Measurement methods



Methods for measurement of thermal expansion


-   (Mechanical) Dilatometry
-   Thermomechanical Analyser
-   Interferometry
-   X-Ray diffraction
-   Line-width camera
-   Strain gauge technique


-   Magnetic suspension
-   Rise of meniscus in capillary 


Dilatometers (an early version is shown above)
are the most common measurement devices
for thermal expansion measurement.

Expansion measurement methods for solids

The most commonly used technique on a suitable test-piece is one based on mechanical dilatometry the change in length of a known length is recorded as a function of temperature by a contacting push-rod. The movement of this push-rod is determined by one of several techniques, including a simple dial gauge, a capacitance transducer, an LVDT or interferometer. This technique works well from liquid helium temperature to over 2000 C, provided that the materials of the supporting system and the push-rod are stable. There are commercial instruments that make direct measurements on individual test-pieces, or compare the movement in an unknown with that in a reference material.

The accuracy of such instruments is typically no better than 0.1 x 10-6 C in expansion coefficient or expansivity, for data obtained over a 100 C temperature interval. In the polymer field, the Thermomechanical Analyser is a simple form of dilatometer, but is not capable of the same level of accuracy as purpose-built dilatometers on materials of low thermal expansion.

Commercial dilatometers are available from various suppliers, like that shown above from Netzsch.

The use of interferometry to measure length change directly from the test-piece is less common but potentially more accurate since it is less reliant on mechanical contact movements. The test-piece is placed on a mirror, has a small mirror placed on top, and the relative movement of the mirrors as the test-piece is heated and cooled is determined by multiple beam interferometry. Preferably, the test-piece itself is made with mirror surfaces. The accuracy of this type of arrangement is perhaps an order of magnitude improvement over mechanical dilatometry, but is
Laser interferometer for expansion measurement on pulse-heated samples at OGI, Austria.
limited by achievable temperature homogeneity. The technique is also more expensive, more limited in temperature range, and more restricted in terms of test-piece type and geometry.

Direct optical expansion measurement is in use for high-expansion plastics materials and has been used extensively in the past. In fact, certified reference materials have been calibrated using this method. Fiducial marks are placed on a long test-piece and viewed laterally using a long focal length microscope attached to an accurately calibrated length scale parallel to the test-piece. As the test-piece is heated or cooled, the position of the fiducial marks are recorded manually. Modern versions of this method involving analysis of video-images have also been employed for complex structures.

There are a number of other techniques that have their place, but are less commonly used for data generation, and they include:

  • X-ray diffraction measures lattice cell expansion, but may not produce the same results as whole body methods because the effects of local residual stresses may not be taken into account

  • electrical heating with servo displacement allows expansion to be measured when subjected to a given force

  • line-width camera useful for measuring size changes of very hot objects which can be imaged, but where other direct dilatometric methods are not appropriate, but the accuracy may be limited by resolution limitations

  • strain gauge this technique has value for determining local behaviour of complex bodies, such as composite structures, but the gauges have to be carefully calibrated for their response with respect to changing temperature.

Expansion measurement methods for fluids

Techniques for the direct measurement of fluid volume are less well developed than for linear dimensions. The volume of a known mass of liquid can be tracked as a function of temperature as its meniscus rises up a capillary exiting from a filled rigid vessel.

More sophisticated magnetic suspension devices that operate over wide ranges of temperature and pressure are available for accurate determinations.


Density measurement methods for solids

The most common method is the Archimedean immersion method, whereby the loss of weight of an object when suspended in a fluid of known density is equal to the mass of fluid displaced, from which its volume and hence density can be calculated. Unless there are good reasons for not selecting it, water is the most common immersion medium, the primary reason being its low sensitivity of density to temperature compared with many organic liquids.

Varying degrees of sophistication can be built into the technique. Ensuring that no bubbles are trapped on the immersed object, and that the suspension wire is clean and has a consistent immersion depth, are key experimental factors. For materials that have open porosity, appropriate conditioning of the material is important before liquid immersion to eliminate or stabilise the residual gas content. Techniques include evacuation and re-pressurisation under the immersion liquid, boiling while immersed in the liquid followed by equilibration, or evacuation followed by high-level pressurisation. From such tests, bulk density and apparent solid density can be determined.

The following drawing shows the legendary Archimedes weighing method of measuring the density of a solid object. (Archimedes used this to detect a jeweler's fraud of admixing silver into gold of the crown of Hiero II, the king of Syracuse). The object is suspended on a thin thread and weighed twice - measuring the force of pull on the thread when suspended in air and immersed in the liquid.  If a balance from which the thread can be suspended is not available, a modification of the method is to simply weigh the object on a top loading balance followed by weighing the container with the liquid with and without the object immersed (suspended) in the liquid.

Other less commonly used methods for density determination include:

  • pyknometry (or pycnometry): the internal volume of a vessel with and without a solid material present is evacuated and filled with gas, often helium; the volume of gas used, corrected for its pressure, is used to determine the apparent solid volume

  • porosimetry: a liquid, such as mercury, is forced into the material under a progressively rising pressure until a stable infiltrated volume is achieved. The amount of mercury used provides a measure of the total porosity, and the pressure/volume curve gives a measure of the open pore channel size distribution

  • X-ray diffraction: the density can be estimated from the unit cell dimensions for the given crystalline phase; but this does not take defects, strain or pores into account

  • gamma densitometry: the attenuation of gamma radiation transmitted through a solid body can be related to its density via some form of calibration with artefacts of known density. This technique is typically used for continuous measurement of apparent density on production lines.

Density measurement methods for liquids

Liquid density at or near room temperature is most conveniently measured using either:

- density bottle: filling the bottle with an unknown liquid and separately with water and measuring the respective masses can be used, provided the temperature is kept constant; or
- hydrometer: a flotation device with a calibrated immersion scale is commonly used for a rapid density check; the lower the liquid density the lower the hydrometer sinks.

Varying degrees of sophistication and automation have been incorporated into these principles.

Measurement at higher temperatures is rather more difficult, and requires the volume of a given mass to be determined as a function of temperature. A so-called PVT device has been
Commercial density bottles used for liquid density measurement.
used successfully for polymers and waxes, incorporating pressure as a further variable.

Piston dilatometry has been used successfully for molten metals, provided that no leakage occurs. A given mass of metal is held between pistons in a cylinder. As the metal melts to fill the gap it pushes the pistons outwards and the change in entrained volume is determined.

Other techniques include:

  • pressure method: maximum bubble pressure (for liquid oxides/glasses)

  • levitation: for liquid metals, the size of a droplet levitated in an RF field

For on-line use:

  • vibrating cell, vibrating wire, vibrating tube techniques: the vibration frequency is controlled by the density of the surrounding medium; works best for liquids or slurries;

  • X-ray or gamma-ray densitometers based on absorption through the fluid; particularly useful for slurries and foods.

Methods for measurement of density


-   Archimedean immersion
-   Pyknometry
-   Porosimetry
-   X-Ray diffraction
-   Gamma densitometry


-   Density bottle
-   Hydrometer
-   Piston dilatometer
-   Maximum bubble pressure method
-   Levitation
-   PVT-apparatus


-   Closed vessel method
-   Velocity-of-sound method
-   Flow meter
-   Refractometry


A levitated molten nickel specimen at DLR,
Cologne, Germany.

Density measurement methods for gases

Direct methods include measuring the mass of a closed vessel:

1. when evacuated,
2. after filling with the unknown gas, and
3. after filling with a known gas or liquid.

Key control parameters are the pressure and temperature, and the method is prone to significant errors resulting from parasitic effects, such as the small mass of the gas compared with that of the container. Devices are now available commercially for accurate measurement of the equation of state of a fluid (including density) over a wide temperature range, including the critical region.

Other simpler, but less direct methods have been employed for industrial use, particularly for on-line monitoring, including:

  • flowmeter, in which the float is supported by a given mass flow rate;

  • refractometry: in which the refractive index and its change with pressure or temperature is determined interferometrically, and related to density through the equation of state;

  • velocity-of-sound method: this is directly linked to density through bulk modulus, which needs to be known;

  • vibration method: the vibration frequency of a fork or other device changes with surrounding gas density; requires calibration

  • centrifugal method: based on the pressure differential when a gas is subjected to angular velocity; requires calibration.