物性 i: 鉱物の結晶と胸の谷間

Minerals are inorganic substances found in the Earth, with unique properties that aid in identification and analysis. 

Many minerals exhibit crystalline structure. These crystalline materials have highly ordered atomic arrangements, made up of repeating atomic groupings, called unit cells. Because unit cells are identical within a crystal, they are responsible for the symmetry of the crystal on the micro- and macro-scale.

This symmetry causes mineral crystals to break, or cleave, in a predictable way. Cleavage is the tendency of a crystal to break along weak structural planes. Thus, the way a mineral cleaves provides insight into its crystal structure. 

This video will demonstrate the analysis of macro-scale mineral crystal forms by breaking mineral samples and observing their cleavage. 

Crystalline solids contain atoms organized in a repeated pattern, whereas amorphous solids have no order. For example, carbon can be found in many forms. The atoms in amorphous carbon are randomly organized, whereas the atoms in diamond are arranged in an ordered crystal.

A crystal is an array of repeating, identical unit cells, which are defined by the length of the unit cell edges and the angles between them. These repeated structures extend infinitely in three spatial directions, and define the uniformity and properties of the crystal.

There are seven basic unit cells. The simplest unit cell, the cube, has equal edge lengths, and an atom at each corner. Variations include tetragonal and orthorhombic, which possess different edge lengths. 

Rhombohedral crystal structures possess similar parallel face geometry without right angles. Monoclinic and triclinic are similar in shape, but with varied angles and edge lengths. Finally, the hexagonal structure is composed of two parallel hexagonal faces, with six rectangular faces. 

Variations in these structures arise when additional atoms are contained in the crystal face, called face-centered, or in the crystal body, called body centered. 

When crystals are broken, they tend to cleave along structurally weak crystal planes. The cleavage quality depends on the strength of the bonds in and across the plane. Good cleavage occurs when the strength of the bonds within the place are stronger than those across the plane. Poor cleavage can occur when the bond strength is strong across the crystal plane. Crystals may cleave in one direction, called basal cleavage, resulting in two cleaved faces. This results from strong atomic bonds within the plane, but weak bonds between the planes.

Similarly, crystals may cleave in two directions, due to two weak planes, resulting in four cleaved faces and two fractured faces. Cubic and rhombohedral forms result from cleavage in three directions. Octahedral and dodecahedral forms arise from four and six fracture planes, respectively.

Some minerals don’t cleave along a crystal plane at all, due to strong bonds in all directions, and instead result in irregular fracture.

Now that we’ve covered the basics of crystal structure, and the different types of crystal cleavage, let’s look at these properties in real mineral samples. 

To analyze crystal forms, first collect a group of mineral samples, such as quartz, halite, calcite, garnet, biotite, and muscovite.

Place the sample on the observation surface. Rotate the sample in order to observe all sides. Look for crystal faces, crystal edges, and crystal vertices.

Where possible, measure the interfacial angles using a goniometer. To do so, lay one side of the goniometer on a particular crystal face, and the other side of the goniometer on an adjoining face. Then read the angle.

Compare the observations to the set of characteristic crystalline polyhedra. Repeat these steps for other minerals, and note the differences.

Quartz samples have a hexagonal dipyramidal crystal form, as indicated by the 6 sides.

The calcite material, exhibits scalenohedron form, as shown by the 8 faces of the twinned pyramid structure.

Halite, shows characteristic cubic structure, with 90° angles.

Garnet has angled surfaces with 12 sides, indicative of its dodecahedron form.

Finally, biotite can show an apparent hexagonal form. 

Next, to observe crystal cleavage, first put on eye protection.

Place a piece of quartz on the breaking surface. Using a hammer, break the piece of quartz. Using a hand lens, observe the broken piece of quartz for cleavage surfaces. Notice that quartz has none.

The unit cells in the quartz crystal lattice have comparably equal bond strengths in all directions, resulting in a crystal with no preferred breaking planes, called conchoidal fracture.

Next, repeat this breaking step for other specimens. Use a hand lens to evaluate different cleavage qualities.

When there is a dramatic difference in bond strengths in a particular orientation, such as between sheets of silicate groupings in the case of mica, a nearly perfect cleavage is generated between these sheets, called basal cleavage.

Biotite and muscovite each display basal cleavage, with a single break plane.

Halite displays cubic cleavage, resulting from three cleavage planes at 90°.

Calcite displays rhombohedral cleavage, resulting from three cleavage planes at 120 and 60°.

The analysis of crystal structure is important to understanding the types of minerals found in the field.

The quantitative analysis of crystal structure can be performed using X-ray diffraction, or XRD.

In this example, the crystal structure of an iron oxide was synthesized from a mixture of hematite and iron at high temperature and pressure in a diamond anvil cell. The XRD scattering pattern was analyzed throughout the reaction to determine the crystal structure.

The results showed smooth or spotty Debye rings, which indicate crystallinity. The location of each ring elucidates the crystal structure, as each ring corresponds to a crystal plane.

Due to its planar cleavage property, and therefore atomically flat surface, mica is frequently used as a substrate for small molecule imaging.

In this example, mica was used as a substrate for the imaging of photoreceptor molecules using atomic force microscopy, or AFM. The protein sample was adsorbed to a freshly cleaved mica sheet, and then rinsed with buffer.

The sample was then imaged using a fluid cell. The mica substrate enabled high resolution imaging of the protein sample due to its atomically flat surface.

You’ve just watched JoVE’s introduction to physical properties of minerals. You should now understand the basics of crystal unit cells, and how to determine crystal cleavage planes. Thanks for watching!