Introduction

Directional freeze-casting [1,2,3] is a solidification technique that is used to create anisotropic porous metallic [4], ceramic [5], and polymeric [6] materials. For metallic and ceramic material processing, the process typically involves solidification of particle suspensions under the presence of a thermal gradient. As solidification progresses, the suspension fluid solidifies into dendrites, which grow along the direction of the thermal gradient. Suspended particles are first rejected by advancing dendrites and later incorporated within interdendritic space. After solidification, a porous structure is obtained by removing the solidified, particle-depleted fluid regions via sublimation. For metal and ceramic material processing, particle-packed walls are then sintered to form a solid matrix [1, 2].

A key benefit of the freeze-casting approach is the capacity to tune microstructural parameters by manipulating suspension characteristics and solidification conditions. The final pore structure of freeze-cast materials is templated by the morphology of the solidified suspension fluid; thus, the pore shape of freeze-cast materials is largely determined by the choice of suspending fluid [1, 2, 7]. The most commonly employed freeze-casting suspending fluids include water, camphene, and tert-butyl alcohol [1, 7]. Aqueous processing results in a range of lamellar [8] to dendritic pore structures [9] depending on the solidification velocity (higher velocities promote a transition from lamellar to dendritic structures [8]) and employment of suspension additives (where higher additive concentrations also promote a transition from lamellar to dendritic structures [9]). Camphene [10] and tert-butyl alcohol [11] result in highly dendritic and elongated tubular structures, respectively. A camphor–naphthalene fluid system has also been reported [12,13,14]; in this case, pore structures can be adjusted by changing the composition of the fluid mixture, i.e., from dendrites, to rods, to plates for hypoeutectic, eutectic, and hypereutectic compositions of camphor–naphthalene, respectively [14]. However, the microstructure images accompanying these camphor–naphthalene reports show a relatively disordered microstructure, where pores do not appear homogeneously aligned throughout these samples [12,13,14].

Here, we utilize only naphthalene (an apolar, polycyclic aromatic hydrocarbon) as the freeze-casting suspending fluid; naphthalene/Cu particle suspensions are sterically stabilized and directionally solidified to characterize the corresponding microstructure. As naphthalene solidifies with faceted interfaces [15], it should yield anisotropic pore structures when employed as a freeze-casting suspension fluid. The relatively high melting temperature of naphthalene (80 °C [16]) and vapor pressure (130 Pa at 52 °C [12]) allows for sublimation at room temperature/ambient pressure, as reported elsewhere [12,13,14]. Here, we investigate the as-solidified microstructure to better correlate processing conditions to microstructural characteristics, because post-solidification processing steps, which result in anisotropic shrinkage during sublimation [17] and sintering [18], often obscure these processing-structure connections.

Results and discussion

Suspension stability

Naphthalene/Cu particle suspensions (5-vol% Cu particles, corresponding to 32 wt% in suspension) were sterically stabilized using 1-wt% Hypermer KD-13 dispersant with respect to Cu particle mass (0.5 wt% with respect to naphthalene mass) and suspension stability was assessed by measuring the height of macroscopic particle-depleted regions in solidified samples. As samples are solidified vertically upward, particle sedimentation in the liquid results in particle-enriched and particle-depleted regions; in the solidified samples, the particle-enriched regions begin at the bottom of the samples (first-to-solidify regions) and particle-depleted regions end at the top (last-to-solidify regions). These regions present a color change in the solidified samples, with particle-enriched regions appearing darker due to the dark color of Cu particles relative to naphthalene and particle-depleted regions presenting as light orange to nearly clear (practically devoid of particles).

Figure 1 shows the average measured height of the particle depletion regions as percentages of the total solidified sample height (~ 20 cm) for samples solidified using furnace translation velocities of 6.5, 38, and 80 μm s−1). Samples solidified at the highest furnace translation velocity (V = 80 μm s−1) show particle depletion region heights that correspond to 30 ± 7% of the total sample height. Particle depletion region height increases nearly double to 58 ± 15% for samples solidified using the slowest translation velocity (V = 6.5 μm s−1), where longer solidification times promote increased particle sedimentation. The Stokes’ sedimentation velocity for 1-μm Cu particles in liquid naphthalene is ~ 2.7 μm s−1; this corresponds to a particle depletion region comprising ~ 3, 7, and 42% of sample heights for samples solidified at 80, 38, and 6.5 μm s−1, respectively, well below the values reported in Fig. 1. Suspensions containing 0.1- and 2.5-wt% dispersant (with respect to Cu mass) were produced to assess whether the sedimentation rates could be reduced by modifying dispersant concentration; as the resulting suspensions showed extensive particle sedimentation immediately after preparation, they were not tested further.

Figure 1
figure 1

Plot of particle depletion layer height (as a percentage of total sample height of ~ 20 cm) vs. solidification velocity for naphthalene/Cu particle suspensions stabilized with Hypermer KD-13. Error bars represent standard deviation.

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Solidified microstructures

Figures 2 and 3 show optical micrographs of solidified structures obtained by directionally solidifying the Cu particle suspensions using furnace translation velocities of V = 80 and 38 μm s−1, respectively. In these images, transparent naphthalene appears black, whereas Cu particles appear golden. Figures 2(a) and 3(a) are taken perpendicular to the freezing direction (the freezing direction is out-of-the-page) and images in Figs. 2(b) and 3(b) are taken parallel to the freezing direction (shown by the white arrow). For both translation velocities, naphthalene is lamellar (or plate like) with dendritic features (i.e., minor secondary arm growth of naphthalene, resulting in relatively small protrusions on particle-packed walls [8]), some of which are highlighted using small white arrows in Figs. 2(a) and 3(a). The observation of highly anisotropic structures is consistent with facetted growth [15], i.e., relatively high interfacial anisotropy of the solidifying solid. Microstructural directionality with respect to the imposed thermal gradient (white arrows in Figs. 2(b) and 3(b) are largely retained over the height of these samples.

Figure 2
figure 2

Optical micrographs of naphthalene/Cu particle suspensions directionally solidified under the fastest translation velocity studied (V = 80 μm s−1, where cross-sections (a) and (b) are taken perpendicular and parallel to the freezing direction, respectively; the white arrow in (b) shows the freezing direction. Naphthalene lamellae have dark contrast, and copper particle-packed interlamellar regions have a golden color. Asymmetric secondary arms in naphthalene are highlighted with small white arrows in (a).

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Figure 3
figure 3

Optical micrographs of naphthalene/Cu particle suspensions directionally solidified under the intermediate translation velocity studied (V = 38 μm s−1), where cross-sections (a) and (b) were taken perpendicular and parallel to the freezing direction, respectively; the white arrow in (b) shows the freezing direction. Macro-regions of naphthalene show as dark regions in these images; copper particle-packed walls are golden in color. Asymmetric secondary arm growth of naphthalene is highlighted with small white arrows in (a).

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Preliminary directional solidification tests of Cu particle/naphthalene suspensions were conducted using a typical directional freeze-casting set-up [1], wherein a Teflon mold containing the suspension was temperature controlled at the top and bottom faces, defining the macroscopic thermal gradient in the solidifying sample, but not the thermal gradient within the interfacial region, specifically. Microstructures similar to those reported in the literature for the camphor–naphthalene fluid system [12,13,14] were obtained: some local, directional growth of naphthalene was observed, but directionality was not retained over the solidification height for these samples. Fabietti et al. [19] reported that instability mechanisms during directional solidification of naphthalene are strongly dependent on the orientation of the solid/liquid interface (which can be influenced by a lack of control over the thermal gradient at the interface [20, 21]). The improved microstructural directionality shown here was obtained only using a Bridgman furnace. While use of the Bridgman furnace provides better control over the thermal gradient at the solid/liquid interface (thus may have improved directionality by itself [20, 21]), it also necessitated use of increased sample heights (~ 60 mm vs. 5–15 mm in refs. [12,13,14] and ~ 10 mm in our initial studies that used a typical freeze-casting set-up). Grains that are initially misaligned with respect to the thermal gradient will typically rotate such that the preferred crystallographic growth direction is aligned with the thermal gradient; how fast this occurs is dependent on factors, such as pulling velocity, thermal gradient, and crystal anisotropy [20]. Thus, the use of increased solidification heights may have contributed to the improved directionality observed here as misoriented grains were provided a longer length scale for orientation corrections.

As noted above, the images in Figs. 2 and 3 show evidence of secondary arm growth of naphthalene [small white arrows in Figs. 2(a) and 3(a)], but the resulting particle–wall protrusions are primarily observed on only one side of particle walls. Asymmetric dendritic features on lamellae, often referred to as “one-sided dendrites” [8], can be promoted due to the presence of interdendritic convective flow during solidification. Similar asymmetric dendritic features were reported in our previous investigation of aqueous TiO2 suspensions [22]; there, it was proposed that rotating fluid cells between lamellae were promoted due to a shear flow existing at the solid/liquid interface, and the interaction between these fluid flow regimes promoted growth of secondary arms on the upstream side (where heat is more easily transported away from lamellae via the fluid flow) and the warmer fluid on the downstream side promoted melting and fragmentation of secondary arms [23]. A similar mechanism can be invoked here to explain the asymmetric dendritic features observed in Figs. 2(a) and 3(a).

Figure 4 shows optical micrographs of solidified structures obtained by directionally solidifying the suspensions at a translation velocity, at V = 6.5 μm s−1. Cross-sections Fig. 4(a) and Fig. 4(b) are taken perpendicular to the freezing direction, and the images in Fig. 4(c) and (d) are taken parallel to the freezing direction (shown by large white arrows). Cross-sections Fig. 4(a) and (c) are taken from the outer region of the sample (closest to the ampoule wall) and Fig. 4(b) and (d) are taken from the central region. Increased wall thickness (or wall merging) is observed in Fig. 4(b) relative to Fig. 4(a), which is suggestive of a microstructural transition from dendrites to banding (bands are naphthalene plates orientated perpendicular to the freezing direction, which are templated into cracks after sublimation [24]; these are best viewed in parallel cross-sections). The left side of the parallel cross-section in Fig. 4(c) is toward the outer region of the sample; moving toward the right in the image, the width of the particle walls increases (i.e., wall width increases with increasing distance from the ampoule wall). A dramatic increase in wall width is further observed in Fig. 4(d), which represents the central region of the same sample where banding is observed [small white arrows in Fig. 4(d)]. Figure 4(d) shows the central region of the same sample where particle wall width has increased dramatically, and banding is observed (small white arrows in Fig. 4).

Figure 4
figure 4

Optical micrographs of naphthalene/Cu particle suspensions directionally solidified under the slowest translation velocity studied (V = 6.5 μm s−1), where cross-sections (a, b) were taken perpendicular to the freezing direction and (c, d) were taken parallel to the freezing direction (the large white arrows in (c, d) show the freezing direction). Images (a) and (c) were taken from the outer regions of samples (closest to the ampoule wall) whereas (b) and (d) were taken from central regions. Macro-regions of naphthalene show as dark regions in these images; copper particle-packed walls are golden in color; asymmetric dendritic features (a) and banding defects (d) are marked with small white arrows.

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Radial segregation

Figure 5 shows box and whisker plots describing thickness of lamellae. Measurements obtained from the “outer” (or peripheral, closest to the ampoule wall) regions of cross-sections are summarized in the leftmost plot, and the rightmost plot summarizes measurements taken from inner/central regions of samples. The minimum and maximum values of boxes represent the first and third quartiles, respectively; medians are shown as horizontal lines inside the boxes, means are represented by black diamonds, and whiskers represent 1.5 times the interquartile range. Numerical values for the data described in Fig. 5 are provided in Table 1.

Figure 5
figure 5

Box and whisker plots summarizing thickness of naphthalene lamellae in sterically stabilized naphthalene/Cu particle suspensions after directionally solidification using furnace translation velocities, V = 6.5, 38, and 80 μm s−1. “Outer,” “outer-middle,” “middle-inner,” and “inner” measurements are described in text and illustrated in insert. The minimum and maximum values of boxes represent the first and third quartiles, respectively; medians are shown as horizontal lines inside the boxes, means are represented by black diamonds, and whiskers represent 1.5 times the interquartile range.

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TABLE 1 Thickness of naphthalene lamellae in suspensions of Cu microparticles that were directionally solidified at furnace translation velocities of 6.5, 38, and 80 μm s−1.
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Naphthalene lamellar thickness is expected to increase with decreasing solidification velocity [8]; taking the furnace translation velocity as roughly equivalent to solidification velocity, this relationship is observed for all regions. For all translation velocities, lamellae are thickest in the outer region of the samples and a decrease in thickness is observed with decreasing distance from the center (e.g., for samples solidified at V = 6.5 μm s−1, lamellae thickness at the outer and inner regions is 74 ± 30 and 36 ± 15 μm, respectively; for V = 80 μm s−1, these values decrease to 45 ± 23 and 19 ± 10 μm, respectively). This trend—increasing lamellar thickness at outer/peripheral regions of samples relative to inner/central regions—indicates that the local solidification velocity is higher in the central region of the sample relative to the outer region, which is suggestive of macroscopic curvature of the interface during solidification and corresponding convective fluid motion [25]. Similar observations were described in our previous study investigating directional solidification of aqueous TiO2 suspensions [22, 26] solidified in a buoyancy unstable configuration (which for water, is vertically upward), wherein a macroscopic curvature of the solid/liquid interface was proposed to explain radial variation in particle wall width (dependent on distance from the center) and banding (solidified fluid, separated by particle-packed regions, and oriented perpendicular to the solidification direction) present in the central regions of samples. Banding was attributed to particle build-up within the central region of the samples, resulting from the interface curvature itself as well as from convective mixing within the bulk liquid (ahead of the solid/liquid interface) leading to orthokinetic particle aggregation. Here, suspensions are solidified in the buoyancy-stable configuration for naphthalene (vertically upward, with denser solid naphthalene below and the lighter liquid suspension above); thus, convective fluid motion is likely promoted due to the presence of radial thermal gradients at the solid/liquid interface and resulting, orthokinetic aggregation may be contributing to the lensing observed here.

Model comparison

You et al. [24] developed a model for predicting freeze-cast microstructures, including dendrites and lenses, where lensing includes both banding (solidified fluid oriented perpendicular to the solidification direction) and “spears,” (highly interconnected dendrites whose sidearms merge). The boundary between dendritic and lensing is determined by the relationship between two dimensionless parameters, including the Darcy coefficient (D), which describes fluid flow through the particle accumulation layer, given by

$$D = \frac{{\mu VT_{m} }}{k\rho LG}$$
(1)

where \(\mu\) is the dynamic viscosity of the suspending fluid, V is the solidification velocity (taken as the furnace translation velocity, V = 6.5, 38, and 80 μm s−1), \({T}_{m}\) is the melting temperature of the pure fluid (80.23 °C for naphthalene [27]), \(\rho\) is the density of the solid, pure fluid (976.7 kg m3 for naphthalene [28]), L is the latent heat of fusion of the pure fluid (146 J/g for naphthalene [29]), G is the imposed thermal gradient (here, G = 35 °C cm−1), and k is the permeability of the accumulated particle region given by

$$k = \frac{{r^{2} \left( {1 - \phi_{p} } \right)^{3} }}{{45\phi_{p}^{2} }}$$
(2)

where \(r\) is the particle radius (here, r = 0.5 μm) and ϕp is the volume fraction of particles in the accumulation region, taken as the random close-packed value of 0.64. The second dimensionless parameter, ϕ, is given by

$$\Phi = \frac{{\phi_{0} }}{{\phi_{p} - \phi_{0} }}$$
(3)

where ϕ0 is the particle volume fraction in the bulk suspension (here, ϕ0 = 0.05). Dendritic structures are predicted when \(D/(1+\upphi )>1\), whereas lensing regimes are predicted when this value is less than one. Thus, transitions from dendritic to lensing regimes are predicted as the solidification velocity decreases or with increases in thermal gradient, particle volume fraction, or particle radius (here, G, \({\phi }_{0}\), and r are held constant, while V is varied from 6.5 to 80 μm s−1).

The microstructures for all translation velocities explored here are predicted to be within the lensing regime (\(D/(1+\upphi )\) is less than one for all translation velocities). Inconsistent with model predictions, anisotropic, directional lamellar structures are observed for V = 38 and 80 μm s−1. This model does not account for solute effects; the dispersant used in our suspensions likely contributed to the breakdown of the solid/liquid interface [30] and may have promoted the development of anisotropic structures outside model predictions. At V = 6.5 μm s−1, a transition between dendritic to lensing microstructures is observed from the outer to inner region of the samples. The transition to lensing with decreasing V is qualitatively consistent with this model, but it is notable that lensing is observed in the central regions of samples only; this observation may be attributable to convective effects [22], which are also not accounted for in the model. We described similar observations previously for directional solidification of aqueous TiO2 suspensions [22], wherein macroscopic curvature of the solid/liquid interface (resulting from convection) leads to radial variation in particle wall width (dependent on distance from the center) and banding in the central regions of samples; as described earlier, we attributed banding to particle build-up within the central region of samples from both the interface curvature itself as well as convective mixing in the bulk liquid (ahead of the interface).

Conclusion

To investigate the suitability of naphthalene as a suspending fluid for freeze-casting applications, suspensions of 5-vol% (32 wt%) Cu microparticles in naphthalene, sterically stabilized by the polymeric surfactant Hypermer KD-13 (1 wt% with respect to Cu particle mass), were directionally solidified in a Bridgman furnace at translation velocities, V = 6.5, 38, and 80 μm s−1. The following main conclusions are drawn:

  1. 1.

    Directional microstructures are predominantly observed, comprising colonies of nearly particle-free naphthalene lamellae interspersed with particle-enriched interlamellar regions.

  2. 2.

    At V = 38 and 80 μm s−1, a preferred growth direction is observed along the thermal gradient imposed during solidification, over the full height of solidified samples.

  3. 3.

    At V = 6.5 μm s−1, a transition from lamellar to lensing microstructures is observed from the regions closest to the ampoule wall to the central regions, suggestive of a macroscopic curvature of the solid/liquid interface during solidification.

  4. 4.

    For all V, the thickness of lamellae increases with increasing distance from the region near the ampoule wall (with lamellae thinnest in the central regions of samples) and lamellae show secondary arms on one, not both, of their sides.

  5. 5.

    Both the presence of asymmetric dendritic features and radial variation in lamellar thickness are suggestive of buoyancy-driven convective fluid flow during solidification. As suspensions were solidified in a buoyancy-stable configuration for naphthalene (vertically upward, with denser solid naphthalene below and lighter liquid above), convective fluid motion is likely introduced due to radial temperature gradients which are often present during Bridgman solidification.

Experimental methods

Specimen preparation

As-received naphthalene (C10H8, 99.6% purity, Sigma-Aldrich, St. Louis, MO, USA) was first vacuum distilled at ~ 90 °C. Due to the relatively high solubility of atmospheric gases in liquid naphthalene [19, 31,32,33,34], suspensions were prepared under helium atmosphere using a Schlenk line. The polymeric surfactant Hypermer KD-13 (Croda Inc., Edison, NJ, USA) was incorporated at a concentration of 1 wt% (with respect to intended Cu mass) into the distilled naphthalene and equilibrated via stirring for ~ 12 h at ~ 90 °C. Copper microparticles (1 µm, SkySpring Nanomaterials, Inc., Houston, TX, USA), which were first dried for 12 h under vacuum at ~ 100 °C to remove moisture adsorbed on their surfaces, were then added to naphthalene/dispersant solutions at a volume fraction of 5% (corresponding to a Cu particle weight fraction of 32%). These suspensions were stirred for 12 h at ~ 90 °C and sonicated for 2 h in a ~ 90 °C water bath. Suspensions were prepared at volumes of either 50 or 100 mL (with equilibration times remaining the same regardless of volume).

Particle suspensions were transferred to quartz ampoules (10 mm inner diameter, ~ 20 cm in length) and directionally solidified using a Bridgman furnace (preheated to ~ 130 °C). For this furnace, the ampoule is held stationary, while the furnace is translated vertically upward, promoting “upward” (against gravity) solidification. Furnace translation velocity was controlled using an Arduino microcontroller, where physical measurements were obtained to produce calibration tables corresponding furnace translation velocities to software and motor driver settings. Samples were solidified at three translation velocities, V = 6.5, 38, and 80 μm s−1 under a constant thermal gradient of 35 °C cm−1.

Microstructural investigation

Directionally solidified samples were mounted in epoxy, polished, and imaged using a Wild M3Z Stereoscope. Naphthalene lamellae thickness was measured using ImageJ/Fiji [35] from stitched cross-section images taken perpendicular to the freezing direction. These measurements were regionalized using guides: “outer” measurements were taken from a circle drawn at the periphery of cross-sections and “inner” measurements taken from a circle drawn at the center of cross-sections having a diameter of ~ 2.5 mm. “Outer-middle” and “middle-inner” measurements were taken from equally spaced circles drawn between the outer and inner circles (thus, distance between any given circle is ~ 1.25 mm as the sample diameters are ~ 10 mm). Only lamellae crossing drawn guides were measured. Nine samples were analyzed (three samples for each furnace translation velocity) with 500 measurements taken for each region (at each velocity).