1. Bibliographic Information

1.1. Title

Densification of 0·99SnO2–0·01CuO Mixture: Evidence for Liquid Phase Sintering

1.2. Authors

• Nathalie Dolet, Jean-Marc Heintz, Marc Onillon & Jean-Pierre Bonnet
• Affiliation: Laboratoire de Chimie du Solide du CNRS, Talence Cédex, France.
• Background: The authors are affiliated with the CNRS (French National Centre for Scientific Research), specifically in a solid-state chemistry laboratory, indicating expertise in materials science, ceramics, and thermodynamics.

1.3. Journal/Conference

• Journal: Based on the formatting and citation style (e.g., "Received... revised... accepted"), this paper was published in a peer-reviewed materials science journal, likely the Journal of the European Ceramic Society or a similar archival journal in the field of ceramics (e.g., Journal of Materials Science or Ceramics International), given the date and content.
• Status: Published (Accepted 13 June 1991).

1.4. Publication Year

1991

1.5. Abstract

The paper investigates the sintering (densification) process of tin dioxide ($SnO_2$) doped with 1 mol% copper oxide (CuO) at 1150°C in air. The study reports rapid and high densification, reaching 98.7% relative density. Through dilatometric analysis (measuring shrinkage over time) and microstructural observation, the authors demonstrate that the densification mechanism is Liquid Phase Sintering (LPS). Furthermore, electrical conductivity measurements suggest that copper ions dissolve into the $SnO_2$ lattice in interstitial positions, rather than substituting for tin atoms.

1.6. Original Source Link

/files/papers/69424d3653092c97c18dda64/paper.pdf

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2. Executive Summary

2.1. Background & Motivation

• Core Problem: Pure tin dioxide ($SnO_2$) is a technologically important material (used in sensors, electrodes, etc.) but is notoriously difficult to sinter into a dense ceramic. This is because, at the high temperatures required for sintering ($>1100^{\circ}C$), $SnO_2$ tends to evaporate (sublime) rather than densify.
• Importance: To use $SnO_2$ in solid components, it must be densified. Additives like $MnO_2$, ZnO, and CuO are known to aid this process. CuO is particularly efficient.
• Research Gap: While it was known that CuO helps $SnO_2$ sinter, the underlying mechanism was debated.
  • Hypothesis A (Duvigneaud & Reihnard): Formation of a liquid phase that glues particles together.
  • Hypothesis B (Varela et al.): Solid-state diffusion enhanced by oxygen vacancies created by copper substitution.
• Innovation: This paper provides a definitive answer by combining kinetic analysis (shrinkage rates), thermodynamic calculations (phase diagrams), and electrical property measurements to rule out the solid-state mechanism and confirm the liquid phase mechanism.

2.2. Main Contributions / Findings

1. Mechanism Confirmation: The paper conclusively proves that the fast densification of $SnO_2-CuO$ is due to Liquid Phase Sintering. A copper-rich liquid forms above $1092^{\circ}C$, promoting particle rearrangement and diffusion.

2. Kinetic Modeling: The authors successfully fit experimental shrinkage data to Kingery’s liquid phase sintering models, showing the process is controlled by diffusion through the liquid phase.

3. Defect Chemistry: By analyzing electrical conductivity, the authors provide evidence that copper acts as an interstitial impurity (sitting between lattice sites) rather than a substitutional one (replacing tin atoms). This challenges the assumption that simple substitution drives the defect chemistry.

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3. Prerequisite Knowledge & Related Work

3.1. Foundational Concepts

To understand this paper, a beginner needs to grasp three core concepts:

• Sintering: The process of compacting and forming a solid mass of material by heat or pressure without melting it to the point of liquefaction. The goal is to remove pores (voids) between powder particles to increase density.

  • Solid State Sintering: Atoms diffuse through the solid particles to fill gaps.
  • Liquid Phase Sintering (LPS): A small amount of additive melts at the sintering temperature. This liquid wets the solid particles, pulling them together via capillary forces (like water pulling sand grains together) and acting as a fast path for atoms to move and fill pores.

• Dilatometry: An experimental technique used to measure the change in length (shrinkage) of a sample as it is heated. In sintering studies, the "relative shrinkage" $\Delta L/L_0$ is plotted against time to understand how fast the material is densifying. The slope of this curve in a log-log plot reveals the underlying physical mechanism (kinetics).

• Kröger-Vink Notation: A standard notation used in defect chemistry to describe point defects in crystals.

  • $V_{O}^{\bullet\bullet}$: An oxygen vacancy with a +2 relative charge (missing $O^{2-}$ ion).
  • $Cu_{Sn}''$: A copper ion sitting on a tin site. Since Cu is typically +2 and Sn is +4, the site has a -2 relative charge.
  • $Cu_{i}^{\bullet\bullet}$: A copper ion squeezed into an interstitial space (between atoms). It carries its full +2 charge relative to the empty space.
  • $e'$: A free electron (negative charge).

3.2. Previous Works

The authors position their work between two conflicting theories regarding CuO additives:

• Duvigneaud & Reihnard (Ref 4): Proposed that a liquid phase forms, facilitating densification.
• Varela et al. (Ref 2): Proposed a solid-state mechanism where CuO substitutes into $SnO_2$ ($Cu \rightarrow Sn$), creating oxygen vacancies ($V_O^{\bullet\bullet}$) that speed up diffusion.
  • Implied Formula: The substitution reaction proposed by Varela is: $CuO \xrightarrow{SnO_2} Cu_{Sn}'' + O_O^x + V_O^{\bullet\bullet}$

3.3. Differentiation Analysis

This paper differentiates itself by not just proposing a mechanism but rigorously testing it against multiple data sources:

1. Kinetic Fit: They don't just observe shrinkage; they mathematically fit the shrinkage rate to specific physical laws derived by Kingery.

2. Thermodynamics: They use phase diagrams to prove a liquid can theoretically exist at the specific temperature and partial pressure of oxygen used.

3. Electrical Testing: They use conductivity to determine where the copper goes in the atomic lattice, providing a complete picture of the material's state.

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4. Methodology

4.1. Principles

The core approach relies on Isothermal Sintering Kinetics. By holding the temperature constant ($1150^{\circ}C$) and measuring how the sample shrinks over time, the authors can determine the "rate-limiting step" of the process.

Theory states that shrinkage follows a power law: $\frac{\Delta L}{L_0} \propto t^n$. The exponent $n$ (the slope on a log-log plot) differs depending on the mechanism (e.g., rearrangement, diffusion, dissolution).

4.2. Core Methodology In-depth

Step 1: Material Preparation

• Mixing: $SnO_2$ (99.9% pure) and CuO (99% pure) are mixed in a molar ratio of 0.99 : 0.01.
• Calcination: The mixture is heated at $400^{\circ}C$ for 3 hours to remove volatiles and ensure mixing.
• Compaction: The powder is pressed into cylinders at 100 MPa. Green density (density before sintering) is $\approx 2.8 \, g \cdot cm^{-3}$.

Step 2: Dilatometry (Shrinkage Measurement)

Samples are heated to $1150^{\circ}C$. The change in length is recorded. The data is analyzed using log-log plots of shrinkage ($\Delta L / L_0$) vs. time ($t$).

The following figure (Fig. 3 from the paper) shows the experimental shrinkage data. Note the two distinct linear regions (slopes $p_1$ and $p_2$).

该图像是图表，展示了相对收缩率随着时间的演变关系。横轴为 $\ln(t_r)$（以秒为单位），纵轴为 $\ln \left| \Delta L / L_0 \right|$。数据点显示出在特定时间范围内收缩率迅速变化的趋势，支持了液相烧结机制的假设。

Step 3: Mathematical Modeling of Kinetics

The authors analyze the second stage of sintering (after the initial 7 minutes of rapid rearrangement). They compare experimental data against two theoretical models for Liquid Phase Sintering (LPS) derived by Kingery (Ref 8).

Model A: Diffusion Controlled If the process is limited by the diffusion of atoms through the liquid film surrounding particles: $$\Delta L / L_{\circ} = A (r)^{-4/3} (t)^{1/3}$$

• Symbol Explanation:
  • $\Delta L / L_{\circ}$: Relative shrinkage.
  • $A$: A constant.
  • $r$: Average grain radius.
  • $t$: Sintering time.

Model B: Dissolution Controlled If the process is limited by the rate at which the solid dissolves into the liquid at the interface: $$\Delta L / L_{\circ} = B (r)^{-1} (t)^{1/2}$$

• Symbol Explanation:
  • $B$: A constant.

Integrating Grain Growth: The grain size $r$ is not constant; grains grow during sintering. The authors measured grain growth experimentally (using SEM images) and found it follows a power law: $$r = C (t)^{1/5}$$

• Symbol Explanation:

  • $C$: A constant.

  • $1/5$: The grain growth exponent ($p \approx 0.20$).

    The following figure (Fig. 5 from the paper) shows this linear relationship between log grain radius and log time, confirming the $t^{1/5}$ growth law.

    

    Final Derived Equations: To see which model fits, the authors substitute the grain growth equation ($r \propto t^{1/5}$) into the sintering models.

1. For Diffusion Control: Substitute $r \propto t^{1/5}$ into Model A: $$\Delta L / L_{\circ} \propto (t^{1/5})^{-4/3} \cdot t^{1/3} = t^{-4/15} \cdot t^{5/15} = t^{1/15}$$

   • Result: Slope should be 1/15 (approx 0.067).

2. For Dissolution Control: Substitute $r \propto t^{1/5}$ into Model B: $$\Delta L / L_{\circ} \propto (t^{1/5})^{-1} \cdot t^{1/2} = t^{-1/5} \cdot t^{1/2} = t^{-2/10} \cdot t^{5/10} = t^{3/10}$$

   • Result: Slope should be 3/10 (0.30).

     The authors then compare the experimental slope ($p_2$ from Fig 3) to these predicted values to identify the mechanism.

Step 4: Thermodynamic Verification

The authors verify if a liquid phase is thermodynamically stable using the Cu-O phase diagram. They analyze the Gibbs energy of formation ($\Delta_f G^\circ$) to determine the oxygen partial pressure ($pO_2$) ranges where liquid copper oxide exists.

The following figure (Fig. 6 from the paper) displays the $Cu_2O - CuO$ phase diagram used for this analysis.

该图像是$ext{Cu}_2 ext{O} - ext{CuO}$相图。图中显示了在多个温度下的平衡氧分压，以及液相区域的信息。主要温度范围在1000°C至1200°C之间，标注了不同氧分压下的温度值。

Step 5: Electrical Characterization

To determine where Cu sits in the lattice, they measure electrical conductivity ($\sigma$).

• Hypothesis 1 (Substitution): $Cu^{2+}$ replaces $Sn^{4+}$. This creates oxygen vacancies ($V_O^{\bullet\bullet}$) which trap electrons or reduce electron concentration. Predicted Result: Lower conductivity than pure $SnO_2$.

• Hypothesis 2 (Interstitial): $Cu^{2+}$ enters interstitial sites ($Cu_i^{\bullet\bullet}$). This increases tin vacancies ($V_{Sn}''''$) and decreases oxygen vacancies via Schottky equilibrium, ultimately increasing free electron concentration. Predicted Result: Higher conductivity than pure $SnO_2$.

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5. Experimental Setup

5.1. Materials

• Powders:
  • $SnO_2$: Aldrich, 99.9% purity, specific surface area $7.33 \, m^2 g^{-1}$.
  • CuO: Prolabo Normapur, 99% purity, specific surface area $14.8 \, m^2 g^{-1}$.
• Sample Shape: Cylindrical pellets ($\phi \approx 6-8 \, mm$, thickness $\approx 2.5 \, mm$).

5.2. Evaluation Metrics

1. Relative Shrinkage ($\Delta L / L_0$):
   • Definition: The ratio of the change in length to the original length. It quantifies how much the material has compacted.
   • Formula: $\frac{L(t) - L_0}{L_0}$
2. Compactness (Relative Density):
   • Definition: The density of the sintered ceramic divided by the theoretical density of the material.
   • Measurement: Archimedes method (British Standard 1902).
3. Average Grain Radius ($r$):
   • Definition: The mean size of the crystalline grains within the ceramic.
   • Measurement: estimated from Scanning Electron Microscope (SEM) micrographs of polished and etched samples.
4. Electrical Conductivity ($\sigma$):
   • Definition: A measure of the material's ability to conduct an electric current. Used here as a probe for defect chemistry.
   • Measurement: Four-probe method with platinum leads.

5.3. Baselines

• Pure $SnO_2$ Single Crystal: Used as a baseline for electrical conductivity to see if adding copper increases or decreases conductivity.

• Reference Models: Kingery’s theoretical models for sintering serve as the mathematical baseline for mechanism identification.

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6. Results & Analysis

6.1. Core Results Analysis

Densification Behavior

The sintering was extremely fast. As shown in Figure 3, the material reached 94% density in just 8 minutes. This rapid densification is characteristic of Liquid Phase Sintering, where a liquid acts as a lubricant, allowing particles to rearrange quickly under capillary pressure.

Kinetic Mechanism Identification

The log-log plot of shrinkage vs. time (Figure 3) revealed two slopes:

1. Slope $p_1$ (0 to 7 min): $1.20 \pm 0.05$. This corresponds to the Grain Rearrangement stage, where the liquid forms and particles slide past each other.

2. Slope $p_2$ (7 to 80 min): $0.05 \pm 0.02$.

   Comparing $p_2$ to the derived models in Section 4.2:

• Predicted Slope for Diffusion Control: 0.067 (1/15)

• Predicted Slope for Dissolution Control: 0.30 (3/10)

• Experimental Slope: 0.05

  Conclusion: The experimental slope (0.05) is very close to the diffusion-controlled prediction (0.067). Therefore, the sintering mechanism is Liquid Phase Sintering controlled by diffusion through the liquid.

Microstructural Evidence

Direct visual evidence supported the kinetic data.

• Figure 4 (see below) shows copper-rich coagulated droplets on the surface, confirming a liquid was present at high temperatures.

• Figure 9 (see below) shows an intergranular phase surrounding the grains in quenched samples.

  Figure 4: Surface droplets proving liquid phase existence.

  该图像是图4，显示了在空气中以1150°C烧结1小时后，再以1100°C加热30分钟得到的陶瓷表面的二次电子图像(a)和反向散射电子图像(b)。该陶瓷为$0.99 ext{SnO}_2 - 0.01 ext{CuO}$混合物，表面结构呈现出特征性的颗粒排列与形态。

  Figure 9: Intergranular phase surrounding grains.

  该图像是扫描电子显微镜（SEM）所拍摄的陶瓷材料图像，显示了在 $1150^{ ext{°C}}$ 下，空气中烧结 30 分钟后的相间结构。图中可见不同形状和大小的晶粒间相，证实了液相烧结机制。

Thermodynamic Validation

Using the phase diagram data (Figure 6) and Gibbs energy calculations, the authors determined that in air ($pO_2 = 0.21$ atm), a copper-rich liquid phase is stable at temperatures $> 1092^{\circ}C$. Since the sintering was performed at $1150^{\circ}C$, the existence of the liquid is thermodynamically guaranteed.

6.2. Electrical Properties & Defect Chemistry

The authors measured the conductivity of the sintered ceramic and compared it to a pure $SnO_2$ crystal.

Figure 12 below shows the results. The open circles (Ceramics) show significantly higher conductivity than the solid dots (Crystal).

Analysis:

• If Cu substituted for Sn ($Cu_{Sn}''$), it would act as an acceptor, reducing n-type conductivity (lowering the curve).
• Since conductivity increased, Cu must be acting as a donor or facilitating the creation of donors.
• The authors propose the interstitial model: $CuO \xrightarrow{SnO_2} Cu_i^{\bullet\bullet} + O_O^x + \frac{1}{2} V_{Sn}''''$ Through the Schottky equilibrium ($null \rightleftharpoons 2V_O^{\bullet\bullet} + V_{Sn}''''$), an increase in tin vacancies ($V_{Sn}''''$) suppresses oxygen vacancies ($V_O^{\bullet\bullet}$). Wait, let's re-read the author's logic carefully in section 4.5.2.

  • Correction on Author's Logic: The authors state: "interstitial copper... must be associated with an increase in tin vacancy concentration... and a decrease of oxygen vacancy concentration."

  • Then they refer to Eq 11: $O_O \rightleftharpoons 1/2 O_2 + 2e' + V_O^{\bullet\bullet}$.

  • Equilibrium constant $K_{11} = [V_O^{\bullet\bullet}] [e']^2 (pO_2)^{1/2}$.

  • If $[V_O^{\bullet\bullet}]$ decreases, then to keep $K_{11}$ constant, [e'] must increase.

  • Increase in [e'] $\rightarrow$ Higher n-type conductivity.

  • This matches the experimental data in Figure 12.

    Conclusion: Copper dissolves into the rutile structure of $SnO_2$ in an interstitial position.

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7. Conclusion & Reflections

7.1. Conclusion Summary

This paper definitively characterizes the sintering of 0.99SnO_2-0.01CuO.

1. Mechanism: The fast densification is caused by Liquid Phase Sintering. A Cu-rich liquid forms above $1092^{\circ}C$.
2. Process Stages:
   • Stage 1: Rapid grain rearrangement (liquid acts as lubricant).
   • Stage 2: Solution-precipitation controlled by diffusion through the liquid phase.
3. Atomic Structure: Copper acts as an interstitial dopant in $SnO_2$, evidenced by the increased n-type electrical conductivity.

7.2. Limitations & Future Work

• Cooling Effects: The authors note that upon cooling, the liquid phase crystallizes into $Cu_2O$ and then oxidizes to CuO. This oxidation involves a volume expansion that can generate micro-stresses or cracks in the ceramic.
• Solubility Limit: Over long sintering times (e.g., > 4 hours), the copper diffuses entirely into the grains, and the liquid phase disappears. Densification then slows down significantly (as seen in Figure 11), shifting to a solid-state mechanism.

7.3. Personal Insights & Critique

• Methodological Rigor: The combination of kinetic modeling (math) with physical evidence (microscopy) and property testing (electricity) makes the conclusion very robust. It is a textbook example of how to characterize sintering mechanisms.
• Practical Implication: The finding about interstitial copper is crucial for semiconductor sensor applications. If copper sits interstitially, it affects the electronic band structure differently than if it were substitutional. This informs how to tune $SnO_2$ for gas sensing (where surface conductivity is key).
• Complexity of "Simple" Systems: Even a simple binary mixture like $SnO_2-CuO$ involves complex phase equilibria and defect interactions. The reliance on accurate thermodynamic data underscores that sintering is as much about chemistry (phase stability) as it is about physics (diffusion).