Reticulated open-cellular aluminum nitride ceramic foams: Effect of sintering aids on microstructural, thermal, and mechanical properties

Abstract

Open-celled aluminum nitride ceramic foams were prepared by the polymer sponge replication technique involving aqueous dispersions of passivated AlN. The amount of the Y₂O₃ and Dy₂O₃ as sintering aid was varied, and the effects on the densification, microstructure formation, phase composition, and finally, the thermal conductivity were investigated. A typical thermal conductivity of 1.1 W m⁻¹ K⁻¹ was determined for foams at a porosity level of 94.3 vol.%, on average. This measured foam thermal conductivity was subsequently modeled using different porosity ↔ thermal conductivity relations considering the different hierarchical levels of porosity in these foams. From these models, the thermal conductivity of the bulk AlN strut material was determined, correlated with the strut microstructure and the phase composition, and compared to literature data.

1 INTRODUCTION

The most prominent manufacturing technique for open-celled ceramic foams is the polymer sponge replication, or the Schwartzwalder technique.¹ It makes use of open-celled, reticulated polymer foams (usually polyurethane), which are coated with a suitable ceramic dispersion, and form—after thermal processing—a ceramic replica of the polymer foam. The Schwartzwalder or replica process has been applied in manufacturing foams of several ceramic materials, most prominently silica-bonded alumina, oxide-bonded silicon carbide, and zirconia.^{2, 3} These materials are mostly used for the industrial production of ceramic foam filters for foundry applications in quantities exceeding 10⁸ pieces per year.⁴ Nevertheless, the process has also been adapted for more specialized engineering and functional ceramics, for example, Al₂O₃–ZrO₂ composites (ZTA),^{5, 6} ZnO,⁷ CeO₂,⁸ Si₃N₄,⁹ and also, AlN.¹⁰

Aluminum nitride features the unique combination of being an electrical insulator and possessing a high thermal conductivity of up to 180 W m⁻¹ K⁻¹ for typical sintered parts of AlN.^{11, 12} The drawback of AlN—being hydrolytically instable—can be compensated by a passivation of AlN powder with phosphate species like orthophosphoric acid or an Al(H₂PO₄)₃ solution prior to processing.^13-15 This passivated AlN powder can then be conventionally processed in aqueous dispersions.^{10, 16} Nevertheless, the other drawback of AlN remains: Due to its high degree of covalent bonding, usually high temperatures and/or additives, which enable a liquid phase sintering process, are necessary for the densification of AlN ceramics. Typically, yttria (Y₂O₃), sometimes combined with calcia (CaO), is used for this purpose. These sintering aids form a liquid phase of yttrium/calcium aluminates, which reduces the sintering temperature and collects oxide impurities from the AlN starting material.^17-20 As oxide contamination leads to the formation of crystallographic defects within the AlN phase and therefore to a decrease of the thermal conductivity, this scavenging effect is mandatory for achieving a high thermal conductivity in the sintered AlN parts.²¹ Besides yttria, other rare-earth sesquioxides, RE₂O₃ proved to be suitable as sintering aid for the densification of aluminum nitride. In this context, Dy₂O₃ was most effective in extracting oxygen impurities from AlN resulting in an increased thermal conductivity of the respective AlN–Dy₂O₃ ceramics.^{18, 22}

In most cases, AlN is processed into simple geometric forms, for example, substrates for electronics, by using dispersion-based processes like slip casting or tape casting.^{16, 23} Examples for more geometrically complex structures made from aluminum nitride are the previously mentioned AlN replica foams,¹⁰ or most recently, AlN scaffolds manufactured by stereolithography.²⁴

The present work deals with the manufacturing of cellular AlN structures with a focus on thermal conductivity. Open-cellular (ceramic) structures are promising candidates for heat-managing devices, for example, as supports for zeolites as active materials in adsorption-driven heat pumps.²⁵ For this purpose, AlN ceramic foams were prepared by the Schwartzwalder replica technique using aqueous dispersions of phosphatized AlN powders. The effect of the concentration of the rare-earth oxide sintering aid was investigated and Y₂O₃ and Dy₂O₃ as sintering aids were compared with respect to their effect on the microstructure, phase composition, as well as thermal properties of the processed AlN foams.

2 EXPERIMENTAL PROCEDURES

2.1 AlN foam preparation

Aluminum nitride (AlN) ceramic foams were prepared by the Schwartzwalder sponge replication process using an aqueous AlN dispersion and polyurethane foam templates with 20 pores per (linear) inch (ppi).¹ The amount of the sintering aid RE₂O₃ (RE = Y, Dy) was varied between 1.7 and 2.5 mol%.

To avoid hydrolysis, a passivation of the AlN powder with Al(H₂PO₄)₃ solution was performed according to Refs. [10, 15]: Aluminum nitride powder of 100 g (grade C, d₅₀ = 1.3 μm, Höganäs Germany GmbH, Goslar, Germany) was stirred for 15 min in 200 ml of a 6.3 mmol L⁻¹ solution of Al(H₂PO₄)₃ at 70°C. Afterward, the phosphatized AlN particles were collected by vacuum filtration, washed with demineralized water, and finally, dried at 70°C.

The AlN dispersions were prepared according to a previous work in Ref. [10]. An ethylammonium citrate–based deflocculant, Dolapix CE 64, a polyvinyl alcohol (PVA) binder, Optapix PA 4G, and a nonionic alkyl polyalkylene glycol ether-based anti-foaming agent, Contraspum K 1012, used as processing aids, were obtained from Zschimmer & Schwarz GmbH & Co. KG, Lahnstein, Germany. Table 1 provides the composition of the respective dispersions. Phosphatized AlN, RE₂O₃ (Y₂O₃: grade C, d₅₀ = 0.8 μm, Höganäs Germany GmbH, Goslar, Germany; Dy₂O₃: 99.9%, d₅₀ = 5 μm, abcr Chemie GmbH, Karlsruhe, Germany), and Dolapix CE 64 (1.0 ma.% of AlN + RE₂O₃ solid content) were dispersed in demineralized water, which has been acidified with orthophosphoric acid. The addition of H₃PO₄ is mandatory, otherwise the phosphatization layer on the AlN particles might be destroyed during mixing resulting in a catastrophic hydrolytic decomposition of the AlN powder. A first mixing step was performed in a planetary centrifugal mixer (THINKY Mixer ARE-250, THINKY Corp. Tokyo, Japan) at 2000 rpm for 5 min while monitoring the temperature of the dispersion. Excessive heating of the dispersion during the mixing step must be avoided to minimize the hydrolysis of the AlN powder. Subsequently, the PVA binder (1.5 ma.% of AlN + RE2O3 solid content) and the anti-foaming agent (0.1 ma.% of AlN + RE₂O₃ solid content) were added followed by a second mixing step (2000 rpm, 5 min). The resulting AlN dispersions were characterized by a total solid loading of 73.7–75.8 ma.%, which is 45.4–46.1 vol.% and were suitable for the polymer sponge replication technique.

TABLE 1. Dispersion compositions used for the manufacturing of AlN foams

component/g	sample series//mol% RE2O3
	1.7 Y	2.5 Y	2.5 Dy
Dolapix CE 64	0.44	0.46	0.49
Demineralized H2O	13.7	13.7	13.7
H3PO4	0.80	0.80	0.80
Phosphatized AlN powder	40.0	40.0	40.0
RE2O3 powder	3.78	5.67	9.36
Optapix PA 4G	0.66	0.69	0.74
Contraspum K 1012	0.04	0.04	0.05
Total solid loading/wt.%	73.7	74.4	75.8
Total solid loading/vol.%	45.4	46.1	46.1

The obtained AlN dispersions were then coated on polyester polyurethane foam templates (SP30P20R, Koepp Schaum GmbH, Oestrich-Winkel, Germany) with a linear cell count of 20 ppi and a dimension of 50 mm × 50 mm × 20 mm (samples for thermal conductivity measurements) and 20 mm × 20 mm × 20 mm, respectively (samples for porosity and compressive strength analysis). The polymeric sponge pieces were immersed into the AlN dispersion; the excess slurry was removed manually until the coated foam templates reached a weight of ∼2.0 g (8 cm³ templates) or 12.5 g (50 cm³ templates), respectively, corresponding to a porosity of ∼94% in the final foam parts. After drying at ambient conditions, thermal template removal was performed in three steps (110°C/2 h, 250°C/3 h, and 400°C/3 h, heating/cooling rate for each step: 1 K min⁻¹) in a circulating air furnace (KU 40/04/A, THERMCONCEPT Dr. Fischer GmbH, Bremen, Germany). For sintering, the green foams were transferred into a tube furnace (HTRH 70‑600/1800, Carbolite Gero GmbH & Co. KG, Neuhausen, Germany) and heated free standing without powder bed in an atmosphere of flowing N₂ to 1650°C for 3 h (heating/cooling rate 5 K min⁻¹).

2.2 Characterization

For porosity analysis, the foams made from the 8 cm³ templates were used; at least 10 specimens per sample series were analyzed, and the results were averaged. The total porosity of the AlN foams (V_pores/V_foam) was calculated from the geometric foam density and the theoretical density of the strut material. The strut material density was calculated by the rule of mixture from the densities of AlN (3.26 g cm⁻³) and RE₂O₃ (5.01 g cm⁻³, Y₂O₃; 7.81 g cm⁻³, Dy₂O₃).^{12, 26} The strut porosity (V_{strut pores}/V_struts) was calculated from the dry, buoyant, and water-filled weight of the foams (water immersion/Archimedes’ method according to the DIN EN 623‑2:1993‑11 standard).²⁷ The porosity in the ceramic phase was separated from the hollow strut cavity caused by the burnout of the PU foam template. For this, the volume of the PU foam struts (calculated from the average template weight of 0.244 g for an 8 cm³ foam and a PU skeletal density of 1.1 g cm⁻³ according to He-pycnometry results) was subtracted from the total strut pore volume as determined by the water immersion technique. Beforehand, the PU foam strut volume was corrected by the observed volumetric shrinkage of the AlN foam sample of ≈15 vol.%. This procedure allows the separation of the pore volume being present in the strut material, in the hollow strut cavities and—under consideration of the volume of the AlN strut material itself—also in the foam cells (cell porosity).

The microstructure of particular struts of the AlN foams was characterized by scanning electron microscopy using a backscattered-electron detector (XL30 ESEM-FEG, FEI/Philips, Hillsboro/OR, USA). The AlN foam samples were embedded in an epoxy resin, grinded, polished, and sputter-coated with gold prior to the measurement.

The quantitative phase composition of the grinded aluminum nitride strut material was determined by powder X-ray diffraction (XRD) analysis with a D8 Discover diffractometer (Bruker AXS GmbH, Karlsruhe, Germany) in the Bragg–Brentano reflection geometry with Co K_α1/2 radiation. The X-ray tube was operated with 35 kV and 40 mA; a fixed divergence slit of 0.6 mm and 2.5° primary and secondary soller slits were used as optical components. The diffracted intensities were recorded in a 2θ range from 10° to 160° using a LYNXEYE XE-T energy-dispersive detector operated in 1D mode. The quantitative phase analysis was performed by the Rietveld analysis with the software TOPAS V6 (Coelho Software, Brisbane, Australia/Bruker AXS GmbH, Karlsruhe, Germany).^{28, 29} The oxide content of the AlN strut material was calculated from the phase content of free Al₂O₃ as determined by the Rietveld analysis.

The thermal conductivity of the aluminum nitride foams was determined by the transient plane source (TPS) technique (TPS 2500 S, Hot disk SE, Gothenburg, Sweden).³⁰ A TPS sensor with 9.908 mm in diameter was placed between two identical AlN foams manufactured from the 50 cm³ templates. Beforehand, the surface of the foams was sanded carefully. The sensor was heated with 200 mW for a 5 s measurement, and the thermal conductivity was calculated from the sensor temperature change.³¹ Each combination of the sides of both rectangular specimens was measured for five times, and the resulting 20 measurements were finally averaged.

The compressive strength was determined using a TIRAtest 2825 testing machine that was equipped with circular loading plates with 150 mm in diameter (TIRA GmbH, Schalkau, Germany). To ensure a more homogeneous load on the samples, a cardboard piece with 1 mm thickness was placed between the foam part and the loading plates. The applied loading rate was set to 1 mm min⁻¹. The compressive strength was calculated from the maximum force of the respective foam sample. At least 10 specimens were measured per sample series. The average compressive strength was calculated using the three-parameter Weibull distribution as implemented in the Visual-XSel 14 software.^{32, 33} This gives the average compressive strength σ_cf and the minimum compressive strength σ_cf,min together with the Weibull modulus m as a measure of the scattering of the individual strength results.

3 RESULTS AND DISCUSSION

For all three AlN–RE₂O₃ compositions, mechanically stable foams were obtained (Figure 1). The linear shrinkage during the sintering process is 5% for the samples containing 1.7 and 2.5 mol% Y₂O₃ and 3% for the foams made with 2.5 mol% Dy₂O₃, respectively. This is significantly lower compared to fully densified AlN ceramics. For these, a linear shrinkage in the order of magnitude of 20% is usually observed.²⁴ Thus, the strut material of the AlN foams exhibits a significant amount of residual porosity, which ranges between 22 vol.% (2.5 mol% Y₂O₃) and 37 vol.% (1.7 mol% Y₂O₃) with respect to the strut volume (excluding the hollow strut cavities). Accordingly, with increasing concentration of the Y₂O₃ sintering aid, a decrease in strut material porosity has been observed (Table 2). The foam samples made with Dy₂O₃ as sintering aid exhibit a higher porosity in the strut material (31 vol.%) compared to the cellular ceramics made with the same concentration of yttria. This might be explained by the larger particle size of Dy₂O₃ (5 μm) compared to the Y₂O₃ powder (0.8 μm) used within this study. Consequently, the sintering activity of the AlN–Dy₂O₃ starting material is lower, which reflects in the decreased shrinkage as well as increased residual strut porosity.

FIGURE 1

Open-celled aluminum nitride ceramic foams containing 1.7 mol% Y₂O₃, 2.5 mol% Y₂O₃, and 2.5 mol% Dy₂O₃ as sintering aid (from left to right). The smaller foams are used for porosity and strength analysis, and the larger specimens are for thermal conductivity measurements.

TABLE 2. Properties of cellular aluminum nitride; the total porosity (P_tot.) and cell porosity (P_cell) correspond to the geometric foam volume and the ratio V_pores/V_foam, whereas the strut porosity (P_strut) refers to the ratio V_{strut pores}/V_struts (excluding the hollow strut cavities remaining after template burnout and sintering)

Foam sample (mol%)	Ptot./%	Pcell^a/%	Pstrut^b/%	Second phases/ma.%	λfoam/W m^−1 K^−1	λstrut^c/W m^−1 K^−1	λbulk^d/W m^−1 K^−1
AlN 1.7 Y	94.0(4)	90.5(4)	37(3)	12.7(2)	1.24(6)	38	72
AlN 2.5 Y	94.3(3)	92.8(3)	22(3)	16.3(2)	1.01(4)	41	58
AlN 2.5 Dy	94.6(6)	92.2(6)	31(3)	20.2(3)	1.05(1)	39	66

• ^a Including the cavities resulting from the PU template burnout.
• ^b Related to the volume of the strut material excluding the cavities resulting from the PU template burnout; V_{strut material pores}/(V_{strut material pores} + V_solid)
• ^c Extrapolated strut thermal conductivity (Equation. 2).
• ^d Extrapolated bulk thermal conductivity (Equations (2) and (3))

In general, the densification behavior of the AlN–RE₂O₃ mixtures is far from optimal, which is mostly caused by the sintering temperature being limited to 1650°C. Commonly, sintering of AlN is performed at temperatures exceeding 1700°C (with multiphase sintering aids, e.g., CaO–Y₂O₃), or even 1800°C, when only rare-earth oxides are used.^{19, 22}

The microstructure of the AlN strut material of all foam samples is inhomogeneous and shows a significant amount of pores in the submicrometer regime (Figure 2). The shape of the AlN grains is irregular, and no significant grain growth has taken place as the majority of grains is smaller than 1 μm. Some larger aggregates of 2–5 μm in size were formed, indicating that a certain amount of sintering has taken place in these areas. For the foams made with dysprosia as sintering aid, the number of aggregates is larger compared to the samples made with yttria.

FIGURE 2

Backscattered-electron micrographs of strut cross sections of AlN foams with different amounts of rare-earth oxide sintering aids (top: 1.7 mol% Y₂O₃; middle: 2.5 mol% Y₂O₃; bottom: 2.5 mol% Dy₂O₃). The secondary phases (rare-earth aluminates) are shown in white/light gray.

The rare-earth aluminate secondary phases are evenly distributed throughout the microstructure of the AlN strut material. For the foams made with Y₂O₃, the size of the rare-earth aluminate inclusions ranges between 0.5 and 2 μm, whereas for the Dy-containing samples, the secondary phases are significantly larger (2–10 μm). This is a direct consequence of the Dy₂O₃ powder used being coarser than the Y₂O₃.

Interestingly, the microstructure of all foams investigated differs from the typical microstructure of liquid-phase sintered ceramics, which show the formation of secondary phases from a molten phase at the grain boundaries as well as grain triple points.^{7, 19, 24} For high contents of sintering aids, even a percolating arrangement of secondary phases is formed.¹⁶ Consequently, the particulate arrangement of secondary phases for the AlN foam samples in this work indicates that no formation of a liquid phase has taken place over larger areas in the microstructure. This is a direct consequence of the low sintering temperature compared to conventional thermal processing of AlN ceramics and in good agreement with the significant amount of residual porosity in the strut material.

Phase determination by XRD and the Rietveld analysis revealed a significantly reduced amount of a free aluminum oxide phase with corundum structure compared to a previous study of cellular AlN (Figure 3).¹⁰ The Al₂O₃ concentration decreased from 3.2 ma.% for foams with 0.9 mol% yttria sintering aid¹⁰ to 0.6–0.9 ma.% for the specimens with 1.7 and 2.5 mol% RE₂O₃ (this work). As the processing conditions during foam preparation and sintering were identical to the previously prepared samples, the increased amount of rare-earth oxide sintering aid proved to be effective for the reduction of the oxide content in the AlN phase.

FIGURE 3

Left: powder X-ray diffraction (XRD) patterns of the strut material of AlN foams with different rare-earth oxide sintering aids (black/gray symbols: measured data, colored lines: Rietveld fit); right: phase composition obtained from the Rietveld analysis (left column extracted from Ref. [10], second, third, and fourth column: this work)

As secondary phases, the rare-earth aluminates RE₃Al₅O₁₂ (garnet structure, RE = Y, Dy), REAlO₃ (perovskite structure, RE = Y, Dy), as well as monoclinic RE₄Al₂O₉ (RE = Y, Dy) were identified. As expected, the total amount of secondary phases increased with an increasing concentration of rare-earth oxide sintering aids and range between 10 ma.% (samples with 0.9 mol% Y₂O₃¹⁰) and 20 ma.% (samples with 2.5 mol% Dy₂O₃). Furthermore, an increasing content of phases with a higher RE:Al ratio (for RE₃Al₅O₁₂: 0.6, REAlO₃: 1, and RE₄Al₂O₉: 2) became apparent for an increasing RE₂O₃ sintering aid concentration: For the foams made with 2.5 mol% yttria, monoclinic Y₄Al₂O₉ is the main secondary phase, and for the samples containing 0.9 mol% Y₂O₃, only the aluminum-rich garnet phase Y₃Al₅O₁₂ is formed. In the samples containing dysprosia, however, a significant fraction of DyAlO₃ is observed. This might be explained by a different thermodynamic stability of the corresponding dysprosium aluminates, or—more likely—by the larger particle size and thus lower reactivity of the Dy₂O₃ powder used.

The compressive strength data of all AlN foam series were approximated by a three-parameter Weibull distribution (Figure 4). The mean compressive strength at a failure probability of 63.2% is 0.18 ± 0.11 MPa for the foams made with 1.7 mol% yttria, 0.14 ± 0.07 MPa (2.5 mol% Y₂O₃), and 0.07 ± 0.03 MPa (2.5 mol% Dy₂O₃), respectively. The overall strength is low due to the high total porosity of 94 vol.% or above, and it is in good agreement with cellular ceramics made of other materials like ZnO (0.15 MPa at P = 93.6 vol.%)⁷ and Al₂O₃ (0.19 MPa at P = 94 vol.%).³⁴ The course of the strength results fits well with the trend in the average total porosity, which is highest for the foams made with 2.5 mol% Dy₂O₃ (94.6 vol.%) and lowest for the samples with 1.7 mol% Y₂O₃ (94.0 vol.%).

FIGURE 4

Top: three-parameter Weibull distribution of the strength data measured for different AlN ceramic foams. Bottom: The (averaged) compressive strength is well approximated with the Gibson–Ashby model for brittle cellular structures (Y: Y₂O₃; Dy: Dy₂O₃).

In order to evaluate the effect of porosity on the compressive strength, all data were modeled with the following Gibson–Ashby relation for brittle, cellular structures (Equation 1)³⁵:

$$$$\begin{equation}{\sigma _{{\rm{cf}}}} = {C_6} \cdot {\left( {{\rho _{{\rm{rel}}{\rm{.}}}}} \right)^n} \cdot {\sigma _{{\rm{fs}}}}\end{equation}$$$$(1)

The compressive strength of a porous ceramic σ_cf is a function of the relative density ρ _rel. (which is 1–P_tot./100) and the flexural strength of the bulk strut material σ_fs. The parameter C₆ is a constant, and it is related to the cell geometry; typically, it is set to 0.16.³⁶ The exponent n is left at 1.5 as given in the original Gibson–Ashby model; it defines the effect of a porosity change on the compressive strength.³⁵ For modeling of the AlN strength data, the parameter σ_fs was varied and finally converged to a value of σ_fs = 60 MPa. This is significantly lower compared to the flexural strength of AlN in the literature (300 MPa and above).^{24, 37, 38} The reason for the considerably reduced flexural strength of the AlN strut material is the significant amount of residual strut porosity of 30 vol.% on average, as well as the incomplete sintering of the AlN phase.

The thermal conductivity of the AlN foams investigated within this work is 1.24 ± 0.06 W m⁻¹ K⁻¹ for the sample made with 1.7 mol% yttria, 1.01 ± 0.04 W m⁻¹ K⁻¹ (2.5 mol% yttria), and 1.05 ± 0.01 W m⁻¹ K⁻¹ (2.5 mol% dysprosia), respectively. These values are in the same order of magnitude as reported previously for cellular AlN (1.16 W m⁻¹ K⁻¹; see Ref. [10]), but at a significantly increased porosity level. Therefore, in order to evaluate the thermal conductivity results and for comparision with other (cellular) materials, the modeling of the porosity effect is mandatory. The foams presented within this work exhibit porosity on different hierarchical levels: (1) cell porosity: mm range; (2) hollow strut cavities: 100 μm range; (3) strut material porosity: sub-μm range. Therefore, a combined approach of different porosity ↔ thermal conductivity models is applied: The effect of cell porosity P_cell (which also contains the hollow strut cavities) on the thermal conductivity was modeled following a rule-of-mixture-based approach by Ashby, which assumes that heat is conducted equally in all three spatial directions within the foam lattice (Equation 2)³⁹:

$$$$\begin{equation}{\lambda _{{\rm{strut}}}} = \frac{{{\lambda _{{\rm{foam}}}} - {P_{{\rm{cell}}}} \cdot {\lambda _{{\rm{gas}}}}}}{{{1/3} \cdot (1 - {P_{{\rm{cell}}}})}}\end{equation}$$$$(2)

Equation (2) gives an approximation of the thermal conductivity of the strut material λ_strut of a cellular structure based on the measured foam conductivity λ_foam and the thermal conductivity of the surrounding gas phase λ_gas (a value of 0.0264 W m⁻¹ K⁻¹ was used⁴⁰). For the AlN foams investigated within this work, λ_strut ranges between 38 and 41 W m⁻¹ K⁻¹ (Table 2) and corresponds to the thermal conductivity of the AlN strut material still containing the residual porosity of ∼30 vol.%. In a second step, the effect of this residual strut material porosity was estimated by using the following model of Eucken (Equation 3)⁴¹:

$$$${\selectfont\fontsize{9}{11} \begin{equation} {\lambda}_{\mathrm{strut}}={\lambda}_{\mathrm{bulk}}\cdot \frac{1+2{P}_{\mathrm{strut}}\cdot (1-{\lambda}_{\mathrm{bulk}}/ \vphantom{{\lambda}_{\mathrm{bulk}}{\lambda}_{\mathrm{gas}})/(2}{\lambda}_{\mathrm{gas}})/(2{\lambda}_{\mathrm{bulk}}/{\lambda}_{\mathrm{gas}}+1)} {1-2{P}_{\mathrm{strut}}\cdot (1-{\lambda}_{\mathrm{bulk}}/\vphantom{{\lambda}_{\mathrm{bulk}}{\lambda}_{\mathrm{gas}})/(2}{\lambda}_{\mathrm{gas}})/(2{\lambda}_{\mathrm{bulk}}/{\lambda}_{\mathrm{gas}}+1)} \end{equation}}$$$$(3)

Equation (3) is solved analytically, and the bulk thermal conductivity λ_bulk of the nonporous strut material is extrapolated from the measured strut material porosity P_strut, the thermal conductivity of the gas phase λ_gas, and the thermal conductivity of the porous strut material λ_strut as determined by Equation (2). The bulk thermal conductivity of the AlN strut material ranges between 58 W m⁻¹ K⁻¹ for the samples made with 2.5 mol% yttria and 72 W m⁻¹ K⁻¹ (1.7 mol% Y₂O₃; Table 2). The specimens containing dysprosia as sintering aid show an extrapolated bulk thermal conductivity of 66 W m⁻¹ K⁻¹ and are in between the two Y‑containing foam sample series. Two effects were identified: (1) The bulk thermal conductivity decreases with increasing concentration of sintering aid (λ_{2.5% Y} < λ_{1.7% Y}), and (2) Dy₂O₃ as sintering aid results in an improved (bulk) thermal conductivity (λ_{2.5% Y} < λ_{2.5% Dy}). The latter finding is in good agreement with the literature^{18, 22} and was the actual reason for selecting Dy₂O₃. The decreasing bulk thermal conductivity with increasing yttria concentration in the strut material is attributed to the larger quantities of yttrium aluminate secondary phases, which itself have a thermal conductivity significantly lower than pure AlN.^{42, 43} Consequently, further increasing the amount of RE₂O₃ sintering aid is expected to re-degrade the thermal conductivity.

Nevertheless, the extrapolated bulk thermal conductivity of all samples is significantly lower than the range of 140–180 W m⁻¹ K⁻¹ expected for technical AlN ceramics.^{12, 24}

The reason for this is the share of oxide phases, which is still present in the AlN strut material. The substitution of N³⁻ by O²⁻ results in the formation of point defects in the Al³⁺ sub-lattice in order to maintain the charges balanced. These defects are strong phonon scattering centers and result in a reduction of the thermal conductivity. The following linear correlation of the thermal resistivity (1/λ) with the oxide content of AlN has been intensively studied by Slack (Equation 4)²¹:

$$$$\begin{equation}\frac{1}{\lambda } \approx \frac{1}{{{\lambda _0}}} + \alpha \frac{{\Delta n}}{{{n_0}}}\end{equation}$$$$(4)

The parameter λ₀ is the thermal conductivity of pure AlN (320 W m⁻¹ K−¹), n₀ is the number of N³⁻ ions per unit volume of pure AlN, which is 4.79∙10²² cm⁻³, and Δn is the number of N³⁻ substituted by O²⁻. The empirical constant α has a value of 0.43 m K W⁻¹. This empirical model has been confirmed by numerous measurements of AlN ceramics with different quantities of oxygen (Figure 5).^{17, 19-21, 44} The concentration of O²⁻ within the AlN strut material of the foams investigated within this work has been calculated from the results of the Rietveld analysis, and it ranges between 0.4 and 0.6 mol%. Consequently, a thermal conductivity in the order of magnitude of 130 W m⁻¹ K⁻¹ might be expected from Equation (4), which is higher than the actually determined values. The reason for this deviation is most likely found in the different sources of measurement errors during the porosity determination, the thermal conductivity measurement and extrapolation as well as the determination of the oxygen content. Thus, these thermal conductivity values should be considered conservative estimates. Nevertheless, a significant improvement of the (bulk) thermal conductivity compared to AlN cellular ceramics made with 0.9 mol% yttria was observed. For these samples, which contained a significantly higher oxygen concentration, an AlN bulk thermal conductivity of only 48 W m⁻¹ K⁻¹ has been determined.¹⁰ Consequently, by increasing the amount of rare-earth sintering aid, an improvement of the (bulk) thermal conductivity by up to 50%—or in other context: maintaining the foam thermal conductivity constant while increasing the total porosity by ≈2 vol.%—has been achieved.

FIGURE 5

Extrapolated bulk thermal conductivity of the AlN foam strut material (red squares) as a function of the oxygen content within the material. The dashed line represents the empirical correlation of Slack (Equation 4, Ref. [21]), which gives a good approximation of the AlN thermal conductivity data from the literature.

4 CONCLUSION

The effect of the rare-earth sintering aid addition on the microstructure and thermal properties of AlN ceramic foams manufactured by the polymer sponge replication technique has been investigated. The typical thermal conductivity of the foams was 1.1 W m⁻¹ K⁻¹ at a porosity of 94.3 vol.%, on average. By increasing the concentration of RE₂O₃ to the doubled or tripled amount of what is usually applied for the densification of AlN by sintering, the extrapolated bulk thermal conductivity of the AlN strut material was increased by ∼50%. This was caused by the reduction of the oxide contamination within the AlN phase. Nevertheless, the foam strut material was not fully densified and contained about 30 vol.% residual strut porosity. Consequently, future work is focused on the sintering regime—both the optimization of the sintering additives, for example, multicomponent additives, and increasing the sintering temperature. With fully densified ceramic struts, AlN foams might reach a thermal conductivity in the order of magnitude of ≈4 W∙m⁻¹ K⁻¹ at a porosity exceeding 90 vol.% significantly, and they may be promising candidates for heat managing and heat conversion applications.

ACKNOWLEDGMENTS

Open Access funding enabled and organized by Projekt DEAL.