Mechano-Chemical Model of Sintered Tantalum Capacitor Pellets

This article by Vladimir Azbel, an independent consultant on tantalum capacitors, introduces Mechanochemical Model of Structurally Disordered Transition Layer Formation in Sintered Tantalum Pellets that helps to understand internal tantalum capacitor anode structure, its mechanics to potentially decrease DCL leakage current and improve reliability of tantalum capacitors.

Traditionally, the quality of sintered tantalum pellets for tantalum capacitors is evaluated using shrinkage parameters and total oxygen content (O₂), benchmarked against values obtained from qualified devices. However, the experimental results presented in this study demonstrate that the determining factor is not the absolute oxygen concentration but the morphology and structural state of oxygen distribution, which are governed by internal mechanical stresses within the porous skeleton.

The oxygen passivation process in sintered tantalum pellets is analyzed within a mechanochemical framework. It is shown that the coupled action of exothermic oxidation reactions and internally stored mechanical stresses leads to the formation of a structurally disordered nanostructured transition layer with a characteristic scale of approximately 15–50 nm at the Ta/TaOₓ interface. X-ray diffraction peak broadening indicates the absence of long-range crystallographic order in this region. Based on these observations, the transition layer is described as a structurally disordered (quasi-amorphous) nanostructured mesophase.

The proposed model treats this layer as an ensemble of oxygen-enriched nanoclusters (sub-oxide regions) with suppressed long-range order. The presence of such a layer at the surface of sintering necks eliminates a sharp crystallographic and elastic boundary during subsequent electrochemical growth of the anodic amorphous Ta₂O₅ film. This creates conditions for a continuous, energetically favorable interface, identified as a critical factor in reducing leakage currents in finished tantalum capacitors.

1. Results: Oxygen Accumulation Kinetics and Suppression of Nonlinear Oxidation

In this work, the term nonlinear (“explosive”) oxidation kinetics refers to an abnormally high rate of oxygen uptake observed during certain processing routes, characterized by abrupt increases in both oxygen content and mechanical strengthening parameters. Suppression of this regime is shown to be essential for stabilizing the anodic oxide interface.

Determination of yield strength (Aᵧ) and strain hardening coefficient (K) is a destructive testing method. However, statistical sampling of 5–10 pellets from an industrial batch consisting of several thousand units provides sufficient reliability for diagnosing the structural state of the entire lot prior to anodization, while preserving the majority of the production volume.

1.1 Comparative Analysis of Oxygen Uptake

Experimental data obtained for tantalum powder with a specific surface area of 23 kCV/g and an initial oxygen content of approximately 1300 ppm reveal the existence of two fundamentally different oxidation regimes (Fig. 1).

Uncontrolled nonlinear oxidation. Sequential sintering without intermediate stress relaxation (1st sintering + 2nd sintering) results in a sharp increase in oxygen content from approximately 3030 ppm to 3600 ppm. This increase occurs against the background of an already elevated oxygen level and is accompanied by a pronounced rise in yield strength Aᵧ from 9.96 to 13.5 kg/mm², indicating a highly stressed surface state of the porous skeleton.

Decelerated oxidation after deoxidation. Introduction of a deoxidation (Deox) stage leads to a substantial reduction in oxygen content to approximately 1230 ppm and a decrease in Aᵧ to 6.5 kg/mm², corresponding to a relaxed “clean porous skeleton” state. Under these conditions, the subsequent sintering cycle (1st sintering + Deox + 2nd sintering) results in a significantly smaller oxygen increase, reaching only about 1710 ppm. The corresponding primary mechanical response of the porous skeleton for these states is illustrated by the stress–strain curves in Figure 2, where the distinct separation between high-stress and relaxed states is clearly visible.

1.2 Empirical Evidence for Suppression of Nonlinear Oxidation

The observed oxygen uptake behavior leads to the following conclusions:

• Pellets subjected to preliminary stress relaxation via deoxidation exhibit a markedly lower oxygen accumulation rate during subsequent sintering.
• Oxygen levels comparable to those observed in the nonlinear regime are reached only after an additional sintering cycle (1st sintering + Deox + 3 × 2nd sintering), at which point the oxygen content approaches ~3960 ppm.
• The decelerated oxidation regime correlates with smoother and more predictable evolution of both Aᵧ and K.

These observations provide indirect but consistent evidence that stress relaxation weakens the conditions required for nonlinear oxidation behavior.

2. Discussion: Mechanochemical Origin of the Structurally Disordered Transition Layer

The sintered tantalum pellet can be regarded as a metastable system in which internal mechanical stresses (σ) play a decisive role in determining the morphology and structural state of the oxygen-enriched surface region.

2.1 Mechanochemical Genesis of the Nanostructured Interface

Formation of the oxygen passivation layer is interpreted as a mechanochemical process driven by the coupled action of two energy contributions:

• Chemical (exothermic) energy, released during the formation of tantalum sub-oxides.
• Mechanical energy, stored in the form of local stresses arising from differences in coefficients of thermal expansion between metallic tantalum and its oxides, as well as from the substantial volume expansion associated with the Ta → TaOₓ transformation (Pilling–Bedworth ratio ≈ 2.5).

The interaction of these factors promotes dissipation of excess energy through localized plastic deformation and fragmentation of the metallic lattice in the near-surface region of sintering necks. As a result, a nanostructured transition layer with a characteristic structural scale of approximately 15–50 nm forms at the Ta/TaOₓ interface.

2.2 Universal Nanostructural Hardening Analogy

The experimentally observed maximum strengthening of the pellet surface (Aᵧ ≈ 13.5–14.4 kg/mm²) corresponds to a characteristic nanostructural scale at which mechanical response is dominated by interface-controlled deformation mechanisms. Similar maxima in hardness or strength have been widely reported for nanocrystalline and nanocomposite systems, where the transition from intragranular dislocation-dominated plasticity to intergranular and interface-mediated mechanisms occurs at characteristic structural dimensions on the order of ~10 nm.

This behavior is commonly illustrated by Musil-type hardness–grain–size relationships, in which a peak mechanical response is observed in the nanocrystalline regime between fully amorphous and microcrystalline states. In these models, enhanced strengthening arises from the combined effect of structural disorder, a high density of interfaces, and suppression of conventional dislocation motion.

By analogy, the structurally disordered nanostructured TaOₓ transition layer formed during oxygen passivation of sintered tantalum pellets can be expected to exhibit a similar strengthening maximum. In the present system, this manifests as an increase in Aᵧ rather than directly measured hardness, reflecting the integral mechanical response of the porous skeleton. The analogy is used here as a universal physical framework rather than as a quantitative equivalence between Aᵧ and hardness.

2.3 Structurally Disordered (Quasi-Amorphous) Mesophase

X-ray diffraction peak broadening observed for oxidized pellets indicates a pronounced reduction in coherent scattering domain size combined with significant lattice distortion. Within the resolution limits of the available experimental methods, no evidence of a well-defined crystalline oxide phase with long-range order is detected in the interfacial region.

Accordingly, the transition layer is described as a structurally disordered nanostructured mesophase, consisting of oxygen-enriched nanoregions (sub-oxide clusters) with suppressed long-range crystallographic order. While local short-range atomic correlations may persist, the absence of extended periodicity makes this structure functionally equivalent to an amorphous interlayer in terms of mechanical response and interfacial behavior.

2.4 Formation of a Continuous Anodic Interface

Stress relaxation of the porous skeleton through deoxidation suppresses nonlinear oxidation and promotes controlled formation of the structurally disordered mesophase. During subsequent anodization, growth of the amorphous Ta₂O₅ film occurs on a surface that already lacks a sharp crystallographic and elastic contrast.

As a result, the Ta/Ta₂O₅ interface is characterized by a gradual transition in structural order and mechanical properties rather than an abrupt boundary. This reduces local electric field enhancement, suppresses field-induced crystallization, and contributes to long-term stability of leakage currents in finished tantalum capacitors.

2.5. Relationship between Oxygen Content and Microhardness in Bulk Tantalum (Foil)

To provide a baseline for the mechanical response, the relationship between oxygen content and microhardness was investigated using bulk tantalum foil (Table 1).

Table 1. Oxygen content and Vickers microhardness (HV) of bulk Tantalum foil.

Processing State	Oxygen, ppm	Microhardness (HV), kg/mm2	STDEV
Ta -(foil)	550	99.8	3.5
Ta +DEOX	210	83	4
Ta+2000°C/20min	1100	245	7.9
Ta+2000°C/20min+DEOX	150	72.8	4.5

The initial state (550 ppm oxygen) represents a metal near the solubility limit, with a hardness of 99.8 HV. High-temperature vacuum annealing at 2000°C/20min leads to a significant increase in oxygen content (1100 ppm) due to passivation upon removal, which triggers a dramatic rise in hardness to 245 HV. This confirms that oxygen-induced lattice distortion is a primary driver of mechanical hardening even in non-porous systems. Crucially, the introduction of a deoxidation (Deox) stage effectively restores the material to a low-stress state (72.8–83.0 HV) with oxygen levels significantly below the solubility threshold (150–210 ppm). This reference study confirms that the mechanical properties of tantalum are fundamentally governed by oxygen-induced lattice distortion, providing a solid baseline for interpreting the behavior of complex porous structures

3. Internal Stresses and Process Control Strategy

3.1 Origins of Internal Stresses in the Porous Skeleton

Internal stresses in sintered tantalum pellets arise from multiple sources:

• Mechanical factors, including particle deformation and stress concentration at contact points during powder pressing.
• Thermal factors, associated with mismatched coefficients of thermal expansion between tantalum and its oxides during heating and cooling cycles.
• Structural factors, related to volumetric expansion during oxidation within an already rigid sintering-neck framework.

3.2 Stress-Driven Nanostructuring Mechanism

At temperatures below approximately 1100 °C, the solubility of oxygen in tantalum decreases sharply. Under these conditions, the combined action of oxidation exothermicity and accumulated mechanical stresses promotes localized lattice fragmentation rather than uniform diffusion-controlled oxidation. This mechanochemical pathway leads to the formation of the structurally disordered nanostructured transition layer.

3.3 Role of Deoxidation as a Stress-Control Tool

Two distinct processing paths can be identified within the proposed framework.

Uncontrolled path.
In the absence of stress relaxation, internal stresses accumulated during pressing and sintering remain stored within the rigid porous skeleton. Under subsequent thermal exposure, these stresses act as an effective trigger for nonlinear oxidation behavior. Oxygen uptake proceeds in an accelerated, non-uniform manner, accompanied by abrupt increases in oxygen content and a pronounced rise in yield strength. This response reflects the formation of a highly stressed, structurally heterogeneous interfacial region, which is unfavorable for subsequent anodic oxide growth.

Controlled path.
Introduction of a deoxidation stage before re-sintering fundamentally alters the system response. Deoxidation reduces the overall oxygen content and, more importantly, enables relaxation of internal mechanical stresses accumulated in the sintering necks. As a result, the porous skeleton returns to a low-stress “clean porous skeleton” state, characterized by a reduced yield strength (Aᵧ ≈ 6.5 kg/mm²). Under these conditions, subsequent oxidation proceeds in a controlled and decelerated manner, favoring the formation of a structurally disordered nanostructured transition layer rather than triggering nonlinear oxidation.

From a mechanochemical perspective, deoxidation suppresses the positive feedback between oxidation-induced volume expansion and stress accumulation. By lowering the stored elastic energy before renewed oxygen exposure, the system is shifted away from the instability threshold associated with nonlinear oxidation kinetics. This establishes a reproducible structural pathway toward the formation of a stress-tolerant interfacial mesophase.

Conclusions

1. Validation of the virtual structural probe concept.
   Measurement of yield strength (Ay) and strain hardening coefficient (K) on a limited statistical sample of sintered pellets is demonstrated to be a reliable virtual structural probe. These parameters provide direct insight into the internal stress state and surface morphology of the porous skeleton for an entire industrial batch before anodization.
2. Experimental baseline from bulk tantalum.
   Complementary experiments on dense tantalum foil establish a fundamental baseline for interpreting the behavior of porous systems. Exceeding the oxygen solubility limit under typical processing conditions leads to pronounced lattice distortion and more than a twofold increase in microhardness. This confirms that oxygen-induced mechanical hardening is an intrinsic property of the Ta–O system and is not specific to porosity or pellet geometry.
3. Dominant role of internal stresses over absolute oxygen content.
   The results demonstrate that the absolute oxygen concentration alone is insufficient to characterize pellet quality. Instead, the spatial distribution and structural state of oxygen, governed by the level and distribution of accumulated elastic energy in the porous skeleton, determine whether oxidation proceeds along a controlled pathway or transitions into an unfavorable nonlinear regime.
4. Mechanochemical formation of a structurally disordered interfacial mesophase.
   At temperatures below approximately 1100 °C, the coupled action of oxidation exothermicity and internally stored mechanical stresses promotes localized lattice fragmentation rather than uniform diffusion-controlled oxidation. This mechanochemical pathway results in the formation of a structurally disordered nanostructured transition layer with a characteristic scale of approximately 15-50 nm at the Ta/TaO_x interface, effectively eliminating a sharp crystallographic and elastic boundary.
5. Quasi-amorphous mesophase as an interfacial buffer during anodization.
   Owing to the absence of long-range crystallographic order, the transition layer functions as a quasi-amorphous mesophase that provides a gradual transition in structural and mechanical properties between metallic tantalum and the anodic amorphous Ta₂O₅ film. This continuity suppresses local electric field enhancement and reduces the likelihood of field-induced crystallization during anodic oxide growth.
6. Technological implications for process control and capacitor reliability.
   Stress relaxation of the porous skeleton, exemplified in this study by deoxidation, shifts the system away from the instability threshold associated with nonlinear oxidation kinetics. By promoting the formation of a stress-tolerant interfacial mesophase, such processing strategies provide a physical basis for improved leakage-current stability and enhanced long-term reliability of tantalum capacitors. Importantly, deoxidation is not unique in this role; any processing route capable of reducing stored mechanical energy before renewed oxygen exposure may lead to similar interfacial stabilization.

Final Remarks on Processing Routes and Model Applicability

It should be emphasized that deoxidation is not considered in this work as the only technologically viable method for achieving controlled oxidation behavior in sintered tantalum pellets. Rather, it is employed as a model and experimentally transparent stress-relaxation tool that allows the role of internal mechanical stresses in interfacial structure formation to be isolated and analyzed.

From a mechanochemical standpoint, the decisive factor governing the morphology of the Ta/TaOₓ transition region is the level and spatial distribution of stored mechanical energy in the porous skeleton. Any processing route capable of reducing this stored energy before renewed oxygen exposure—such as multi-step or two-stage sintering schedules, modified thermal ramps, or alternative stress-relief treatments—may, in principle, lead to a similar suppression of nonlinear oxidation and promote formation of a structurally disordered TaOₓ mesophase.

The present results, therefore, do not prescribe a specific technological recipe, but instead establish a general physical framework that links the internal stress state, oxidation kinetics, and interfacial nanostructure. Within this framework, deoxidation serves as a representative and well-controlled example rather than a unique solution.

The author is grateful to A. Agulyansky for fruitful discussions that helped clarify the physical nature of the transition layer. In particular, his insights regarding the low probability of crystalline phase formation during sintering and the explanation of XRD peak broadening for 15–50 nm particles were instrumental in refining the proposed mechanochemical model.”