. The USANS cross-section dΣ sm (Q)/dΩ in absolute scale were converted to the pin-hole SANS cross-sections dΣ(Q)/dΩ by multiplying a Δq V /Q, where Δq V is the vertical divergence of the one-dimensional detector 33 to estimate the invariant quantity.

Multiple scattering measurement.
Multiple scattering is proportional to the size of heterogeneity of the scatterer (D) as well as the sample thickness (t), the volume fraction of scatterers (φ), the square of neutron wavelength (λ 2 ), and the contrast (i.e., λ ∼ Δ tD ( SLD) 2 2 ). Since the USANS measures the microscale heterogeneity, multiple scattering is more concerning than in SANS, which measures on the nano scale. In order to assure that a neutron scatters only once (i.e., no multiple scattering) in the BMG alloys with the large rough surfaces, multiple scattering was estimated by comparing the sample transmissions measured with two independent detectors, a transmission detector and a detector bank (see Fig. 7), in the following manner: after aligning both monochromator and analyzer crystals to satisfy Bragg's law, the peak intensity of rocking curve is measured at Q = 0 with the detector bank by rotating the analyzer step-by-step through the rocking peak of the main beam. The ratio, T I(0) /I(0) rock sample empty = , of the rocking peak intensity with and without sample is the sample transmission attenuated by absorption, incoherent scattering, and coherent small angle scattering. A second transmission is measured from the transmission detector at non-Bragg condition. The detector located behind the first analyzer reflector captures all transmitted neutrons not to satisfy the Bragg's law for the analyzer, which was achieved by rotating the analyzer to a relatively wide angle (Q→∞,afewdegree) from the aligned rocking peak position (Q = 0). The transmission detector measures both the direct beam and forward coherent small angle scattering. The neutron counts collected by the transmission detector are decreased due to absorption and incoherent scattering. Thus, the ratio, T wide = <I(∞) sample >/<I(∞) empty >, of averaged count rate on the transmission detector with and without the sample represents the sample transmission attenuated by absorption and incoherent scattering.
The ratio t T T /T ( exp( )) sas rock wide = = −Σ ⋅ of these two separate transmissions is used to estimate the amount of multiple scattering. If the USANS measurements are free of multiple scattering, T rock ≈ T wide . Thus, (1 − T sas ) is the measured scattering probability including multiple scattering. As a rule of thumb, multiple scattering can be neglected when T sas ≥ 90% or t 0 1 Σ ⋅ ≤ . where Σ is the macroscopic scattering cross section (i.e., cross section per unit volume) that estimate the attenuation due to small angle scattering and t is the sample thickness 34,35 . If any significant multiple scattering occurs, it can also be shown as a broadening (i.e., flattening) of the sample rocking curve, which can cause an artificial Guinier-like scattering shape. In this study, two independent transmissions were more than 92% for all measurements, ≥ . T 0 95 sas , and only power law scattering was observed, which confirms that multiple scattering is negligible and the USANS measurements are reliable. Based on this argument, USANS can be measured for homogeneous Cu50Zr50 alloy samples with a thickness (t 0 1/ ) = . Σ of up to 1.5 mm. If only power law scattering is observed, USANS can also be measured for thicker samples.

Appendix: Propagation of Uncertainty in the Contrast Matching Plot
The propagation of uncertainty in the two contrast matching methods, the squared root zero angle scattering method and the squared root invariant method, was treated in the following manner; A1. Propagation of Uncertainty (vertical error bar) in the zero-angle scattering (or near zero-angle) plot. The measured USANS count (I SAM ) of the sample is corrected in absolute scale (unit cm −1 sr −1 ), I cor (Q), with empty count (or, buffer scattering), (I EMP ), sample transmission (T tran ), sample thickness (t), detector solid angle (dΩ) and a constant background (I BKG ) in the following manner; where sf is an absolute scale factor containing sample transmission (T wide ) measured in a background region, and a rocking curve peak count of the empty run (pk EMP ). Thus, the propagation of uncertainty of Eq. (S1) is . When the analyzer is rotated by an angle q, only the ultra-small angle scattering corresponding to the same angle q is reflected (see . When the analyzer is turned further to a large angle (non-Bragg condition), all incident neutrons (except for absorption and incoherent scattering) are transmitted to the transmission detector.
, since the USANS intensity was measured with different intervals of Q for each angular region. For simplicity in the notation I i is used for representing The invariant including the error propagation is expressed as Q inv Q inv σ ± . In the contrast matching plot where the y axis is Q inv , the vertical error bar is given by Note that in Fig. 6(a) (in the main text), the vertical error bars within the symbols. Apparently, the squared root invariant matching method shows smaller error bars than the squared root of the extrapolated zero angle scattering, Σ Ω d d (0)/ , method. However, regardless of the method, the densities estimated from both methods are identical within experimental error.