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Recent innovations in dilatometer hardware and software design promise to increase the power of thermal expansion measurement. These include applying new thermokinetic analysis techniques to model and construct optimized firing and sintering processes, combining dilatometry with simultaneous DTA (differential thermal analysis) for better understanding of thermal behavior, and new hardware designs to improve low-temperature thermal expansion measurements.
The Principle of DilatometryTo perform a dilatometric analysis, a sample is placed in a special holder inside a moveable furnace. A push-rod placed directly against the sample transmits length change to a linear variable displacement transducer (LVDT). As sample length changes during the temperature program, the LVDT core is moved, and an output signal proportional to the displacement is recorded. The temperature program is normally controlled using a thermocouple located next to the heating element or next to the sample.
Tube-type and rod-type sample holders of fused silica, alumina and graphite are typically used for temperatures up to 1100, 1680 and 2800°C, respectively. Rod-type holders usually provide the best heat transfer to the sample. The measured length change of the sample includes both the sample holder expansion and the length change of the sample itself. The measurement is automatically corrected against the expansion behavior of a suitable standard reference material under identical conditions as the sample. The coefficient of thermal expansion (CTE) is determined by comparing the sample length change with the initial length over a temperature range.
Modern dilatometers often use horizontal furnace designs to reduce thermal gradients across samples found to occur in vertical furnaces. It may be crucial in some cases to tightly control gas atmospheres inside the furnace (for example, samples subject to oxidation). For this reason, vacuum-tight furnace designs are becoming increasingly important, allowing work in pure gas atmospheres or under vacuum conditions.1
Advances in Sintering OptimizationAn important application for dilatometry is optimizing the sintering process of high-tech ceramic materials. In the production of modern high-performance technical ceramics, a green body is often made by mixing a ceramic powder and a binder material. The green body is fired afterwards to achieve the final product. The temperature program during the firing process, especially during the binder burn-out and sintering phase, has a significant influence on product quality. By modifying the temperature program, it is possible to optimize the properties of the sintering products, such as densification and grain size distribution.
A new method to optimize the sintering process has recently been developed by combining dilatometric measurements with thermokinetic analysis.2 The basis for thermokinetic analysis is a series of dilatometer measurements made at different heating rates. The result is a multi-step formal kinetic approximation of the measurement results. Based on this data, the material behavior for different temperature profiles or for certain sintering processes (such as constant sintering rates) can be calculated.
For example, cold-pressed green bodies of silicon nitride (Si3N4) powder (from TeCe Technical Ceramics) were examined using measurements made at three different heating rates. The samples contained 5% of Y2O3 and 5% of Al2O3 (by molecular weight) as sintering additives. A push-rod dilatometer (see Figure 1) was used for the measurements from room temperature to 1850°C, with constant heating rates of 5, 10 and 20°C per minute. Over this same temperature range, measurements were carried out using rate-controlled sintering software at constant sintering rates of 0.087 and 0.174% per minute.
For the kinetic description of the measurement results, a four-step model indicated in Figure 2 was used. Based on this model, non-linear regression was performed by adjusting the different reaction parameters, such as the pre-exponential factors and activation energies. The results are shown in Figure 2 as straight lines. The kinetic model chosen enables a good description of the experimental results. With the help of this model, sintering processes can be calculated with different temperature programs or heating rates. It also provides the possibility to determine temperature programs necessary for sintering the sample at a constant linear shrinkage rate.
Temperature programs for constant sintering rates can also be directly determined with a dilatometer using rate-controlled sintering (RCS) software.3 Using these same silicon nitride samples, appropriate measurements were carried out at different constant sintering rates. The results were compared with the predictions obtained from the thermokinetic analysis software.
Dilatometry with Calculated DTAInterpretation of transitions occurring in the sample during the thermal treatment is sometimes difficult using only thermal expansion data. A new type of differential thermal analysis known as "calculated DTA" (c-DTA*) can offer even a more detailed insight into material behavior. Differential thermal analysis is well-known for the characterization of transformation energetics (exo- and endothermal effects) of materials. Calculating the c-DTA signal on a thermal expansion curve yields information similar to the DTA method.
The c-DTA calculation is a mathematical routine based on the temperature measurement at the sample. Transitions connected with exo- or endothermal effects are known to slightly influence the temperature change of the sample during dynamic heating or cooling. By comparing the measured temperature change with the theoretical one, these exo- or endothermal effects can be determined. A calibration run that is carried out on a standard sample prior to the sample run is also considered in the calculation process. However, quantification of the measured effects is not practical using this new routine since, in this sample format, the true energetics of the heat-flow behavior cannot be accurately calibrated to any standard.
Characterizing a Floor TileThe thermal expansion and sintering of a floor tile during firing is shown in Figure 5.
The measurement was carried out at 10°C per minute in a static air atmosphere. The different sintering steps are clearly visible in the thermal expansion curve. c-DTA allowed more detailed insight into the thermal behavior of the material. The endothermal effect up to 150°C is due to dehydration. The exothermal peak at 316°C is due to the burnout of organic additives. Dehydration of the clays was measured at 581°C (peak temperature). The exothermal effect at 917°C (extrapolated onset) is due to a solid-state transition in the sample. The endothermal effect during sintering is most probably due to formation of a liquid phase.
Figure 6 shows the thermal expansion and c-DTA analysis of a porcelain green body between room temperature and 1375°C.
Analyzing Tungsten CarbideTungsten carbide is a well-known hard metal used for industrial cutting tools. In most cases, tungsten carbide parts are produced by a sintering process. Cobalt is used as an additive to reduce the sintering temperature. Figure 7 shows the thermal expansion and the c-DTA analysis of a tungsten carbide green body during heating and cooling at 10°C per minute.
The atmosphere was dynamic argon (gas flow rate: 75 ml/min). Increasing sample length was measured up to approximately 800°C, and sintering was detected above this point. The shrinkage rate increased with rising temperature. It can be seen that sintering suddenly stops at 1373°C. During cooling, a small step was detected at 1364°C. This effect is most likely due to formation and solidification of a liquid phase in the sample. The c-DTA calculation (endo- and exothermal effects during heating and cooling, respectively) is another indication for this assumption.
Improvements in Low-Temperature Dilatometer MeasurementsOver the past few years, the industry has increased its efforts to introduce new materials for high performance applications. For example, glass ceramics are often used for the production of modern earth telescopes and in satellites. In many cases, accurate knowledge of thermal expansion is crucial for the application of these new materials. Measurements are necessary in the temperature range of interest to overcome any problems, such as formation of tension between two different materials in contact.
Recent advances in low-temperature dilatometry allow measurements of the thermal expansion between -180 and 500°C with higher levels of performance. Employing vacuum-tight designs allows testing under defined atmospheres. Evacuation and backfilling with inert atmospheres removes any influences from humidity. A completely thermostatted housing around the Invar (very low CTE metal alloy) high-resolution inductive transducer system (1.25 nm/digit) reduces system drift. Therefore, sub-ambient measurements are now possible with higher reproducibility and accuracy than previously observed (see Figure 8).
Examining a Low-Expansion GlassShown in Figure 9 is the thermal expansion of Zerodur, a material often used as mirror carrier in earth telescopes, between -150 and 100°C. Two runs were carried out on the same sample. The reproducibility of the coefficient of thermal expansion between 0 and 50°C was 0.3x10-9 1/°C. The coefficient of thermal expansion was in good agreement with the manufacturer's values (Schott Glasses in Mainz-Germany).
Optimizing Thermal AnalysisNew developments in hardware and software design have increased the power and capabilities of dilatometer measurements. Applying advanced thermokinetic analysis techniques to thermal expansion data permits fast, cost-effective offline optimization of firing and sintering processes. The comparison between predicted temperature profiles and real measurements at constant sintering rates proved the capability of this method.
Additionally, as demonstrated through measurements on ceramic green bodies and a powder metal, combining dilatometry with a powerful new c-DTA calculation technique can offer a more thorough understanding of thermal behavior by directly correlating exo- and endothermal DTA effects with length changes. Finally, new hardware designs permit low-temperature thermal expansion measurements with higher accuracy than previously observed.