Crystallography Class Notes PDF

Programme: B.Sc. with Geology as Major / Minor Course: Fundamentals of Geology – I Unit - Crystallography CLASS NOTE - 1 Prof. Santanu Sarma, Department of Geology, Cotton Universi...

Programme: B.Sc. with Geology as Major / Minor Course: Fundamentals of Geology – I Unit - Crystallography CLASS NOTE - 1 Prof. Santanu Sarma, Department of Geology, Cotton University. Prof. Santanu Sarma, Department of Geology, Cotton University. Class notes of Crystallography Recommended Books - 1. Manual of Mineralogy (After J.D. Dana) – Cornelis Klein & C.S. Hurlbut 2. A text book of Mineralogy – E.S. Dana & W.E. Ford 3. Rutley’s Elements of Mineralogy – H.H. Read Crystallography The word "mineral" is used in many different ways A formal definition preferred by geologists Mineral is a substance that must meet five requirements: – Naturally occurring (people did not make it.) – Inorganic (not made by an organism.) – Solid (not a liquid or a gas at standard temperature and pressure.) – Definite chemical composition (all occurrences of that mineral have a chemical composition that varies within a specific limited range.) – Ordered internal structure (atoms in a mineral are arranged in a systematic and repeating pattern.) Minerals are chemical compounds that are normally crystalline and formed by geological processes. They much also have a well defined chemical composition. Crystalline means having an orderly and repetitive atomic structure. Exceptions: – Some biogenic crystalline substances such as Calcium Phosphate (apatite) in bones or teeth, Calcium Carbonate (Calcite) in shells are also considered to be minerals. – Chalcedony [SiO2] and Malachite [Cu₂CO₃(OH)₂] are minerals but non-crystalline in nature – Some mineral like substances are there but they do not fit the definition of minerals – Synthetic Diamond and rubies are not mineral because they are nor natural. Prof. Santanu Sarma, Department of Geology, Cotton University. Class notes of Crystallography  – Refined sugar is crystalline but is not considered mineral because it is human made and organic. – Rust is not a mineral but goethite with nearly the same composition and properties is a mineral. The general term crystalline solid is characterized by the possession of ordered internal arrangement of atoms or internal atomic structure. When conditions are favorable during the solidification of the substances from the solution or fluid state, they may be bounded by smooth plane surfaces and assume regular geometric forms known as crystals. Minerals, with few exceptions, possess the internal, ordered arrangement that is characteristic of crystalline solids. Two major factors set the minerals apart from other crystalline materials: – Temperature / Pressure – Time High temperature and long period of time lead to highly ordered crystal structure that synthetic and organic processes can not normally imitate. To most people, a crystal is a sparkling gem like solid with well-formed faces and a geometric shape. To a mineralogist or a crystallographer A crystal or crystalline solid is a solid material whose constituent atoms, ions and molecules are arranged in an orderly, repeating pattern extending in all three spatial dimensions resulting a definite atomic structure. When conditions are favorable during the solidification of the substances from the solution or fluid state, they may be bounded by smooth plane surfaces and assume regular geometric forms (Gemmy appearance). Most material scientists use the term crystal to describe any solid with an ordered Prof. Santanu Sarma, Department of Geology, Cotton University. Class notes of Crystallography internal structure, regardless of whether it possesses external faces. Because bounding faces are mostly an accident of growth and their absence in no way changes the fundamental properties of a crystal, this usage is reasonable. Thus we may frame a broader definition of a crystal as a homogeneous solid possessing long range, three-dimensional internal order. The study of crystalline solids and the principles that govern their growth, external shape, and internal structure is called crystallography. Although crystallography was originally developed as a branch of mineralogy, today it has become separate science dealing not only with minerals but with all crystalline matter. Crystal is also used in its broader sense with modifiers indicating perfection of development. Thus, a crystalline solid with well-formed faces is euhedral; if it has imperfectly developed faces, it is subhedral; and without faces, anhedral. Morphological crystallography deals mainly with those aspects of crystallography that relate to the external form, or morphology, of crystals. This subject is known as morphological crystallography. In the discussion of the external form of crystals we must, however, incorporate many of the findings that relate to the internal order of crystals. Depending on the grain size, the crystalline substances may be Macrocrystalline: Crystalline substances large enough to easily be identified by sight. Microcrystalline: Crystalline substances occur in such fine grained aggregates that their crystalline nature (or crystallinity) can be determined only with the aid of a microscope. Cryptocrystalline: If the crystalline aggregates are so fine that the individual crystals cannot be resolved with the microscope but can be detected by X-ray diffraction techniques. Prof. Santanu Sarma, Department of Geology, Cotton University. Class notes of Crystallography Solids can be divided in to two distinct classes. CRYSTALLINE SOLIDS Crystalline solids have the following fundamentals properties. 1. They have highly ordered definite atomic structure.. 2. They have characteristic geometrical shape. (if condition permits at the time of growth) 3. They are bounded by PLANES or FACES. (if condition permits at the time of growth) 4. Planes of a crystal intersect at particular angles. 5. They have sharp melting and boiling points. Examples: Copper Sulphate (CuSO4), Diamond, Graphite, NaCl, Sugar etc AMORPHOUS SOLIDS Solids that have a random atomic structure are known as Amorphous Solids. 1. In these solids, particles are randomly arranged in three dimension. 2. They do not have a characteristic geometrical shape. 3. They don’t have sharp melting points. (Melt over a wide range of temperature) 4. Amorphous solids are formed due to sudden cooling of liquid. Examples: Coal, Glass, Plastic, rubber etc Naturally occurring amorphous substances are designated as mineraloids. Prof. Santanu Sarma, Department of Geology, Cotton University. Class notes of Crystallography  CRYSTALLIZATION – How crystals are formed ? Crystals are formed from solutions, melts, and vapors. The atoms in these disordered states have a random distribution but with changing temperature, pressure, and concentration they may join in an ordered arrangement characteristic of the crystalline state. Crystallization from solution Crystallization from solution may be formed by 1. Evaporation of the solvent 2. Lowering of Temperature 3. Lowering of pressure They will increase the concentration of the dissolved substance in the solvent. Example : Consider sodium chloride dissolved in water. If the water is allowed to evaporate, the solution contains more and more Na+ and CI- per unit volume ie the concentration of Na+ and Cl- will increase in the solution. Ultimately, the point is reached when the remaining water can no longer retain all the salt in solution, and solid salt begins to precipitate. If the evaporation of the water is very slow, the ions of sodium and chlorine will group themselves together to form one or a few crystals with characteristic shapes and often with a common orientation. If evaporation is rapid, many centers of crystallization will be set up, usually resulting in many small, randomly oriented crystals. Prof. Santanu Sarma, Department of Geology, Cotton University. Class notes of Crystallography Crystals also form from solution by lowering the temperature or pressure. Hot water will dissolve slightly more salt, for instance, than cold water; and, if a hot solution is allowed to cool, a point will be reached where the solution becomes sufficiently concentrated that salt will crystallize. Again, the higher the pressure, the more salt water can hold in solution. Thus, with lowering the pressure of a saturated solution, supersaturation will result and crystals will form. A crystal is formed from a melt in much the same way as from a solution. Examples: Formation of ice crystals when water freezes. When the temperature is lowered sufficiently, the H2O molecules, which were free to move in any direction in the liquid state, become fixed and arrange themselves in a definite order to build up a solid, crystalline mass. The formation of igneous rocks from molten magmas, In the magma there are ions of many elements in an uncombined state. As the magma cools, the various ions are attracted to one another to form crystal nuclei of the different minerals. Crystallization proceeds with the addition of more ions to the crystal nuclei to form the mineral grains of the resulting rock. Although crystallization from a vapor is less common than from a solution or a melt, the underlying principles are much the same. As the vapor is cooled, the dissociated atoms or molecules are brought closer together, eventually locking themselves into a crystalline solid. The most familiar example of this mode of crystallization is the formation of snowflakes from air laden with water vapor. Prof. Santanu Sarma, Department of Geology, Cotton University. Class notes of Crystallography  Crystal Growth Anyone who has collected minerals or has viewed mineralogical exhibits in museums, in rock shops, or in jeweler's display cases, knows the aesthetic beauty and attraction of a well-formed crystal. Well developed crystals are the result of chemical deposition from a solution (or a melt) in an open space, such as a vug, or cavity in a rock formation. The formation of crystal involves the bringing together and ordering of constituent elements. Crystal grow from a small single molecule to their final visible form. The question that arises is "how do such well formed crystals grow from little to bigger ones?" Or One might rephrase the same question in chemical terms such as "how are the chemical building blocks (atoms, ions, or ionic clusters) incorporated into a well-ordered crystalline pattern?" Basic aspects of crystal growth: From melt Kinetic energy in magma is very high because of its higher temperature. Because of the high kinetic energy, atoms are always in motion. Atoms collide and may form bonds temporally before breaking them apart. As long as bonds break as fast as they form, there will be no net crystallization. Magma will be completely molten at high temperature. When magma cools down sufficiently, kinetic energy will get reduced and the atoms slow down. As a result some bonds begin to persist to form nuclei and that is the beginning of the formation of crystal, from the melt. From aqueous solution Atoms dissolved in water and as long as the water is not saturated, no crystals will form. Atoms will bond temporarily, only to break apart and return to solution. Most substance Prof. Santanu Sarma, Department of Geology, Cotton University. Class notes of Crystallography are more soluble in water at high temperature and pressure. A decrease in temperature and pressure may lead to oversaturation, nucleation and precipitation of aqueous minerals. Changes in composition or pH my also lead to the formation of aqueous crystal. So whether in a melt or aqueous solution, the first stage in the growth of a crystal is that of nucleation, which implies that growth can commence only after a nucleus (or seed) has been formed. The nucleus is the result of the coming together of various ions/atoms to form the initial regular structural pattern of a crystalline solid. Many nuclei continue as the centers of continued crystal growth. Most nuclei may not lead to further crystal growth, because in a saturated solution or high energy melt, there is also a tendency for nuclei to go back into solution (to be redissolved) or melt. This is because, these very small beginnings of an ordered structure have a very large surface area with respect to volume (Surface Area / Volume is very high). This is referred to as a high free energy per unit volume, and implies a high solubility. If a nucleus is to survive, it can do this by rapid growth so that it reduces its surface energy (the ratio of surface area to volume). If a nucleus reaches a critical size through rapid deposition of further layers of ions, it will have a high chance of surviving as a crystal. Large crystals are chemically stable because Molecules in the interior of the crystals are less reactive and have lower energy than those on the outside. Low free energy per unit area There is often more than one way for atoms to combine to form crystal. As atoms bond, they naturally tend to arrange themselves in a way to minimize the chemical energy. There are more than half dozen of naturally occurring crystalline forms of SiO2, each having its own distinctive arrangement of atoms and bonds. – α-Quartz – Crittobalite – Coesite – Tridymite – Stishovite Prof. Santanu Sarma, Department of Geology, Cotton University. Class notes of Crystallography Factors that control the crystal size and perfection are Temperature – Crystals that form at high temperature have simpler atomic structure than those that are stable at low temperature. – Low temperature minerals have the ability to be large and well ordered. Time – If crystals have longer time to grow, it will naturally be larger and better ordered that one that grow quickly. – More atoms have time to migrate to the growing crystal and to order themselves in a regular way. Presence of necessary element Flux – Fluids such as interstitial water or a magma act as flux, transporting atoms to growing crystal. – If flux is present, elements may be carried long distances to sites of mineral growth and even minerals composed of rare elements may grow to be large. Prof. Santanu Sarma, Department of Geology, Cotton University. Class notes of Crystallography