POLDI: Pulse Overlap time-of-flight Diffractometer

 

 

 

 

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Background

Introduction

POLDI is a neutron diffraction instrument designed for strain measurements, i.e. the accurate determination of lattice spacings. In a stressed material the lattice spacing acts as a kind of strain gauge. If d0 and d are, respectively, the stress-free and actual lattice constant then the strain is given by:

Using Hooke's law, the measured strain can be converted to a stress. The knowledge of the stress components in a material is of great importance for both engineering applications and material science.


Diffraction

In diffraction experiments a diffraction peak is characterized by its position, width and intensity. The position is a measure for the average strain, whereas the width is related to strain fluctuations. Peak intensities can be used to obtain information about texture. Diffraction can be understood in terms of the Bragg's law:

where d is the lattice spacing, λ the wavelength and 2θ the diffraction angle. POLDI is a so-called time-of-flight instrument which means that the detector is placed at a fixed diffraction angle and that in contrast to constant wave length instruments a broad wave length spectrum is used. The wave length of the neutrons is determined by the time they need to travel a certain distance (see also here). The strain is then given by:

The main applications of POLDI are:


Residual stresses - strain mapping

Figure 1. The principle of strain mapping.

Residual stresses are the auto-balancing stresses that exist in a material free off any applied stress at constant temperature. They have an important influence on the behaviour of materials. A well known example is the presence of residual stresses in welds, which typically produces large tensile stresses whose maximum value is approximately equal to the yield strength of the materials being joined, balanced by lower compressive residual stresses elsewhere in the component.


Neutrons are highly penetrating and therefore well suited for strain mapping in engineering materials. The principle is shown in figure 1. The incoming neutron beam is defined by a slit in front of the specimen whereas the diffracted beam is defined by a slit between the specimen and detector. The diffraction angle is close to 90 degrees. This defines a small sampling volume as indicated by the green square in figure 1. By translating the specimen in the neutron beam diffraction data from defined volume elements can be acquired. This geometry is common for most strain scanners because the gauge volumes should have the shape of a cube or at least a square in the scattering plane, since only for these geometries perpendicular strain directions of the identical stress state are measured within the same volume, a necessary requirement for a correct calculation of the stress.


Study of deformation mechanisms

Figure 2. Load transfer in steel.

Neutron diffraction is particulary well suited for the study of deformation mechanisms in engineering materials. In single phase materials the behavior of the different families give insight in the complex interplay between elastic and plastic anisotropy. This is demonstrated for the simple case of a low carbon steel in figure 2, which displays the change of the axial strains determined by the {111} and {200} diffraction peaks as function of applied load. In the elastic regime the axial strains increase linearly with applied stress. The different slopes are due to elastic anisotropy; in this material the [111] direction is relatively harder compared to the [200] direction. When entering the plastic regime deviations from linearity can be observed. For the interpretation of the behaviour of the different diffraction peak often computational modeling has to be done, describing the very complex interactions between grains during deformation.

Similar information can be obtained for composite materials where the diffraction peaks of each phase can be followed during mechanical loading. This allows studying effects such as load transfer and the consequent build-up of residual stresses.


Examples

Two examples of recent POLDI measurements:

Recommended references

  1. Analysis of Residual Stress by Diffraction using Neutron and Synchrotron Radiation
    M.E. FitzPatrick, A. Lodini (editors)
    Taylor&Francis 2003