Mechanisms of Self-Sustained Reaction in Mechanically Induced

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C: Physical Processes in Nanomaterials and Nanostructures

Mechanisms of Self-Sustained Reaction in Mechanically Induced Nanocomposites: Titanium Nitride and Boron Joshua M Pauls, Natalia F Shkodich, and Alexander S. Mukasyan J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.9b01521 • Publication Date (Web): 03 Apr 2019 Downloaded from http://pubs.acs.org on April 3, 2019

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The Journal of Physical Chemistry

Mechanisms of Self-Sustained Reaction in Mechanically Induced Nanocomposites: Titanium Nitride and Boron Authors: J. M. Pauls1,N.F. Shkodich2, A. S. Mukasyan1* 1Department

of Chemical and Biomolecular Engineering, University of Notre Dame,

Notre Dame, Indiana, 46556, USA. 2National

University of Science and Technology MISiS, Moscow, 119049, Russia

*corresponding author: [email protected]

ACS Paragon Plus Environment

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ABSTRACT We report the results from investigation of the mechanisms of self-sustained reaction in mechanically-induced TiN/B nanocomposites. The exothermic displacement reaction, 3B+TiN->BN+TiB2, with an adiabatic reaction temperature of 1905 K, was initiated through two different means; localized thermal heating and mechanical stimulation by high-energy ball milling (HEBM). Comprehensive studies strongly indicate that chemical interaction in the system involves three main stages. Solid-state mass transfer, likely the substitutional diffusion of B into a nitrogen deficient TiNx crystal lattice, is responsible for the formation of TiB2 during the first stage of the reaction (1350 – 1500 K) under ambient pressure. Thermal gravimetric analysis coupled with mass spectrometry demonstrated the evolution of gas phase nitrogen from TiN during an intermediate stage of the reaction in the temperature range of 1500–1800 K. Electron microscopy results show the formation of h-BN along the pores present in the initial composite thus indicating reaction of gaseous nitrogen with boron during the final reaction stage. In addition, propagation characteristics of an oscillatory spin combustion regime in the TiN3B system were analyzed using high-speed infrared imaging, which suggest a strongly nonlinear spin combustion mode.


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1. INTRODUCTION Self-sustained reactions, reactions that once initiated proceed without any external energy sources, are widely used for a variety of applications, such as the fabrication of materials via combustion synthesis (CS), joining and cutting of refractory solids, and as high-density energy sources1–3. A wide range of different reactions may proceed in a selfsustained manner, including: (i) between elements, such as metal-metal (e.g. Ni-Al), metal – nonmetal (e.g. Ti-B), or metal/nonmetal – gas (e.g. Ti-N2; B-N2); and (ii) between a compound and an element, such as thermites, metal oxide – reducing metal (e.g. Co2O3-Al). In order to control the material properties of the reaction products, the mechanism of chemical processes under CS conditions must be understood, and many studies have investigated the fundamentals of self-sustained reactions for the systems mentioned above3. Reactions including compounds are typically subjected to further classification. Single displacement reactions (1) are reactions in which one reactant replaces one component of the other reactant. Thermite reactions (2) represent a specific type of displacement reactions, but have historically been considered a separate class of reaction. Metathesis reactions (3) are double displacement reactions that involve the exchange of cations and anions between the reactants to form products. AB + C →AC + B (example: Fe + CuSO4 → FeSO4 + Cu)

(1)

MeIO + MeII → MeIIO + MeI (example: Fe2O3 + Al → Fe + Al2O3)

(2)

AB + CD → AD + CB (example: MoCl5+ Na2S → MoS2 +NaCl)

(3)

It has been demonstrated that both single and double displacement (metathesis) reactions can be exothermic enough to react in a self-sustained regime and both lead to the


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formation of a wide variety of materials. To the best of the authors’ knowledge, metathesis systems were introduced to the field of CS by I. Parkin4. However, only recently have breakthroughs taken place permitting this type of reaction to fabricate a variety of bulk materials, including borides, nitrides and carbides5,6. Titanium nitride (TiN) and boron (B) is an interesting example of a single displacement reaction that allows the use of a solid nitrogen source (TiN) to fabricate a refractory BN-TiB2 composite ceramic. Boron nitride (BN) and titanium diboride (TiB2) are refractory materials with favorable electric and thermal properties as well as chemical stability at high temperatures (T > 1000 K)7,8. In general, boride and nitride-containing composites are known for their high melting points, oxidation resistance, hardness, as well as chemical and thermal stability. Applications such as thermal shields, coatings during refractory processing, and cutting tools have been suggested for such materials9–11. A high pressure polymorph of BN, cubic BN, possesses mechanical properties comparable to those of diamond. This reactive system was used in the reactive sintering mode by Matsudaira et al.12 to produce a TiB2-rich ceramic powder. The combustion synthesis routes in this system were also investigated by Manukyan et al.13. Their conclusion was that the reaction is not exothermic enough and allows the self-sustained regime of propagation only after chemical activation, i.e. addition of pure Ti to the system or conducting the reaction in a nitrogen atmosphere with excess boron, both of which increase the total heat release either due to reaction of Ti with excess B to form TiB2, or due to N2 gas reacting with B to form BN.


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However, we recently demonstrated another method to enhance reactivity in this system by applying a technique known as mechanical activation (MA)14. Specifically, high-energy ball milling (HEBM) of the initial mixture of boron and titanium nitride powders produces finely mixed TiN/B composite particles with greatly increased surface contact area between the reactants, where native oxide layers, which inhibit diffusion, have been disrupted, and the overall diffusion scales necessary for reaction have been reduced by two to three orders of magnitude. This allowed us to develop a novel route for the synthesis of the super-hard BN polymorph, cubic boron nitride, under shock-induced reaction conditions. The reaction mechanism in this system remains unknown. As it was previously shown15, and will be further discussed below, this system theoretically belongs to the solid-flame type of self-sustained reactions. This means that the adiabatic reaction temperature is well below any phase transformation temperature for all precursors, potential intermediates, and final products. In this case, the transport of nitrogen and boron is expected to occur via solid-state pathways within the composite TiN/B particles. In this paper we present results on the combustion propagation characteristics and the reaction mechanism of a high-purity mixture of TiN+3B, prepared using high-energy ball milling, and reacted under inert atmosphere. The conditions studied included reactions initiated by localized thermal heating and mechanically stimulated reaction occurring during HEBM. 2. METHODS 2.1.Thermodynamic Calculations


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Thermodynamic analysis of the TiN-B system was performed using the software package THERMO16. The adiabatic reaction temperature (Tad), or the maximum attainable temperature for complete reaction in a thermally isolated system depends on the initial conditions and ratio of the reactants. Tad are shown in Figure S1 for TiN/B molar ratios of 1:X (for X, 2-4) and an initial temperature and pressure of 300 K and 1 atm. Tad for the 1:3 TiN/B mole ratio, the most exothermic stoichiometry, is 1905 K. This ratio was therefore selected as the primary composition for use in this study. Thermodynamic analysis also indicates that the equilibrium products for the selected ratio of precursors are boron nitride (BN) and titanium diboride (TiB2), which may form according to the following overall reaction: 𝑇𝑖𝑁 + 3𝐵→𝑇𝑖𝐵2 +𝐵𝑁 + 192 𝑘𝐽/mol

(4)

Based on a comparison of the thermodynamic analysis and known dissociation and melting temperatures of all possible phases (Table 1) involved in the reaction, it can be concluded that Tad is lower than any phase transformation temperature in the Ti-B-N ternary system. Therefore, this reaction, if carried out in an inert atmosphere, may be considered a solid flame type of reaction17. Solid flame reactions are defined as any selfsustaining reaction that is not catalyzed by the presence of impurities and does not produce a liquid or gaseous phase at any step of the process. For example, tantalumcarbon is a classical solid-flame system, which has been studied for several decades18. Recently, a few other compositions have shown reaction characteristics typical of solid flames15. However, all previously investigated systems were binary and involved direct reactions between a metal and a nonmetal. This work considers a ternary and displacement-type reaction, TiN+B, in order to elucidate its reaction mechanisms. The


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main question to address is: What sequence of transformations allows rapid formation of BN/TiB2 composite at temperatures well below the melting points of the precursors, intermediates, or product phases in this ternary system? Table 1: Congruent melting/dissociation temperatures of reactants and products Species

T (K)

Transformation

TiN19

3550

melting

B20

2350

melting

TiB220

3500

melting

BN21

3400

dissociation

2.2.Reaction Mixture Preparation Titanium nitride (< 10 um, 99.9% purity) (Alfa Aesar) and β-boron (< 44 um, 98% purity) (Alfa Aesar) powders were used to prepare reactive nanostructured B/TiN particles. First, the powders were thoroughly mixed at a 1:3 molar ratio using a mortar and pestle. Composite TiN/B particles, containing both reactants, were then fabricated using a planetary ball mill (PM-100 Retsch) operated at 650 RPM with a milling regimen divided into segments of 5 minute milling periods and 15 minute cool down periods. These cool down periods prevent premature reaction due to elevated temperatures resulting from friction in the milling jar. A powder to ball mass ratio of 1:40 was used for all preparations. A 500 mL stainless steel (SS) milling jar was filled with 5 grams of mixed precursors and then 200 grams of 3/8” SS media. The jar was then sealed and purged 4 times with argon (99.999% purity).


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The scale of reactant size is reduced through shearing and fracturing of TiN and B particles which has primarily been attributed to the collisions of milling media, however for materials differing in hardness the harder material, in this case boron, may also aid these comminution processes22. Increased milling duration typically results in a higher degree of mixing between reactants within the composite particles; however, at an empirically determined critical time, conversion to product will begin to occur. 2.3. Thermal Initiated Reaction The critical milling time for this system under dry milling conditions was found to be greater than 45 minutes. Unless otherwise stated, all reactive composite powders used in this study were prepared by HEBM for 45 minutes and are, from here on, referred to as the initial composite material. Composite powder was cold pressed into pellets, with diameter 13 mm and height 11 mm, to 60% of the theoretical maximum density (TMD). TMD was determined by measurement of the external dimensions of the pellet with a micrometer. The pellet was then inserted into a 1 L stainless steel reactor, vacuum purged 4 times with argon (99.999%, purity), and pressurized to 0.4 MPa with the same gas. Reaction was initiated using a resistively heated tungsten coil and the reaction temperature profile was measured using a 100 μm diameter C-type thermocouple. 2.4. Mechanically Induced Reaction The mechanically intensive conditions of HEBM expose the reactant precursors to moderately high temperatures, from inelastic collisions of powder and SS balls, and pressures, from the collisions both between balls and the jar wall23. Continuation of the HEBM process in excess of the critical time (in this case above 45 min) results in


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gradually increasing conversion to product. Material was milled to twice the critical time in order to more easily locate reaction zones by increasing the degree of conversion. 2.5. Infrared Video and Thermocouple Measurements High-speed infrared (IR) video recording (FLIR Systems, SC6000) was used to obtain a 2D temperature-time maps of the reaction process. This device functions by sequential recording of multiple temperature ranges, the highest of which can accurately record temperatures up to 2300 K, with overall frame rates of up to 20,000 fps. Emissivity was calibrated by setting the maximum temperature observed by IR to equal the maximum temperature measured via thermocouple. Propagation velocity of the reaction front and other propagation characteristics were calculated based on frame-byframe analysis of the IR recording. Spatial resolution for the acquired recordings was 64 ± 3 μm/pixel, and temporal resolution was 2 ms/frame. For ignition temperature measurements, a thin disc was pressed from the TiN/3B composite powder with a C-type thermocouple imbedded into the center of the disc. The test material was placed on a graphite strip. An electrical current was passed through the graphite to heat the surface to 1900 K at 200 K/s. The temperature rise of the test material is recorded via the thermocouple and the ignition temperature is calculated from this data. 2.6. TGA/DSC + Mass Spectrometry A dual use thermal gravimetric analyzer - differential scanning calorimeter (TGA-DSC 1; Mettler Toledo) coupled with a mass spectrometer (Thermostar-GSD 320/quadrupole mass analyzer, Pfeiffer Vacuum) was used to analyze the change in mass during reaction and to observe formation of any potential gas phases. The experiment was performed at a heating rate of 50 K/s with an Ar flow rate of 200 mL/s. Simultaneously


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the MS scanned across the m/z range 10-60. The parameters of this analysis were selected to determine whether nitrogen (m/z 28) was released from the sample during heating. 2.7. Sample Characterization Powder X-ray diffraction analysis was performed using a Bruker D-8 Advance Diffractometer with a Cu Kα (0.15418 nm) radiation source and all samples were analyzed using identical instrument parameters. In addition, a Bruker D-8 Discover diffractometer with a Cu Kα (0.15418 nm) radiation source and stage control was used to determine the lattice parameter of the initial TiN powder. A HELIOS Nanolab 600 operating in secondary electron mode (resolution: 0.9 nm at 15 kV) with a focused gallium ion beam (FIB) attachment was used for initial cross-sectional microstructure imaging and preparation of TEM samples. A Magellan 400 (FEI) operating in backscattered electron mode was used to provide enhanced phase contrast in imaging of crosssectioned microstructures with more than two compounds present. A TITAN (FEI) transmission electron microscope operating at 300 kV (point resolution: 0.2 nm, STEM resolution: 0.136 nm) with energy dispersive X-ray (EDX) capabilities was used to determine phase identities and elemental distributions. SEM and TEM techniques were used to characterize microstructural features, the distribution of phases, and to identify specific crystalline phases. 3. RESULTS As was mentioned previously, the reaction of initial TiN-3B composite reactive particles was investigated under two different conditions, i.e. after thermal initiation of the combustion wave and during HEBM. Analysis and characterization of the product


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phase identities, phase distribution, and scale of product crystallites provides evidence for determining the mechanism of reaction under varied conditions. 3.1. Initial Reactive Composite Particles The typical microstructure of the fabricated TiN/B composite particles is shown in Figure 1. It can be seen that the particle sizes range from 1 to 30 μm (Figure 1a). The surface morphology (Figure 1b) suggests that the formation of the particles during HEBM occurs both through cold welding of the initial precursors as well as through agglomeration of the previously formed composite particles. The particle cross-section (Figure 1c) reveals a dark phase and a bright phase. In secondary electron imaging, darker contrast corresponds to lighter elements while brighter contrast corresponds to heavier elements, in this case B and TiN, respectively. The bright phase, TiN, does not contain any discernible granular features, while the dark phase, B, exhibits a very wide size distribution ranging from well less than 100 nm up to 1 μm. Cross-section analysis of multiple particles reveals that although porosity exists throughout the composite particles, the center typically shows a higher degree of densification (Figure 1c).


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100 μm (d)

(c)

(b)

(a)

10 μm

2 μm (f)

(e) 0.212 nm TiN (200)

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0.498 nm t-B (112)

Figure 1: SEM images of 45 minute dry milled TiN/3B composite particles (a), particle morphology (b), FIB cross-section (c); bright field TEM images at low magnification (d), high resolution (e), and SAD imaging of the same region (f). TEM imaging and electron diffraction analysis (Figures 1d-f) confirmed that the composite particles consist of regions with nano-scale (as small as 5 nm) boron and other regions with micron-scale boron (> 100 nm). In bright field (BF) TEM imaging, darker phases typically correspond to heavier elements and brighter phases to lighter elements. Finely mixed regions of nanocrystalline B and TiN were found in layers of ~100 nm surrounding the micron-scale boron crystals. Titanium nitride crystallites of approximately 5-10 nm in size are closely adjacent to a large B crystallite (Figure 1e). The electron diffraction pattern in Figure 1f shows diffraction rings indicating highly polycrystalline TiN and largely mono-crystalline B. Therefore, we may conclude that


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initial composite TiN/B particles involve uniformly distributed TiN crystallites with average size ~10 nm and B crystallites with size ranges from 5 nm to 1 μm. An XRD pattern of the initial composite particles is shown in Figure 2a. It can be seen that only broad peaks of the TiN phase were detected. The Scherrer method, which relates peak width to crystal size, was used to obtain an approximation of the average crystallite size in the materials24. XRD patterns from the reactant precursors are shown in Figure S2. Results from applying the Scherrer equation, presented in Table 2, indicate that there has been a ten-fold reduction in TiN crystallite size after HEBM and this value (7.2±0.1nm) is in good agreement with TEM observations. XRD analysis also implies that the boron phase has become x-ray amorphous. A similar effect has been observed for carbon during HEBM of Ti-C mixtures25. 3000

(a)

2500 2000 Intensity (a.u.)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


TiN TiB2 h-BN

1500 1000

(b)

500 (c)

0 20

25

30

35 40 45 2θ (degrees)

50

55

Figure 2: X-ray diffraction patterns from the initial (a), thermally initiated product (b), and mechanically induced product (c) composite powders. The application of HEBM reduces the average crystallite size and significantly increases surface contact area between the reactants. Both of these phenomena are the


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direct result of reduction in reactant particle size via fracturing and shearing actions accompanied by intimate intermixing and agglomeration into composite particles under severe mechanical treatment. Table 2: Crystallite size analysis using Scherrer approach. Crystalline

Reactant

HEBM

HEBM

Thermal

Species

Precursors

45 min

90 min

Initiated

TiN (nm)

76 ± 13

7.2 ± 0.1

6±2

-

B (nm)

102 ± 5

-

-

-

TiB2 (nm)

-

-

5

50 ± 7

BN (nm)

-

-

-

17

The reactions in as-fabricated TiN/3B nanostructured composite particles were investigated under two different conditions: after thermal initiation of the combustion wave and during further HEBM. 3.2. Thermally Initiated Reaction Determining the reaction onset, or ignition, temperature, relative to the melting or dissociation points of the precursors can provide insight into the reaction mechanism. Onset temperatures near a reactant’s melting point typically indicate a melt-spreading type of initiation, whereas onset temperatures well below the melting or eutectic points of any reactants indicates a solid-state diffusion mechanism. For example, both of these features can be observed in the Ni-Al system15,26. Figure 3 represents a typical temperature-time profile obtained from an ignition temperature experiment. The ignition temperature is defined as the point when the rate of


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temperature rise shifts from linear to exponential increase. Analysis of five experiments indicated that Tign for 45 minute HEBM mixtures of TiN-3B was 1340 ± 35 K, which is well below any phase transformation temperatures in the considered system (Table 1). Note that within the investigated temperature range, 1000 – 1900 K, reaction could not be initiated in a TiN-3B mixture prepared using mortar and pestle. 1700 1500 Temperature (K)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Tign

1300 1100 900 700 500 300 2.0

4.0 6.0 Time (s)

8.0

Figure 3: Ignition temperature for the TiN/3B initial composite powder measured for a 200 K/s heating rate. 3.2.1. Combustion Wave Propagation It was shown that the reaction front in the TiN/B system propagated along the sample in a periodic mode, which is typical for systems with relatively low exothermicity27–31.

However, the observed combustion regime is distinct in that it

includes features of both spin and oscillation modes of propagation (Figure 4). After local initiation at the top of the pellet, the reaction transitions to an established, but not steadystate, propagating regime that oscillates between two stages. First, the reaction front traverses the sample circumference with velocity (𝜃avg) and zone width (δ) during an


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active stage. This is followed by stagnation of the reaction for a period of time (τ) and then a return to the active mode. Frame-by-frame statistical analysis of high-speed IR recordings of experiments permits calculation of the average rate of front propagation, oscillation period (τ), as well as the above defined δ and 𝜃avg. (Table 3). It was observed that the average rate of combustion front propagation, żavg, was 3.77 ± 0.15 mm/s, while the circumferential velocity, 𝜃avg, was an order of magnitude faster at 35 ± 13 mm/s. Here it should be noted that the standard deviations listed in Table 3 are representative of the stochastic nature of the observed phenomenon, with negligible uncertainty attributable to the method of measurement.

The velocity ratio between axial and

circumferential propagation fits the prediction of a strongly nonlinear spin mode suggested by Novozilov and investigated for gas-solid systems by Filimonov32,33. Table 3: Oscillating reaction front characteristics of the TiN+3B reaction. Reaction HEBM 45 min Characteristics 𝑧avg (mm/s)

3.77 ± 0.15

τ (s)

0.255 ± 0.143

δ (mm)

0.99 ± 0.40

𝜃avg (mm/s)

34.5 ± 12.9


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1796 1383 0.000 s

3.360 s

1.832 s

4.032 s

5.634 s

5 mm

6.621 s

4.688 s

Oscillation Layer

Spin Direction

7.387 s

8.007 s

(K) 742

8.921 s

473

Figure 4: Select frames from infrared video recording of reaction propagation. 1800 1600 Temperature (K)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1400 1200 1000 800 600 400 3

5

7 Time (s)

9

Figure 5: Reaction temperature profile from IR video. A typical temperature profile acquired at a single point in the central region of the reacting pellet is shown in Figure 5. The maximum combustion temperature is on the order of 1700 K, which is below the adiabatic value (1900 K). This may indicate that the degree of conversion in the combustion front is less than 100% and that reaction proceeds further in the post-combustion zone. Of note though, is the fact that the measured maximum combustion temperature is well below the melting points of precursors and any considered product phases in this system. An important observation is made that the temperature profile has two distinct peaks. The first peak has a maximum value of 1700


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K, which rapidly decreases and is then followed by a second peak with a slightly lower value near 1500 K. This is a direct indication that the combustion reaction scheme involves several stages. It is worth noting again that pellets prepared with the same dimensions and to the same relative density from a conventional mixture of the initial TiN and B powders were found to not ignite when exposed to the same conditions. Data from powder XRD analysis of the thermally initiated product is shown in Figure 2b. The presence of TiB2 and h-BN with only one TiN peak at the level of the background signal indicates essentially complete conversion to product in the combustion wave. The average crystallite sizes estimated based on the Scherrer approach are 50 nm and 17 nm for TiB2 and BN, respectively (Table 2). (a)

(b)

(c) (d)

(c)

100 μm (d)

2 μm

10 μm (e)

(f) 0.332 nm h-BN (002) 0.324 nm TiB2 (001)

5 1/nm

Figure 6: SEM images of thermally initiated TiN/3B composite particles (a), particle morphology (b), FIB cross-section (c); bright field TEM images at low magnification (d), high resolution (e), and SAD imaging of the same region (f).


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Typical microstructures of the synthesized BN/TiB2 particles are presented in Figures 6 a-b. Qualitative comparison of these SEM images, with those for the initial particles (Figures 1 a-b) allows us to conclude that the particle microstructure remains essentially unchanged. The internal porosity of the product particles (Figure 6c) also appears qualitatively similar to that of the initial material (Figure 1 c). SEM analysis shows that product particles from the thermally initiated reaction are essentially the same size as the initial composite material indicating that inter-particle interactions are limited to heat transfer. This corresponds well with the limited mobility of the reactant phases, and mass transfer can thus be assumed to only occur within the volume of the initial composite particles. These features suggest the absence of liquid phases during the combustion process, which typically leads to significant changes in the initial microstructure and porosity. SEM and TEM analysis (Figures 6 c-d) also confirm that there are no identifiable regions containing unreacted material. h-BN was observed to have consistently formed along the pore boundaries, whereas TiB2 crystallites appear to have formed in dense clusters (Figure 6c). In Figure 6e a grain boundary between h-BN and TiB2 is shown in which the basal planes of both hexagonal phases are parallel to each other and normal to the probable direction of grain growth. The identification of phases was confirmed by the analysis of the electron diffraction patterns (Figure 6f). 3.2.2. Additional Experiments In situ experiments employing a dual use TGA/DSC coupled with simultaneous mass spectrometry (MS) for identical reactive composite TiN/B particles showed a twostep decrease in sample mass coinciding with two qualitative increases in the MS signal


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from m/z 28, which corresponds to N2 (Figure 7). The first step, beginning at 1500 K and representing loss of 1% of the total sample mass, corresponds to a 7% loss of the total nitrogen. Due to the high rate of mass loss at the maximum temperature, the TGA measurement period was extended to observe mass change during the slower cooling period. Inclusion of this section revealed that mass loss continued until the sample temperature returned to 1550 K. During this period there was an overall 4% decrease in sample mass, equivalent to a 28% loss in total nitrogen. An exothermic event beginning at 1400 K preceded the change in mass (Figure S3) by 100 K. XRD analysis (Figure S4) of the product detected only TiB2, while SEM imaging and EDS area analysis indicated a reduced amount of BN, corresponding approximately to the observed nitrogen loss. These results suggest two important conclusions: (1) gas phase nitrogen appeared during the TiN+3B reaction; (2) the relatively low heating rates present in TGA/DSC, as compared to the combustion wave, provide ample time for a significant portion of the gas-phase nitrogen to escape and thus allowing only a small amount of h-BN to form. 100.0

4.0E-09

Ion Current for m/z 28 (A)

99.8

Percent of Initial Mass

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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3.5E-09 99.6 99.4

3.0E-09

99.2

2.5E-09 99.0 98.8 900

1200 1500 Temperature (K)

2.0E-09 1800


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Figure 7: Mass spectrometry results for m/z 28 and thermal gravimetric analysis results from the TGA/DSC heating of TiN+3B at 50 K/s from 900 K to 1770 K. 3.3. Mechanically Induced Reaction Continued HEBM processing of TiN-3B beyond the empirically determined critical time leads to a gradual conversion to product. The low intensity and broad widths of peaks in the XRD pattern, Figure 2 c for the 90 min HEBM powder indicate very fine crystallite size scales for TiN and TiB2, while BN was not detected. SEM investigation of the mechanically induced product, Figures 8 a-c, showed a microstructure that was qualitatively very similar to that of the initial composite, however with relatively reduced porosity consistent with continued densification of the particles. Additionally, average composite particle size increased, corresponding to a continued agglomeration process, and a lamellar-like structure not seen in the initial composite was also identified. This new feature was observed to be present in regions similar to those previously identified as containing nano-crystallites of B mixed with TiN. A TEM sample was prepared from a region containing several of these features (Figure 8 d). High-resolution TEM (HRTEM) imaging and select area diffraction (SAD) both confirmed that these regions contained unreacted TiN and B along with the product phase, TiB2 (Figures 8 e-f). In regions without the lamellar features, no TiB2 was identified. The scale of crystallite sizes in these regions ranged from 5 to 20 nm for all phases. In no case were any features of a BN phase observed indicating that under HEBM conditions reaction produces TiB2, while nitrogen does not react with boron to form BN.


21


(a)

(b)(c)

100 μm

5 μm

(d)

(e)

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(c)

1 μm (f) 0.767 nm t-B (101)

0.260 nm TiB2 (100) 5 1/nm

Figure 8: SEM images of mechanically induced reacted TiN/3B composite particles (a), particle morphology (b), FIB cross-section (c); bright field TEM images at low magnification (d), high resolution (e), and SAD imaging of the same region (f). 4. DISCUSSION 4.1. General Reaction Mechanisms for Combustion Synthesis In general, self-sustaining combustion reactions may occur through several mechanisms including (1) melt-spreading followed by dissolution of the higher melting point reactant into the melt, followed by product phases crystallization from the melt34,35, (2) solid-state interdiffusion of reactants with formation of solid solutions36,37, (3) solidstate diffusion of reactants with nucleation and growth of intermediate phases38, (4) infiltration of the gas phase reactant to the surface of the solid reactant followed by diffusion through the product phase39,40, and (5) local generation of a gas phase reactant that enables reaction by catalyzing mass transport18.


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The above-described experimental results are considered to formulate the mechanism of displacement reaction for TiN+B within the combustion wave. First, considering that the ignition temperature and the maximum measured combustion temperature in this system are well below the reported melting temperatures of all possible phases (Table 1) involved in this reaction, we may conclude that solid-state diffusion, probably a modification of mechanisms 2 and 3, is responsible for the observed interactions. These liquid-free mechanisms are also supported by comparison of the microstructure of the initial particles to that of the reaction products, which do not exhibit significant changes. Second, the oscillatory spin mode of propagation and two-peak temperature time profiles suggest at least two distinct stages to reaction. Third, the TGA/DSC + MS study demonstrates that significant amounts of gas phase nitrogen evolve during heating from 1500 – 1800 K, which indicates that the gas phase mechanisms 4 and 5 should also be considered. Fourth, the products of reaction during HEBM imply that reaction in this system may occur without BN formation. The exothermic event observed in the TGA/DSC between 1400-1500 K and the absence of BN from HEBM reaction products allows us to conclude that formation of TiB2 phase is a leading stage of the process. In general, three scenarios based on these findings can be formulated to explain the reaction mechanism occurring in the high temperature, ambient pressure reaction between titanium nitride and boron. 4.2. Scenario I: Formation of Ti-B-N Solid Solutions The first scenario is based on the assumed presence of a ternary TiNxBy phase or TiN/B solid solution. At some critical concentration, this TiNxBy phase or solution


23


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rapidly transforms into both product phases (TiB2 and BN). A similar mechanism was observed for the reduction combustion reaction in the CoO-Al system41. However, it is worth noting that, this mechanism does not explain the appearance of the gas phase nitrogen during reaction in the system. Close examination of the reported behavior of the Ti-B-N ternary system reveals a disagreement over the absence or presence of ternary phases and solid solutions. Despite several studies reporting the solubility limit of B in TiN1-x as approximately of only 1 at.% and zero solubility of nitrogen in TiB242–45, authors have reported the preparation of solid-solutions of TiN containing a wide range of B concentrations46–48 and have even claimed the presence of a ternary phase49. Additional TEM investigations of multilayer films showed regions containing all three elements, Ti, B, and N50. However, DFT calculations51 indicate that both nitrogen-deficient and boron-deficient solid solutions, such as those reported, are far from equilibrium and would decompose to TiN-TiB2 and TiN-BN, respectively. Therefore we can conclude that these phases are only preserved due to kinetic limitations during preparation, and they have in fact been shown to phase separate under additional heat treatment48. No evidence for such ternary solutions was observed during the course of this study. However, the potential role of boron diffusion into titanium sub-nitride must be considered. Trapping the system at such a meta-stable state and identifying it are both difficult tasks, since the lattice spacing of TiN and ternary TiNxBy (or solid solutions of boron in titanium nitride) phases should be very similar and would phase separate if not quenched. In our opinion, the best opportunity for observation of this phase is the


24

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application of high-resolution in situ time-resolved x-ray diffraction. This investigation is currently underway. It is also clear that in order for this step to occur the sub-nitride phase must be present first. This may occur through two ways, either the TiN present in the initial composite is already nitrogen-deficient or it becomes so through the loss of nitrogen during the reaction. The high-resolution X-ray diffraction scan indicated a lattice parameter of 0.4235 ± 0.0001 nm for the used initial TiNx, which corresponds to x = 0.93 ± 0.01 as based on reported stoichiometries19. A second and third scenario account for the observed appearance of gas phase nitrogen during the reaction and are based on the fact that nitrides possess an equilibrium vapor pressure of nitrogen above the solid surface, which is known to increase with temperature52. 4.3. Scenario II: Gas-Solid Leading Reaction then Solid-Solid Diffusion In the second scenario, nitrogen vapor pressure builds during the initial heating of the sample or, once propagation is achieved, during the previous oscillation. In this scenario, boron promptly reacts with the small amount of available nitrogen, simultaneously reducing the vapor pressure of nitrogen and increasing the local temperature through exothermic reaction. As noted above, nitrides possess a vapor pressure of nitrogen above the solid surface, which increases with temperature (Figure 9)53–57. Since gas phase nitrogen is reactive with boron39,58, this nitrogen (for TiN0.93, ~1 Pa at 1900 K) may be rapidly consumed through the formation of boron nitride.

The observed mass loss and N2

release support the hypothesis of N2 evolution.


25


1.0E+02 TiNx Partial Pressure, N2 (Pa)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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1.0E+00 1.0E-02 Pollard 1950 1.0E-04 1.0E-06

Hoch 1955 Hojo 1977 Andrievskii 1983

1.0E-08 1300

2300 Temperature (K)

Figure 9: Temperature dependence of nitrogen partial pressure for TiNx for values of x (0.7-0.93). The reduced vapor pressure spurs on continued dissociation and the increased temperature speeds up the rate of all processes. In this case, reaction spreads as further nitrogen is released and the leftover boron diffuses into and reacts with the remaining titanium. A similar mechanism, termed a chemical pump, was suggested to explain combustion in the silicon-nitrogen system, which also occurs in an oscillatory mode59. It is clear that for scenario II reaction between boron and gas phase nitrogen is critical. 4.4. Scenario III: Solid-Solid Diffusion and Dissociation of the Sub-Nitride In the third scenario, at Tig, the nitrogen partial pressure along the internal pores is sufficient to form small pockets of nitrogen gas leaving behind thin, nitrogen deficient TiNx layers. Boron diffuses into the TiNx matrix substituting the nitrogen and forming TiB2 nuclei. The exothermic process of TiB2 formation spurs on further nitrogen release, which by this time has begun to react with the remaining boron to form boron nitride.


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Once this process begins, there is sufficient heat released to sustain reaction across the bulk. The exothermic event observed between 1400 K and 1500 K during TGA/DSC indicates that a solid-state interaction leads the reaction process. Considered in context of the self-propagating behavior, these results strongly suggest that the reaction rate is limited by solid-solid diffusion of boron into the TiNx crystal lattice during the active stage of the oscillation process. The results from mechanically induced reaction that occurred during HEBM provide additional insight into the reaction pathway. While XRD results show a gradual conversion to product, reaction was likely repeatedly initiated in localized regions followed by rapid extinction. This is supported by the observation that in the reaction product, TiB2, is only found within the lamellar regions. With estimated local temperatures approaching 1000 K, a nitrogen deficient TiNx phase allows substitutive diffusion of B into the TiNx lattice. As the reaction proceeds and heat release causes increased temperature, further nitrogen deficient TiNx is formed, typically spurring on continued reaction. However, during HEBM, the high heat loss conditions likely prevent formation of BN and nitrogen escapes to the atmosphere inside the milling jar. Note that solid-solid interactions play a major role in the reaction mechanism for scenario III, however the primary distinction from scenario I is that the formation of a ternary phase is not required. As such, the solid-state interactions of phases present in the initial composite must be evaluated at, or near, the ignition temperature (1340 K). Potential solid-state diffusion pairs based on current understanding include boron through titanium nitride47 (3.0 x 10-18 m2/s, 1225 K), boron through titanium diboride60 (1.7 x 10-


27


13

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m2/s, 1340 K, extrapolated) and nitrogen through titanium nitride61 (1.8 x 10-16 m2/s,

1340 K). To the best of the authors’ knowledge, diffusion data for titanium through boron and nitrogen through boron do not exist. The characteristic reaction time, or rapid temperature increase (Figure 5), is on the order of 0.5 s. Considering the diffusion coefficients and the characteristic time scale of the combustion front, B can diffuse ~1 nm into TiN; ~200 nm into TiB2 and N can diffuse ~10 nm through TiN. With an average crystal size of 7 nm for TiN, these estimations imply that bulk diffusion of B can be responsible for up to ~50% of conversion. They also indicate that the product, TiB2, does not act as a significant diffusion barrier for the considered length scales. In the above context, it is interesting to discuss results obtained by Matsudaira from reaction sintering in the TiN-B system12. Employing a 1:2 molar ratio for submicron powder mixtures of TiN and B the previous study reported the formation of solely TiB2 under long term (0-6 hr) sintering conditions (1300 – 1800 K) and inert atmospheres. However, they reported that no reaction occurred under nitrogen atmosphere. The first result implies that formation of TiB2 is the leading reaction in this system, since diboride can be formed without the appearance of BN. More interestingly, the second result suggests that increasing nitrogen pressure over the TiN surface prevents the formation of the nitrogen deficient TiN lattice, which in turn inhibits the diffusion of B into TiN and therefore the reaction that forms TiB2 . Two additional thermal initiation experiments for the TiN/B system were performed under similar conditions to investigate these observations. We cannot exactly repeat Matsudaira’s experiment in the combustion mode, as localized heating of a pellet


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of initial HEBM composite particles with a 1:2 TiN/B molar ratio under argon gas at 0.4 MPa does not produce a self-sustaining reaction. However, experiments performed under 0.4 MPa nitrogen with the 1:3 TiN/B ratio provided an interesting result, namely the system switched from oscillating to steady state propagation. XRD scans of the reaction products from these additional experiments are included in Figure S4. To explain the switch to a steady state reaction mode, it should first be noted that a pure boron sample pressed to the same initial relative density as the TiN/B mixture did not burn under the same nitrogen pressure. This again implies that reaction between boron and nitrogen is not the leading reaction in the TiN/B system. However, addition of nitrogen to the pores of the sample appears to bypass the limiting kinetics of the stagnation stage of the oscillation process, which is otherwise controlled by the dissociation of TiN. This steadier regime of reaction propagation is instead entirely controlled by the diffusion rate of boron into titanium sub-nitride. Additionally, sintering and TGA/DSC experiments show that low heating rates appears to dramatically reduce, or inhibit, the formation of BN, but not TiB2. This observation further supports the critical function of solid-state diffusion during the initiation stage of reaction. The fact that a nitrogen atmosphere did not suppress reaction, and indeed led to steady reaction propagation, strongly suggests the dependence of the oscillation step, τ, on the TiN dissociation process. A schematic of the hypothesized reaction mechanism under ambient pressure conditions along with initial and final states is shown in Figure 10. Reaction begins with the diffusion of B into the adjacent nitrogen deficient TiNx. The solid solution of B in TiNx forms primarily in the nano-mixed layers surrounding the larger B crystallites while


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nitrogen gas escapes along grain boundaries and fills the pores. TiB2 begins to nucleate and grow from the solid solution, B continues to diffuse into the surrounding TiNx, and BN begins to nucleate along the pores. The growth of TiB2 and h-BN continues until all reactants are consumed, with reaction of B+N2 continuing up to several seconds after the primary reaction front passes.

TiB2 B TiNx /B Layer

BN

TiB2

B

B

TiNx By

N2 Pore

TiNx /B Layer

N2

B

N2

Figure 10: Proposed TiN+3B reaction pathway for ambient pressure conditions. 5. CONCLUSIONS Reaction propagation characteristics and an analysis of reaction mechanism in the mechanically activated TiN-B system for a 1:3 molar ratio at ambient pressure have been reported. Additionally, this reaction has been demonstrated to occur under a range of experimental conditions. (1) Results from DSC and mechanically-induced reaction via HEBM provide strong evidence that TiB2 is the first reaction product to form. The presence of sub-stoichiometric TiNx is believed to permit the substitutional diffusion of B into the nitride lattice. (2) The vapor pressure of nitrogen for TiNx is non-negligible for 1300-1900 K, and TGA/DSC + MS results indicate that nitride dissociation is an


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intermediate feature of the TiN+3B reaction. (3) The oscillatory spin mode of reaction propagation is defined by two stages: an active stage limited by solid-state diffusion, and a stagnation stage limited by dissociation of TiNx. Further evaluation of the validity of these conclusions would be strongly supported by the application of time resolved in-situ x-ray diffraction to observe the sequence of phase transformations. ACKNOWLEDGEMENT This work was supported by the Department of Energy, National Nuclear Security Administration, under the award number DE-NA0002377 as part of the Predictive Science Academic Alliance Program II. An author (N.F. Shkodich) acknowledge the financial support of the Ministry of Science and Higher Education of the Russian Federation in the framework of Increase Competitiveness Program of NUST «MISiS» (№ К2-2017-083), implemented by a governmental decree dated 16 th of March 2013, N 211. We are also grateful to T. A. Orlova for her skillful FIB-preparation of TEM samples. We thank the ND Energy Materials Characterization Facility (MCF) for the use of the TGA/DSC coupled with mass spectrometer, and the Molecular Structure Facility for the use of x-ray diffractometers. SUPPORTING INFORMATION DESCRIPTION Calculated adiabatic reaction temperature for TiN/xB as a function of x; XRD profiles of the reactant precursors; TGA/DSC profiles; XRD profiles of TiN/B reaction products for different compositions and gas environments. This material is available free of charge via the Internet at http://pubs.acs.org.


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