Thermodilatometry

 

Thermodilatometry is a rather vain glorious term for what is mostly known as the measurement of thermal expansion. Most solids expand with temperature and the change is defined by the following equation,

 

 

                        where (l₁) is the length at (T₁) and (l₂) is the length at (T₂)

                             and () is the coefficient of linear expansion.

 

  If () is small i.e () then the above equation can be simplified to,

 

 

The coefficient of linear expansion is related to the physical structure of the sample. It is also in some cases anisotropic, for example in a crystal, drawn fibers and liquid crystals. The value of the coefficient of expansion for strongly bonded solids (ionic materials) tend to be lower than for say molecularly bonded materials. 

 

In the determining the thermal expansion of solids, the measurements can be absolute or relative in which case the expansion of the sample of interest is compared with the expansion of that of a standard reference material. The sample can be horizontally or vertically placed but the sensor should be loaded against the sample surface as, in some substances that are anisotropic there may be a contraction as apposed to an expansion as the temperature is increased. The movement due to thermal expansion can be measured in a number of ways. It can be measured magnetically employing a variable differential transformer where the movement of a central magnetic core relative a set of transformer coils produces a directional output that can be extremely sensitive. The design of a magnetic motion transducer is shown in figure 14.

 

Figure 14. Diagram of a Magnetic Motion Transducer

 

A magnetic core (that is connected to a rod that is in contact with the sample situated in the oven) is located in the center of the primary coil of a transformer. The secondary coils on either side of primary coil are connected in opposition and so when the core is directly in the center there is no electrical output from the secondary coils. If the sample expands or contracts then a sign sensitive output appears at the output of the secondary coil, which is acquired by a computer and appropriately processed.

 

Alternatively an optical sensing system can be used as diagrammatically depicted in figure 15.

 

Figure 15. Optical System for Measuring Thermal Expansion

 

A plane mirror is placed on the surface of both the sample and the reference standard. A laser produces a light beam that strikes a half silvered mirror and half the light is reflected to the reference standard plane mirror, which is then reflected back through the half mirror onto a photocell. The laser light that initially passed through half silvered mirror strikes another plane mirror and is reflected to the surface of the sample plane mirror. The reflected light from the sample plane mirror passes back to the plane mirror and then to the half silvered mirror where it is reflected onto the photocell.

 

Both beams of light have been attenuated by first passing through the half silvered mirror and then by being reflected from the half silvered mirror. As a consequence each beam will have the same intensity (viz. one quarter of the original laser light intensity). The two beams will interfere and, thus, produce interference fringes. The output from the photocells are passed to a computer and as the sample expands or contracts relative to the standard, the interference fringes pass across the photocell and are counted. The counts are directly converted to relative changes in sample and reference standard dimensions. The measurements are accurate to one quarter of the wavelength of the laser light,

 

The results are usually presented as a curve relating change in sample dimensions to the temperature. The coefficient of expansion can be obtained from the slope of the curve but it is usually the inflections and slope changes that provide information regarding the physical condition of the sample. An example of such a curve relating change in sample dimensions with change in temperature is shown in figure 16. It is seen that initially as the temperature is increased there is the expected increase in sample dimension. However, at a certain temperature dehydration occurs and the sample begins to shrink and the sample dimensions are steadily reduced. Eventually the rate of shrinkage suddenly increases significantly and there is an inflection in the curve and the downward slope of the curve indicates some physical change is taking place; this is interpreted as the onset of crystallization.

 

 

Figure 16. The Thermodilatometry Curve for a Clay Sample

 

At an even higher temperature the derivative increases to an even greater extent and this inflection is interpreted as the onset of sintering. It is clear that the thermodilatometry can indeed be very informative regarding physical changes that occur as the temperature of the sample is changed.