# Attenuated Total Internal Reflectance

## 38. Attenuated Total Internal Reflectance (often abbreviated as A.T.R.)

One of the school physics experiments many of us will have performed is to observe total internal reflection. If you carry out the experiment drawn below

you will note the phenomenon called refraction. If the indices of refraction Ng and Na are those for glass and air respectively, then

Sin(i)/Sin(r) = Na/Ng i.e. r >

a law due to the very early physicist, one Snell.

39. If you increase i there comes a point where r runs away to 90°. It is when Sin(i) = Na/Ng. At greater angles of incidence than this the light stays inside the glass and reflects – none is refracted.

40. Although few people do the experiment at school, you can place any two materials in ‘optical contact’, say glass and oil, and observe the same effects. The same relationships apply except that now Nair becomes Noil. This phenomenon makes the optical fibre possible

Index Nglass or Nquartz > Nsilicone rubber

The rays totally internally reflect down the core and none leaks into the sheath.

41. In 19 I said that in an absorbing material the index of refraction changes as one crosses an absorption band. As a result, if one carried out the total internal reflection experiment using infrared radiation, the angle at which total internal reflection would occur would vary as one crossed an absorption band. You would need an infrared optical crystal of high index – say, zinc selenide or ThBrI(KRS-5) and a method of placing your sample on its surface. If the angle of incidence was just right, as one crossed an absorption band internal reflection would be switched off and on. All a bit difficult but possible. It turns out life can be a bit simpler than this. If the experiment is set up so that total internal reflection is comfortably occurring, i.e.

Sin(i) > Nsample/Ncrystal

a different but related phenomenon occurs.

42. Light comes in at incident angle i and reflects at r where i = r. Now total internal reflection is occurring at the interface but the radiation is not perfectly confined inside the crystal. Over a very short distance, (a shallow penetration) the radiation permeates the sample. The jargon is that the ‘Evanescent wave’ penetrates the sample – to a depth of the order of the wavelength of the radiation (but this penetration depends amongst other things on angle i). As a result, the totally internally reflected light carries information about the infrared absorption of the sample. The attenuation of the infrared beam is subtle, so in most ATR accessories multiple reflections are used e.g. in the horizontal ATR systems the optical arrangement is

43. The sample is poured, spread or squashed onto the upper surface of the crystal. Ours, from Grazeby Specac, has a ZnSe crystal with dimensions 60x7mm x 4.5mm thick and it fits into the sample area of our 1720 or 2000 Perkin Elmers. The spectrum produced is very close to the absorption spectrum of the sample. Because the penetration of the beam is so small, a thin smear of a liquid gives excellent results. ATR has recently been extended a great deal and is now a really versatile, supremely easy, and fast sampling system and we will cover the technique in detail in future editions. You do not have to restrict yourself to oils or squashy solids, powders, films, solutions, minerals, hard plastics -almost anything other than a gas can now be examined.

44. So, we have a set of reflection methods, applicable in the infrared. All have their attractions, some can give unique data whilst others are more routine in their application. All can be used on commercial spectrometers, thanks to the accessory manufacturers and incidentally all are useable in infrared microscopes – another subject to be covered in future editions.

REF: Int.J. Vib. Spect.,[www.irdg.org/ijvs] 1, 4, 38-44 (1997)