Expansivity and density FAQs

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B1.  What is thermal expansivity?

B2.  What is density?

B3.  What is the difference between expansion coefficient and expansivity?

B4.  I have seen expansions recorded in parts per million; what does this mean?

B5.  How accurately can expansion coefficients be measured?

B6.  How good are strain gauges at measuring expansion coefficients?

B7.  What is a pyknometer?

B8.  How does a push-rod dilatometer work?

B9.  What does CTE mean?

B10.  Which inert gas should be used for dilatometer measurements?

B11.  Which reference temperatures are used for dL/L0 and CTE values?

B12.  Which heating rates should be used for dynamic dL/LO measurements?

B13.  Is there a way to statically measure dL/LO?

B14.  Which techniques are most common used to determine thermal expansivity?

B15.  What is the coefficient of linear thermal expansion?

B16.  Are there any simple rules to presume thermal expansion?

B17.  What techniques are used to determine thermal expansivity?

B18.  What is the reason for thermal expansion?

B19.  How does the density (expansion) change during at the melting transition?

B20.  What is the difference between linear thermal expansion and volume expansion?

B21.  What is the coefficient of thermal expansion of [your material]?

B22.  How can volume expansion be measured during an ohmic pulse-heating experiment?

B23.  How does thermal expansion correlate with temperature?

B24.  What is the difference between a TMA and a dilatometer?

B25. What types of push-rod dilatometer are there?


B1.  What is thermal expansivity?

Most materials (with few exceptions) will expand or grow in size when heated. This expansion depends on the type of material, the pressure (notably in gases) and the material temperature.                     

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B2.  What is density?

The density (r) of a substance is the ratio of the mass (m) to the volume (V), that is,  r = m/V. The SI unit for density is kg/m3, and as a reference value the density of water (1000 kg/m3) is often used.

B3.  What is the difference between expansion coefficient and expansivity?

A mean expansion coefficient is the fractional increase in length per unit temperature rise when averaged over a known temperature interval, i.e. it is the chord slope of the curve of fractional increase in length as a function of temperature, between two specific temperatures. An 'expansivity' is the fractional increase in length per unit temperature rise at a given temperature, i.e. it is the tangent to the curve of fractional increase in length as a function of temperature. Since the fractional increase in length with temperature is seldom a linear relationship, these two parameters are NOT numerically the same.                                       

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B4.  I have seen expansions recorded in parts per million; what does this mean?

Thermal expansion is quite a small effect, but is very significant in engineering terms when things jam or buckle or need to be joined rigidly to each other, e.g. railway lines without adequate expansion gaps in hot weather. A fractional increase in length can be expressed as parts per million, ppm. Expansion coefficients of solid materials are typically in the range 0 x 10-6 C-1 to 200 x 10-6 C-1, which units can also be presented as ppm/C.

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B5.  How accurately can expansion coefficients be measured?

A typical mechanical dilatometer operated with a temperature ramp, up or down, is typically capable of giving a measurement uncertainty of about 1% in fractional length change over a temperature range of typically 100 C. Over smaller temperature ranges, the accuracy is less. The fundamental limitation is the mechanical stability and repeatability of the system and the test-piece being measured. To improve upon this level of accuracy it is generally necessary to use optical interferometry, and to employ a series of steady-state temperatures at which the lengths are measured. Accuracies of about 1 ppm in length are achievable under optimum conditions. Few materials are stable enough to warrant such accurate measurements. 

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B6.  How good are strain gauges at measuring expansion coefficients?

Strain gauges are generally designed for use at the temperature at which they are glued to the test surface. Changing the temperature can lead to parasitic effects due to expansion mismatch between the gauge and the test material, and to changes in calibrated gauge factor. Accuracies of typically 5% can be achieved.                                             

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B7.  What is a pyknometer?

A pyknometer is any vessel of defined volume that can be used for measuring the volume of a mass placed inside it. A simple example is a density bottle. Weighing the bottle empty, full of a liquid of known density, and then with the weighed unknown object immersed in the liquid filled to the same level allows the object's density to be determined. More sophisticated devices include helium pyknometers, in which the solid volume can be determined from the volume of helium gas displaced.    

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B8.  How does a push-rod dilatometer work?

A push-rod dilatometer measures linear thermal expansion. The thermal expansion of a test specimen is determined relative to that of a standard reference specimen. The specimen is placed in a furnace and alumina push-rods that extend from the furnace to a thermally isolated linearly variable displacement transducer (LVDT) bear on the specimens. The expansion of the specimens results in a movement of the push-rod, thus allowing the linear thermal expansion of the sample to be determined. The temperature of the specimen is usually measured with a thermocouple (e.g. Pt vs. Pt-10Rh).                                                                           

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B9.  What does CTE mean?

The Coefficient of Thermal Expansion (CTE) is defined as the fractional increase in length per unit rise in temperature. It can be defined at either a precise temperature or over a temperature range.                   

B10.  Which inert gas should be used for dilatometer measurements?

Preferably an inert gas with a high thermal conductivity, e.g. argon.

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B11.  Which reference temperatures are used for dL/L0 and CTE values?

Recommended reference temperatures are between 20 and 30 C. The international reference temperature for dimensional metrology is 20 C.

B12.  Which heating rates should be used for dynamic dL/L0 measurements?

The heating rates should be as low possible and yet not too low to make the total measurement time unacceptably long. Reliable heating rates are no greater than 2 K/min.                                                                    

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B13.  Is there a way to statically measure dL/L0?

Yes, step-by-step from temperature to temperature.

B14.  Which techniques are most commonly used to determine thermal expansivity?

The most common technique for determination of thermal expansivity is dilatometric analysis with inductive sensor.

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B15.  What is the coefficient of linear thermal expansion?

In its simplest form, the coefficient of linear thermal expansion of any material can be defined as the fractional increase in length (linear dimension) per unit rise in temperature. It can be defined at a precise temperature or over a temperature range.

B16.  Are there any simple rules to presume thermal expansion? 

Touloukian gives the following rule of thumb: materials that melt above 600C have a linear expansion of about 2% when heated from room temperature to their melting point.

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B17.  What techniques are used to measure thermal expansivity?

Techniques for determination of thermal expansivity are as follows: (i) dilatometric analysis with inductive, capacitive or optical sensors, (ii) X-ray-analysis and (iii) interferometric based.

B18.  What is the reason for thermal expansion?

A physical explanation for this behaviour is commonly based on a simplified model of crystalline solids, where the atoms are held together in a regular array (the lattice) by electrical forces. The forces between atoms are like those that would be exerted by a set of springs connecting the atoms. At any temperature the atoms of the solid are vibrating. When the temperature increases, the amplitude of the vibrations increases and thus the average distance between neighbouring atoms itself increases. This leads to an expansion of the whole solid body as the temperature is increased. For gases, this situation changes a little bit, as the atoms or molecules are no longer situated in a regular array or lattice but can be seen as moving freely. In this case, an increase in temperature causes an increase in kinetic energy (meaning an increase in atomic velocity) and so the pressure of the gas increases, leading to expansion.

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B19.  How does the density (expansion) change during the melting transition?

Melting is a first order phase transition. Density and expansion will change discontinuously during melting: density decreases and expansion increases abruptly at the melting transition.

B20.  What is the difference between linear thermal expansion and volume expansion?

Linear thermal expansion defines the fractional increase in length, whereas the volumetric expansion defines the fractional increase in volume per unit rise in temperature. For an isotropic material the true coefficient of volumetric thermal expansion is equal to three times the true coefficient of linear thermal expansion. For non-isotropic materials this relation can lead to significant deviations.

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B21.  What is the coefficient of thermal expansion of [your material]?

When looking for the coefficient of thermal expansion (CTE) you should know the composition of your material. For example, 300 and 400 series stainless steels have CTE around 10 x 10-6 C-1 and 18 x 10-6 C-1 respectively. If you do not know which you have, the uncertainty in the CTE is quite large.

B22.  How can volume expansion be measured during an ohmic pulse-heating experiment?

For fast expansivity measurements to be made in a pulse-heating apparatus various techniques have been developed, namely: interferometry (double Michelson interferometer), streak cameras, x-ray cameras, schlieren techniques, shadowgraph techniques or electron diffraction, to name a few.

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B23.  How does thermal expansion correlate with temperature?

It is important to note that the CTE is a temperature dependent property and will, for most metals and alloys, gradually increase with temperature. However, in some instances the occurrence of phase changes will cause discontinuities in the value of the coefficient - for example a sharp contraction occurs on heating iron-based materials through the austenitic transition as the crystal lattice changes from body-centred cubic to the more compact face-centred cubic structure.

B24.  What is the difference between a TMA and a dilatometer?

Both a dilatometer and a TMA (ThermoMechanical Analysis) measure the dimensional changes of a sample as a function of temperature or time. In TMA the sample is subjected to a defined mechanical load, while in the dilatometer the load may not have influence on the thermal extension of the sample.

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B25. What types of push-rod dilatometer are there?

There is the horizontal and vertical push-rod dilatometer, single and dual push-rod dilatometer or push-rod dilatometer with ceramic or fused silica sample holder.

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