Introduction

Titanium carbide (TiC) and titanium diboride (TiB2) ceramics possess desired properties such as low densities, high melting points, good thermal and chemical stability, high hardness and excellent wear resistance. In particular, use of these ceramics in composites offers the advantage of enhanced fracture toughness and wear resistance over the monolithic constituent, making them attractive for applications as advanced structural materials [1, 2].

Several techniques including reactive hot pressing [1, 3–5], transient plastic phase processing [6, 7], self-propagating high temperature synthesis (SHS) (also termed combustion synthesis) [2, 8–10], and spark plasma sintering [11] have been utilized to prepare the TiC–TiB2 composites using Ti–B–C [2, 10], Ti–B4C [1, 3–9], and Ti–B4C–C [8, 9, 11] systems with proper proportions of the reactants. The reaction in these systems, however, is somewhat difficult to initiate because of the high melting temperatures of the reactants and lack of a preactivation reaction. Once initiated, however, it is explosive. The final products, on the other hand, are usually poorly consolidated and contain many cracks even though a dynamic compaction was employed immediately after the reaction was completed [8]. A possible solution to these problems is to incorporate the metals with low melting points and/or reasonable reactivity with titanium for formation of low-melting intermetallics into the reactants, as did in the Al–Ti–C [12, 13] and Ni–Ti–BN systems [14], where the addition of Al to Ti–C reactants was reported to significantly lower the reaction activation energy and decrease the exothermic extent [12, 13], and a small addition (1–3 wt.%) of Ni to Ti–BN reactants was found to substantially decrease the consolidation energy and time, promote the densification and improve the fracture toughness of the synthesized composites [14]. Such studies, however, were few in the Me(metal)–Ti–B4C systems [3, 15]. For instance, with respect to the reaction in the Al–Ti–B4C system, the first and simple investigation was performed by Gotman et al. [16], who fabricated the TiC and TiB2 reinforced Al matrix composite with appreciable TiAl3 phase via the SHS reaction from a 57.6 wt.% Al–Ti–B4C preform with Ti:B4C = 3:1 (in molar ratio). The maximum combustion temperature was reported to be 1,428 K and the combustion velocity to be 0.8 mm s−1. Another indirectly relevant study was from Taheri-Nassaj et al. [17], who obtained the final products of the Al–TiB2–TiC composites, without the detectable TiAl3 phase, by reactive spontaneous infiltration of molten Al into Ti–B4C powder mixtures at 1,473 K. In addition, they suggested the following reactions:

$$ 3{\text{Al}} + {\text{Ti}} \rightarrow {\text{TiAl}}_3 $$
(1)
$$ 3{\text{TiAl}}_3 + {\text{B}}_4 {\text{C}} \rightarrow 2{\text{TiB}}_2 + {\text{TiC}} + 9{\text{Al}} $$
(2)

More details on the reaction behavior and mechanism, however, were not presented. The lack of understanding of the reaction behavior and mechanism will certainly hinder the optimization of the processing, the resultant phases and their microstructure, and eventually the properties of the composites.

In a previous article [18], we have investigated the reaction mechanism in the self-propagating reactions of the Al–Ti–B4C compacts, and in this article, we present the reaction behaviors and the resultant products. It is expected that the understanding of the reaction behaviors and mechanism would not only permit a better control of the reaction process through the regulation of processing variables, but also provide a concrete basis for the formulation of theoretical models that could be used as a guide for producing the TiC–TiB2/Al composites with tailored microstructures and properties.

Experimental procedure

The raw materials used were commercial powders of Al (99 wt.% purity, ≤29 μm particle size), Ti (99 wt.%), and B4C (∼95 wt.%). The impurities in the B4C powders were mainly free boron and carbon together with <1 wt.% Fe2O3. To examine the effect of the particle size, the B4C particles with sizes of mainly ≤3.5 μm and within 3.5–50 μm (hereafter abbreviated as ≤50 μm) and the Ti particles varying from −500 mesh (≤28 μm) to −100 mesh (74–165 μm) were used [in most runs, however, the Ti particles of −300 mesh (37–48 μm) were used, except for those specifically indicated cases]. The proportion of Ti to B4C was fixed to 3:1 in molar ratio and the Al content varied from 10 wt.% to 60 wt.% of the total weight of the mixtures. The reactant powders were mixed in a stainless-steel container for 8 h to ensure homogeneity. After mixing, the powders with suitable weights were uniaxially pressed into cylindrical compacts of ∼22 mm in diameter and ∼15 mm in height with green densities of ∼65 ± 2% of theoretical, as determined from weight and geometric measurements. For comparison, limited numbers of the Ti–B4C compacts were also prepared with the same dimensions and density.

The SHS experiments were conducted in a self-made vacuum vessel. The compact was placed on a graphite plate with a thickness of ∼2.5 mm, below which a tungsten electrode was set up as the reaction ignition source. The vessel was first evacuated and then filled with Ar at 1 atm. The reaction was initiated by an arc heating, which was generated by passing a strong current between the tungsten electrode and the graphite plate. As soon as the reaction was initiated, the power was switched off. The temperature in close vicinity to the center of the compacts was measured by W5-Re26 thermocouples and the signals were recorded and processed by a data acquisition system using an acquisition speed of 50 ms/point. The combustion process was recorded by a CCD video camera using scanning speeds of 30–60 frames per second (depending on the reaction violent extent) to evaluate the combustion wave velocity. The phase compositions in the reacted samples were identified by X-ray diffraction (XRD, Rigaku D/Max 2500PC, Japan) and their morphology at the fracture surfaces was examined by scanning electron microscopy (SEM, JSM 5310, Japan) and field emission SEM (FESEM, JSM 6700F, Japan).

Results and discussion

Theoretical calculation of adiabatic temperature

The adiabatic temperature, T ad, defined as the final theoretical temperature attained by a system undergoing an adiabatic condition, is a good measure of the exothermicity of the reaction and the state of the various phases. Providing (i) the self-propagating mode is initiated at room temperature (298 K) without any preheat, (ii) the reaction follows the overall equation of

$$ x{\text{Al}} + 3{\text{Ti}} + {\text{B}}_4 {\text{C}} \rightarrow 2{\text{TiB}}_2 + {\text{TiC}} + x{\text{Al}} $$
(3)

and (iii) no eutectic transformation (TiC + TiB2 ⇔ Liquid [19]) occurs in the resultant TiC and TiB2 phases, the value of T ad for the reaction in the Al–Ti–B4C system could be calculated using thermodynamic data from references [20, 21] according to the following equation [22],

$$ \Updelta H(298) + \int_{298}^{T_{{\text{ad}}} (298)} {\sum {n_j } } C_{\text{p}} (P_j )dT + \sum\limits_{298 - T_{{\text{ad}}} (298)} {n_j L(P_j )} = 0 $$
(4)

where ΔH(298) is the reaction enthalpy at 298 K, n j is the stoichiometric numbers, C p and L are the heat capacity and latent heat (including melting and boiling), and P j refers to the product, respectively. The calculated T ad values as a function of the reactant Al weight percent are shown in Fig. 1 together with the experimentally determined maximum combustion temperatures (T c), as will be described later. It may be mentioned that the phase and microstructural examinations on the synthesized samples with high Al contents revealed the presence of some intermediate phases such as TiAl3 and Al4C3, which were not considered here. According to Merzhanov’s empirical criterion, for the reaction to be self-sustaining in the absence of preheat, T ad should not be less than 1,800 K [23], implying a maximum addition of 52.2 wt.% Al in the reactants.

Fig. 1
figure 1

Variations in the theoretically calculated adiabatic temperature, T ad, and experimentally determined maximum combustion temperature, T c, with the Al weight percent (w Al) using two sizes of the B4C particles. It is worthwhile to mention that the T c values for the Ti–B4C samples are far beyond 2,573 K and they were determined by extrapolation from the available temperature-electromotive force function, which might have a relatively large error. On the other hand, T c for the samples with 60 wt.% Al and 50 wt.% Al with B4C ≤ 50 μm could be affected by the prolonged arc heating since the reaction was unable to self-sustain after removal of the heater. Therefore, the corresponding T c values are connected by dashed lines in the figure

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Reaction behavior and phase identification

The variation in the maximum combustion temperature, T c, with the Al weight percent (w Al) in the case of using two sizes of the B4C particles is shown in Fig. 1 for a better comparison with the value and the behavior of T ad. With the increase in w Al, both T ad and T c decrease substantially. The effect of the B4C particle size on the combustion temperature, however, is insignificant except for w Al > 40%. It was experimentally observed that when w Al = 50%, the self-sustaining reaction was successful in the samples with ≤3.5 μm B4C particles but failed in those with ≤50 μm B4C particles unless a prolonged arc heating was supplied. For w Al ≥ 60%, the reaction in all the samples could no longer be self-sustaining without a noticeable preheating effect, regardless of the B4C particle size. Such a behavior is generally consistent with the aforementioned theoretical prediction of the maximum addition of 52.2 wt.% Al in the reactants for the reaction to be self-sustaining. The measured T c values, on the other hand, are smaller than T ad when w Al ≤ 50% because of heat loss. However, the difference between them seems to decrease with an increase in the amount of Al when the small B4C particles were used. A prolonged heating for the ignition could bring a preheating effect in high Al content (w Al ≥ 50%) samples and thus increases the combustion temperature. Besides, the decreasing maximum combustion temperature with the increasing Al content also reduces the heat loss in unit time, thus making the difference between T c and T ad smaller.

Figure 2 shows the variation in the ignition delay time (t ig), which represents the time interval from the onset of heating to the initiation of the SHS reaction, with w Al when the B4C particle was 3.5 μm. As can be seen, t ig first decreases and then increases with the increase of w Al, indicating that the SHS reaction initiated more readily at a specific amount of Al (e.g., 30 wt.% Al in the present study). Previous examinations [18] on the reaction and phase formation mechanisms have demonstrated that the primary reaction between Ti and B4C could be promoted by the addition of Al through the formation of low-melting TiAln intermetallics (initially, the TiAl3 phase), which provides a much better particle contact and thus reduces atomic diffusion distance and decreases the diffusion and reaction activation energies. However, with the further increase of w Al, t ig increases substantially because the heat liberated by the reaction decreases significantly, as reflected by T ad and T c in Fig. 1. Consequently, the value of t ig shows first a decrease and then an increase behavior.

Fig. 2
figure 2

Variation in the ignition delay time (t ig) with the Al weight percent (w Al)

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Figure 3 shows the dependence of the combustion wave velocity on the Al content as well as on the B4C particle size. Clearly, the wave velocity decreases monotonically with the increase in the Al content. This result is somewhat different from that observed in the Al–Ti–C system, where the wave velocity displays a maximum value for the Al content in the range of 15–25 wt.% [12]. The B4C particle size has a significant effect on the combustion wave velocity. The velocity decreases rapidly as the B4C particle size changes from ≤3.5 μm to ≤50 μm, particularly when the Al content is low. This could be explained by the expression for the velocity of propagation based on a diffusion model [24]

$$ V^2 = \frac{{2K}} {{d^2 c_{\text{p}} \rho S}}D_0 \exp ( - E/RT_{\text{c}} ) $$
(5)

where V is the wave velocity, c p is the heat capacity of the product, ρ is the density of the product, d is the particle size of one of the reactants, S is the stoichiometric ratio of the reactants, D 0 is the diffusion preexponential coefficient, K is a constant, R is the gas constant, and E is the activation energy for the process. Assuming that the other parameters do not vary significantly with the B4C particle size, an increase in the particle size could lead to a decrease in the wave velocity in an equivalent scale.

Fig. 3
figure 3

Dependence of the combustion wave velocity on the Al content for two sizes of the B4C particles used

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Figure 4 shows the XRD results of the reaction products for the samples with various Al contents and two different B4C particles. As indicated, the reaction products depend not only on the Al content but also on the B4C particle size. For w Al ≤ 20%, the reaction products consist of TiB2 and TiC binary phases in the reacted Ti–B4C samples and TiB2, TiC, and Al in the reacted Al–Ti–B4C samples, without any intermediate phases, indicating that the reactions are complete even when the coarse B4C particles (≤50 μm) were used. For w Al = 30–40%, the reaction products are slightly different in the samples with different sizes of the B4C particles. Only TiB2, TiC, and Al are detected in the samples with ≤3.5 μm B4C particles, but in those with ≤50 μm B4C particles, in addition to the aforementioned primary phases, a small amount of TiAl3 is also observed. With a further increase in w Al, the reaction products are substantially different in these two kinds of the samples. For the samples with the fine B4C (≤3.5 μm) particles, the reaction products consist of the primary Al, TiB2, and TiC phases together with some TiAl3 or/and Al4C3 intermediate phases; while for the samples with the coarse ones (≤50 μm), the primary phases are TiAl3, Al, and unreacted B4C, suggesting that the dominating reaction occurs between Al and Ti. These results, in turn, explain the dependence of the combustion temperature on the Al content and the B4C particle size, as shown in Fig. 1.

Fig. 4
figure 4

XRD patterns of the SHS reaction products in the samples with various Al contents for two sizes of the B4C particles [(a) B4C ≤ 3.5 μm and (b) B4C ≤ 50 μm] used: (1) 0 wt.% Al, (2) 10 wt.% Al, (3) 20 wt.% Al, (4) 30 wt.% Al, (5) 40 wt.% Al, (6) 50 wt.% Al, and (7) 60 wt.% Al

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Figure 5 shows the effects of the Ti particle size on the maximum combustion temperature and combustion wave velocity for the 40 wt.% Al–Ti–B4C samples, and Fig. 6 gives the selected XRD results of the reaction products. Compared with that of B4C, the effect of the Ti particle size is far less significant. With the decrease in the Ti particle size, the combustion temperature does not vary considerably and the wave velocity first exhibits an appreciable increase and then tends to be constant. The reaction products consist of the Al, TiB2, and TiC phases except for the case of using the −100 mesh (74–165 μm) Ti particles, in which a small amount of TiAl3 phase was found. This is not difficult to understand since most of the Ti particles react with Al to form titanium aluminides and the maximum combustion temperatures are generally higher than the melting points of both titanium aluminides and Ti. The titanium aluminides and the Ti particles (if not completely consumed) would melt during the passage of the combustion wave, making the role of the Ti particle size not so significant as that of B4C. Likewise, the effect of the Al particle size, although not examined in the present study, is thought to be of little importance.

Fig. 5
figure 5

Effects of the Ti particle size on the maximum combustion temperature and combustion wave velocity for the 40 wt.% Al–Ti–B4C samples

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Fig. 6
figure 6

XRD patterns of the SHS reaction products in the 40 wt.% Al–Ti–B4C samples with the Ti particle sizes of (a) −100 mesh, (b) −300 mesh, and (c) −500 mesh

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Microstructures

Figure 7 shows the typical agglomeration microstructures at the fracture surfaces of the reacted Ti–B4C samples. For the small B4C particles (≤3.5 μm) used, a fine hypereutectic-type structure was observed in the products (Fig. 7a), suggesting that a eutectic reaction involving the TiC and TiB2 phases might progress during the synthesis process. For the large B4C particles (≤50 μm) used, however, no such eutectic structure but a large amount of bulky TiB2 clusters were observed (Fig. 7b). It was reported by Gusev [19] that the eutectic reactions could take place in the TiCx–TiB2 system. The eutectic composition and temperature are dependent on the stoichiometry (x) of TiCx, e.g., when x = 0.6, the eutectic point is for 40.1 mol.% TiB2 at 2,910 K, and when x = 1.0, the eutectic point is for 40.2 mol.% TiB2 at 2,936 K. The experimentally determined maximum combustion temperatures in the samples with the small B4C particles (≤3.5 μm) are about 2,965–3,045 K, slightly above the aforementioned eutectic temperatures. Therefore, the occurrence of the eutectic transformation is possible in those samples and the microstructure in Fig. 7a consists of the primary TiB2 phase and the encircled eutectic TiCx–TiB2 phases, i.e., a hypereutectic microstructure because of 66.7 mol.% TiB2 in the products. On the other hand, the maximum combustion temperatures in the samples with the large B4C particles are about 2,883–2,948 K, just close to or even lower than the eutectic temperatures. Hence, the eutectic structure was unable to develop or was only weakly developed.

Fig. 7
figure 7

FESEM micrographs showing the typical agglomeration microstructures at the fracture surfaces of the reacted Ti–B4C samples for two sizes of the B4C particles used: (a) ≤3.5 μm and (b) ≤50 μm

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Figure 8 shows the typical microstructures at the fracture surfaces of the reacted Al–Ti–B4C samples (B4C ≤ 3.5 μm) with various Al contents. As indicated, the microstructures in the Al–Ti–B4C samples are quite different from those in the Ti–B4C samples. The individual TiC and TiB2 grains were largely developed, without forming a eutectic-like structure. TiC exhibits sphere or round shapes and TiB2 presents hexagonal or rectangular shapes. With the increase in the Al amount, the quantity of the TiC and TiB2 grains decreases and their size changes from several micrometers to several hundreds of nanometer. The reduction in size is mainly caused by the decrease in the maximum combustion temperature as a function of increasing w Al. Moreover, in some regions, the TiC and TiB2 grains are separately located (e.g., only the large and small TiC grains were found in Fig. 8b), which could be essentially attributed to the much higher dissociation and diffusion rates of carbon from the B4C crystal into the Ti–Al melt than those of boron, as we have described thoroughly in a previous paper [18].

Fig. 8
figure 8

SEM (a, b) and FESEM (c, d) micrographs showing the typical microstructures at the fracture surfaces of the reacted Al–Ti–B4C samples (B4C ≤ 3.5 μm) with various Al contents: (a) 10 wt.% Al, (b) 20 wt.% Al, (c) 40 wt.% Al, and (d) 60 wt.% Al

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Conclusions

Based on the preceding results, the following conclusions could be drawn:

  1. (1)

    Theoretical estimation of adiabatic temperatures shows that the reaction in the Al–Ti–B4C system could be self-sustainable for the presence of no more than 52.2 wt.% Al in the reactants without any preheat, which is generally consistent with the experimental observation.

  2. (2)

    The proper addition of Al to the Ti–B4C reactants not only lowers the ignition delay time but also reduces the reaction exothermicity and modifies the resultant microstructures. Increasing the Al content in the reactants considerably decreases the maximum combustion temperature and combustion wave velocity.

  3. (3)

    The B4C particle size has a significant effect on the ignition behavior and combustion wave velocity while that of Ti has only a limited influence. Increasing the B4C particle size retards the reaction initiation and remarkably lowers the combustion velocity. The maximum combustion temperature, however, is not significantly affected as long as the reaction could get to completion.

  4. (4)

    The reaction products are dependent on the B4C particle size and the Al content. Ideal phases consisting of only TiC, TiB2, and Al could be obtained by a cooperative control of the B4C particle size and the Al content.