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Analysis of Thermal Expansion via Dilatometry
##### Science Education (Materials Engineering)
Directional Solidification and Phase Stabilization
##### Science Education (Materials Engineering)
Electrochemical Impedance Spectroscopy

# Analysis of Thermal Expansion via Dilatometry

### Overview

Source: J. Jacob Chavez, Ryan T. Davis, and Taylor D. Sparks, Department of Materials Science and Engineering, The University of Utah, Salt Lake City, UT

Thermal expansion is extremely important when considering which materials will be used in systems that experience fluctuations in temperature. A high or low thermal expansion in a material may or may not be desirable, depending on the application. For instance, in a common liquid thermometer, a material with a high thermal expansion would be desirable due to its sensitivity to temperature changes. On the other hand, a component in a system that experiences high temperatures, such as a space shuttle re-entering the atmosphere, will need a material that will not expand and contract with large temperature fluctuations in order to prevent thermal stresses and fracture.

Dilatometry is a technique used to measure the dimensions of area, shape, length or volume changes of a material as a function of temperature. A principal use for a dilatometer is the calculation of thermal expansion of a substance. The dimensions of most materials increase when they are heated at a constant pressure. The thermal expansion is obtained by recording the contraction or expansion in response to changes in temperature.

### Principles

Dilatometry is performed by first measuring the initial length of the sample by hand using calipers, and then measuring the length of the sample while it is subjected to specified temperatures for specified amounts of time, this measurement will be recorded by a sensitive gauge in the dilatometer. While the sample is being measured a purge gas will be flowing through the furnace; (argon, nitrogen, etc) this will provide consistent atmosphere conditions, as well to keep the sample from oxidizing with oxygen in the air. Next, the sample is heated to a specified temperature at a specified rate, and the changes in dimensions are recorded with a sensitive measuring gauge. The change in dimensions could be either expansion or contraction. Thermal expansion is then calculated by dividing the change in length (L) by the initial length of the sample (). This process yields the average linear thermal expansion of the material. Several measurements of each sample yields more accurate results.

Thermal expansion can be instantaneous (the slope of the length vs temperature) or average (net change in length over a temperature range). The value can either be linear if only length is measured or volumetric if the change in volume of the sample is assessed.

Dilatometry can be conducted through several methods. The Dilatometer in this experiment uses a vertical push-bar method. (Figure 1) The thermal expansion experienced by the sample is transferred to the displacement sensor by the connected rod. However, since the rod is also exposed to the high temperature in the furnace, it too experiences thermal expansion. Thus, the resulting measurement must be corrected.

Figure 1: A schematic of a standard vertical push-rod dilatometer.

A comparable technology for measurement of thermal expansion is Michelson laser interferometry. The technique uses high precision lasers and mirrors to measure thermal expansion. Quality optics, photodetectors and interpolation techniques allow length resolution to about a nanometer. A unique feature of interferometry is the little restriction on size or shape of the sample. Another comparable technique is X-ray diffraction with the sample on a heated stage. Since X-ray diffraction can easily determine lattice parameter, it is possible to measure how the lattice parameter changes with temperature and extract a thermal expansion coefficient.

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### Procedure

1. Machine Start Up and Set Up. Begin with powering the computer, equilibrating the sample temperature ensuring it is at room temperature (about 20°C), and dilatometer on. Make sure cooling system is running and nitrogen gas is flowing along with all other necessary systems. The nitrogen gas will need to be turned on between when the furnace is turned on and when the sample is inserted for testing. The pressure for the gas will be specific to the dilatometer, for ours it is 10 psi.
2. Determine which experiment will be conducted: calibration or expansion. For any set of expansion tests, a calibration test must be performed prior for reference. When doing an expansion test, select the most recent calibration that meets or exceeds your maximum temperature range and preferably is run at the same temperature ramp rate. When making a calibration for subsequent experiments, utilize a known standard. We will use a previously run calibration measurement of the known standard Crystallox. (Whether a calibration or expansion test is being run, the process for sample preparation, machine set-up, and establishment of parameters will be the same.)
3. Sample Preparation. For our experiment we will be testing a metal material. Accurately measure the length of the sample using high-quality calipers before inserting the sample into the furnace. Take several measurements along the length in order to establish measurement error. The sample should be long enough to allow the pushrod to exert some force on the top of the sample. If the sample is not tall enough, use spacers of a known material (measure the height of these so that the expansion can be subtracted from the results). The ends of the sample must be parallel within 1 degree.
4. Insert Sample. Clean the bottom surface of the furnace to ensure the sample has a flat place to stand. Lower the pushrod until it contacts the top of the sample. Lower the tube back into the furnace and ensure that the sample did not shift during lowering by checking the displacement gauge.
5. Establish Parameters. Follow ASTM E 228 standards for the material type. The important parameters include max temperature, heating ramp rate, dwell time, cooling ramp rate, number of repeats, and dwell time between repeats. Your parameters should match the calibration that you are using as closely as possible. Allow the temperature of the sample to reach equilibrium within the loading tube environment, at room temperature. The metal sample with be taken from a temperature of 20°C to 1000°C. Heat or cool at a constant rate equal to or less than 5°C/min. We will be not be doing any repeats in this test. The maximum furnace temperature for this device is 1200°C.
6. Verify Set Up. Before starting the test and walking away, double check that all systems are on and functioning, especially the furnace. Many dilatometers use a flow of nitrogen gas to keep the atmosphere of the test inert and constant, verify nitrogen purge gas is flowing.
7. Initiate Test. Start test and real-time data will be available for monitoring. If needed, the test can be canceled.
8. Save Data. Export and save data to the user's desired format, this will vary depending on how the data will be analyzed and presented. Typically, each sample should be run three times, with the first set of data discarded due to more significant expansion and contraction because of the thermal annealing of the sample.
9. Shut-Down. Verify all systems are powered down including the furnace, cooling system, and purge gas. Remove the samples from the furnace after ensuring that the furnace is cooled to near room temperature. Clean up workspace.
10. Analyze Data. Import data and create graphs and visuals to effectively represent your data.

The thermal expansion of a material is extremely important when considering its use in a system with fluctuating temperature. Dilatometry is a technique used to measure the area, shape, length, or volume changes of a material as it experiences fluctuations in temperature. Thereby enabling the calculation of thermal expansion. In this video we will introduce the dilatometer, and demonstrate how to measure the thermal expansion of a metal sample in the laboratory.

Dilatometry is first performed by measuring the initial length of the sample using calipers. Then the sample is placed in a furnace, and in the case of this experiment, connected to a vertical push bar. A purge gas flows through the furnace to provide consistent conditions and prevent oxidation of the sample during heating. The sample then is heated to a predetermined temperature at a specified rate. The thermal expansion of the sample is transferred to the push bar, which is then transferred to the displacement sensor. Most materials expand with increased temperature and then contract upon cooling. Since the rod is also exposed to the high temperature in the furnace, it too experiences thermal expansion and contraction. Thus the measurement must be corrected to account for this.

The thermal expansion experienced by the sample is calculated by dividing the change in length by the initial length of the sample. This yields the average linear thermal expansion of the material. We can calculate the linear thermal expansion coefficient, αL, by dividing the average linear expansion by the change in temperature experienced. The volumetric expansion coefficient, αV, is then 3-times the linear expansion coefficient for isotropic materials. Some anisotropic materials, meaning a materials whose properties are direction dependent, may exhibit different linear expansion coefficients in different directions. Now that you've learned the basics of thermal expansion using a dilatometer, let's take a look at the technique in the laboratory.

To begin, power up the dilatometer operating system and allow the sample to sit at room temperature to equilibrate. Make sure that the cooling system for the instrument is running, and that nitrogen gas is connected to the furnace. Do not turn the gas flow on yet, the gas will be turned on when the furnace turned is turned on. Now check that the calibration run has been performed on the system prior to testing your sample and select the most recent calibration that meets or exceeds your maximum temperature range and preferably is run at the same temperature ramp rate. Here we will use a previously conducted calibration run of the standard crystal locks. Next, accurately measure the length of the sample using high quality calibers.

Take several measurements along the length in order to establish the measurement error. Ensure that the sample is long enough to allow the push rod to exert some force on top of the sample. If it is not tall enough, use a spacer of a material with known thermal expansion and measure its height so that the spacer can be subtracted from the results. If a spacer is used, it must be parallel to the sample within the 1º. Then power the system on and ensure that the furnace is close to room temperature. Now raise the tube-chamber out of the furnace by pulling the knob on the side to release the tube. Raise up the tube and clean the bottom surface of the chamber with isopropanol and a wipe to ensure that the sample has a flat place to stand. Then, place the sample in the furnace with the flat surfaces towards the bottom of the chamber and the push rod and lower the push rod until it contacts the top of the sample. Lower the tube chamber containing the sample back into the furnace and ensure that the sample did not shift by checking the displacement gauge. Now, input the heating parameters into the dilatometer operating system.

Here the metal sample will be heated 20º-1000ºc at a constant rate of 5º/minute. To cool the furnace, just allow the temperature to equilibrate with room temperature. Before starting the test, double check that all systems are all on and functioning. Turn on the nitrogen purge gas and ensure that it is flowing to the system. Then initiate the test and check back periodically to make sure that it is running appropriately. When the run is complete and the system has cooled back to room temperature, export and save the data. Then repeat the scan another 2 times to account for any exaggerated expansion on the first run. After all runs have been completed and all data saved, ensure that the furnace is cool. Then raise the tube out of the furnace and remove the sample. To raise the tube out of the furnace, pull the black knob on the side of the furnace to release the tube. Finally, shut down the furnace, cooling system, and purge gas.

Now let's take a look at the results. The program returns the values for: 1. Time, 2. Sample Temperature, 3. Gauge Reading, 4. Corrected Expansion, 5. Time in seconds, 6. Dimensionless Gauge Reading, 7. System Correction. First, calculate the change in length of the sample for each temperature point using a spreadsheet program, and then divide each value by the original length to obtain values of ΔL/L. Then plot ΔL/L vs Temperature. As you can see from the plot here, 3 metals were heated to a preset temperature and then cooled back down to room temperature. Though it was heated to a lower temperature, aluminum exhibited a more significant thermal expansion than stainless steel or cold worked steel.

In the case of aluminum and stainless steel, thermal expansion and contraction both follow a linear slope; meaning that thermal expansion was linear. And the linear expansion coefficient was constant. However, the thermal expansion is not always linear, meaning that the linear expansion is not always constant, as we see for cold worked steel. The cold worked steel sample exhibited a non-linear change between 700º and 900º, which can be attributed to defects in the lattice structure of the material called dislocations.

It is important to understand the thermal expansion and contraction of materials for a wide range of applications. For example, it is essential to account for the thermal expansion for materials when designing structures such as railroads and bridges. The thermal expansion of sections of railroad tracks is the main cause of rail buckling, which caused almost 200 train derailments in the US over a period of just 10 years. The measurement of thermal expansion using dilatometry can also be used to examine defects in crystals. Dislocations are defects in a materials lattice structure, and can take many different forms such as a point dislocation where one atom is missing, or an edge dislocation where an extra half plane of atoms is introduced in the lattice. Since dislocations occupy volume, density changes in response to heat treatment. Thus, high resolution dilatometry has extended the technique to study rearrangement of dislocations. Essential to understanding strength and possible areas of failure.

You have just watched Joves introduction to the analysis of thermal expansion via dilatometry. You should now understand the fundamentals of thermal expansion, the dilatometry technique, and some areas where thermal expansion is analyzed in structural and materials engineering. Thanks for watching.

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### Results

The results of dilatometers generally include data of temperatures, expansion lengths, and time. Different softwares used together with dilatometers can return results in different ways. Some softwares only return data points, while others have plotting functions and other analysis features. The software used in the procedure above used WorkHorseTM. This program returns data in a .txt file that can then be plotted using a software such as- Matlab, Qtgrace or Excel. Figure 2 shows three different metals expanding and contracting as temperature is raised and lowered.

Figure 2: The change in length as function of temperature is plotted for stainless steel, cold worked steel, and aluminum. Samples are heated and then cooled with continuous length measurements to observe whether any hysteresis exists.

Thermal expansion is not always a linear function. This means that the coefficient of thermal expansion is not always constant. As seen in Figure 2, there is an unusual thermal expansion event that occurs in cold worked steel between 700oC and 900oC. In the case of stainless steel and aluminum the thermal expansion, as well as contraction, follow a linear slope. However, for the cold worked steel the expansion and contraction follows a non-linear change. This can be attributed to the dislocations in the cold worked steel. Locations where dislocation recovery occurs can experience different expansion/contraction as opposed to locations where normal expansion/contraction occur.

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### Applications and Summary

Dilatometry is a technique for measuring the dimensional thermal expansion of a material. Frequently this value is found by measuring the change in length as a material is heated and cooled. Thermal expansion is quantified by change in length divided by initial length. In addition to thermal expansion, the technique offers insights into vacancy formation, phase changes, and dislocation evolution in response to heat treatments.

While determining thermal expansion of materials is a very popular use for dilatometers, there are other applications for them. For example, these instruments can also be used as a method to monitor phase changes in certain alloys. Determining dislocation densities is another application of dilatometry.

Monitoring Phase Changes: The application of dilatometry in phase change research is due to the change of the specific volume of a sample during a phase transformation. Lattice structure changes when a material undergoes a phase change. By recording the transformations taking place over a range of conditions, it is possible to present the results in a graphical form. This shows the formation temperatures of microstructural constituents that may be obtained for a given cooling or heating condition. This technique is widely used to study the transformation behavior of steels during continuous heating, cooling, and isothermal holding. This has immense value in metallurgical applications. It is important in engineering industries where steels are used for construction.

Dislocation Densities: Dislocations occupy a volume and therefore, as dislocation density changes in response to heat treatments, dilatometry can be used to observe and quantify dislocations. High resolution dilatometry has extended the technique to the study of texture changes and rearrangement and annihilation of dislocations related to the recovery and recrystallization process. High-resolution dilatometry, together with a model of isotropic dilatation and atomic volumes can be used estimate the dislocation density introduced in microstructures due to isothermal decomposition of austenite.

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### Tags

Thermal Expansion Dilatometry Material Temperature Fluctuation Measurement Technique Area Change Shape Change Length Change Volume Change Thermal Expansion Calculation Dilatometer Metal Sample Laboratory Experiment Calipers Furnace Push Bar Purge Gas Oxidation Prevention Heating Predetermined Temperature Specified Rate Displacement Sensor Correction Factor Linear Thermal Expansion

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