Section 1.6.4.9. Fast and slow vibration directions

Before discussing other methods of identifying polarization colours, it is necessary to explain the use of the sensitive-tint plate and the quartz wedge. Both devices consist of a crystal mounted in an elongated holder that can be inserted into a slot in the microscope tube set at 45° to the vibration directions of the polarizer and analyser. The vibration directions of the plates themselves are normally oriented so that the slow ray vibrates NE–SW and the fast ray NW–SE.

The sensitive-tint (or 1) plate is made from a cleavage sheet of the white mica, muscovite, and has a thickness such that R = 560 nm. To determine fast and slow directions in an unknown specimen, the crystal grain is set to an extinction position and then rotated 45° in either direction. Thus its own vibration directions lie in diagonal positions, and when the tint plate is inserted, the vibration directions of plate and grain are parallel to each other. There are two possible cases depending whether the fast and slow directions coincide or not, i.e. slow vibration direction of plate parallel to the slow direction of the crystal (and fast parallel to fast) or slow direction of plate parallel to the fast direction of the crystal.

In the first case, the relative retardation is increased by 560 nm and the observed polarization colour jumps up the scale by one complete order as the plate is inserted. Thus, for example, first-order white (R = 230 nm) changes to second-order yellow/green (R = 790 nm), second-order blue changes to third-order blue etc. When this effect is seen, it shows that the slow direction of the crystal lies NE–SW.

In the converse case, the observed polarization colour also changes, and, if the original colour is at least as high as second-order, will move down the scale by one complete order, e.g. second-order orange (R = 950 nm) changes to first-order yellow/orange (R = 390 nm). If the original colour is, however, within the first order (i.e. R < 560 nm), the new colour is still a consequence of subtracting 580 nm from R, but it is the absolute value of the new R (not the sign) which is relevant. For example, if the original colour is a first-order grey (R = 100 nm), the new colour corresponds to R = 460 nm, i.e. first-order orange. As a rapid mental aid, it is useful to think of the original colour falling to the bottom of the scale (R = 0) and then `bouncing' back up until a change of one order has been reached, e.g. a first-order white, in the middle of the first order, hardly changes (half an order down followed by half an order up); first-order red changes to first-order grey (a fall of 90% of an order, followed by a rise of 10%).

If there is any doubt about the identification of the new colour, the crystal should be rotated through 90° and the second new colour examined. A comparison of the two options available, before and after rotation, rarely leaves any doubt about which is the higher colour (i.e. the slow-parallel-to-slow case). In all cases, whether or not the original colour is in the first order, one of the two new colours is higher than the other.

The sensitive-tint plate is so-called because it allows investigation of crystals showing very low birefringence (e.g. dark greys with or less). In the parallel position, the new colour will lie just on the blue side of sensitive tint, and in the crossed position, just on the red side. These two colours are very easy to distinguish even though they represent only a small change in R.

From the above, it should be clear what an important aid the sensitive-tint plate can be in the actual identification of an unknown polarization colour, whether it be the body colour of the crystal or something observed in a set of grain-margin fringes. There are always two other colours that can be generated using the plate, and their relationship to the original colour is known in terms of R change, so that there are altogether three colours providing information.

The quartz wedge (Fig. 1.6.4.6) is an elongated wedge-shaped plate of progressively increasing thickness, usually cut parallel to the c axis so that the slow vibration direction is parallel to the length of the wedge. In this form it is inserted into a NE–SW slot so that the slow direction has this orientation. Some microscopes are, however, fitted with a NW–SE slot, and are provided with wedges (and sensitive-tint plates) that are `length fast' rather than `length slow'. The optical effects are of course the same in both cases, but it is always a good idea to examine an accessory plate for its vibration directions (marked by the manufacturer) to be on the safe side.

Figure 1.6.4.6 | top | pdf | Polarization colours versus thickness. The lines radiating from the origin are of equal birefringence (numerical values are given at the top and the right-hand side of the figure). The diagram may be used to determine thickness if birefringence is known, or birefringence if thickness is known. For example, the diagonal line for birefringence = 0.009 (e.g. quartz) intersects the standard thin-section thickness (0.03 mm) on first-order white. This is the polarization colour shown by quartz in a standard thin section.

The wedge varies in thickness from almost zero to about 0.2 mm, and typically shows a range of polarization colours from dark first-order grey up to the fourth order or so, as it is progressively inserted into the slot. The wedge can thus be used to change the polarization colour of an observed crystal by any desired amount of R within the available range (roughly 0–2500 nm). By using the two vibration directions of the crystal, these changes can be made additive or subtractive at will. In its simplest possible application, the crystal is set so that slow is against fast and the wedge is inserted until the crystal shows as close to zero birefringence as possible, i.e. the relative retardations of the wedge and the crystal are equal and opposite (this is called compensation). Next, the specimen is removed, the colour shown by the wedge noted, and the wedge is slowly pulled out, counting the orders as they go past. This is an accurate and simple alternative method of determining polarization colours.

The accessory plates are useful in identifying the order of polarization colours, but their most frequent application is in determining which of the vibration directions shown by a crystal is fast and which is slow. For example, in a specimen of a biaxial crystal lying with the optic axial plane in the plane of the slide, the slow ray represents γ and the fast ray α. To determine which is which, the vibration directions are set in the 45° position and the tint plate is inserted. If the polarization colour goes up by an order, then the slow direction of the plate is parallel to the slow direction of the crystal. Conversely, if the colour goes down by an order, or goes up by less than a complete order (when the original R < 560 nm), fast in the crystal is parallel to slow in the plate.