1. Relationship of first and second halves of class
2. This half: optical mineralogy, mineral occurrence and stability + more on earlier topics
3. Crystal chemistry of minerals in the lithosphere: Homework assignment to fill out formulas for major groups (go over in class)
4. Light & minerals: electromagnetic spectrum, many kinds of interaction, refraction and reflection, polarized light, interaction depends on mineral composition and structure
¥ Homework collected today at end of class (answers)
1. Minerals and light (refraction & reflection; isotropic & anisotropic behavior [double refraction], the optical indicatrix)
2. Minerals in plane light (relief / Becke line, color/ dispersion / pleochroism; cleavage, habit, inclusions, zoning, alterationÉ)
3. Minerals with cross-polars (birefringence, extinction angle[s], elongation; compare minerals in reflected light Ð bireflectanceÉ)
4. Minerals in conoscopic illumination (interference figures, optic sign, optic angle [2V], the optical indicatrix again)
5. A strategy for identifying minerals in thin section (mainly next Wednesday)
Refraction follows Snell's law in many familiar materials (fluids, glass, some minerals). In this case, the change in direction corresponds to change in wavelength (light slows down, so frequency is the same) and the wave-normals are still perpendicular to the ray path.
á Illustration of change in wavelength and link to Snell's law in refraction. Note that this change in wavelength with index of refraction becomes important in understanding the property of birefringent colors (next lecture).
Index of refraction correlates with the abundance of electrons (average electron density), hence it is generally higher for dense materials -- i.e., those with relatively high mean atomic weights (e.g., Fe-rich or Pb-rich) or with short bonds (e.g., diamond).
Light interacts with an isotropic material in the same way regardless of direction, whereas the nature of the interaction varies with direction in an anisotropic material (most crystalline materials). The difference results from the symmetry of the materials (more below).
Double refraction, or the splitting of light into two rays, is a characteristic property of anisotropic materials. Calcite is a familiar and spectacular example. Double refraction is also known by its synonym "birefringence" (though the latter often is used to indicate the range of colors seen in thin section with crossed polars).
á Light paths in calcite. Double refraction occurs in all direction but one (parallel to C-axis). (Klein Fig. 7.14).
The two rays have characteristic vibration directions (polarization) that are at right angles to one another. Wavefronts generally are not perpendicular to the ray (travel direction).
á Path of rays for double refraction in calcite. (BlossOC Fig. 6-7)
These rays travel at different speeds through the crystal (i.e., they have different refractive indices) Ñ one is the with the lower effective index of refraction (and travels more quickly) is the fast ray whereas the other, naturally, is called the slow ray.
¯ Given this point about electron density and refractive index and considering that the calcite structure has layers of tightly bonded CO3 groups perpendicular to the C-axis Ð which direction in calcite (a hexagonal mineral) would you expect to have the highest refractive index: 001 (parallel to C) or 100 (perpendicular to C)?
** Calcite experiment on overhead projector with polarizing filters
¯ As the crystal rotates in unpolarized light, which is the ordinary ray (O-PO, above) and which is the extraordinary ray (O-PE, above)?
¯ Inserting the polarizing filter on top should do what to the images as it rotates?
¯ What about putting it on the bottom?
¯ What if we have one on the bottom such that we see only one ray and then put the other at right angles on the top? (This is the case of cross-polars which we will investigate further in the next lecture.)
á Calcite showing double refraction with and without a second polarizing filter.
¯ From the these photos and the preceding figure, can you determine which is the O ray and which is the E ray as labeled in the sketch?
The optical indicatrix is an ellipsoid (a three dimensional figure an central section of which is an ellipse, described by 1 = x2/alpha2 + y2/beta2 + z2/gamma2) that relates the index of refraction and the vibration direction for light traveling through a material. An indicatrix may have 1, 2, or an infinite number of circular sections (the latter is a sphere).
Optic axis / optic axes: these are directions in the crystal that are perpendicular to the one or more circular sections in the optical indicatrix. Light entering a crystal parallel to the optic axis does not exhibit double refraction.
Case 1. If all the axes are all equal (a = b = c) the indicatrix is a sphere. Light behaves the same in all directions, although the refractive index (= radius of indicatrix) typically changes with wavelegth (dispersion). This is the case for isotropic substances. There are not distinct optic axes given the uniform behavior of light.
á Isotropic indicatrix (BlossOC Fig. 6-3). Note all the happens with change in wavelength is a change in radius.
Case 2. If one axis is not equal to the other two (a = b <> c, or a1 = a2 <> c) this is an ellipsoid of revolution. It has one distinct axis and is known as uniaxial. The two common directions have the index omega (after O for "ordinary") because the ray that falls in this plane follows Snell's law, whereas the distinct direction is referred to as epsilon (after E for "extraordinary" ray). A uniaxial mineral has a single circular section (with index omega).
á Two uniaxial indicatrices (Nesse 7-23) Ñ optic sign is discussed below.
Case 3. If the principal Cartsian axes of the indicatrix are all unequal, correspond to the maximum and minimum refractive indices (designated gamma and alpha) and an intermediate value (beta) that corresponds to the third axis. These Cartesian axes are labeled X (alpha), Y (beta), and Z (gamma). In this case there are two circular sections and the material therefore has two optical axes and is known as biaxial. The angle between these axes is known as "2V" (more about 2V later).
á Illustration the biaxial indicatrix and its principal axes.
á Biaxial indicatrix showing sections and optical axes (Nesse Fig. 7.27)
á Hornblende example showing relationship to crystal form, cleavage, and crystal axes (Gribble).
How does crystal symmetry (crystal system) relate to the optical indicatrix? Consider how symmetry operations are consistent with ellipses (including circles).
¯ What about cubic minerals? Glass?
¯ What about hexagonal and tetragonal minerals?
á Examples of orthorhombic, monoclinic, and triclinic symmetry (Nesse Fig. 7-28):
Plane light (light polarized in one direction) is the way we typically start observing minerals in thin section or in grain mounts (grains in some medium, commonly a fluid of known refractive index).
As we have seen above, light entering an anisotropic mineral is split into two polarized rays (vibration direction). Plane polarized light behaves similarly, but there is now only one direction to be split. Consequently the intensity of these two rays depends on the orientation of the mineral. If it is oriented such that the entering polarization is parallel to one of these directions (corresponding to the indicatrix axes), then the intensity of the second ray is zero and the light coming out has the same orientation as going in. This can be used to great advantage for examining minerals in both plane light and cross polars.
BlossOC Fig. 6-17
Optical relief is term used to describe the appearance of a mineral due the contrast in refractive index. High relief minerals have a large contrast; low-relief have little contrast and are hard to see.
á Minerals with different refractive indices in an oil with an index similar to quartz. Note that relief can be positive (higher than medium) or negative (less than medium).
¯ Would you expect relief to change with direction? Why or why not? If so, in what groups of minerals?
Becke lines Ñ a whitish band of light at the boundaries between materials Ñ provide direct evidence of the relative refractive index of adjacent materials. They represent the focusing of light into the higher index material which can be observed as the microscope stage is racked slightly up and down. When the stage goes down Becke lines move toward the higher index material. Although subtle in thin section, they can be helpful to distinguish between minerals of differing relief (index).
á Illustration of Becke lines.
Color Ñ many origins, most commonly due to absorption. Composition has a big effect and transition metals, especially iron, are key to causing color and color changes.
¯ How does the color of the amphiboles change with the addition of from tremolite to actinolite or hornblende? How does the index of refraction change with iron content? (see amphibole descriptions in textbook).
Pleochroism Ñ Changes in color with direction in crystal. This can be seen in unpolarized light (tanzanite example from last lecture), but is best seen in polarized light. In this case, light of a preferred orientation passes into the mineral and one can see the effect of the two rays combined. If the crystal is oriented such that one of the principal directions is parallel to the incoming polarizedlight, you see that color along.
Pleochroism is characterized in terms of the color seen when light passes through a crystal in a single direction (e.g., along the principal vibration directions: X, Y or Z). One needs to remember that both compositional differences and pleochroism can occur in the same minerals.
¯ Can an isotropic mineral show pleochroism? Why not?
¯ How many pleochroic directions are needed to characterize a hexagonal or a tetragonal mineral?
á Tourmaline example showing pale yellow-green to darker blue-green prisms and cross sections in plane polarized light (Gribble). Tourmaline is trigonal (hexagonal). White is quartz; inclusions in tourmaline crystals are dark.
¯ Given that tourmaline is uniaxial, you should be able to deduce in which direction the incoming light is polarized.
Dispersion Ñ Differences in the refractive index with wavelength disperse light in a material leading to a play of colors best known in materials like diamond (Gems & Gemology cover, Fall 2004). A common prism is another classic example. Dispersion is usually subtle in thin section and thus unimportant in routine petrography.
These crystallographically controlled features are also characteristic of minerals at other scales Ð in hand specimen for example Ð but they are often nicely expressed and easier to see in thin section. They can provide some of the most distinctive clues to mineral identification in thin section.
á Cleavage is typically quite helpful, for example, in the common mafic minerals.
á Habit is commonly helpful Ð it reflects both crystallography and growth history.
á Twinning is an excellent tool for distinguishing between some feldspars and from quartz. It occurs in many minerals.
These features are commonly seen in thin section in plane or cross polars; they may or may not reflect crystallography (zoning does, deformation can). There is much to be learned from these features about the minerals themselves (and clues to their identification) and about the rocks which they comprise.
á Plagioclase(movie, next set of pictures), amphibole (following), quartz (last) examples illustrating twinning, habit, cleavage, zoning, inclusions, and alteration.
Thin section billet (about 3 x 2 cm) of a diorite from Chile. Note the big red feldspars?
¯ What would your first guess be about the indentity of a red (vs. gray or white) feldspar?
High-power view of feldspar grain showing tiny (< 1 micron) hematite inclusions that impart the red color.
Same field of view, showing albite twinning in plagioclase.
Same rock, now stained for K-feldspar (yellow).
á Fluid inclusions in quartz. Aqueous fluid (brine) with vapor bubble (dark) and daughter crystal of halite (cube). These represent the room temperature products of original homogeneous high-T brines trapped when the quartz crystal grew.
¯ What can we learn when polarized light passes through a mineral which, in turn, can split that light into two polarized components?
The way to do this is to look at the resulting light with another polarizer, both in direct (perpendicular or orthoscopic) illiumination and in convergent (conoscopic) illumination.
¯ How do you tell if a mineral is isotropic?
Klein 292-309 (Optical Microscopy through reflected light), or Nesse Chapter 7 (p. 114-159) [coverage of optics in Nesse is superior to that in Klein]
¯ Questions about the optical indicatrix (what is it?) and the relationship of different types to the six crystal systems. Examples of minerals that have different kinds of indicatrices.§
Reminder of GEOS 251 notes and lectures
- Press et al. (2004) Understanding Earth, Freeman Ñ Chapter 3 / Minerals
- 251 notes (on-line: http://www.geo.arizona.edu/geo2xx/geo251/)
- Lectures 3 & 4 (pdf file) cover mineralogy
- Quicktime movies of GEOS 251 PowerPoint lectures linked from class web page