# Understanding the competitive nanostructure evolution in V-doped hard metals by in-situ small-angle neutron scattering and thermodynamic-based modelling

Ahmet Bahadir Yildiz, Manon Bonvalet Rolland, R. Prasath Babu, Robert Cubitt, Susanne Norgren, Peter Hedström

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## To cite this version:

Ahmet Bahadir Yildiz, Manon Bonvalet Rolland, R. Prasath Babu, Robert Cubitt, Susanne Norgren, et al.. Understanding the competitive nanostructure evolution in V-doped hard metals by in-situ small-angle neutron scattering and thermodynamic-based modelling. Acta Materialia, 2025, Acta Materialia, 287, pp.120773. 10.1016/j.actamat.2025.120773. hal-04947351

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Full length article

# Understanding the competitive nanostructure evolution in V-doped hard metals by *in-situ* small-angle neutron scattering and thermodynamic-based modelling

Ahmet Bahadir Yildiz<sup>a,1,*</sup> <sup> ID </sup>, Manon Bonvalet Rolland <sup>a,b</sup> <sup> ID </sup>, R. Prasath Babu <sup>a,2 ID</sup>, Robert Cubitt <sup>c ID</sup>, Susanne Norgren <sup>d,e ID</sup>, Peter Hedström <sup>a,*</sup> <sup> ID </sup>

## ARTICLE INFO

### Keywords:

- Hard metals

- Grain refining

- Small-angle neutron scattering (SANS)

- Computational thermodynamics

## ABSTRACT

Grain coarsening inhibition in hard metals is regarded as controlled by formation of interface complexions. To date, however, direct experimental insights into the presence and evolution of interface complexions during sintering of hard metals have been lacking. We here present *in-situ* small-angle neutron scattering (SANS) experiments up to 1500 °C and provide first-hand evidence on the thickness and volume fraction evolution of (V,W)Cₓ interface complexions in V-doped hard metals at various sintering temperatures. The experimental data is complemented by simulations using a thermodynamic-based model to understand the mechanisms behind the nanostructure evolution. We show that there indeed exist (V,W)Cₓ interface complexions at liquid-phase sintering temperatures; and their thickness and volume fraction are strongly related to the presence of bulk (V,W)Cₓ precipitation, the V activity in the Co-rich binder phase, and the temperature. The thermodynamics-based model, including the geometry of the investigated material system, reveals that the formation of (V,W)Cₓ bulk precipitates is energetically favorable over the thickening of complexions in the stability range of bulk precipitation. This, explains the reduction in complexion volume fraction and thickness with increasing temperature up to the dissolution of bulk precipitates. Upon dissolution of bulk precipitates, enhanced interfacial layer formation occurs through the formation of new layers of lower thickness, leading to better coverage of WC grains. The provided understanding of the nanostructure evolution during sintering is expected to foster the further development of representative modelling tools.

## 1. Introduction

The search for alternative hard materials with better performance, replacing the use of high-speed steel, led to the discovery of hard metals with composite structure about 100 years ago [1,2]. WC-Co hard metals have thenceforth become critical structural material for metal cutting and rock drilling tools. They are generally produced through powder metallurgical processing routes, where the final step is liquid-phase sintering at temperatures of about 1300–1400 °C. During sintering, liquid Co-rich binder stimulates the diffusion and the densification of the

composite WC-Co [3]. Concurrently, the coarsening of the WC grains occurs [4].

The control of WC grain coarsening is key for improved tool life and performance; it is achieved effectively by WC/Co interface modification through transition metal, e.g. Cr, Ti, or V, additions [5–10]. Findings have indicated that V is the most effective additive for inhibiting both the continuous and discontinuous grain coarsening of WC at a wide range of sintering temperatures [6,7,11]. Such grain coarsening effect has been widely attributed to the presence of nano-scale (V,W)Cₓ complexions, i.e. interfacial layers, [12] formed at the WC/Co interfaces.

<footnote><sup>a</sup> Department of Materials Science and Engineering, KTH Royal Institute of Technology, SE-100 44 Stockholm, Sweden</footnote>

<footnote><sup>b</sup> UMET – Unité Matériaux et Transformations, Université de Lille, CNRS, INRAE, Centrale Lille, UMR 8207, 59000 Lille, France</footnote>

<footnote><sup>c</sup> Institut Laue Langevin, BP 156 Cedex 9, F-38042 Grenoble, France</footnote>

<footnote><sup>d</sup> Sandvik Coromant R&D, SE-126 80 Stockholm, Sweden</footnote>

<footnote><sup>e</sup> Department of Mechanical Engineering Sciences, Division of Production and Materials Engineering, Lund University, SE-221 00 Lund, Sweden</footnote>

<footnote>* Corresponding authors.
*E-mail addresses:* ahmet@scatterin.com (A.B. Yildiz), pheds@kth.se (P. Hedström).</footnote>

<footnote n="1">¹ Present address: Scatterin AB, SE-114 28 Stockholm, Sweden.</footnote>

<footnote n="2">² Present address: Outokumpu Stainless AB, SE-774 41 Avesta, Sweden.</footnote>
Yildiz et al. [10] have reported that the efficiency of grain coarsening inhibition in V-doped hard metals depends on the degree of V segregation at the WC/Co interface and the coverage of WC grains. Whilst atomic segregation is observed at minor additions, an increasing amount of V doping results in the formation of (V,W)Cₓ interface complexions and enhanced coverage of WC grains. This further reduces the total driving force for grain coarsening and interface mobility during the sintering, hence resulting in smaller WC grains.

When the amount of V addition is above the solubility limit in the Co-rich binder [13], bulk (V,W)Cₓ precipitates form. These precipitates reduce the fracture toughness and cause brittleness, i.e. they are detrimental to the performance of a hard metal [14]. Whilst reports claim that they have no effect on the WC grain coarsening inhibition [15], a recent ex-situ small-angle neutron scattering (SANS) study has shown that the formation of bulk (V,W)Cₓ precipitates during sintering may compete with the growth of (V,W)Cₓ interface complexions and reduce their volume fraction in as-sintered samples [10]. These factors make (V, W)Cₓ complexions and bulk precipitates critical microstructural constituents. The competition between the growth of complexions and the formation of bulk precipitates during the sintering yet needs to be understood.

Liquid-phase sintering of hard metals is a complex process accommodating several structural transitions including passing through solidus and liquidus points of Co-rich binder, formation of bulk precipitates, and formation of nano-scale (V,W)Cₓ interface complexions. The absolute control of the nanostructural evolution during sintering is crucial for developing novel materials and processes providing as-sintered hard metals with improved properties. Until now, nanostructure evolution during the sintering of hard metals has been solely characterized by ex-situ techniques with the most representative investigations being rapidly cooled samples, limiting information to the relative change in as-sintered structure with respect to the cooling rate [8,16–18]. The lack of *in-situ* experimental data hampers the complete understanding of structural evolution during sintering and, hence, the development of representative modelling tools accounting for the correct physics is prevented.

We here perform *in-situ* SANS experiments up to 1500 °C and track how the size and volume fraction of nano-scale (V,W)Cₓ interface complexions evolve at the different sintering temperatures in V-doped WC-Co hard metals. The complementary use of *in-situ* SANS, equilibrium thermodynamics calculations, and thermodynamic-based modelling provide an enhanced understanding of the nanostructure evolution and the nature of competition between (V,W)Cₓ complexions and bulk precipitates.

## 2. Materials and methods

As-sintered WC-11.45 wt% Co reference; and 0.14, 0.22, and 0.39 wt % V-doped WC-10.07 wt% Co hard metals were used for the investigations. The powder mixtures were liquid-phase sintered in a controlled vacuum at 1410 °C for 1 h. The chemical composition of as-sintered samples and the details of powder processing and sintering process can be found in Ref. [10]. Equilibrium thermodynamics calculations were performed by CALPHAD (CALculation of PHAse Diagrams) methodology using Thermo-Calc Software [19] and TCFE9 Steels/Fe alloys database [20] to predict the equilibrium phases together with their chemical composition, volume, and density.

### 2.1. *In-situ* small angle neutron scattering (SANS)

*In-situ* SANS measurements up to 1500 °C were carried out on the D33 beamline at the Institut Laue-Langevin (ILL), Grenoble, France [21, 22]. The experiments were performed using the time-of-flight (TOF) mode with a wavelength span of 2–14 Å at a single experimental setup: 7.8 m collimation length with sample-to-detector distances of 1.2 m (front detector) and 7.8 m (rear detector), resulting in a scattering vector

(Q) range of 0.0067–1.1682 Å⁻¹ ($Q = (4\pi/\lambda)\sin\theta$), where θ is half of the scattering angle). Square samples with a dimension of 12 mm × 12 mm × ~0.2 mm (thickness) were probed by a neutron beam of 8 mm in diameter. An ILL-type high-temperature vacuum furnace was used for the *in-situ* experiments. Since the furnace operates in a vacuum at about 10⁻⁵ mbar, i.e. about two orders of magnitude higher than the vapour pressure of Co at the liquid-phase sintering temperatures, a special sample container made of high-purity alumina was designed for preventing the possible material loss. In Supplementary Fig. S1, we present the sample container and furnace setup. The sample container consists of: (i) flat alumina plate with 1 mm thickness and (ii) alumina plate with 2 mm thickness having 15 mm × 15 mm × 0.1 mm (depth) cavity. The sample was placed in the cavity and by using high-temperature adhesive, the alumina components were sealed. The sample container was then fixed to the furnace stick using Nb wires. The as-sintered hard metals were heated to the measurement temperatures with a heating rate of 100 °C/min, and the SANS data was acquired for 5 min during the dwell time at each temperature. The reduction, correction (including subtraction of scattering originating from the furnace and sample holder), and absolute scaling (dΣ/dΩ [cm⁻¹]) of the raw SANS data were performed on the GRASP software [23]. The scattering invariant and volume fractions were determined by using the Scatterin software [24], and volume-averaged size distributions were modelled on the Irena tool suite [25].

### 2.2. Thermodynamic-based modelling

The thermodynamic-based calculations were performed to understand the competition between the formation of bulk rounded (V,W)Cₓ precipitates and the growth of the already present (V,W)Cₓ interfacial complexions. To evaluate the difference in energetics for nucleating rounded precipitates or nucleating new layers in two dimensions, the Gibbs energy change and nucleation barrier associated with the two situations were estimated in simplified geometrical considerations. Previous studies have shown that the V-rich compound is present only at WC/WC boundaries adjacent to binder pockets with (V,W)Cₓ, while it is abundant at both prismatic WC/Co and basal WC/Co interfaces [10,26]. In this manuscript, we therefore focus on the WC/Co interfacial layers and consider the thickening or thinning of grain boundary interfacial layers as a consequence of changes in the phase boundary interfacial layers.

The initial thermodynamic system consists of WC grains with prismatic grains covered by a layer of (V,W)Cₓ with thickness $h_0$ as depicted in Fig. 1.a. This description of the microstructure is in-line with the commonly observed morphologies of WC grains and (V,W)Cₓ interfacial layers in V-doped WC-Co hard metals [8,10,13]. For the sake of simplicity, the prismatic grains were considered to have the same size, i. e. same height *H* and same prismatic face edges *p*, and assumed to be not truncated. In the first situation, the existing (V,W)Cₓ layer would continue to grow as depicted in Fig. 1.b. In such case, the Gibbs energy change associated with the increase in thickness of the layer is:

<figure><img src="image_4.png" /><figcaption>**Fig. 1.** Schematic illustration of the modelled V-doped hard metal systems. (a) The initial case with a layer of (V,W)Cₓ with thickness $h_0$. (b) The first situation: the (V,W)Cₓ layers continue to grow and reach thickness h. (c) The second situation: a bulk (V,W)Cₓ precipitate with radius *r* is created between the adjacent WC grains.</figcaption></figure>
$$ \Delta G_l = -\Delta G_m V_l + S_l \sigma \quad (1) $$

with $V_l$ the volume of the layer created, $S_l$ the surface of the layer and $\sigma$ the interfacial energy. The surface $S_l$ in this calculation corresponds to the new surface area created compared to the initial situation, which consists of WC grains already covered by a layer of $(V,W)C_x$. $S_l$ is thus associated with the surface that is generated by the height growth of the additional layer, $h_0 \to h$. The expressions thus become:

$$ \begin{aligned} V_l &= 2hHp \\ S_l &= 2hH \end{aligned} \quad (2) $$

where the pre-factor 2 is due to the presence of two $(V,W)C_x$ layers: one at each of the prismatic facets as shown in Fig. 1. The chemical driving force $\Delta G_m$ for creating $(V,W)C_x$ was calculated with Thermo-Calc Software [19] using TCFE9 Steels/Fe alloys database [20] at the binder phase composition.

In the second situation, we consider that bulk $(V,W)C_x$ precipitates in a truncated cylinder shape with radius $r$ are created between two prismatic facets of adjacent WC grains (see Fig. 1.c). Sugiyama et al. [13] have previously reported the formation of island-like $(V,W)C_x$ precipitates with a hemispherical shape along the facets of adjacent WC grains. For simplicity, we here assume the presence of perfectly aligned WC grains and bulk $(V,W)C_x$ precipitates in a truncated cylindrical shape. The section of the truncated cylinder was thus kept constant along with its height. In this case, the Gibbs energy change is associated with the formation of the truncated cylinder by:

$$ \Delta G_c = -\Delta G_m V_c + S_c \sigma - S_{rem} \sigma \quad (3) $$

where $V_c$ and $S_c$ are the volume and surface of the formed truncated cylinder. $S_{rem}$ is the pre-existing surface of the interface existing between the layer of $(V,W)C_x$ and the binder that is removed while a truncated cylinder is created. The angle $\theta$ drawn in Fig. 1.a between the prismatic facets of two adjacent grains affects the volume of the truncated cylinder:

$$ V_c = \frac{\theta r^2 H}{2} \quad (4) $$

Accordingly, the surface of the truncated cylinder and the surface that is removed are:

$$ \begin{aligned} S_c &= \theta r H \\ S_{rem} &= 2Hr \end{aligned} \quad (5) $$

The calculations were performed for 0.39 wt% V-doped sample at 1200 °C. The parameters and geometrical configuration used in the calculations are listed in Supplementary Table S1 and S2, respectively.

### 3. Results

#### 3.1. Interpretation of in-situ SANS data

Fig. 2 shows two examples of in-situ SANS patterns (the differential scattering cross-section $d\Sigma/d\Omega$ vs scattering vector $Q$) during the thermal treatment of 0.22 % V sample, representing 5 min isothermal hold at 1100 °C (Fig. 2.a) and 1500 °C (Fig. 2.b). The sample holder, i.e. empty sample holder, was measured using the same in-situ conditions, and the associated strong scattering contribution (shown as black crosses) is subtracted from the scattering patterns. The remaining patterns, shown as blue dots, represent solely the scattering originating from the nano-structure in the V-doped hard metals. In these particular examples, the comparison between the scattering patterns and background pattern (shown as blue lines) reveals that whilst the overall scattering intensity reduces in the low-Q region including around 0.1 Å⁻¹, more pronounced scattering is observed at the high-Q region at 1500 °C, which could be attributed to the structural refinement in nanostructural features with increasing temperature.

In order to track the temperature evolution of the hard metals' nanostructure, we start analyzing the SANS patterns by calculating the scattering invariant $Q^n$, describing the area under $(d\Sigma/d\Omega)Q^2$ curve over the Q-range [27]:

$$ Q^n = \int_0^\infty \frac{d\Sigma}{d\Omega \cdot Q^2} dQ \quad (6) $$

Fig. 3.a shows the evolution of $Q^n$ in 0 %, 0.14 %, 0.22 %, and 0.39 % V doped hard metals as a function of temperature. A strong decrease in the $Q^n$ up to 1100 °C is observed in all samples. Whilst this reduction in reference (0 % V) sample continues almost linearly at higher temperatures, $Q^n$ in V-doped samples diverges strongly from the reference state. Four reasons can lead to such general temperature-dependent reduction in $Q^n$: (i) reduction in the nuclear scattering length density difference, i. e. scattering contrast, between Co-rich binder and WC ($\Delta SLD_{WC-CO}$) due to its dependence on composition and density of phases; (ii) reduction in magnetic scattering contribution; (iii) thermal expansion of probed sample; and (iv) attenuation due to the thermal motion, i.e. increased displacement of an atom from its average position. The equilibrium compositions and densities of Co-rich binder and WC phases at in-situ experiment temperatures were calculated for the as-sintered compositions. The thermodynamic predictions were later used for calculating the nuclear scattering length density (SLD) values. Increasing temperatures stimulate the W dissolution in the Co-rich binder phase and bring higher binder density. The density of WC on the other hand reduces due to the thermal expansion. Therefore, the SLD of each phase evolve with the compositional changes by [28]:

<figure><img src="image_5.png" /><figcaption>Fig. 2. In-situ SANS patterns of 0.22 wt% V-doped hard metal at 1100 °C (a) and 1500 °C (b) before and after subtracting the scattering associated with the sample holder.</figcaption></figure>
<figure><img src="image_6.png" /><figcaption>Fig. 3. Scattering length density difference ΔSLD between the Co-rich binder phase and WC (a) and the volume evolution of hard metal systems (1 mol) up to 1600 °C calculated by Thermo-Calc Software [19] and TCFE9 Steels/Fe alloys database [20] for the as-sintered compositions given in Ref. [10] (b). Scattering invariant in the measured hard metal systems (c).</figcaption></figure>

$$ SLD_k = \frac{(\sum_i b_i \cdot x_i) \cdot d \cdot N_A}{M} \qquad (7) $$

where $b_i$ and $x_i$ are the bound coherent scattering length and atomic concentration of the element $i$, respectively. $N_A$ is the Avogadro constant; and $d$ and $M$ are the density and molar mass of the phase k. Fig. 3.b shows the evolution of $\Delta SLD_{WC-Co}$ between the Co-rich binder and WC, half of which determines the nuclear scattering length density difference between interfacial (V,W)C$_x$ morphologies with matrix and WC phases. As seen, the $\Delta SLD_{WC-Co}$ is predicted to decrease with increasing temperatures. This should be above the freeze-in temperature of 900 °C, i.e. the temperature below which the diffusion is negligible, causing a reduction in $(d\Sigma/d\Omega)_{NUC}$ as it evolves with the square of $\Delta SLD$. Since the magnetic moment of Co decreases with increasing temperature, a similar reduction in total $d\Sigma/d\Omega$ up to Curie temperature of <1100 °C (for alloyed Co) is expected from the magnetic scattering contribution of ferromagnetic Co-rich binder pockets. Together with the aforementioned SLD effect, the thermal motion may lead to lower $(d\Sigma/d\Omega)_{NUC}$; however, the prediction of its degree is beyond the scope of this work. Finally, a constant slit size is used during in-situ SANS experiments; and, as seen in Fig. 3.c the volume expansion of the hard metal sample takes places at elevated temperatures, meaning the probed mass of the material would be lower; and, accordingly the $d\Sigma/d\Omega$ would reduce with thermal expansion at elevated temperatures. To track the V-doping related nanostructural evolution, interpretation of the SANS patterns thus needs to be done carefully by taking the above-mentioned

temperature effects under consideration.

The volume fraction ($f_v$) of nano-scale features can be calculated using $Q^n$ by [27]:

$$ Q^n = 2\pi^2(\Delta SLD_{WC-Co})^2 f_v (1 - f_v) \qquad (8) $$

Assuming a diluted spherical particle system, the size distribution of scatterers can be calculated by [25,29]:

$$ d\Sigma/d\Omega = (\Delta SLD)^2 \int |F(Q, r)|^2 (V(r))^2 N_p(r) dr + BKG \qquad (9) $$

where $F(Q, r)$ is the sphere form factor, $F(Q, r) = (3(\sin(Qr) - (Qr)\cos(Qr)))/(Qr)^3$ [30], $V(r)$ and $N_p(r)$ are the volume and number distribution of scatterers with radius $r$, respectively. For spherical scatterers, the volume-averaged radius distribution is thus $D_v(r) = N_p(r) \cdot (4/3\pi r^3)$.

Here $f_v$ and $D_v(r)$ accounts for the sum of both the nanoscale Co-rich binder pockets and the (V,W)C$_x$ interfacial layers over the Q-range as the SANS signal in the V-doped WC-Co system is mainly originating from features of this size. The magnetic SANS signal has recently been used for the separation of the scattering contribution of ferromagnetic Co-rich binder pockets [10]. However, above the Curie temperature of Co (1100 °C), the separation of scattering contributions of binder pockets and nanoscale interfacial layers becomes infeasible. Nevertheless, by using the as-sintered samples and due to the grain coarsening inhibition effect, one can make benefit of the in-situ experiments and assume that the size
of Co-rich binder pockets – and accordingly that of WC grains- does not change during the heat treatment. The nanostructural evolution of (V, W)Cₓ can thus still be monitored; however, the reported values of e.g. volume fraction and size distribution amplitudes of (V,W)Cₓ interfacial layers, only give information regarding the relative changes in the sample with temperature and cannot be taken as quantitative.

## 3.2. Nanostructure evolution at sintering temperatures

Fig. 4.a shows the evolution of relative volume fraction ($f_v$) in the hard metals at various in-situ heat treatment temperatures. Fig 4.b, c, and d illustrate the evolution of volume-averaged pseudo-size (thickness) distribution ($D_v(D)$) of (V,W)Cₓ interfacial layers in V-doped hard metals. These calculations were performed using $\Delta SLD_{WC-Co}$ values presented in Fig. 3.b; and, normalization was applied to take the thermal expansion into account (Fig. 3.c). In the un-doped state (0 % V sample), $f_v$ represents the binder pocket volume fraction and serves as a reference to compare with V-doped systems. In this sample, $f_v$ decreases linearly up to 1100 °C; and, above 1200 °C no significant evolution is observed in binder pockets. This reduction in $f_v$ up to 1100 °C is also observed in V-doped hard metals, and it is attributed to the decreased magnetic scattering contribution of binder pockets.

Upon reaching 1200 °C, $f_v$ increases in both the 0.14 % and 0.22 % V-doped hard metals. As shown in the volume-averaged size distributions in Fig 4.b and c, the thickness of the (V,W)Cₓ interfacial layer decreases while the volume fraction, i.e. the area under the $D_v(D)$ curve, increases.

This temperature is above the stability range of bulk (V,W)Cₓ precipitation (see Table 1 for the formation temperature of bulk precipitates and solidus and liquidus temperatures) in both compositions. The increase in $f_v$ and $D_v(D)$ suggests enhanced nanoscale (V,W)Cₓ interfacial layer formation. This likely occurs through consumption of V in binder phase and dissolution of bulk (V,W)Cₓ (in 0.22 % sample) as the interfacial layers decrease the WC/Co interfacial energy [31]. This increase in volume fraction and decrease in thickness indicate that the enhanced interfacial layer formation does not result from growth and coarsening of pre-existing layers. Instead, it occurs through the formation of new layers of lower thickness, leading to better coverage of WC grains. In contrast, in the 0.39 % V sample, we surprisingly observe thinner (V,W) Cₓ interfacial layers (Fig. 4.d) with reduced $f_v$ (Fig. 4.a). In this sample, both (V,W)Cₓ interfacial layers and bulk precipitates are predicted to

<caption>**Table 1**</caption>

Equilibrium thermodynamics calculations. Solidus and liquidus points of Co-rich binder phase and the formation temperature of bulk (V,W)Cₓ precipitates, i.e. the bulk precipitates are not stable above this temperature. The calculations were performed in Thermo-Calc Software [19] using TCFE9 Steels/Fe alloys database [20].

<table><thead><tr><th></th><th>0 % V</th><th>0.14 % V</th><th>0.22 V</th><th>0.39 V</th></tr></thead><tbody><tr><td>Formation T of bulk (V,W)C<sub>x</sub> [°C]</td><td></td><td>1020</td><td>1180</td><td>1314</td></tr><tr><td>Solidus [°C]</td><td>1312</td><td>1312</td><td>1305</td><td>1300</td></tr><tr><td>Liquidus [°C]</td><td>1349</td><td>1348</td><td>1344</td><td>1337</td></tr></tbody></table>

<figure><img src="image_7.png" /></figure>

<figure><img src="image_8.png" /></figure>

<figure><img src="image_9.png" /></figure>

<figure><img src="image_10.png" /><figcaption>**Fig. 4.** In-situ SANS results. (a) Volume fraction evolution. (b-d) Volume-averaged size (thickness) evolution of (V,W)Cₓ interfacial layers in 0.14 % (b), 0.22 % (c), and 0.39 % (d) V-doped WC-Co hard metals. The reported values of volume fraction and size distributions should only be used for studying the relative changes in the sample.</figcaption></figure>
co-exist at 1200 °C, as the temperature is about 100 °C lower than the formation temperature of bulk (V,W)Cx precipitates (Table 1) [10]. This suggests preferential growth or coarsening of bulk (V,W)Cx. Such competition between the interfacial layers and bulk precipitates is further discussed in the following sections.

At 1300 °C, i.e. about the solidus temperature of the Co-rich binder (see Table 1), a reduction in $f_v$ and interfacial layer thickness are accompanied by a strong reduction in the amplitude of the interfacial layer $D_v(D)$ in the 0.14 % V sample. In the 0.22 % V sample, on the other hand, the presence of thinner interfacial layers with decreased $D_v(D)$ amplitude occurs together with an increase in $f_v$. The observed refinement of interfacial layers in both the 0.14 % and 0.22 % V samples is expected due to the higher solubility of V in the binder. However, the divergent scattering behavior, i.e. increase in $f_v$ in 0.22 % V sample, might be attributed to the possible co-existence of the liquid binder phase with different scattering contrast. For the 0.39 % V sample, the temperature is just under the formation temperature of bulk (V,W)Cx precipitates, and it is predicted that the bulk precipitates with lower volume fraction may still co-exist with the interfacial layers. We observed a further reduction in $f_v$, while the amplitude of the interfacial layer $D_v(D)$ remains constant, and the interfacial layer thickness increases. It should be noted that the $D_v(D)$ represents the volume-averaged size distribution and thus even though the amplitude in distribution is maintained, higher thickness value means lower number density. This suggests that some interfacial layers are dissolved while others grow, leading to fewer WC grains being covered by interfacial layers.

At 1350 °C, SANS analysis confirms again the presence of interfacial layers in 0.14 % V sample, while the average thickness of interfacial layers amounts to about ¾ of the ones at 1100 °C. In the 0.22 % V sample, the temperature increase from 1300 to 1350 °C results in a strong reduction in $f_v$, while the reduction in $D_v(D)$ amplitude reveals that there are now fewer WC grains covered by interfacial layers. With the dissolution of bulk (V,W)Cx precipitates in binder phase above 1314 °C, an opposite trend is observed in 0.39 % V sample: a strong increment in $f_v$ comes together with enhanced interfacial layer formation indicated by a strong increase in $D_v(D)$ over a wider range of thickness.

Further temperature increment to 1410 °C, i.e. liquid-phase sintering

temperature, causes a pronounced reduction in $f_v$ in 0.14 % V sample. This is accompanied by thinner interfacial layers with reduced amplitude and width of $D_v(D)$ curve, suggesting decreased WC grain coverage, albeit density-functional theory (DFT) -based interfacial phase-diagram calculations predict no stable interfacial layers above 1370 °C [10,32]. The average thickness of the interfacial layers corresponds to about 60 % of the thickness at 1100 °C. In 0.22 % and 0.39 % V-doped samples, SANS measurements at 1410 °C and 1500 °C reveal that $f_v$ tends to decrease with increasing temperatures. Whilst the thickness of interfacial layers reduces with increasing temperature, surprisingly, their distributions reveal increased amplitude and accordingly enhanced WC coverage even at 1500 °C.

Fig. 5 shows the V activity in solid and liquid Co-rich binder in V-doped hard metals calculated for the as-sintered compositions. We find abrupt changes in V activity in solid and liquid Co-rich binder during melting, which have a strong influence on the $f_v$ (Fig. 4.a). Between 1300 and 1350 °C, the activity graphs reveal three different changes in the V activity corresponding to different V additions. For example, upon reaching 1350 °C in the 0.14 % V sample, i.e. about the liquidus temperature of the Co-rich binder, no important change is observed in $f_v$ and V activity in the binder phase. In the 0.22 % V sample, strong reduction in V activity is accompanied by a reduction in $f_v$. In contrary, in the 0.39 % V sample, we observe a jump in V activity and $f_v$.

### 3.3. Thermodynamic-based modelling

In order to understand the mechanism underlying the preferential formation of bulk (V,W)Cx precipitates, we model two representative situations and investigate the work of formation for creating additional (V,W)Cx interfacial layer or bulk precipitate with truncated-cylinder, i.e. wedge, shape. As schematically illustrated in Fig. 1, the modelled systems include two adjacent hexagonal prism WC grains with $WC_{(0001)}/Co$ and $WC_{(1010)}/Co$ interfaces covered by (V,W)Cx interfacial layers. In Fig. 6, we present the thermodynamic-based modelling results, modelling the equilibrium conditions in the 0.39 % V-doped hard metal system at 1200 °C. Fig. 6 shows the evolution of Gibbs energy change $\Delta G$ as a function of the created volume of (V,W)Cx layer or truncated cylinder bulk precipitate. There is no nucleation barrier in these configurations, i.

<figure><img src="image_11.png" /><figcaption>Fig. 5. Evolution of V activity in solid and liquid Co-rich binder in 0.14 % (a), 0.22 % (b), and 0.39 % (c) V-doped WC-Co hard metals calculated by Thermo-Calc Software [19] using TCFE9 Steels/Fe alloys database [20].</figcaption></figure>
<figure><img src="image_12.png" /><figcaption>**Fig. 6.** Mean-field simulations. Evolution of Gibbs energy change as a function of the created volume of (V,W)Cₓ layer and truncated cylinder bulk precipitate in 0.39 % V-doped hard metal system at 1200 °C.</figcaption></figure>

e. the Gibbs energy change is always negative. For the same (V,W)Cₓ volume, the formation of bulk (V,W)Cₓ between the adjacent WC grains leads to a higher gain in energy compared to the growth of nano-scale (V,W)Cₓ layers. This makes, for the given geometrical and thermodynamic configurations, that the formation of bulk precipitates is always favorable over the growth of interfacial layers. It is here worth noting that the chemical driving force for the (V,W)Cₓ formation (ΔGm in Eqs. (1) and (3)) is indeed the same in the two geometrical configurations. Such a variance in the ΔG thus originates from the evolution of total interfacial energy in the simulated configuration. It is important to point out that the modelling results are only based on thermodynamics and do not involve any kinetics. Therefore, for a small difference in the Gibbs energy change between the two configurations, i.e. for a small precipitate volume created, see Fig. 6, the interfacial layer formation might be favored. From the microstructural evolution point of view, it also indicates that for a small supersaturation of the binder, growing the (V,W)Cₓ layers might be sufficient and faster to reduce the overall energy of the system. When the supersaturation increases, the reduction would not be sufficient to promote the growth and coarsening of the existing layers. Indeed, the expected volume fraction of (V,W)Cₓ that needs to be created increases with the supersaturation. For large precipitate volume, Fig. 6 shows that the competition between the cost of the interface creation and the gain in the created volume of (V,W)Cₓ is largely more favourable for the wedge-shaped bulk precipitates. It is finally important to highlight that the bulk precipitate results in Fig. 6 has been obtained for a specific angle between the prismatic facets θ (See Eq. 4). For example, an increase in this angle denotes that the prismatic grains position further away from each other. In that case, the energy difference in the gain for creating wedges instead of growing the (V,W)Cₓ layers becomes smaller. It is therefore expected to observe more pronounced bulk precipitate formation when the binder volume fraction is smaller.

## 4. Discussion

We here show direct experimental evidence that the volume fraction and thickness of (V,W)Cₓ interfacial layers is strongly affected by the temperature, presence of (V,W)Cₓ bulk precipitates, and V activity in the Co-rich binder phase. A previous TEM study on rapidly-cooled hard metals from liquid-phase sintering temperature (1390 °C) reported that the thickness of (V,W)Cₓ interfacial layers can reach about five atomic layers (about 1.2 nm) at the WC(0001)/Co interface and two atomic layers at the WC(1010)/Co interface [8]. Higher layer thickness observed at the

WC(0001)/Co interface stems from the smaller lattice misfit with (V,W)Cₓ [15] and larger reduction in interfacial energy [31]. In the present work, in-situ SANS analysis at liquid-phase sintering temperature of 1410 °C shows that the volume-averaged pseudo-size (thickness) distributions of (V,W)Cₓ interfacial layers reach maxima at about 15 Å in 0.14 % V and 16 Å in 0.22 % and 0.39 % V samples. These values are thus in-line with the published thickness values in the literature that has been shown to be affected by the C content [18]. The small difference with the TEM investigation is attributed to the sphere form factor [30] used in the analysis. The sphere form factor is widely used for small-angle scattering analysis of non-spherical structural features and provides reliable size information for polydisperse systems [9], though the results become questionable especially in the systems with large aspect-ratio scatterers [33]. For example, Supplementary Fig. S2 shows the simulated SANS patterns of (i) monodisperse spherical [30] scatterers with 10 Å diameter and (ii) monodisperse infinitely large lamellar [34] scatterers with a thickness of 10 Å. As can be seen, the scattering of lamellar objects appears at the lower-Q range. Therefore, the use of lamellar shape factor for modelling of in-situ SANS patterns would bring smaller interfacial layer thickness values; and, for precise measurement of interfacial layer thickness in hard metals, representative form factor needs to be developed. Along with TEM investigations on rapidly-cooled samples, interfacial phase diagrams built by equilibrium thermodynamics and DFT calculations are used for predicting interface structure evolution at the sintering temperatures [10,32]. It has been shown that the formation of two atomic layer thick (V,W)Cₓ at the WC(0001)/Co interface brings the most energetically favourable configuration, and the calculation of interfacial transition temperature was thus performed considering two atomic layers [35]. However, in-situ SANS reveals that the thickness of (V,W)Cₓ interfacial layers changes during the sintering: it reduces with increasing temperature above the liquidus temperature of the Co-rich binder phase. We thus believe that the present in-situ investigations provide important experimental insights into the complex interface structure evolution and will foster further development of representative modelling tools.

Thermodynamic-based modelling reveals that within the stability range of bulk (V,W)Cₓ precipitation, the formation and coarsening of bulk precipitates become energetically favourable over the coarsening of interfacial layers. This process is driven by the reduction in total interfacial energy. Initially, the hard metal system reduces the interfacial energy of WC(0001)/Co and WC(1010)/Co interfaces effectively by the formation of “interfacially stabilized” (V,W)Cₓ layers [12], creating (V, W)Cₓ/Co interfaces. Further reduction in total interfacial energy is then achieved by bulk precipitation between the adjacent WC grains, decreasing the (V, W)Cₓ/Co interface area and accordingly the total interfacial energy. In the investigated hard metal systems, the bulk (V, W)Cₓ precipitation takes place at expense of weakened V segregation at the WC/Co interfaces. As observed in 0.39 % sample, bulk precipitation leads to thinner (V,W)Cₓ interfacial layers with lower volume fractions. Increasing temperatures where the dissolution of bulk precipitates is expected to reach completion, i.e. 1200 °C in 0.22 % V and 1350 °C in 0.39 % V samples, more pronounced interfacial layer formation is observed. Such variance in WC/Co interface structure is of particular importance for grain coarsening inhibition, which is driven by the reduction in the mobility and total interfacial energy of WC/Co interfaces [10]. (V,W)Cₓ interfacial layers act as pinning points, exert back-driving force (Zener force) [36,37], and reduce the WC/Co interface mobility. The applied Zener force would reduce in accordance with the reduction in the volume fraction of (V,W)Cₓ interfacial layers and; therefore, can hamper the grain coarsening inhibition effect. Since the bulk (V,W)Cₓ precipitates form on the existing (V,W)Cₓ interfacial layers, they instead reduce the total interfacial energy of (V, W)Cₓ/Co; and, thus they are likely to have no contribution to the grain coarsening inhibition through the WC/Co interfacial energy reduction. The stability range of bulk precipitation thus needs to be known, and the composition
of the hard metal and sintering parameters should be chosen accordingly.

Along with the temperature and composition, the kinetics of such bulk precipitation would depend on the number of adjacent WC grains, i. e. grain impingement. For example, for a constant V/Co ratio, increasing binder volume fraction reduces the probability of grain impingement to take place [38] and thus the number of nucleation sites for possible bulk precipitation would be diminished. In addition, it is also thermodynamically shown that such an increase in the binder fraction would lead to a smaller energy gain difference between the layer and wedge-shaped bulk precipitate configurations. Furthermore, the binder pocket size evolves proportionally with the WC grain size [9]. Therefore, without the need of changing the hard metal composition, the use of smaller WC grains in the starting powder mixture could lead to a higher number of impingements and adjacent WC grains, facilitating the bulk (V,W)Cₓ precipitation. As this type of (V,W)Cₓ bulk precipitation is shown to be promoted by interface properties, the stability region may extend the temperatures beyond the equilibrium range through the “interface stabilization” effect [12]. The impact of binder volume fraction and WC starting powder size on the kinetics and equilibrium properties of bulk (V,W)Cₓ precipitation remain to be explored.

## 5. Conclusions

In the present work, we have provided the first *in-situ* experimental evidence on the presence of (V,W)Cₓ complexions at sintering temperatures in hard metals. By complementing the experimental data with thermodynamic-based modelling and equilibrium thermodynamic calculations, we have explained how the nanostructure evolves during different stages of sintering.

We have shown that the thickness and volume fraction of complexions varies with the amount of V-doping and temperature, and the reported complexion thickness values are comparable with previous TEM studies. By modelling the thermodynamic stability of different geometrical configurations, we have revealed that the formation and coarsening of bulk (V,W)Cₓ precipitates are favoured over thickness increase in (V, W)Cₓ complexions. During the sintering, the total interfacial energy is initially reduced by the formation of (V,W)Cₓ complexions, i.e. replacement of WC/Co interfaces with (V,W)Cₓ/Co, which generates the grain coarsening inhibition. Within the stability range of bulk precipitates, further reduction in total interfacial energy is then achieved by the formation of bulk precipitates on the existing interface complexions. Around the solidus and liquidus temperatures of the Co-rich binder phase, we have observed abrupt changes in the interface structure. This behaviour is attributed to the distinct alteration of V activity in the Co-rich binder phase. However, further work is needed for the complete understanding of the scattering response around solidus and liquidus temperatures. Finally, the temperatures above the liquidus point have brought thinner complexions, which is further amplified by the reduction in V addition level.

## Data availability

The data that support the findings of this study are available on Ref. [22].

## CRediT authorship contribution statement

**Ahmet Bahadir Yildiz:** Writing – original draft, Visualization, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. **Manon Bonvalet Rolland:** Writing – review & editing, Visualization, Methodology, Investigation, Formal analysis. **R. Prasath Babu:** Writing – review & editing, Methodology, Investigation. **Robert Cubitt:** Writing – review & editing, Resources, Methodology, Investigation. **Susanne Norgren:** Writing – review & editing, Supervision, Resources, Methodology, Funding acquisition, Conceptualization. **Peter

**Hedström:** Writing – review & editing, Supervision, Resources, Project administration, Methodology, Funding acquisition, Conceptualization.

## Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## Acknowledgements

This research was funded by the Swedish Foundation for Strategic Research (SSF) within the Swedish national graduate school in neutron scattering (SwedNess). The work was performed in collaboration with the SSF funded project "Sintering non-homogeneous structures to enhance performance". Authors gratefully acknowledges the financial support provided by KTH Materials Platform and ILL for the costs associated with the SANS experiments.

## Supplementary materials

Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.actamat.2025.120773.

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