Understanding the impact of high-energy ball mill tooling on powder refinement and alloy formation: Microstructural evolution in immiscible W-Cr alloys

Abstract

High-energy ball milling provides an effective means to drive thermodynamically non-favorable solid solutions while also refining the microstructure of powders. Key parameters in this process, such as the size and hardness of the milling media, the hardness of the milling vessel, and the ball-to-powder ratio, can have a major effect on the resultant powders. Using W-10 wt.% Cr as a model system, we establish the relationship between processing/tooling parameters and the resultant powders. Here, we find that the larger milling media provides higher energy per collision, enabling further crystallite refinement but limiting the total frequency of solute-dissolving impacts. Additionally, we find that variation between the first and subsequent milling runs is not significant, indicating negligible “seasoning” effects from prior use of the milling vessel for the reported material system. These findings provide insight into the role of processing parameters in tailoring the microstructure of immiscible and refractory alloys, with implications for extrapolation to the ball milling of a wide range of material systems.

Keywords

ball milling mechanical alloying powder refinement tungsten-chromium alloy microstructural evolution nanocrystalline alloys refractory alloys x-ray diffraction

Introduction

Mechanical attrition serves as a powerful synthesis route for advanced materials by critically deforming and mixing powders to achieve specific objectives, such as nanocrystallinity, metastable phase formation, and dispersion strengthening through uniformly distributed second-phase particles that hinder dislocation motion. It allows for the refinement of crystallite sizes down to the nanometer scale, facilitating the formation of new crystalline and quasicrystalline phases. Additionally, mechanical attrition through mechanical alloying (MA) supports the development of amorphous (glassy) materials, the disordering of ordered intermetallic compounds, and the alloying of elements that are typically difficult to combine. In this way, mechanical attrition offers a versatile approach for producing advanced materials with a range of unique and desirable properties.^1–5 For instance, early work from Benjamin reports successfully producing single-phase Ni-Cr after going through an MA process, providing similar results to conventional cast ingots of similar composition.⁴ Traditionally, MA is performed through high-speed translational, frictional, or vibrational forces that are applied to a vessel containing powder feedstock and a hard media.^6,7 The media and vessels in these processes then exert forces, shear, and impact upon the powder material to cause deformation and mixing.^6,7 Among these methods, high-energy ball milling (HEBM) stands out due to its ability to achieve tremendous deformation and mixing conditions through random, high-energy collisions of the milling media and powder feedstock.^8,9 This is commonly done using a triaxial shaker mill, such as the commercially available SPEX mill, due to its ability to deliver extremely high energy through complex, high-speed oscillations along the X, Y, and Z axes. This motion facilitates intense, random collisions between the milling media and powder. Here, the resulting randomized collisions and high-velocity impacts facilitate thorough mixing of the feed material.^8,9 Fecht et al. and Eckert et al. highlight the effectiveness of HEBM in producing ultrafine grain and nanocrystalline powders, emphasizing how the steady-state plastic deformation induced during the process introduces a significant volume of dislocations, which contributes to grain refinement.^1,2

The efficiency and results of HEBM are significantly affected by various mill parameters, including, but not limited to, rotational speed, motion amplitude, and the temperature of the milling environment. In commercial units, these variables are typically treated as fixed, but adjustable factors, such as the properties of the milling vessel, milling media, milling time and powder charge, can significantly influence the properties of the final synthesized material.^6,7 Milling time is one of the most frequently studied parameters in HEBM, often demonstrating increased microstructural refinement and enhanced solution formation.^1,2,10 This can be attributed to an increased cumulative energy input and collision count over longer periods of time. While processing time remains a dominant focus in the literature, additional parameters such as milling media size and ball-to-powder ratio (BPR) have been shown to influence the efficiency and outcome of HEBM.⁵ For instance, Yang et al. reported a reduction in ignition time during a combustion-driven reaction which was attributed to an increased microstructural refinement when larger ball bearing sizes were used in HEBM.¹¹ More recently, Bor et al. showed the effects of milling time, rotational speed and ball bearing size on crystallite size and powder morphology of pure Cu.¹² Alternatively, Darling et al. utilized HEBM to study Al–Mn alloy formation, with both milling time and energy impacting Mn solubility in Al.¹³ Increased milling energy sped up alloying but did not enhance solubility or crystallite refinement beyond a certain point. Alloying was driven by the interfacial surface area between Mn and Al, but excessive milling led to the formation of the equilibrium Al6Mn phase, limiting further alloying.¹³ After 300 h of milling, Mn solubility reached 3.1 at.%, five times the equilibrium limit, and the crystallite size decreased to around 12 nm.¹³ In general, the collective works on HEBM emphasize the critical need for parametric studies tailored to the specific system being studied, particularly for complex material systems.⁵ These studies are essential for understanding how adjustable parameters influence key properties such as microstructural refinement, solution formation, and powder morphology.

The effectiveness of HEBM in processing advanced chemically engineered systems is particularly important when dealing with challenging systems, such as the immiscible nanocrystalline W-5 wt.% Cr alloy reported by Park et al..^14,15 This system exhibits nanophase separation, where factors like surface energy, interfacial energy, and enhanced atomic mobility promote rapid sintering to near-theoretical density at much lower temperatures than conventional methods allow. In this system, the melting temperature of the matrix (W) is much higher than that of (Cr), and a positive miscibility gap exists. Achieving a high solubility of Cr in W is crucial, as the rapid densification depends on chromium being fully in solution and the powder particles possessing a nanocrystalline microstructure.^14–16 As these features are direct results of MA, the W-Cr system serves as a relevant and difficult testbed for understanding the results of changes in HEBM parameters. To further the challenge of this system and enhance the identification of parametric effects, the chromium content of the alloy in this study was doubled, nominally resulting in a W-10 wt.% Cr alloy. This increase in solute content greatly exceeds the equilibrium solubility limit of Cr in W, making it more difficult to achieve a fully dissolved solid solution through MA. Doubling the Cr content and placing the alloy composition within the immiscibility gap of the equilibrium phase diagram amplifies the phase-separating nature of the alloy, helping to better differentiate between efficient and inefficient parameter sets during alloying. Additionally, it should be noted that nanocrystalline W-Cr exhibits a high hardness which exceeds that of many common HEBM tooling materials.¹⁷ Initial results synthesizing W-5 wt.% Cr show significant tungsten carbide (WC) and other media contamination in the powder after extended milling periods, due to extensive wear.^15,18,19 Excessive contamination can negatively impact material properties, as in the case of WC which can embrittle the material and/or reduce its sinterability. These issues can be mitigated when the milling media and vessel are matched to the feed material; however, this may not always be feasible due to practical challenges related to fabricating custom vessels or milling media.^7,20

The motivation of this study is to address the difficulty in fabricating immiscible and refractory alloy compositions, such as W-10 wt.% Cr, using HEBM. By systematically varying parameters such as ball bearing size, BPR, and tooling hardness, we aim to provide critical insights into how these factors influence microstructural refinement, solution formation, and powder morphology. These findings are intended to guide process optimization for other refractory and immiscible alloy systems, where limited or no systematic data have been reported on how milling parameters influence microstructural refinement and alloy formation. This work will help to bridge gaps in the current understanding of HEBM processing while offering practical recommendations for HEBM applications in such materials.

Experimental

Powder feedstock and tooling

In this work, spherical tungsten (W) powder (EOS, 99.9% pure, −325 mesh) and irregular-shaped chromium (Cr) powder (BeanTown Chemical, 99.9% pure, APS <10 µm) were utilized as feed material. Images are provided of these materials in an as-received state below, in Appendix A. These reveal a size discrepancy in the Cr feed material, which appears to fall within the 10–50 µm range rather than the specified <10 µm. This is due to natural agglomeration during storage, though it does not appear to have impacted the results of this study. Feed powders were ball milled using a singular SPEX 8000M Mixer/Mill at ∼1080 rpm for periods varying from 10 to 30 active milling hours, which refers to the amount of time the mill was actively agitating the vessel. To reduce the accumulation of heat in the milling vessel, protect the tooling, and reduce cold-welding potential, a 30-min on then 15-min off interval was set for all experimental runs. All milling experiments utilized 52100 steel ball bearings with varying sizes as the milling media, with certified hardness between 62–65 HRC. Milling was done within an in-house designed vessel that consists of an aluminum sleeve (6061-T6) and a hardened tool steel (D2) liner for lightweighting purposes. This design allowed for tempering of the vessel tooling to a maximum 62 HRC to study the effects of hardness on the resultant powder, which will be described in later sections. Powder charges were sealed within each vessel under a pure argon environment, due to O-ring seals within the design of these vessels; however, the milling runs were performed in a laboratory atmosphere.

X-ray diffraction and refinement

X-ray diffraction (XRD) was used to identify the microstructural and compositional characteristics of the powder materials within this work. These measurements were made on a Philips X’pert MPD equipped with a Cu Kα source, using the following scan parameters: 0.02° step size, 1 s per step, 10 repetitions, 1/2° divergence slit, and 1° Fixed Anti-Scatter Slits. Refinements were made within Profex XRD using phases from the Inorganic Crystal Structure Database (ICSD), ICSD-43421 and ICSD-44731 (ICSD release 2024.2) for the W and Cr phases, respectively.^21,22 This was done on a sum of the repetition scans and resulted in weighted R values between 2.55 and 3.02 for all the analyzed measurements, with the exact value reported within the appropriate table for each specimen. Information about the lattice parameters, crystallite sizes, and phase make-ups are reported in the following sections from these refined results. Crystallite size was extracted from Rietveld refinement using Profex, which models peak broadening across all reflections to separate size and strain contributions and determine volume-weighted crystallite size. Reported values reflect single refinements per sample; standard deviations were not included, as each parameter set was produced and measured once. Fit uncertainties from the refinement process are available but do not represent experimental repeatability.

Powder characterization

Size analysis was performed on the synthesized powders with an Anton Paar PSA 990, using a 3-min measurement cycle and water as the solvent. The resulting D10, D50, and D90 values are reported from the Rosin-Rammler particle distributions, and the trends between these will be discussed further for each set of experiments. Additionally, images of each powder are provided in Appendix B to support the results from particle size analysis and form a qualitative conclusion about the particle morphologies.

Scanning electron microscopy was conducted with a ThermoFisher Apreo 2 FE-SEM, mainly using an annular backscatter detector under the beam conditions of 15 kV and 0.80 nA. To image, each powder was mounted on carbon tape and blown with compressed air to remove any additional layers and debris.

Results and discussion

Variation within a milling recipe

To establish a baseline recipe for processing, we must consider the initial reporting of 20 h as being effective for this alloy system to reach a steady state of evolution.¹⁵ That is, at 20 h, no further crystallite size reduction occurs, and a complete solid solution is achieved, as evidenced by the peak shifts and phase disappearance shown in Figure 1(a) and (b).¹⁵ The shift in tungsten's peaks and the dissolution of Cr peaks indicate successful solution formation, evidenced by a reduced lattice parameter. The low-angle region shown in Figure 1(b) highlights the peak broadening associated with nano-sized crystallites and the shift due to lattice distortion from Cr incorporation. Please note, these runs were performed with a middle ground ¼ inch ball bearing size and a BPR mass ratio of 10:1 to ensure complete processing of the material. Also, it is vital to understand the reproducibility of results and the deviation when changing parameters; consequently, this parameter set was used four separate times in the same ball mill. These results will serve as an indicator of changes outside of normal deviation in the subsequent resulting powders, and whether they can be considered different from baseline. This is important groundwork for parametric experiments as ball milling can be an intensive process, and it would not be viable to run every parameter set multiple times over to determine individual processing spreads. Table 1 presents the results from four independent runs, summarized with a 95% confidence interval. These results demonstrate consistent processing and provide a statistical framework to evaluate the significance of deviations in subsequent experiments. In addition to developing a representative data spread, this experiment helps to identify that consecutive runs within the same vessel do not have an appreciable effect on the resulting powder. While this does not account for any contamination change run to run, the effect of any ‘seasoning’, that is, changes in vessel behavior due to prior use, such as surface wear, residual buildup, or altered impact efficiency, is not seen in the microstructure or macro morphology of the powder. Images of each powder from this run are available in Appendix A. Moving forward, this serves as a representative refinement for all the synthesized powders in this work. With that in mind, to conduct a parametric study, earlier milling times must be selected. In this case, milling times of 10 to 15 h were used to assess the increase or decrease in milling efficiency compared to the 20-h state.

Figure 1.

(a) XRD measurement showing the peak positions for each phase in mixed and milled W-Cr powders. (b) Representative refinement of milled powder used for reporting the data in this work.

Table 1.

Results from multiple milling runs within the same milling vessel.

Run	Lattice parameter	Crystallite size	Free Cr	R_wp	D₁₀	D₅₀	D₉₀
Run	Å	nm	Wt. Pct.	Pct.	µm	µm	µm
1^st	3.0758	12.3	2.03	2.95	0.71	4.63	15.25
2^nd	3.0772	11.8	2.02	2.88	0.87	5.50	18.02
3^rd	3.0792	13.0	1.98	2.71	0.67	4.84	16.90
4^th	3.0763	12.3	2.01	2.86	0.75	5.03	16.80
	3.077 ± 0.001	12.37 ± 0.37	2.01 ± 0.02	N/A	0.75 ± 0.07	4.99 ± 0.31	16.74 ± 0.96

Provided in the bottom row is the average and 95% confidence interval to provide insight on the repeatability.

Effect of ball bearing size

With our baseline set, it is now important to understand how ball bearings effect powder in the milling process. Previous studies, such as those by Yang et al. and Bor et al., have demonstrated the impact of ball bearing size on reaction kinetics and ignition times in the TaCl₅ system or their impacts in a planetary milling system.¹¹ However, Yang et al. primarily focused on ignition time and reaction products, providing limited insight into structural changes.¹¹ While results such as that by Bor et al. do report the effects on microstructure, they are from planetary ball milling. Unfortunately, this type of milling has a heavier reliance on frictional forces, making it difficult to extrapolate to the high-impact environment of shaker mills.^7,12,23 Here, we aim to investigate how ball bearing size influences lattice parameter, crystallite size, and solute dissolution in a HEBM system.

Figure 2 illustrates that the lattice parameter remains consistent across ball bearing sizes, except when using the smallest bearings. This aligns with trends observed by Yang et al., where ignition times similarly vary with bearing size, indicating a refinement in the material, typically by way of particle and crystallite size reduction.¹¹ These results from Yang et al. additionally show a similar trend where there appears to be a steep change when ball bearing size is shrunk below a certain point.¹¹ To confirm these observed trends, the experiment was duplicated for 10-h milling periods, which produced similar results in trend, but the less-refined state in 10-h runs reflects the reduced cumulative energy input. Also marked on Figure 2 is Vegard's law estimation of lattice parameter for this alloy, which can be calculated as follows²⁴:

\begin{matrix} a_{a l l o y} = x_{W} \cdot a_{W} + x_{C r} \cdot a_{C r} \end{matrix}

(1)

Where:

x_{A} : a t o m i c f r a c t i o n o f A

a_{A} : l a t t i c e c o n s t a n t o f A

This results in a value of 3.086 Å, assuming lattice parameters of 3.165 and 2.884 Å, for W and Cr, respectively.^25,26 Though this method does not account for lattice distortion and assumes an ideal linear relationship between the elements, it serves as a rough estimation that, in this case, provides an upper bound for expected results.²⁷ Lattice parameters for solutions can also be estimated using an apparent atomic radius approximation. This takes into consideration factors such as lattice strain and expansion/contraction of the atoms’ radii to provide an accurate apparent radius for the solute and solvent of a given mixture.²⁷ Application of these values provides atomic volumes that differ from the King's table size factor approximation but are more accurate when used for a linear approximation. These calculations are shown here^25–27:

\begin{matrix} Ω_{A} = \frac{4 π}{3} \cdot r_{A}^{3} \end{matrix}

(2)

\begin{matrix} Ω_{a l l o y} = x_{W} \cdot Ω_{W} + x_{C r} \cdot Ω_{C r} \end{matrix}

(3)

\begin{matrix} a_{a l l o y} = \sqrt[3]{Ω_{a l l o y} \cdot 2} (f o r B C C) \end{matrix}

(4)

Where:

Ω_{A} : a t o m i c v o l u m e f o r A

r_{A} : a p p a r e n t a t o m i c r a d i u s f o r A

Figure 2.

Refined lattice parameter with respect to each ball bearing sized used in milling for 10- and 15-h increments. Labelled with dotted horizontal lines are the Vegard's law estimate and apparent atomic radius approximation for the alloys lattice parameter for reference.

These calculations result in a lattice parameter of 3.076 Å when using the apparent radii values for a Cr-W solution provided by Lubarda et al.²⁷ This provides us with the lower bounds for the possible lattice parameters, as it assumes the perfect circumstances and does not account for any contamination that may be present. Figure 2 accurately shows a trend between these two values, but closer to the apparent atomic radius approximation, which confirms the accuracy of this approximation and application to real-world results.

Though the lattice parameters are consistent between ball bearing sizes, Figure 3 shows us that the crystallite size and dissolved chromium content vary across the ball bearing sizes. The inverse relationship between crystallite size and solute content can be attributed to the competing energy allocation during milling. Larger ball bearings provide higher energy per collision, enabling grain refinement but limiting the frequency of solute-dissolving impacts. Conversely, smaller bearings increase the frequency of collisions, which is beneficial for dissolving solute but not for crystallite refinement. This behavior emphasizes that solute incorporation is strongly dependent on the total number of impact interactions. As ball size increases, fewer collisions occur per unit time, reducing opportunities for Cr atoms to be mechanically driven into solution. This explains the observed increase in undissolved Cr content at larger ball sizes, despite their higher individual impact energies. The plateau at 10–11 nm aligns with the expected minimum stable crystallite size for tungsten-based materials, as discussed by Koch et al.²⁸

Figure 3.

(a) Refined crystallite and (b) refined Cr content as a function of ball bearing size for both 10 and 15 milling hour increments.

Now, when considering how the measured lattice parameters among the runs can remain the same while crystallite size and dissolved solute values can inversely change, we must consider the lattice parameter as an embodiment of the energy input within the system. Applying conservation of energy, the energy input would be the same since each run has about the same mass. This means that the powders must accommodate similar total energies that are input in each run. In the mechanical attrition process, we can describe the resulting energy input as an accumulation of change within the following powder characteristics, assuming a consistent input efficiency from the mill to the powder itself:

\begin{aligned} E n e r g y A c c o m m o d a t i o n = & Δ (Crystallite S i z e) \\ + Δ (D i s s o l v e d S o l u t e) \\ + Δ (P o w d e r M o r p h o l o g y) \end{aligned}

(5)

With Figure 4(a), we see consistent results for the D10, D50, and D90 of each ball bearing size used, indicating that similar energy from the milling process goes into the refinement of these powder particles, making it a constant in our energy association within the materials accommodation. Powders milled with smaller ball bearings exhibit smoother, more rounded particles (Figure 4(b)), likely due to lower collision energies causing surface abrasion rather than fracture. In contrast, larger ball bearings produce fractured and irregular particles (Figure 4(c)), reflecting higher energy impacts capable of breaking larger particles. These morphological differences help to highlight the trade-offs in milling efficiency. Smaller bearings excel at surface interactions that drive solute incorporation, while larger bearings enable bulk deformation and crystallite refinement. Images of each sample produced in these experiments are available within Appendix B.

Figure 4.

(a) Particle size analysis results depicting the D10, D50, and D90 for each ball bearing sizes respective powder. Also included are backscatter electron images of 15 milling hour powders from (b) 1/8th inch and (c) 1/2-inch ball bearing sizes.

From these results, we can further refine the above equation about energy accommodation by assuming that the energy that goes into the change of powder morphology is similar, therefore a constant between runs. This leads us to believe that the energy is accommodated entirely through (1) change in crystallite size and (2) change in the dissolved solute. Both are factors that can influence the lattice parameter of the materials, which we have already established as a consistent value across parameter sets. Furthermore, we can infer that since our energy accommodation should be consistent across all the runs, the measured lattice parameter works as indicator of this energy accommodation. This allows us to change the representative equation to the following:

\begin{aligned} Δ (L a t t i c e P a r a m e t e r) = Δ (Crystallite S i z e) \\ + Δ (D i s s o l v e d S o l u t e) \end{aligned}

(6)

Since the lattice parameter is consistent between the differing runs in this experiment, the energy that goes towards the change in crystallite size must balance the energy used towards dissolving the solute. This is what gives us the relationship seen in Figure 3, and to explain why each trend exists, we must consider the impacts of each differing ball bearing size.

Larger ball bearings result in higher energy collisions with the powder particles, allowing this material to overcome a steep energy barrier that occurs in crystallite refinement, but this is at the detriment to the total number of collisions that occur, to satisfy the conservation of energy. On the other side, smaller ball bearings are unable to drive as much energy per collision, which reduces their ability to refine crystallite size beyond an energy barrier. As stated above, these lower energy collisions are balanced out by having a much higher frequency of collision, resulting in a higher amount of solute dissolved in the materials. To simplify, driving the solution is a lower energy cost process that is dictated by the ability to collide in specific locations that force atoms of the solute into the matrix lattice. This means that it is more of a numerical probability process. Therefore, increasing the frequency of collisions over a given time would affect the solute dissolution in the alloy, whereas greater energy collisions induce more dislocation buildup in the material, refining the crystallite size further. From the results presented for this material, a ball bearing size of ¼ inch appears to be a viable compromise in achieving highly energetic collisions to reduce the microstructure to a relatively minimum crystallite size, while still maintaining a large quantity of solution-driven impacts for adequate alloying.

It is of note that the differing sizes of ball bearings result in varying levels of local heating upon impact due to the energetics of each collision, which could influence the diffusion of solute material and particle welding behavior. However, the reported particle sizes are within error for the range of bearing sizes indicating that the result in particle morphology is largely the same across the experiments. Additionally, randomized temperature measurements of the external surfaces of milling vessels resulted in values slightly above laboratory temperatures, which are largely non-metallurgically relevant to the macro state of these powders.

Effect of ball-to-powder ratio

To further support that the ball milled powder accommodates the energy through grain size reduction and solution formation, varying BPRs were studied while maintaining a constant mass of ball bearings. This variation of BPR change was chosen over changing the ball bearing mass to keep the total energy input consistent between sections of this work. A milling time of 15 h, and ¼ inch 52100 steel ball bearings were used for each run. Reducing the BPR increases the powder charge, dispersing the energy input across a greater mass. As a result, individual particles experience less energy, resulting in coarser crystallite sizes and less refinement of the lattice parameter (Figure 5(a) and (b)). This is also seen in planetary milling studies such as that done by Gotor et al., where it is shown that increasing the powder charge reduces the overall refinement in the particles.^29,30 From these results, there does not seem to be a difference greater than the spread calculated in section “Variation within a milling recipe” for the solute dissolution between the different BPRs used. However, the stagnation of this result may be due to a “smothering” of particle interactions when increasing the volume beyond a certain point. From Figure 5(c) we should consider the morphological changes to the powder as consistent, so the energy accommodation through this pathway is constant between experiments. All images of these powders are in Appendix C, as well as the table containing raw values for the refined data.

Figure 5.

Refined (a) lattice parameters, (b) crystallite sizes and Cr content, and (c) particle size analysis for W-Cr powders milled under varying BPRs for 15 h.

One would expect that milling times can be increased for these lower BPRs to achieve the same resulting powders over a linear scale in time. For example, a powder achieved in 15 h with a 10:1 BPR would sensibly be obtained in 30 h with a 5:1 BPR. As shown in Figure 6(a), increasing milling time for lower BPRs does scale semi-linearly but does not reach the expected range seen for higher BPRs. This deviation likely arises from increased low-energy collisions, which reduce milling efficiency and refinement, extending the time required to achieve similar results. However, this increase in milling time trends how it is expected, where crystallite size is further refined and more solute is dissolved, as shown in Figure 6(b), but not the extent seen for the 10:1 BPR powders. Again, Figure 6(c) shows that no noticeable changes are found in the powder morphology aspect of this process, aside from a slight decrease in D10 value for 10:1, indicating more particle fracturing from the higher energy collisions, though the energy accommodation between these experiments is concluded to be largely constant for this powder morphology factor. These powders are imaged and provided in Appendix C, along with their tabulated refinement results.

Figure 6.

Refined (a) lattice parameter, (b) crystallite size and Cr content, and (c) particle size analysis results from W-Cr powders milled for increasing times with a BPR of 5:1.

Effect of tooling hardness

While powder charge and milling media are important considerations to the efficacy of the milling process, it is also wise to select the appropriate material for the tooling. Works such as that by Ghayour et al. have shown a difference in the milling results based on material selection, but this creates inconsistency since the used materials have varying densities, resulting in different velocities of ball bearings in the process.³¹ To overcome this issue, we utilize D2 tool steel in our custom milling vessels, as it can be tempered to varying hardness easily. With this ability, the true effect of tooling hardness can be observed without other variable changes, such as the mass or toughness of the material. Figure 7 shows the results of milling for 40, 55, and 62 HRC vessels, but only as comparative XRD scans. These were not refined values, such as what has been presented in previous sections, as they did not reach a completely milled state. These experiments were done with a 10:1 BPR, ¼ inch 52100 steel ball bearings, and 15 h of milling time to keep consistent with other experiments in this paper. Through these XRD scans, we see that the powders do not solutionize fully but have some amount, as shown by the bridging in W and Cr peaks at low angles for 40 and 55 HRC specifically. As shown in Figure 7, the sharpness of the W and Cr peaks indicates insufficient grain refinement. This is consistent with a hardness mismatch that is formed when considering the W-Cr powder is harder than the tempered tooling. In this case, the softer tooling accommodates deformation, diverting energy from powder crystallite refinement and resulting in ineffective milling of the powders.

Figure 7.

XRD scans for W-Cr powder milled in vessels of varying hardnesses (40, 55, 62 HRC). Also included are the peak positions for W and Cr phases present in the material.

Additionally, in Figure 8(a) we see that for softer tooling the particle sizes remain larger since there is not as much energy going into fracturing and welding the particles consistently. As previously stated, this energy is instead accommodated within the tooling itself when softened below the hardness of the milled material. Through the sharp W peaks found in the XRD measurements of Figure 7, we expect some amount of powder that is not milled. This is shown in Figure 8(b) and (c), which depicts the powders from 55 HRC and 40 HRC tooling, respectively. These findings highlight the need for tooling materials harder than the processed powder to maximize efficiency in the HEBM process to transfer the energy to the powder elastically versus undergoing plastic deformation.

Figure 8.

(a) Particle size analysis for the powders made in vessels of varying hardness. (b) and (c) Backscatter images for powders made in 55 HRC and 40 HRC vessels.

Conclusion

By analyzing the effects of ball bearing size, BPR, and tooling hardness, this work provides valuable insights into the mechanisms of HEBM for the immiscible W-10 wt.% Cr system. For this system, a balance of crystallite size reduction and solute dissolution was achieved with ¼ inch ball bearings at a BPR of 10:1. These findings and the trends discussed are broadly applicable for optimizing HEBM processing across various systems and highlight the critical role of parameter selection in tailoring synthesis conditions for immiscible and refractory alloys. By elucidating how energy is distributed among crystallite refinement, solute incorporation, and powder morphology, this work offers a comprehensive understanding of how HEBM parameters influence microstructure and composition. These presented results provide the following conclusions for the characterized material system:

Within a hardened tool steel milling vessel, variation between the first and subsequent milling runs is not significant and does not show any impact on the resultant powders from “seasoning” the milling vessel itself.

By varying the size of ball bearings used in the HEBM process, an optimization between crystallite size reduction and percentage of solute driven into solution can be found while achieving similar powder morphological characteristics across the board.

Decreasing BPR can provide a processing route for larger volumes of powder at the cost of milling efficiency due to cushioning effects from the extra powder that can dilute the input energy density.

Optimal milling efficiency is seen when utilizing tooling as hard as can be accessed, and at least harder than the material being produced to prevent excess energy absorption through the tooling.

Footnotes

Author contributions

CG provided the conceptualization, methodology, validation, formal analysis, investigation, data curation, and writing of the original draft. KD and BCH provided conceptualization, review and editing, project administration. GBT provided conceptualization, review and editing, resources, project administration, funding acquisition, and supervision.

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the Army Research Office (grant number ARO-W911NF-15-2-0050).

ORCID iD

Colton A Gilleland

Appendix A

Appendix B

10 h BB size	Lattice parameter	Crystallite size	Free Cr	R_wp	D₁₀	D₅₀	D₉₀
10 h BB size	Å	nm	Wt. Pct.	Pct.	µm	µm	µm
1/8	3.0993	33.2	1.06	3.11	0.62	3.01	8.27
3/16	3.0887	24.4	2.01	2.65	0.73	3.42	9.15
1/4	3.0842	19.9	2.21	2.55	1.21	6.27	17.92
5/16	3.0851	15.3	2.47	2.63	0.91	5.61	17.86
3/8	3.0871	14.8	2.71	2.67	0.88	5.39	17.13
1/2	3.0850	15.5	3.27	2.83	1.19	6.64	19.82

Appendix C

Table C1.

XRD refinement results from milling runs with varying tooling hardness, BPR, and time at a lower BPR.

Run	Lattice parameter	Crystallite size	Free Cr	R_wp	D₁₀	D₅₀	D₉₀
Run	Å	nm	Wt. Pct.	Pct.	µm	µm	µm
7.5:1 BPR 15 h	3.0886	24.9	1.89	2.69	1.06	5.36	14.99
5:1 BPR 15 h	3.0979	31.4	1.87	3.02	0.97	5.03	14.40
5:1 BPR 20 h	3.0919	24.8	1.76	2.67	0.96	4.74	13.07
5:1 BPR 30 h	3.0841	21.7	1.62	2.54	1.01	5.27	15.04

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