Table of Contents:
Thermal expansion
Introduction to thermal expansion
Thermal expansion – also known as thermal expansion – is a physical phenomenon that is equally relevant in everyday life and technology. It describes the change in the geometric dimensions of a body when its temperature changes. Understanding and precisely measuring this property is particularly important in construction, mechanical engineering and materials research.
Fundamentals of thermal expansion
What is thermal expansion?
An increase in temperature increases the molecular movement at the particle level of a material and consequently its space requirement also increases. The resulting effect is then an expansion of the material. On cooling, the space requirement decreases again and thermal contraction occurs accordingly.
Causes and physical principle
- The cause is the increase in the kinetic energy of the particles when heated.
- The distance between the particles increases as a result.
- Each material has a characteristic coefficient of expansion, which indicates how much it expands when the temperature changes, depending on the particles it contains and their degrees of freedom.
Forms of thermal expansion
Thermal expansion can manifest itself in different dimensions depending on the shape of the body and the composition of the material: in length, area or volume.
Linear expansion
With linear expansion, the length of a body changes along an axis, for example in the case of a metal rod, which visibly lengthens when heated. This form of thermal expansion is easy to measure and is the most common application.
Surface expansion
Here, the surface area of a body increases – typically in the case of sheets or foils that expand evenly in two spatial directions.
Volume expansion
Volume expansion refers to the spatial expansion in all three directions. It mainly occurs in liquids and gases, but can also be observed in solids and calculated in part from the linear expansion of an axis.
Mathematical description
Linear expansion
\Delta L = \alpha \cdot L_0 \cdot \Delta T
\quad \text{where} \quad
\begin{cases}
\Delta L : \text{Change in length (m)} \\
\alpha : \text{Linear expansion coefficient (1/K)} \\
L_0 : \text{Initial length (m)} \\
\Delta T : \text{Temperature change (K)}
\end{cases}
\)
Volume expansion
\Delta V = \gamma \cdot V_0 \cdot \Delta T
\quad \text{where} \quad
\begin{cases}
\Delta V : \text{Change in volume (m³)} \\
\gamma : \text{Volumetric expansion coefficient (1/K)} \\
V_0 : \text{Initial volume (m³)} \\
\Delta T : \text{Temperature change (K)}
\end{cases}
\)
Measuring methods for determining thermal expansion
Dilatometer
A dilatometer measures the change in length or volume of a sample of defined temperature and temperature change. The sample is heated or cooled and its change in length is transferred to a displacement transducer via a push rod. The inherent expansion of the measuring system is compensated for or corrected using reference material.
Typical measured variables:
- Linear coefficient of thermal expansion (CTE)
- Sintering temperatures and stages
- Glass transition temperatures (Tg)
- Phase transitions
- Volume and density changes
Areas of application:
- Materials: Metals, ceramics, glasses, polymers, composites
- Possible temperature range: -260 °C to +2800 °C (depending on device configuration)
Thermomechanical analysis (TMA)
Thermomechanical analysis (TMA) is a method for measuring dimensional changes under mechanical load at a defined temperature. A probe presses on the sample with a constant force while the temperature is slowly changed. A sensor, often a differential transformer or LVDT (Linear Variable Differential Transformer), measures the resulting changes in length in real time.
Measured properties:
- Linear expansion and expansion coefficient
- Softening points
- Shrinkage processes during sintering
- Glass transition, melting point, crystallisation
- Creep and relaxation (time-dependent deformation under load)
Typical applications:
- Analysing solids, liquids and pasty materials
- Suitable for: Plastics, elastomers, adhesives, metals, ceramics, composites
- Complements other methods such as DSC, TGA and DMA
Thanks to its high sensitivity, TMA not only allows the determination of expansion, but also the detection of weak physical transitions – such as changes in the crystal lattice, hardening or delamination. This makes it a versatile tool for research and industry.
Use of dilatometers to analyse thermal expansion
Functionality in detail
Dilatometers are essential instruments for determining the thermal expansion of materials. The measurement is carried out either using mechanical components such as a push rod or contactless using optical sensors. The sample is placed in a heatable oven in which a defined temperature profile is run through. As the temperature changes, a high-precision displacement transducer measures the change in length of the sample material. This measurement allows the linear coefficient of thermal expansion (CTE) to be determined – a key parameter for describing the thermal behaviour of materials.
Key steps in the measurement process:
- The sample is heated or cooled in a controlled manner.
- The resulting change in length is recorded with high accuracy.
- The CTE is calculated from the ratio of the change in length to the change in temperature.
This method allows a resolution in the sub-micrometre range and is suitable for both routine quality controls and research applications.
Applications and typical measured variables
Dilatometers provide a variety of measurable parameters that are of central importance for material development and industrial processes:
Typical applications:
- Determination of glass transitions and phase transitions
- Analysis of shrinkage behaviour in sintering processes
- Measurement of volume and density changes
- Use in quality assurance, material development and research
Differences between materials
Comparison of expansion coefficients
- Plastics: e.g. PE = 2,10-4 K-1 K
- Metals: aluminium = 23,8·10-6 K-1, Stahl = 11–1310-6 K-1
- Ceramics/glass: Al₂O₃ = 7,5·10-6 K-1
- Special materials: Invar = 0,55–1,2·10-6 K-1
Significance for technical applications
- Large differences can lead to stresses and material failure.
- Precise material selection is crucial for durable designs.
Practical applications and challenges
Cross-industry significance
Thermal expansion is a key issue in numerous technical disciplines. Depending on the area of application, it can be utilised in a targeted manner or must be actively compensated for in order to avoid component damage or functional losses. Well thought-out design measures are essential, particularly in the case of permanent temperature changes, as occur in many technical environments.
Typical areas of application:
- Construction: Expansion joints in bridges, carriageways or pipelines ensure that materials can expand or contract with temperature changes without causing cracks or structural damage.
- Mechanical engineering: In machines and systems, components with different expansion behaviour often have to function together. If these differences are not taken into account, there is a risk of tension, leaks or premature wear.
- Electronics: Printed circuit boards, semiconductors and housings are often made of different materials. An incorrect combination with different CTE values can lead to solder joint fractures or material cracks.
- Aerospace: The requirements here are particularly high. Components must be able to withstand extreme cold in space as well as extreme heat when exposed to the atmosphere – without deforming or losing their function.
Examples from practice
- Railway tracks are laid with gaps to prevent deformation due to thermal expansion.
- Borosilicate glass in laboratory and cooking vessels withstands thermal shocks thanks to its low coefficient of expansion.
- Water expands when it freezes – an exception that ensures that ice floats on water and insulates it.
Conclusion
Thermal expansion is a central phenomenon in physics and technology. Its exact knowledge and precise measurement using dilatometers or TMA makes it possible to optimise materials for their application. This makes it possible to develop products that function reliably even under extreme conditions – whether in industry, research or everyday life.
Recommended sources for in depth study
- LEIFIphysik: Volumen- und Längenänderung von Festkörpern
(Grundlagen der Wärmeausdehnung anschaulich erklärt) - Wikipedia: Wärmeausdehnung
(Überblick über Formen, Formeln und typische Werte) - Studyflix: Wärmeausdehnungskoeffizient
(Kompakte Erklärung mit Formeln und Beispielen) - TU Dresden Praktikumsanleitung: Thermische Analyse
(Wissenschaftlich fundierte Messmethoden, inkl. TMA und Dilatometer) - PTB – Physikalisch-Technische Bundesanstalt: Dilatometer
(Ausführliche technische Beschreibung von Dilatometern) - Polymer Service Wiki: Thermomechanische Analyse
(Spezifische Anwendung und Funktionsweise von TMA) - Universität Duisburg-Essen: Dilatometrie
(Hintergrundinformationen zur thermischen Analyse fester Stoffe)
