Titanium sintering science: A review of atomic events during densification

Journal Pre-proof Titanium sintering science: A review of atomic events during densification

Randall M. German PII:

S0263-4368(20)30090-1

DOI:

https://doi.org/10.1016/j.ijrmhm.2020.105214

Reference:

RMHM 105214

To appear in:

International Journal of Refractory Metals and Hard Materials

Received date:

6 November 2019

Revised date:

26 January 2020

Accepted date:

7 February 2020

Please cite this article as: R.M. German, Titanium sintering science: A review of atomic events during densification, International Journal of Refractory Metals and Hard Materials(2020), https://doi.org/10.1016/j.ijrmhm.2020.105214

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© 2020 Published by Elsevier.

Journal Pre-proof

Titanium Sintering Science: A Review of Atomic Events during Densification Randall M. German Research Professor, College of Engineering, San Diego State University 282 Surfview Court, Del Mar, CA 92014 email [email protected]

Keywords

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Titanium Sintering Densification Master Sintering Curve Microstructure Evolution Impurity

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Abstract

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The sintering densification trajectory for titanium powder is identified in terms of the interaction between mass transport processes and microstructure evolution. During initial heating, as surface oxides dissolve, surface diffusion forms bonds between contacting particles without densification. Grain boundaries form in the bonds due to random crystal orientations at the contacts. Except for mixed powder Kirkendall swelling, subsequent diffusion in these interparticle grain boundaries leads to densification. Most importantly, the alpha-beta transformation provides strain, defects, and interfaces that accelerate densification in the 800 to 1100°C temperature range. This is below a typical peak sintering temperature. Final densification involves beta phase volume diffusion and grain boundary diffusion. Densification slows due to grain growth and the loss of grain boundary area. Pores close near 92 % density to trap impurities and reaction products inside the closed pores, often limiting sintered density to about 95 % of theoretical. High final density requires slow heating or long holds at intermediate temperatures to evaporate impurities prior to pore closure. The master sintering curve is a means to link densification to process parameters without concern over detailing this cascade of transport mechanisms and microstructure changes.

Introduction In 1949, Duwez [1] labeled titanium a most promising metal. A difficulty with sintered titanium was post-sintering deformation required to reach full density, a problem that persists [2,3]. This article reviews titanium sintering behavior to identify factors controlling densification. Understanding how the transport mechanisms interact with the 1

Journal Pre-proof evolving microstructure provides a basis for innovating cycles to attain full density without resorting to pressure-assisted sintering options such as hot isostatic pressing.

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Titanium components are formed from powder using injection molding, die compaction, cold isostatic pressing, centrifugal or vibratory forming, binder-assisted extrusion, and binder jetting options, each followed by a sintering step. Performance factors, such as fatigue life and corrosion resistance, depend on composition, sintered density, and microstructure. In turn, sintered density depends on the powder and processing cycle. These linkages are conceptually outlined in Figure 1. Fundamental to performance is the elimination of pores during sintering. Although titanium sintering occurs at relatively low homologous temperatures (absolute temperature divided by absolute melting temperature), full densification by sintering is elusive. Toward that end, this analysis reviews the factors that determine the sintering trajectory and inhibit densification.

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Significant Parameters

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A total of 94 detailed experimental reports were extracted from 60 articles to form the statistical basis for this study [4-63]. The processing parameter combinations cover the following experimental conditions: Particle size – 3 to 374 μm Powder type – atomized, dehydride/hydride, sponge, milled, blended, prealloyed, rotating electrode, and various mixtures Alloying – pure Ti, Ti-3Al-2V, Ti-3Al-2.5V, Ti-6Al-4V, and TiH or TiH2 Shaping approach – loose powder, die compaction, injection molding, binder jetting, and cold isostatic pressing Green density – 49 to 89 % of theoretical Heating rate – 3 to 1000°C/min Atmosphere – vacuum, argon, hydrogen, and partial pressure variants Peak temperature – 850 to 1420°C Furnace type – refractory metal, graphite, induction, and microwave Hold time – 1 to 5760 min Initial oxygen content – 0.13 to 0.66 %. Example combinations of these parameters are compared using eleven examples (out of 94) in Table 1. Sintered density ranges up to 99 %. More typical is a lower terminal density of 95 %. At this density, using various powders, Figure 2 compares the time-temperature cycles. The cycles include temperature-time extremes such as 29 μm prealloyed spherical Ti-6Al-4V sintered at 980°C for 5760 min [57] to 35 μm spherical prealloyed Ti-6Al-4V powder sintered at 1400°C for 60 min [41]. The typical heating rate is 10°C/min in a refractory metal vacuum sintering furnace; a few experiments were conducted in argon or hydrogen as the atmosphere. To handle differences in starting green density, densification is used to compare experiments. It is defined as the change in porosity in sintering divided by the initial 2

Journal Pre-proof porosity. For example, a 75 % green density is sintered to 89.7 % density, giving a change in porosity of 14.7 % out of 25 % initial porosity, or 59 % densification. Full densification implies 100 % final density.

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The 94 experiments enabled statistical analysis. Statistically significant factors with regard to densification are a smaller particle size, slower heating rate, and higher peak temperature. In some cases the impact of a statistically significant factor was small. On the other hand, factors such as hold time at the peak temperature is not statistically significant, nor is the initial oxygen content. The absence of an oxygen effect probably reflects the variable deoxidation and contamination effects coming from sintering substrates, furnaces, and residual atmospheres – effectively masking the starting oxygen level. Powder type is not significant; thus, prealloyed, elemental, blended elemental, hydride, and titanium mixed with master alloy powders are included. Although differences exist in the densification at intermediate temperatures, final densification is relatively insensitive to the starting condition. In some cases swelling occurs at lower temperatures when a master alloy dissolves into the titanium, but final density fails to link to the starting powder condition. Alloying improves densification, probably reflecting shifts in the alpha-beta transformation temperature and faster diffusion mobility of aluminum [64,65]. However, final density is not significantly improved by alloying. For example, comparing Ti, Ti-3Al-2V, and Ti-6Al-4V shows similar final density if sintered with comparable conditions of particle size, peak temperature, and hold time [49,66,67]. The tradeoff in sintering parameters enables similar final densities via different pathways, as illustrated by these examples using holds of 120 min at 1250°C:  Kyogoku et al. [8] sintered 30 μm mixture of 10 % hydride and 90 % dehydride Ti powders to 95.8 % density.  Bolzoni et al. [49] milled dehydride and master alloy powders to give the Ti-3Al-2V composition with a 39 μm particle size that sintered at to 96.1 % density.  Ebel et al. [45] sintered 13 μm spherical atomized prealloyed Ti-6Al-4V powder to 96.2 % density.  Miura et al. [34] sintered 21 μm gas atomized spherical prealloyed Ti-6Al-4V powder to 94.9 % density.  Ferri et al. [41] sintered Ti-6Al-4V gas atomized -45 μm (nominally 30 μm) powder to 96.5 % density. Equivalent densification is possible using the interplay between various parameters such as particle size, sintering temperature, and hold time. For example, 15 μm titanium, heated at 10°C/min reaches plateau densification (about 95 %) after 10 min at 1350°C, while 75 μm powder requires 240 min to reach the same densification. A low sintering temperature requires a longer hold. However, with higher temperatures hold time is not an dominant factor. For example, 23 μm powder held at 1200°C exhibits a sintered density of 94.8 % after 60 min with an increase to 96.1 % after 240 min and 97.4 % after 480 min [32].

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Journal Pre-proof Densification slows once pore closure occurs at approximately 92 % density [ 47]. Swelling occurs with excess temperature or time, indicative of trapped vapor in the pores.

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Dilatometry helps understand the densification events. An example plot of shrinkage versus temperature is given in Figure 3 [41]. The heating rate is 10°C/min to 1400°C for a prealloyed 35 μm Ti-6Al-4V powder. Little densification occurs until about 700°C, awaiting oxide adsorption and neck growth between particles. The peak shrinkage rate, estimated near 0.6 %/min (10-4 1/s), occurs during the alpha-beta phase change [6,9,41,50,64,69-75]. Strains arising from polymorphic transformations assist densification [64,76,77]. Most of the sintering shrinkage occurs prior to the isothermal hold, progressively slowing once heating stops.

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Predominantly titanium sintering is measured using mechanical properties [3,78,79]. However, densification is required to reach high properties. With respect to densification the prior studies reveal several facts:  Smaller particles start to densify at a lower temperature, but do not necessarily sinter to a higher final density [13,17,28].  Powders with low impurity contents improve densification [17].  When sintered in a high vacuum, there is no significant change in final density due to powder type; gas atomized, dehydride, blended elemental, mater alloy, or other variants all tend to reach 95 % density [20,40].  Bimodal powder mixtures do not necessarily improve sintered density [29,56,80,81].  Mixed powder chemistries, such as titanium with master alloy, initially sinter faster due to chemical gradients, but often swell such that final density is similar to that from prealloyed powder [49,66].  Adding titanium hydride to titanium lowers sintered performance [ 8].  Higher green density usually improves sintered density for a fixed heating cycle although sintering densification is not dramatically improved [3,11,13,37,38,46].  Standard heating rates between 3 and 10°C/min have little impact on final density especially for peak temperatures of 1200°C or higher [11], but fast heating is detrimental [59,61].  Temperature is a strong factor up to about 95 % density, incomplete densification results from too low a peak temperature [15,33,45,82].  The most intense shrinkage is near the end of the alpha-beta transformation, which is delayed above the equilibrium temperature during heating [11,64].  After reaching about 95 % densification, generally there is little gain from longer holds or higher temperatures [14,26,29,44].  Upon pore closure, at about 92 to 95 % density, some systems swell with prolonged holds [15,32,38,47].  Impurity levels usually increase during sintering; substrates are a contributor to increased impurity levels [11,17,20,23,24,26,49,53,83,84]. 4

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Argon as the sintering atmosphere lowers final density and adds to the impurity level [11,33,54,64]. Vacuum sintering requires partial pressures below 10 -4 Pa to avoid impurities [4]. Hydrogen as the sintering atmosphere refines the microstructure [3,42,62,85]. Grain size and porosity are inversely related [31,86]. Pore growth occurs while porosity declines [52]. Strength increases with the elimination of porosity but declines with a high sintering temperature due to grain and pore coarsening [44,48,87]. Ductility declines with higher sintering temperatures due to pore coarsening [44,48]. Retained impurities generally improve sintered strength but degrade ductility [ 88]. Hot isostatic pressing is able to deliver full density but has only a small impact on important performance factors such as fatigue strength [7,57].

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The following sections analyze for mechanistic aspects in the densification trajectory.

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Densification Mechanisms

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For titanium, sintering densification involves several interacting events. These form a cascade impacted by changes in temperature and microstructure during heating. First surface oxide films must dissolve to allow metallurgical bonds. For a gas atomized powder, the starting titanium oxide surface layer is 4.4 nm thick [89]. Its removal starts about 700°C and is mostly complete by 1000°C [69]. As particle bonding initiates, the transport events progress through a standard morphological trajectory [90]. Initially surface area is consumed as interparticle sinter bonds form by surface diffusion. With the loss of surface area the role of surface diffusion declines. On the other hand, grain boundaries are created in the interparticle sinter bonds, leading to densification via grain boundary diffusion in the newly formed grain boundaries between the particles. These diffusion rates increase with temperature. Considerable densification occurs during the α-β phase transformation. The volume strain and defect structure in the alpha-beta interface promote rapid densification. After the transformation, as temperature increases, grain growth reduces grain boundary area, shifting dominance to volume diffusion. Diffusion data are known for titanium and its key alloying ingredients, in both the alpha hexagonal close-packed and beta body-centered cubic crystal structures [54,69,73,74,87,91-93]. Although alloying elements differ in diffusion rates, this is a secondary factor as homogenization occurs. Diffusion data are plotted in Figure 4 for the surface, volume, and grain boundary transport paths in the two crystal structures. The units are m2/s. The alpha and beta phases exhibit similar surface diffusion rates, while grain boundary and volume diffusion are faster in the beta phase after it forms. Grain boundary diffusion is often given in m3/s to include the boundary thickness, but it is assumed to be five atoms thick here. The beta phase grain boundary diffusion rate is taken from sintering data [54]. 5

Journal Pre-proof Diffusivity is only part of the analysis, since the diffusion rate couples with the microstructure parameters (surface area, grain boundary area, pore area, α-β interface area) to determine the overall flux contributing to sintering; surface diffusion is most active with a high surface area, grain boundary diffusion requires a high grain boundary area, volume diffusion requires a high pore surface area, and α-β interface transport depends on the interface area during the phase change. The combination of temperature dependent diffusivities and concomitant microstructure changes shift the relative priority of each pathway during the sintering cycle.

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Surface diffusion occurs in a relatively thin surface layer. It is active once surface oxides are dissolved. During sintering the surface area continuously declines due to bonding and densification, reducing the relative importance of surface diffusion [94]. Sintering starts with an initial surface area per unit mass SO as determined by the particle size D,

(1)

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where ρ is the theoretical density. For example, spherical 20 μm Ti powder starts with 67 m2/kg surface area and surface diffusion is dominant up to about 850°C [54].

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Sintering densification results in an increase in fractional density f with a decline in surface area per unit mass S,

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𝑆 = 𝑎 −𝑏 𝑓 (2)

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where for typical titanium powders a = 2.875 and b = 3.125. The surface area reaches zero at 92 % density when pores close, although internal pore surface area remains [47]. A high initial surface area enables surface diffusion to form sinter bonds at particle contacts with little densification [95]. Surface diffusion continues at higher temperatures where it acts to smooth pores. The emergence of grain boundaries in the particle contacts initiates densification by grain boundary diffusion. The grain boundaries away from the interparticle contacts do not contribute to densification, since particle center-center motion requires mass transport perpendicular to the interparticle contact. A grain boundary forms in the sinter bond due to crystallographic misalignment between contacting particles. The number of contacts increases with densification. Assume spherical powder of diameter D with a starting fractional green density fG. The coordination number NC tells the number of sinter bonds each particle has with neighboring particles, and for spherical powder it is a function of the fractional density f as follows [96]: 𝑁𝐶 = 2 + 11 𝑓 2

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Journal Pre-proof (3) For a loose powder compact the green density is usually 60 to 65 % of theoretical, giving a starting coordination number of 6.0 to 6.6. Once densification starts, the coordination increases, initiating new bonds that form by surface diffusion. At full density the typical polygonal grain consists of 12 to 14 boundaries.

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𝑓𝐺 1/3 𝑌 = 1− [ ] 𝑓𝑆

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The grain boundaries enable densification by grain boundary diffusion. For an idealized isothermal sintering situation, sintering by grain boundary diffusion causes component shrinkage. For isotropic green bodies, sintering shrinkage, densification, and sintered density are related to one another. Shrinkage, Y = Δ L/LO, is the change in compact dimension divided by the initial dimension and relates to fractional green density fG and sintered density fS as follows:

(4)

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Densification φ is a function of the fractional green density fG and fractional sintered density fS. It normalizes differences in green density, 𝑓𝑆 − 𝑓𝐺 1 − 𝑓𝐺 (5)

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Densification is linearly proportional to sintered density for a fixed green density. Isothermal sintering shrinkage depends on several factors [91]. The generalized form applicable to about 90 % density involves hold time t, absolute temperature T, and grain size G as follows: 𝑌𝑁 =

𝐶𝑡 𝑄 exp [− ] 𝐺𝑀 𝑅𝑇 (6)

Here Q is the activation energy, R is the gas constant, N = 3 and M = 4 for grain boundary diffusion. The factor C combines geometric and material parameters, such as surface energy, atomic volume, grain boundary width, vibrational frequency, and crystal structure. Equation 6 helps explain isothermal dilatometry data. Unfortunately, most experimental data are taken using a slow heating rate, enabling significant densification prior to reaching the hold temperature. In such cases a time or shrinkage correction is required that adds to the analysis difficulty. For an 18 μm titanium powder sintered in the beta temperature range Q = 153 kJ/mol and C = 2.1∙10-25 m4/s [58]. At 1000°C for 60 min, the prediction is 75.0 % density while the actual value is 75.2 %. Modified models are required in other temperature or density ranges. Due to the complexity, computer simulations are required, 7

Journal Pre-proof but those models rely on an extensive array of input parameters, such as the diffusivity date shown earlier in Figure 4. As densification occurs, grain boundary area responsible for densification at the particle contacts initially increases due to neck growth, then decreases due to grain growth. The grain size trajectory starts with the particle size D and increases with the elimination of porosity (1 – fS) as follows [96]: 𝐺 =𝜃

𝐷 √(1 − 𝑓𝑆 ) (7)

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with θ ≈ 0.6, depending on the initial porosity. An example of this behavior is plotted in Figure 5 for 21 μm Ti-6Al-4V spherical powder [34]. The grain boundary area for densification depends on the sinter bond area (diameter X) and coordination number (NC). The neck diameter X saturates at about 0.55 G. Thus, the grain boundary area per unit mass SG over which sintering shrinkage occurs is approximated as follows, assuming a typical polygonal grain shape:

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𝑆𝐺 =

(8)

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A plot of grain boundary area per unit mass versus density is given in Figure 6 for 20 μm titanium starting at 60 % density. Only grain boundaries located at the sintered necks are relevant to shrinkage. Note the interparticle boundary area increases, plateaus, and declines. Accordingly, grain boundary diffusion is less effective as density passes about 80 % [97-100]. In normal sintering cycles this point occurs during heating, so the loss of grain boundary area is compensated for by the temperature increase. Up to about 90 to 95 % density, pore size d tracks with grain size G and porosity (1 – fS) as follows [96]: 𝑑 = 0.4 𝐺 √(1 − 𝑓𝑆 ) (9) After pore closure the elongated pores spheroidize and enlarge, so the relation shifts slightly, 𝑑 = 0.5 𝐺 (1 − 𝑓𝑆 )1/3 (10)

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Journal Pre-proof In titanium, pore closure occurs over a range of densities, so a spline fit is applied from 89 to 96 % density [47]. The calculated shift in pore size with density is plotted in Figure 7, ignoring pore swelling due to trapped impurities or gaseous reactions inside closed pores.

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Diffusion rate changes are associated with temperature and the alpha-beta phase transformation. Figure 8 illustrates densification during heating to 1250°C for titanium hydride and gas atomized Ti-6Al-4V powders [6,41]. Rapid densification occurs near 950°C when a mixed alpha-beta microstructure still exists; enhanced diffusion is associated with the alpha-beta interface [74,101]. At low temperatures the interface area is small and the diffusion rate is low, but by about 900°C or 70 to 75 % density, the interface area is high and diffusion rates are high. During heating, the endothermic transform from alpha to beta is slow [73,102,103]. Thus, the two phases coexist to temperatures above the equilibrium beta transus, up to about 1000°C. Most studies focus on phase content during cooling [65,87,102,104,105]. Note the rapid cooling associated with powder atomization results in about 20 % beta phase at room temperature prior to sintering. As illustrated in Figure 9, alpha is retained to higher temperatures during heating [106]. The conjecture is dislocations generated by the transformation strain provides enhanced densification by grain boundary diffusion assisted grain sliding [71,107,108]. Low angle grain boundaries are an example of dislocation arrays that induce rapid mass transport; the transformation strain induces dislocations and the resulting defective α-β interface acts similar to a thick grain boundary. The alpha-beta interface area is low at the start of sintering, increases during heating and peaks with near 950°C [104,106], then declines to zero by 10501100°C. Alpha-beta interface transport is important to densification and behaves similar to grain boundary diffusion.

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To illustrate the transient role, assume the beta phase nucleates a rod of width Z emanating from the alpha grain boundaries, as sketched in Figure 10. Based on cross-section micrographs of atomized powders, these are assumed to be 2 μm wide features spanning the grains [109]. Each rod forms a defective sleeve of thickness δ responsible for rapid sintering. The phase interface area SP depends on the volume fraction. If the predominant phase is alpha, then these rods are beta, and if the predominant phase is beta, then the rods are alpha. The grain boundary area is known from the degree of bonding and grain size, so for a volume fraction F of second phase (maximum of 0.5) the relative interface area is given as the grain boundary area times the fraction of second phase times a geometric factor Φ calculated as follows: 𝑍2 𝛷 =1− (𝑍 + 2𝛿)2 (11) Based on quenched microstructures, Φ is about 0.3 based with an interface thickness δ of as 0.2 μm [101]. The interface area is calculated as, 𝑆𝐼 = 𝐹 𝑆𝐺 𝛷 9

Journal Pre-proof (12) Figure 11 is a corresponding plot of the interface area versus density for a 20 μm powder starting with 20 % retained beta phase, assuming the initial beta phase is present as an isolated phase. The interface area peaks near 75 % density.

𝑑 𝜌 𝐺2

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Finally, after the transformation, especially by 1250°C, beta phase grain boundary diffusion and volume diffusion are the dominant transport mechanisms. Final densification occurs by pore filling via volume diffusion, effectively treating the pores as accumulations of vacancies [96]. This ignores any residual gas in the pores and focuses on the pore acting as a vacancy emission site that fills with atoms by volume diffusion. The pore surface area per unit mass SP changes with densification and grain growth,

(13)

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This relation is plotted in Figure 12 for 20 μm titanium powder starting at 60 % green density. One difficulty is pore growth late in sintering [57]. Internal pressure from trapped vapors stabilize the closed pores to retard final densification [47].

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For titanium, sintering involves a cascade of mechanisms. The geometric progression is summarized in Figure 13 calculated for 20 μm spherical powder starting at 60 % green density. The curves give surface area, grain boundary area, pore area, and alpha-beta interface area in units of m2/kg. In turn, the diffusion mechanisms are identified versus temperature in Figure 4. The combination of temperature-dependent diffusivity with the morphological evolution determines the rate of sintering densification.

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Surface diffusion induced bonds create grain boundaries at the interparticle bonds such that alpha phase grain boundary diffusion gives first densification. Some beta might initially exist from the powder production process, but should anneal into alpha phase. From about 800 to 1000°C this alpha transforms to beta, leading to a decrease in alpha phase content with increasing temperature. This endothermic reaction is sluggish, so alpha phase and the accompanying alpha-beta interface remain during heating to temperatures above the beta transus temperature. Oxygen also delays the transformation during heating [72]. High densification rates are associated with the strain and interface zone diffusion concomitant with the α-β transformation [41,101]. Grain boundary diffusion is associated with an interface about 1.5 nm wide. However, the much thicker alpha-beta interface zone adds significantly to shrinkage. Note superplastic forming relies on the same phase structure and temperature range, leading to similar strain rates [110]. After full conversion to beta, pores continue to shrink. Grain boundary diffusion depends on the grain boundary area, which peaks at about 75 % density. However, the pore surface area provides for volume diffusion controlled shrinkage, where porosity declines while pores coarsen [94]. Thus, as sketched in Figure 14, several events happen somewhat in sequence during heating in a typical sintering cycle. 10

Journal Pre-proof Figure 15 adds the sense of sequential mechanisms using a previous plot of density versus temperature (Figure 8) for gas atomized Ti-6Al-4V and titanium hydride [6,41]. The upper box indicates the dominant mechanism during heating. Densification is most active in the mixed alpha + beta zone. Most of the sintering densification occurs prior to reaching the peak temperature of 1250°C. The details change with atmosphere, oxygen content, impurities, alloying, powder characteristics, and other process factors, but clearly sintering densification is most active prior to reaching the typical peak hold temperature.

Impurities and Incomplete Densification

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Impurities in titanium powder largely depend on the synthesis details [111]. Titanium sintering densification is sensitive to these impurities, in terms of transformation, performance (strength, ductility, corrosion rate), and sinter densitfication. Often the impurity contents increases during sintering. This is due to residual gas in the vacuum furnace as well as substrate sources. For example, 18 μm powder sintered at 1200°C for 180 min increases oxygen from 0.17 % to 0.25 % in a 10-4 Pa vacuum, but reaches 0.91 % oxygen in a 0.1 Pa vacuum [53]. Indeed, increased impurity levels are detected with vacuum sintering unless the operating pressure is sustained below 10-4 Pa [4]. Higher peak temperatures contribute to impurity accumulation [49]; sintering gas atomized powder with 0.088 % oxygen results in 0.21 % oxygen after 120 min at 1250°C and 0.23 % oxygen after 120 min at 1350°C [22]. Besides surface oxides, other oxygen sources include the residual atmosphere, oxygen in the support substrates, lubricant or binder burnout products adhering to the furnace cold walls, and back-streaming vapors from the vacuum system. Scavenger additives are an option for combating the impurity effects [41,112-126]. Sintered density is slightly improved using scavenging additives, but the compositions are then outside the range covered by standard specifications.

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Titanium hydride is another means to reduce impurities [62,127]. Generally, initial oxygen levels range from 0.2 to 0.4 wt. %, while nitrogen, carbon, and chlorine are lower. Sintered strength and ductility are affected by both impurities and porosity. For example, yield strength increases with the impurity content and decreases with a lower fractional density [128]. In a related manner, ductility declines as the impurity level increases. To understand the impurities, spectroscopy is applied during vacuum sintering. Water vapor is released during heating up to 800°C with reduced release at higher temperatures [127,129]. Powder exposure to air results in hydrated oxides that are difficult to remove during sintering. Also, chlorine impurities forms vapor species during heating [122,123,127,130-132]. Once the pores close at about 92 % density, the internal vapor pressurizes to form spherical gas-filled pores that resist densification [47,57,81,120,122,123,130,133,134]. Pore spheroidization is a clear indication of trapped vapor and surface diffusion transport. Coarsening by impurity species diffusion in the beta solid allows the pores to enlarge; the larger pores grow while the small pores disappear. Eventually the pores are larger than the initial particle size. These pores are stabilized by trapped gas such as water, carbon monoxide, carbon dioxide, or oxygen-chlorine 11

Journal Pre-proof complexes. Powders with high impurity contents swell during prolonged holds [30,52,57,134]. In one report using a 28 μm gas atomized powder sintered at 1250°C, the median pore size was 11 μm after 60 min (94.0 % dense) and 15 μm after 300 min (96.3 % dense) [52]. The pores grow by Ostwald ripening, occurring due to partial solubility of the gas species in the solid. Coarsening results in progressive growth in pore size as the number of pores declines.

4𝛾 𝑑

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Titanium sintering densification is limited by gas pressure generated in the pores by impurities or reaction species (CO, CO2, or such). After pore closure, at approximately 92 % density, the impurities continue to react and generate internal pressure that resists the capillary stress acting to shrink the pore [91,135-137]. For a spherical pore, densification terminates when the gas pressure inside a pore PG reaches the pore capillary stress,

(14)

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where γ is the solid-vapor surface energy and d is the pore diameter. Note the pressure decreases as pore size enlarges, a reason for swelling during pore growth. The surface energy of titanium is 1.7 J/m2. Assume the pore is 10 μm and the porosity is 5 %, then the pore gas pressure needed to halt pore shrinkage is 0.68 MPa (nearly 7 atmospheres pressure). At a sintering temperature of 1350°C, the corresponding gas required to halt densification for that pore is 2.6∙10-14 mol. For carbon monoxide, at a molecular weight of 28 g/mol, this amounts to 7.4∙10-11 g gas mass at temperature. This is a nearly undetectable 16 ppm impurity level. Such contamination is possible from a reaction between residual carbon and oxygen. Both are soluble at 1350°C in beta titanium, carbon is soluble up to 0.27 wt. % and oxygen saturates at 1.40 wt. %. Other gas generation options, such as carbon dioxide, water, or chloride species, result in similarly low impurity levels to halt densification [122]. Pore coarsening causes swelling. Again assume 5 % porosity. Then if two 10 μm pores with 0.68 MPa internal pressure coalesce to form a single pore, the resulting single pore is 14.5 μm in diameter and the internal pressure is reduced to 0.47 MPa (assuming gas mass is preserved). Due to the pressure reduction, the porosity swells to 7.5 %. Such ideas are the basis for forming foamed metals [138,139]. If the gas in the pores is soluble in the solid, then over time the degree of swelling decreases [137]. Thus, pores are stabilized by internal gas, generated by impurity species diffusing and reacting to form insoluble molecules. For this reason, slow vacuum heating, sintering in hydrogen, or adding scavengers are options to remove impurities prior to pore closure, leading to higher sintering densification [15,42,57,125].

Integral Work of Sintering

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Journal Pre-proof Titanium sintering involves a complex interplay of mass transport mechanisms and microstructure changes. To counter this complexity, one idea is to ignore the complications of the different diffusion, phase transformation, and microstructure changes using the work of sintering [140-143]. The integral work of sintering model captures green density, particle size, heating rate, peak temperature, and hold time into a single parameter that enables prediction of densification. Robertson and Schaffer [13,38,47] consolidated their titanium sintering data using this idea using a single activation energy. Related to Equation 6, the integral work of sintering θ includes particle size D (related to grain size), absolute temperature T, time t, and activation energy Q as follows:

(15)

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𝑡 1 1 𝑄 𝜃= 𝑀 ∫ 𝑒𝑥𝑝[− ] 𝑑𝑡 𝐷 𝑅𝑇 0 𝑇

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The work term results from manipulation of equations for shrinkage (Equation 6) and shrinkage-densification (Equations 4 and 5). The effective activation energy of 160 kJ/mol reflects an approximation over a broad range of temperatures; a lower activation ener gy is evident at higher temperatures and higher activation energy is evident at lower temperatures [54,144]. Diffusion activation energies measured during the alpha-beta transformation are similar, in the 153-158 kJ/mol range [145]. Convenient units for θ are min/(K μm2). The integral is over the sintering cycle from the start at t = 0 and 20°C to completion of the hold at the peak temperature. The parameter R is the universal gas constant. For titanium vacuum sintering, Robertson and Schaffer found M ≈ 2. The predicted densification φP as a function of the integral work of sintering is calculated from a sigmoid relation: 𝐴 1 + exp(𝐵 − ln 𝜃)

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𝜑𝑃 =

(16)

with A = 0.93 reflecting saturation at 93 % densification and B = -24.5, reflecting the approximate work needed to initiate sintering densification. This form reflects the inability to reach full density by sintering. For any experiment, the predicted final density fP is calculated from the green density and densification as, 𝑓𝑃 = 𝑓𝐺 + 𝜑𝑃 (1 − 𝑓𝐺 ) (17) As noted earlier, a total of 94 experimental reports were collected with sufficient information to calculate an integral work of sintering (median particle size, green density, heating rate, peak temperature, hold time, and sintered density). The majority relied on vacuum sintering, but a few hydrogen, argon, or partial pressure experiments were included. The resulting relation between densification and work of sintering is given in 13

Journal Pre-proof Figure 16, where θ is in units of min/(K μm2). Included is the best fit sigmoid curve. Some results are anomalous, but inspection finds they are cases of sintering in one atmosphere argon (retarded densification) or in one case microwave heating. An integral work of about 10-9 min/(K μm2) is required to reach 93 % densification.

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Detailed comparisons were conducted against several reports to assess the accuracy of this approach. As an example, 28 μm Ti-6Al-4V starting at 65 % green density and vacuum sintered at 1250°C for 120 min is predicted to undergo 88 % densification (experimental 90 %), reach a grain size of 95 μm (experimental 117 μm), and pore size of 19 μm (experimental 16 μm) [41]. However, with argon as the sintering atmosphere late stage densification is retarded; for 18 μm titanium sintered at 1250°C for 60 min the densification is just 45 % [54], while the prediction is 88 % for vacuum sintering.

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Novel Cycles

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A prediction of isothermal densification using the work of sintering is illustrated in Figure 17 for 20 μm titanium powder instantly heated to 1250°C. More typical is progressive heating to the peak temperature which is held for an appropriate time. An example with 20 μm titanium powder and 10°C/min heating to 1200°C is given in Figure 18. Here densification is plotted versus cycle time. In agreement with dilatometry data, almost all of the densification occurs during the heating portion of the sintering cycle. Excessive sintering results in significant grain growth (and strength loss) [38,45]. On the other hand, titanium powder densifies using long holds at lower temperatures [57]. Along these lines, Figure 19 provides an examination of the calculated time-temperature tradeoffs for a 20 μm powder heated to temperature at 10°C/min. The curve corresponds to the temperature-time combinations for 95 % sintered density at a work of sintering of 10-9 min/(K μm2). The required hold time shifts with the inverse of the particle size squared. For example, a change to 40 μm requires quadruple the hold time; a 40 μm powder at 1350°C would require a hold in excess of 360 min to densify the same degree as a 20 μm powder in 90 min at that temperature.

The discussion has focused on traditional cycles, mostly in vacuum with a heating rate about 10°C/min. Commonly the peak temperature is from 1200 to 1400°C with a hold of 120 to 240 min, depending on particle size. Some novel sintering cycles favor long-term holds at lower temperatures. In terms of final density, the extended outgassing prior to pore closure is helpful, assuming the furnace is held to a very low pressure (below 10-4 Pa). This prevents impurity accumulation from substrates, residual gas, and furnace back-streaming. Some examples of novel sintering cycles are collected in Table 2. Cycle N1 sinters in argon using 45 μm powder with a high peak temperature and long hold time (1400°C, 480 min). The 67 % densification results in a 92.5 % final density, far below that associated with vacuum sintering. Extensive surface impurities are a difficulty. 14

Journal Pre-proof Cyclic heating through a polymorphic phase transformation induces a volume strain beneficial to densification [15,64,146]. In one example, approximately 28 μm spherical powder at 66 % green density is taken to 99.6 % density using multiple oscillations between 1000°C and 1280°C. Full details are not reported, but total furnace time is close to a day. Note one hour at 1280°C contributes 2∙10-10 μm2/(K min) to the sintering work, so repeat cycles add to the total work of sintering. The cycle designated N2 relies on a low green density dehydride titanium powder. Oscillating temperature changes, as employed in this approach, deliver some densification, but such cycles are difficult to implement and control in production sintering furnaces.

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Cycle N3 sinters titanium hydride in hydrogen as used for decorative watch components [147]. Hydrogen sintering has the benefit of faster diffusion and smaller grains, increasing the densification rate in the 800 to 900°C range [42,95,148]. After densification, the atmosphere is switched to vacuum and then nitrogen to produce a gold color (titanium nitride). To fully remove the hydrogen requires a long vacuum soak (720 min at 750°C for 15 mm wall thickness). For a Ti-6Al-4V composition formed from TiH2 and a master alloy, the final sintered density is 99 % with high ductility and strength, in spite of 0.31 % oxygen. For thin wall structures the use of hydrogen is attractive, but thick sections are problematic.

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Cycle N4 involves slow heating and liquid phase sintering for titanium treated with yttria to react with residual chlorine [123]. For an alloy of Ti-5Si treated with 500 ppm yttria, a three stage vacuum sintering cycle of 650°C for 240 min, 1000°C for 240 min, and 1300°C for 240 min results in almost full density. The cycle is restricted to liquid phase sintering where the fast transport rates prove effective and formation of yttrium-oxygen-chlorine complexes removes residual chlorine.

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Finally, cycle N5 illustrates the densification possible using low temperature sintering. A gas atomized 29 μm spherical prealloyed Ti-6Al-4V powder is held for 5760 min (four days or 96 h) at 980°C in vacuum [57]. This prolonged hold produced 98.8 % density with 0.25 % oxygen (the initial oxygen level is not reported). The tensile strength is 931 MPa with 18.3 % elongation, delivering 475 MPa fatigue endurance limit. This same powder sintered at 1350°C for 240 min gave a lower density (97.4 %), strength (837 MPa), ductility (15.1 %), and fatigue strength (291 MPa). Sintering in the two phase alpha-beta region is clearly beneficial.

Summary Properties from sintered titanium and titanium alloy powders depend on many factors. It is possible to arrive at significantly different property combinations depending on a change to just one parameter. Sintering titanium to full density is elusive. Everything is important, from the powder purity to the sintering substrate. It is a challenge to suggest there is any single optimal cycle. Several factors are noted here. This analysis reflects the 80-20 rule, where a few 15

Journal Pre-proof

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factors (20 %) control 80 % of sintering densification. Many of the parameters, such as powder type or green density, impact the densification pathway, but largely do not impact final density. For this analysis a default situation is assumed based on 20 μm prealloyed powder heated at 10°C/min to 1250°C with a 120 min hold in high vacuum. During that cycle a sequence of events occurs as follows:  at temperatures over 300°C residual binder decomposes and must be removed to avoid powder contamination,  up to 800°C outgassing occurs, dominated by the release of water,  oxide adsorption starts between 600 and 700°C and extends to 1000°C,  surface diffusion acts to grow initial sinter necks without densification up to approximately 900°C,  if powders are mixed, such as with a master alloy, the chemical gradients initially enhance diffusion during heating, possibly forming Kirkendall pores, but these effects are transients during heating,  densification starts at temperatures higher than 700°C based on grain boundary diffusion, occurring in interparticle grain boundaries formed by surface diffusion induced neck growth,  during heating the alpha to beta phase transformation starts about 800°C (depending on alloy composition and impurity content) and continues to 1000 and even 1100°C (beyond the equilibrium transformation temperature),  strain associated with the transformation generates defective regions, dislocations, and thick interfaces, all contributing to mass transport and intensive densification during the transformation,  interface diffusion at the alpha-beta boundary gives alpha phase morphology changes and rapid mass transport; the combination of microstructure and transport events results in significant densification with about 25 vol. % alpha phase,  beta phase grain growth reduces grain boundary area and slows grain boundary diffusion contributions to densification,  volume diffusion in the beta phase becomes dominant after completion of the phase transformation, diffusion is from the pores to the remaining grain boundaries,  after conversion to beta titanium, densification slows due to loss of interfaces and grain boundaries,  pore closure occurs at about 92 % density,  gas generation occurs from reacting impurities - oxygen, carbon, and chlorine, creating gas filled spherical pores,  pore coarsening occurs due to solubility of the impurity species in titanium at the sintering temperature, the large pores grow and the small pores disappear,  at temperatures over 1250°C swelling occurs due to pore coarsening since small pores have higher gas pressure and growing pores increase porosity giving swelling,  grain growth continues and couples with pore growth to result in decreased strength and other performance characteristics with excessive sintering, 16

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hot isostatic pressing squeezes the residual pores, but does not remove the trapped impurities.

Future Research Needs

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The science behind titanium sintering needs careful experiments to correct or confirm the conceptualizations presented here. A major problem relates to impurities. Most studies report the starting impurity levels, but often fail to report final levels. Furnaces, substrates, and adsorbed species increase the impurity level. Without final measurement of impurity levels it is not possible to link densification protocols to impurity removal. Residual gas analysis is needed during the entire sintering cycle to identify species and quantities of gas release versus temperatures or degree of sintering. Based on such data, heating cycles are possible for improved impurity release. Fracture of sintered samples inside an analysis device would identify the species in the pores. In turn, heating cycle changes or additives might be employed to avoid stable residual pores.

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Most post-sintering microstructure reports correspond to slow furnace cooling. Only a few studies quench the microstructure from temperature [65,104-106]. Unfortunately, a slow cooled microstructure is not informative on what phases exist at the sintering temperature. Thus, quenching experiments are needed in coordination with dilatometry, allowing better identification of the phases, geometric arrangements, and transport mechanisms.

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The alpha-beta interface is important to densification. Experiments are needed to measure transport rates in that interface. For now the sense is behavior is akin to grain boundary diffusion. Experiments need to focus on measuring transport rates in the interface, similar to how superplastic forming rates are measured.

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The integral work of sintering idea provides a simplification useful in treating densification data. More accurate versions would spline fit alpha and beta phase behavior [149]. The increased complexity should significantly improve accuracy. Further, impurity effects might be included. If the retained impurities resisting full densification are identified, then the master sintering curve might embrace impurities with respect to prediction of terminal density.

Acknowledgements Titanium sintering research was conducted with support from several companies and agencies. Professor Zak Fang’s enthusiasm is much appreciated since he encouraged the presentation of this information.

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Journal Pre-proof Table 1. Examples of traditional titanium sintering cycles (D50 = median particle size)

18

55 61

25 75

68 88

74 15

0.13 0.15 0.16

89.6 67.6 96.1

65

10

1400

120

vac

0.19

97.5

69

5

1300

120

93.5

68

10

1250

69 89

10 600

1300 1300

52 67

50 3.3

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54

vac vac vac

0.40

60

Ar

0.25

82.5

180 10

Ar vac

0.14 0.40

95.9 94.0

850 1050

60 120

Ar vac

0.20 0.17

63.5 95.5

vac

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39

120 120 240

-p

49

1000 1100 1200

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3.3 10 ---

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67 64 65

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23 65 23

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16 28 32

powder type Ti irregular Ti sphere Ti sphere Ti-6Al-4V sphere Ti-6Al-4V sphere Ti-3Al2.5V irregular Ti irregular Ti sphere Ti irregular Ti sphere Ti sphere

heat peak hold initial final rate temp. time atmos- oxygen dense °C/min °C min phere wt. % % 3 1250 120 vac 0.34 95.8

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D50 μm 30

green dense % 60

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Journal Pre-proof Table 2. Novel titanium sintering cycles. N1: 45 μm dehydride powder, compacted at 400 MPa to 77 % green density, heated in graphite furnace first in vacuum of 0.1 Pa at 5°C/min to 850°C, then pressurized furnace using 0.11 MPa atmosphere argon, continued heating to 1400°C for 480 min, final density 92.6 % [60] N2: approximately 30 μm dehydride powder, compacted 35 MPa to 49 % green density, heated in helium using sawtooth temperature cycle near alpha-beta transformation, from 840°C to 920°C in approximately 1 min holds, delivering 20 % densification after 30 min [64]

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N3: titanium hydride powder of 10 μm size is shaped by injection molding, debound, and sintered in hydrogen at 1200°C in a 5 to 7 hour heating cycle, after densification of the hydride, the furnace switched to nitrogen, argon, or vacuum for 20 min, then cooling occurred at 5°C/min; if nitrogen is the cooling gas, then the product is titanium nitride coated (gold color) with 98.5 % density [147]

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N4: dehydride titanium powder with added 5 % silicon or 6 % nickel and 500 ppm yttria is liquid phase sintered in vacuum using a cycle of slow heating at 4°C/min with holds at 650°C, 1000°C, and 1300°C each for 240 min, resulting in densities approaching 100 % [123]

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N5: gas atomized 29 μm prealloyed T-6Al-4V powder is injection molded at 65 vol. % solids loading and sintered (after debinding) at 980°C for 96 hours to deliver 98.8 % density [57].

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Journal Pre-proof

Figure Captions Figure 1. Component performance depends on sintered properties, processing factors, and powder characteristics, showing the complexity associated with reaching optimal behavior. Figure 2. Scatter plot of time-temperature combinations reported to deliver at least 95 % sintered density for titanium or its alloys. The average temperature is 1487 K (1214°C), time is 4.9 h (294 min), particle size is 26 μm, and almost all relied on vacuum sintering.

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Figure 3. Dilatometer results for sintering dimensional change (mostly shrinkage) during heating a Ti-6Al-4V powder compact starting with a 65 % green density [41]. Heating is at 10°C/min to the peak temperature of 1400°C which is held for 120 min. The fastest shrinkage rate is in the mixed alpha-beta transformation temperature range.

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Figure 4. Natural logarithm of diffusivity in m2/s for the two phases and three transport mechanisms (VD = volume diffusion, GBD = grain boundary diffusion, SD = surface diffusion) versus inverse absolute temperature. During sintering the heating pathway is from the right to the left.

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Figure 5. Plot of sintered grain size versus inverse square root of the fractional porosity for 21 μm spherical Ti-6Al-4V, showing agreement with Equation 7 [34].

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Figure 6. Interparticle grain boundary area available for sintering shrinkage shown as a function of the sintered density; calculated for 20 μm titanium powder sintering at 1250°C starting at 60 % green density.

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Figure 7. Early in sintering the pore size remains essentially constant, but due to pore closure and spheroidization the late stage pore size enlarges while the total porosity declines; calculated for 20 μm powder sintering at 1250°C starting at 60 % density.

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Figure 8. Density versus temperature during heating to 1250°C for two different powders [6,41]. The similar plots illustrate the significant density gain associated with the temperature range where alpha converts into beta. Figure 9. During heating the transformation of alpha into beta occurs over a range of temperatures, and the transformation is displaced to higher temperatures for conditions representative of sintering [65,73,87,102,105,106]. Figure 10. Representation of a grain during transformation, where second phase rods of width Z radiate from the grain boundaries. Figure 11. Plot of the interface area evolution during sintering densification with a peak near 75 % sintered density for 20 μm powder sintering at 1250°C starting at 60 % density . Figure 12. Pore surface area versus density for 20 μm powder sintering at 1250°C starting at 60 % density. The onset of pore closure is evident by the changes near 90 % density.

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Journal Pre-proof Figure 13. Composite plot of the geometric transport areas (m 2/kg) calculated for sintering 20 μm titanium powder sintering at 1250°C. Figure 14. The cascade of events that occur during heating titanium powder to the sintering temperature. The temperature range for each is only approximate. Figure 15. Overlay of the main densification mechanisms to illustrate the density versus temperature during dilatometer sintering of two powders. Figure 16. Scatter plot of sintering densification results from 94 experimental reports using the integral work of sintering. The model line corresponds to the Equation 16 sigmoid fit to these experiments.

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Figure 17. Sintering profile of density versus hold time for 20 μm titanium powder held isothermally at 1250°C using the work of sintering to calculate the density.

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Figure 18. Calculated densification for a sintering cycle consisting of heating from room temperature to 1200°C at 10°C/min for a 20 μm powder.

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Figure 19. A plot of the time and temperature combinations that deliver 95 % sintered density, showing the conditions that represent excess sintering. Long times are projected to deliver high sintered density at low temperatures.

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Journal Pre-proof Author Statement

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Other than the conceptualization request from Zak Fang this article was the sole effort of Randall M. German.

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Journal Pre-proof Declaration of interests

☒ 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.

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☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:

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Journal Pre-proof Highlights “Titanium Sintering Science: A Review of Atomic Events during Densification”

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Titanium sintering is explored to sort out the mass transport mechanisms and evolving microstructure allowing densification at modest temperatures. The complex interplay of diffusion events is heavily influenced by the strain and defect structure induced during heating as alpha (HCP) converts to lower density beta (BCC) titanium. Evolutionary microstructure factors, such as grain boundary area and alpha-beta interface area, are identified to provide a mechanistic interpretation for titanium sintering. Impurity stabilize residual pores to prevent full densification, leading to identification of slow heating cycles for optimized sintering.

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Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Figure 7

Figure 8

Figure 9

Figure 10

Figure 11

Figure 12

Figure 13

Figure 14

Figure 15

Figure 16

Figure 17

Figure 18

Figure 19