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Finding the needle

August 26, 2014

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In Depth

Bob Newport, Professor of Materials Physics at the University of Kent, has nominated the work of John Enderby and Peter Egelstaff in the 1960s on neutron diffraction as his Great British Scientific breakthrough The phrase ‘looking for a needle in a haystack’ was born as an idiom for the supremely difficult task of sifting out the kernel of an answer from the vastness or complexity of the particular situation in question. Neutron diffraction with isotope substitution, NDIS, is one of the methods developed in the physical sciences to tackle just such a situation. This is a sketch of its story and of its origins in the work of two remarkable scientists almost five decades ago. Last year saw the centenary of x-ray diffraction¹ and a celebration of the work of the Nobel prize-winning Braggs, and in 2020 we’ll reach the analogous landmark for Chadwick’s discovery of the neutron² – worthy of its own article in this series; the early decades of the 20^th Century were heady times for the physical sciences. Whilst the exploitation of x-rays for research happened relatively swiftly after their discovery by Röntgen in 1895, and demonstrations of the analogous potential for neutrons appeared as early as 1936³, it wasn’t until the mid-1940s that the first diffraction experiments using genuinely practicable beam intensities were conducted by Clifford Shull and Ernest Wollan. There is a reason for this. X-ray beams could be produced in abundance and the x-ray interacts strongly with matter whereas, by contrast, neutron beams are necessarily of much lower flux and interact only weakly with the nuclei of atoms. However, the neutron has attributes – including its weakly interacting nature – which make it a wonderful probe of liquids and solids, and once this had been established there was, and continues to be, a strong desire to use neutron beams to the full. Because the neutron has no charge, its primary interaction is not with the electron cloud surrounding an atom (as it would be with the x-ray) but with the central nucleus; the very weakness of this interaction makes a fully quantitative analysis of the resultant data far more tractable, even if the sample is held within a relatively massive containment vessel. Moreover, the neutron has mass and this means one can not only use its wave-like properties for diffraction experiments on the positions of atoms, but it becomes possible to probe the dynamics of a material’s atoms as well – as first demonstrated in the 1950s by Betram Brockhouse. Crucially for this story, there is more: because neutrons scatter from the nuclei of atoms within a material, the nature of that event is affected by the particular isotopes present. Thus, whilst x-rays are sensitive only to the elements present, neutrons are also sensitive to the admixture of isotopes associated with those elements …suffice it to say that neutrons are marvellous. Returning now to the problem at hand, we need to consider the ‘haystack’. In the May edition of Laboratory News I wrote a short piece about disordered materials: obtaining information on the positions of atoms within the regular array that is a crystal is one thing – take away that sample-wide order and one faces a more challenging problem altogether. Given a liquid or an amorphous solid (e.g. a glass), neither of which possess order to the arrangement of their atoms beyond that driven by short-range chemical/electrostatic forces (i.e. over a distance corresponding to only a few atomic diameters), how does one extract quantitative information about the distribution of atoms of one element with respect to the other elements present? We may illustrate the complexity of this question by considering a ‘simple’ amorphous material containing only two elements: A and B. For a full understanding of the atomic-scale structure of the material one needs to know the distribution of A atoms around Bs (and equivalently, Bs around As), A atoms around other As, and Bs around other Bs. Thus, from one diffraction experiment yielding a single ‘combined’ data set – the structure factor – we must attempt to extract three distinct distributions, the partial structure factors: this is, self-evidently, not possible. The complexity of the puzzle increases rapidly if we add more elements; in general, there are _N(N+1) partial structure factors for a sample comprising N elements. Tissue-regenerative/anti-bacterial bioactive glasses studied by my own team in recent years, for instance, include materials containing up to six elements: there would in this case be 21 distinct partial structure factors contributing to the single experimentally determined curve. Add to this the fact that the scientifically key partial structure factor may be associated with an element present at low concentration and/or which scatters neutrons only weakly, and therefore making a relatively weak contribution, and the problem truly begins to warrant the idiom ‘looking for a needle in a haystack’. At this point our two scientific ‘heroes’, Peter Egelstaff and John Enderby (later Prof. Sir John Enderby FRS in recognition of his contribution) enter the fray. In a paper⁴ published in July 1966 in Philosophical Magazine, with research team member D.M. North, they successfully demonstrated an elegant method by which one might overcome these limitations in the right circumstances. The key step was to make use of the isotope-dependency of neutron scattering. If we return for a moment to our A+B sample, imagine that element A has a stable isotope, let’s designate it A^*, which scatters neutrons with a different ‘strength’ to the naturally occurring mixture of isotopes that make up A. Imagine now two samples, identical in all respects save for the fact that in one of them the natural A is replaced with isotope A^*; x-ray diffraction data gathered from these two samples would be indistinguishable from one another. If, however, we conduct separate neutron diffraction experiments on them we’d obtain a total structure factor for A+B and another for A^*+B, each of these totals will of course be the combination of three distinct partial structure factors: AB, AA and BB in the one case, and A^*B, A^*A^* and BB in the other. Subtracting one data set from the other means that we have immediately removed the BB partial term since it is common to both – leaving only those partial structure factors related to element A. If we take this further by adding a third sample, and corresponding diffraction results, in which the mix of stable isotopes varies again (e.g. a mix of A with A^*, or perhaps using a stable isotope of element B) then we’ll have another data set to add to our armoury. At this point, by analogy with the basic methods for solving simultaneous equations in mathematics, we have reached the point at which all three of our partial structure factors may be derived: we had three ‘variables’ (A around B, A around A, and B around B) and now we have the necessary three ‘equations’.

CGBS image 2 Total structure factors (top) for the sample containing natural Ca and for it's 'twin' in which 44Ca is substituted, and the difference between them (bottom) which comprises only those components associated with calcium

It is not always necessary to be able to derive every single distinct partial structure factor of course; sometimes all that is needed is to narrow the field a little. Take for instance some of my own team’s work on bioactive glasses. A ‘simple’ silicate glass containing some calcium and hydrogen will, if the composition is right, dissolve in body fluid (e.g. blood plasma) and supply a chemical signal to the body which promotes the formation of the mineral component of bone: these materials can provide a scaffold for bone regeneration. Central to the understanding of how this material works is gaining an understanding of why it is that Ca leaves the glass at the rate it does. In other words, we need to know where the Ca sits in relation to its surrounding atoms: we need the partial structure factors associated with Ca. Now, given the presence of four elements (Si, Ca, O, H) a single neutron diffraction experiment yields a structure factor comprising 10 partial components; calcium’s contribution to this is effectively hidden within the total. Thankfully, nature has provided us with a suitable stable isotope of calcium, ⁴⁴Ca, which enables precisely the sort of experiment outlined above. The majority silica component to our diffraction data could be subtracted out, along with the OH terms, leaving only the partial structure factors associated with calcium’s environment, as shown left. Of the six oxygen atoms surrounding the average Ca atom, only two of them tie the Ca into the silicate glass network by forming bridges to Si – the others bridge only to H or are non-bridging. The mystery of calcium dissolution is thereby solved⁵. This is but one example of the continuing beauty and the strength represented by John Enderby and Peter Egelstaff’s breakthrough; here is a method by which, metaphorically speaking, the ‘hay’ may be removed in order to see the ‘needle’. From their first experiments in the 1960s, through the development of high flux neutron sources of the 1970s, and on to the remarkably powerful and diverse facilities UK scientists have access to today, their ground-breaking work continues to enable exciting new science. Indeed, earlier this year the Royal Society elected another talented expert in the use of isotopic substitution to their pantheon of Fellows: Alan Soper. Although the use of hugely important complementary probes such as solid state NMR and x-ray absorption spectroscopy have emerged in the intervening years, together with computer modelling, NDIS remains a powerful technique in the worldwide study of materials, and there is little sign yet of any decline to its scientific impact.

Acknowledgement

I am indebted to colleagues Alan Soper and Robert McGreevy at ISIS for their helpful advice and input.

Author

Bob Newport is Professor of Materials Physics at the University of Kent and has been publishing research in the field of liquids and amorphous materials for more than three decades.