PRINCIPLES OF PUSH-ROD DILATOMETRY

(Technical Note #69)

Principle of Operation | Definitions | Types of Dilatometers | Common Configurations |
Advanced Configurations | Test Procedure | Sample Considerations | Furnace Construction |
Temperature Sensors

A dilatometer measures the expansion of a material when it is heated. A small sample of the material is placed into the instrument and then heated (or cooled) according to a schedule picked by the investigator.

1.)   PRINCIPLE OF OPERATION

Pushrod dilatometry, as its name implies, involves intermediary machine members to transmit the dimensional change caused by subjecting a sample to a change in temperature. The need for these members is a practical one, since the transducer that registers this change cannot normally be subjected to the same temperature excursion as the sample. The closer the transducer can be coupled to the sample, the less the transmission member can influence the results, and, consequently, the more ideal the dilatometer becomes. Specifically, the more one can reduce the contributions made by any such intervening machine members, the more purely the data will represent true values.

In principle, one can devise a simple arrangement in which the movement is transmitted out of the controlled environments and into the ambient by holding the sample between two rods which extend outside of the heated region as shown on Figure 1. The sample pushes the two rods (A and B) as it is being heated, hence the name "pushrod". The sample will expand an amount shown by the shaded area, DL_S. By examining the experimental model, it becomes immediately clear that this configuration will not produce the desired DL_S. Since portions of both rods A and B are in the controlled environment, it is inevitable that they themselves will also expand (DL_A and DL_B respectively). Thus, the measured value of (DX_A+DX_B) will contain (DL_A+DL_B) in addition to DL_S. The sample’s length change, DL_S, can therefore be written as:

(Eq. 1)                DL_S = ( DX_A - DL_A) + ( DX_B - DL_B)

Unless one can assign values to DL_A and DL_B, the true magnitude of DL_S cannot be determined from the measured values of DX_A and DX_B alone. Obviously, if DL_A and DL_B are not present at all, the measurement becomes absolute, but as long as this is not the case, the measurement is, in principle, a relative one.

Figure 1

Figure 2

The most tempting prospect is to minimize the magnitudes of DL_A and DL_B in comparison to DL_S and then to neglect them. If the material of rods A and B do not expand appreciably compared to the sample, or not at all, the conditions become favorable to obtain results with reasonable accuracy. A good example of this would be to use light beams that do not expand when entering the controlled environment in place of rods A and B. More frequently, very low expansion materials such as fused silica are used for rods A and B, and, for many applications, this is enough to reduce inaccuracies to a small fraction of the measured values when high expansion materials such as plastics are tested.

In general usage, however, one must determine the magnitude of DL_A and DL_B accurately. Most commonly, one tests a sample from a material already well-defined by some other absolute method (twin telescopes, interferometer, etc.), which then leaves only the combined values of DL_A and DL_B unknown. This process is known as "calibration" for the dilatometer; the well-defined material is referred to as a "standard" or "reference;" and the combined value of DL_A and DL_B and is known as "system correction." Upon closer examination, it is clear that the correction obtained with a standard will be true only if this sample is of the same length, ensuring that the protruding lengths of rods A and B into the controlled environment region are identical during the calibration and during the test. Furthermore, what may be true at one value of temperature T may not be true at another. To ensure that a calibration is indeed applicable:

• the sample and reference lengths must be close to each other.
• the calibration thermal cycle must closely approximate the test cycle (or vice versa).
• the reference's expansion must be close to the expected expansion of the sample.

(The last criterion is often difficult to visualize as being important, yet experience bears it out to be true.)

A more common variation of this device involves both rods' entering the controlled environment from the same side (Figure 2). For sake of continuity in this discussion, rod B, now longer than before, is divided into two sections: the part that is equal in length with A and as before noted to expand DL_B, and the portion that happens to be equal to and running alongside of the sample, C, that expands DL_C. When heated, both legs (A+sample) and (B+C) will expand. Since they move in the same direction, the transducer will register DX, the difference between the two movements. Thus:

(Eq. 2)                DX = (DL_S + DL_A) - (DL_B + DL_C)

By fabricating A and B from identical material and keeping them close to each other, it is reasonable to postulate that they will behave identically under most conditions. This assumption makes DL_A = DL_B, reducing Equation 2 to:

(Eq. 3)                DX = DL_S - DL_C

which states that a dilatometer of this configuration always measures the difference between the expansion of the sample and that of its own material passing alongside the sample. As with the previous configuration before, the value of DL_C can be determined by first calibrating the dilatometer with a standard. (The criteria discussed earlier for a valid calibration are still holding true.)

A natural extension of the above model is another configuration known as a "differential" dilatometer. In this design, sections B and C are indeed two separate pieces. B is made of the same material as A, so DL_A cancels out DL_B. Section C can be made of any benchmark material usually referred to as the "reference", often the same type used for calibrating an ordinary dilatometer. Equation 3 established earlier that the measured value is the difference in expansion between the sample and section C. This arrangement can offer advantages in certain applications where:

• direct comparison of two samples is desired, when it is more important to know their relative performance than their absolute expansion (for example, screening studies, quality control testing, formulation evaluation, etc.).
• absolute expansion determination in case C is actually a standard.
• the effects of non-uniform heating, and inaccurate temperature (T) measurement are to be minimized.

Differential dilatometers usually measure very small differences with high magnification. A major drawback of this configuration is its susceptibility to errors due to transducer gain misadjustments or malfunctions. As an extreme condition, one can obtain seemingly valid data (that is, the sample appears to expand exactly at the same rate as the reference) with the transducer literally turned off. Additionally, the high magnification severely restricts the range of measurable displacement. For these reasons, the use of differential dilatometers should be limited to applications in which the advantages clearly outweigh these drawbacks. If a temperature change from T_O to T has caused this expansion in a sample of initial length L_O, the average coefficient of linear thermal expansion can be calculated as:
                          _
(Eq. 4)              a = (DL_S/DL_O)/(T - T_O)

This coefficient, often referred to as CTE, is only true for the temperature range T_O to T. (Note that the word "linear" should never precede the word "coefficient", as it always implies uniaxial expansion rather than linearity of the coefficient.)

2.)   DEFINITIONS   [ back to top]

Linear Thermal Expansion:
The change in length of a material resulting from a temperature change. Linear thermal expansion is symbolically represented by DL/L₀, where DL is the observed change in length (DL = L₁ - L_O), and L_O and L₁ are the lengths of the specimen at reference temperature T₀ and test temperatures T₁. Linear thermal expansion is dimensionless, it is often expressed as a percentage, or in parts per million (such as mm/m) units.

Mean Coefficient of Linear Thermal Expansion:
The linear thermal expansion per change in temperature. The mean coefficient of linear thermal expansion, a, is defined as:

      a = 1/L₀ [(L₁ - L₀) / (T₁ - T₀)] = [1/L₀ (DL/DT)]

(It is customary to designate the coefficient of thermal expansion with the greek letter alpha (a). For the mean coefficient, a bar is placed over it, and is referred to as alpha-bar. In industry, frequently the whole process is referred to as "CTE testing".)

The value of the mean coefficient must be accompanied by the values of the two temperatures.

Instantaneous Coefficient of Linear Thermal Expansion:
The slope of the linear thermal expansion curve at temperature T. Instantaneous coefficient of linear thermal expansion represented by:

      a_T = (1/L₀) dL/dT

The value of the instantaneous coefficient must be accompanied by the temperature at which it is determined.

3.)   TYPES OF DILATOMETERS   [ back to top]

There are two basic types:

a.   Standard Dilatometer:
It is the basic device (described earlier in section 1). To calibrate this kind of device, a Standard or Reference sample is tested repeatedly first and a calibration factor for the tube is then computed from these tests. The calibration factor is used when unknown materials are tested.

b.   Differential Dilatometer:
This device always measures the difference between two samples. The two samples are placed into the dilatometer tube, side-by-side, and two push-rods are used to track each sample independently. Since the measurement is one vs. the other sample, the tube has no other purpose than to support the samples. A differential dilatometer can be calibrated similarly to the standard dilatometer, but most frequently it is operated with the Reference in place of one sample. This type of instrument has been greatly overrated for its sensitivity, disregarding drawbacks such as short stroke. Often the device is favored purely on personal preference with not much fundamental reasoning behind it.

4.)   COMMON CONFIGURATIONS   [ back to top]

There are two configurations that are most common among commercial devices. Researchers frequently come up with clever new seemingly different configurations, but on close scrutiny, they all fall within the two basic ones or are not practical due to complexity, cost, or requiring very high skills from the operator.

a.   Horizontal Dilatometer:
As the name implies, this device has a horizontal tube with the sample laying on its side. Advantage of this configuration is better thermal uniformity along the sample. Disadvantage, especially for samples with large shrinkage, is the high push-rod pressures needed to slide the sample along to keep it in contract with the end-plate of the tube. Usually no provision available for push-rod counterbalancing (see later).

b.   Vertical Dilatometer:
The sample stands up on the end-plate of the dilatometer tube with the push-rod resting on it. It does not suffer from the tracking problems noted with horizontal instruments, and therefore is especially useful for measuring large shrinkages (sintering, etc.). As with every vertical system, thermal uniformity is not as good as in a horizontal device, however, one can limit sample size to be still within a nearly uniform thermal zone. Counterbalancing with dead weight is possible. Tracking pressures can be greatly reduced, but not below a minimum needed for smooth and continuous movement.

The Unitherm™ line is structured so that almost any dilatometer can be configured either as a Standard or as a Differential device. There are both horizontal and vertical units available in every model.

5.)   ADVANCED CONFIGURATIONS   [ back to top]

a.   Multi Sample Dilatometer:
Unique to the Unitherm™ line is the ability to test several samples concurrently in the same furnace and to run several devices parallel with the same computer. This greatly increases testing capacity at a fraction of the cost of multiple instruments. (It is often possible to add further testing capacity to an already existing system at a later date.)

b.   Large Sample Dilatometer:
Frequently the need arises to test materials that are not homogeneous, and therefore necessitating samples larger than ordinary dilatometers can accommodate. Natural substances (rocks, mineral deposits, food stuffs), plastic foams, certain ceramics, large grain carbon and graphites, etc. fall into this category. Sometimes it is the poor load bearing ability, at other times it is the size of the particles in a mix (concrete, for example), or grain size that necessitates the size increases.

The Unitherm™ line contains several models that are also available in the large sample configuration.

6.)   TEST PROCEDURE   [ back to top]

a.   Expansion Measurement:
The sample is placed into a holder, usually called the dilatometer tube. This may be horizontal or vertical. A rod in the axis of the tube contacts the sample to transmit the size increase. This is called the push-rod. The sample, when it expands, pushes the tube and the push-rod in opposite directions. This movement is sensed by a transducer. The tube and the transducer are fixed to the same reference surface with the moving member of the transducer coupled to the push-rod. The transducer may be an ordinary dial indicator, an LVDT, or some other type of displacement sensor.

The Unitherm™ line only uses digital transducers which have very high accuracy and do not require periodic recalibration. This is unique among all dilatometers made anywhere in the world.

b.   Temperature Control and Measurement:
Usually thermocouples are used, except for the Ultra High Temperature system which employs a pyrometer. It is imperative to know the temperature of the sample region (not only the sample itself) well, and to control the furnace to provide uniform sample temperature. It is often promoted that the sample temperature must be determined closely and investigators have even attached thermocouples or embedded the couples into the sample. This is not a good practice, as it will interfere with the free movement of the sample and will totally ignore the temperature of the dilatometer tube running along the sample. A best solution is to keep the thermocouple in between the two.

c.   Calibration:
Since the push-rod movement is always the difference between the expansion of the sample and the dilatometer tube, the latter one must be defined accurately. This is done by using a well characterized sample whose expansion is known, called a Standard or Reference.

d.   Heating Programs:
There are no right and wrong heating schedules. Very often they resemble a schedule used in production, other times they are designed to bring about an expected change. Generally there are two major kinds: ramp heating and stepwise heating. With a ramp, the sample is heated continuously to maintain a constant rate of temperature rise. With stepwise heating, the sample is allowed to come to thermal equilibrium at selected temperatures. Unitherm™ dilatometers can do both kinds of heating programs or even a mixture.

7.)   SAMPLE CONSIDERATIONS   [ back to top]

a.   Machining:
It is unimportant to finish machining the entire sample. Only the ends contacting the end-plate of the dilatometer tube and the tip of the push-rod must be flat (RMS 60 or better) and parallel (±0.001 inch; ±0.025mm).

b.   Soft Samples:
Foams, plastics, thermal insulators, and other materials having a low load bearing capacity are difficult to test because the push-rod tends to indent into the sample. Two solutions can be used either separately or together.

  (1)   Reduction of push-rod pressure. It helps but is can also result in jerky movement (ratcheting) when very low tracking force is used. It is better to limit this action and to rely on (b). Vertical dilatometers (such as the Model 1161) with static weight counterbalancing lend themselves best to this approach.

  (2)   Using a pressure distribution plate. This is a thin sheet of very stiff material, similar in nature to the material of construction for the dilatometer itself. Quartz plates for quartz dilatometers, alumina plates for alumina dilatometers, etc. Often stainless steel is used where temperature limitation permits it. When a dissimilar material is used, its contribution to the results must be computed first. If the plate is kept thin, it is usually insignificant.

  (3)   Pressure distribution plates for Model 1054. This is a special case, for this model uses flat plate samples and thin strips on the ends by themselves would not be stiff enough to do the job. The strips are bent into small angles and these are placed over the two end faces of the sample where the push-rod and the back-up rod make contact. With high expansion materials (such as plastics), plate thickness up to 0.010 inch were found to be insignificant.

c.   Stacking of Samples:
Often samples are available in short sections only. To build up a reasonable sample length, several short sections can be stacked up. Vertical dilatometers are best to accommodate this condition.

d.   Thin Films (flexible):

  (1)   Auxiliary Fixturing
In some instances, if the film has a stiff nature, it is possible to test it flat in the Model 1054 with an aluminum pressure bar resting on it. This bar is made slightly shorter than the sample, so the push-rod and the back-up rod are only contacting the ends of the sample. For higher temperatures, jigs can be made out of two bars with a present gap between them to accommodate the sample. Horizontal dilatometers are better suited to deal with this configuration.

  (2)   Shaping
Rolling up the film to produce a cylinder has been used with success. Also folding a crease into the sample may help to stiffen it.

  (3)   Combination
Combination of (a) and (b) may be used, such as folding up both lengthwise edges of a foil sample and also placing a weigh-down bar on the center section.

e.   Yarns or Thin Filaments:
These can be tested only in tension and therefore it requires special fixturing. Vertical dilatometers with counterbalancing can be adapted readily to this task.

8.)   FURNACE CONSTRUCTION   [back to top]

Depending on the temperature range alone (not the model number), different types of furnaces can be employed even in the same instrument. These are:

• Cryogenic to 500°C maximum, aluminum alloy block furnace. Advantage is very good temperature uniformity, superior control, and fast heat up. Very often the sample is not isolated from the furnace block for enhanced temperature uniformity and heat transfer.


• Ambient to 1200°C maximum, Nichrome wire heaters in coiled form are used. These are supported on ceramic half-shells. (Although these are rated to 1200°C, it is preferred to run them to 1000°C and no higher.) Surrounding the half-shells is fibrous insulation. These are the least attractive furnaces in the entire instrument line. They are comparatively slow, and less uniform than the aluminum alloy block furnace.


• High speed IR radiant furnaces. Fast heating system, limited to 1200°C.


• Ambient to 1700°C range is serviced by Kanthal Super S hairpin heaters suspended in a cavity formed by high temperature fibrous insulation. This furnace is very fast heating and somewhat slow cooling due to the excellent insulator shell.


• Ambient to 3000°C range is serviced by graphite furnaces that are built integrally with the dilatometer.

9.)   TEMPERATURE SENSORS   [back to top]

Depending on the maximum temperature, a device will have:

• up to 1000°C, Type K thermocouple (Chromel/Alumel).
• up to 1700°C, Type S thermocouple (Platinum/Platinum-10% Rhodium).
• up to 3000°C, optical pyrometers.