This document last updated on 22-Sep-2014EENS 2110 MineralogyTulane University Prof. Stephen A. NelsonCrystal ChemistryAs we have been discussing for the last several weeks, crystals, and thus minerals, are made up of a 3-dimensional array of atoms arranged in an orderly fashion. Now we explore what these atoms are and how they interact with one another to determine the physical and structural properties of crystals. So, first we explore the properties of the atom.AtomsAtoms make up the chemical elements. Each chemical element has nearly identical atoms. An atom is composed of three different particles: z Protons -- positively charged, reside in the center of the atom called the nucleus.z Electrons -- negatively charged, orbit in a cloud around nucleus.z Neutrons -- no charge, reside in the nucleus. In a neutrally charged atom, each element has the same number of protons and the same number of electrons. z Number of protons = Number of electrons. z Number of protons = atomic number. z Number of protons + Number of neutrons = atomic weight. Isotopes are atoms of the same element with differing numbers of neutrons. i.e. the number of neutrons may vary within atoms of the same element. Some isotopes are unstable which results in radioactivity. z Example: K (potassium) has 19 protons. Every atom of K has 19 protons. The Atomic number of K=19. Some atoms of K have 20 neutrons, others have 21, and others have 22. Thus atomic weight of K can be 39, 40, or 41. 40K is radioactive and decays to 40Ar and 40Ca. It is the electrons in the atoms that are responsible for the chemical properties of atoms. The electronic configuration determines the types of atoms that can be bound to one another, the strength of the bonds, and the types of bonds. Thus, we need to look closely at the electrons and the electronic configuration of atoms. Page 1 of 14Crystal Chemistry9/22/2014http://www.tulane.edu/~sanelson/eens211/crystal_chemistry.htmBohr AtomElectrons orbit around the nucleus in different shells, labeled from the innermost shell as K, L, M, N, etc. Each shell can have a certain number of electrons. The K-shell can have 2 Electrons, the L-shell, 8, the M-shell 18, N-shell 32. Each shell is associated with a principal quantum number, n, where nK = 1, nL = 2, nM = 3, nN = 4, etc. The number of electrons in each shell is controlled by this principal quantum number by the following relationship: # electrons = 2n2Thus, the K-shell can contain 2 electrons, the L-shell, 8 electrons, the M-shell, 18 electrons, and the N-shell, 32 electrons. Electrons in the outermost shells have higher energy than those in the inner shells. This is because the electrons in the outermost shells would release more energy if they were to fall into the inner shells. When such electronic transitions occur, the energy is released as photons, such as X-rays, as we discussed previously. Planck found that the energy released in the electronic transitions is only released in distinct packets, which he called "quanta", and that these packets of energy are related to a constant (now called Planck's constant, and the frequency or wavelength of the radiation released.E = hν = hc/λwhere E = energyh = Planck's constant, 6.62517 x 10-27 erg.sec ν = frequencyc = velocity of light = 2.99793 x 1010 cm/secλ = wavelengthThis led to the quantum mechanical view of the atom. Page 2 of 14Crystal Chemistry9/22/2014http://www.tulane.edu/~sanelson/eens211/crystal_chemistry.htmQuantum Mechanical View of the AtomThe quantum mechanical view of the atom suggests that the electrons are located within specific regions of probability. These probability regions are described by the azimuthal quantum number or orbital shape quantum number, l. A maximum of 2 electrons can be found in each probability region, each electron have a spin quantum number with a value of either +½ or -½. The orbital shape quantum number has the following values and designations for the shape of the probability region in which the electrons are most probably to be found.Value of l 1 2 3 4Sub-shell designation s p d fThe sub-shell designations stand for sharp, principal, diffuse, and fundamental. The probability regions described by these sub-shells are as follows:z s - orbitals - are spherical shaped probability regions. The radius of these spherical regions increases with increasing principal quantum number, n. Again, each of these orbitals can contain a maximum of 2 electrons. z p - orbitals - these can only be present if the principal quantum number is 2 or greater. There are 3 different types of p orbitals, designated px, py, and pz. These are approximately peanut shaped orbitals, with the axis oriented vertically (pz ) and horizontally (px & py). Since 2 electrons can occur in each of the different p orbitals, a maximum of 6 electrons Page 3 of 14Crystal Chemistry9/22/2014http://www.tulane.edu/~sanelson/eens211/crystal_chemistry.htmare associated with p-orbitals in each principal shell.z d - orbitals - These can only be present if the principal quantum number is 3 or greater. There are 5 different probability regions of d orbitals. These are seen in the drawings below, and are designated dz2, dx2- y2, dxy, dyz, and dxz. Since 2 electrons can occur in each of the different d orbitals, a maximum of 10 electrons can occur in d-orbitals for each principal shell.z f - orbitals - these are more difficult to describe in a graphical sense, but it turns out there are 7 possible f -orbitals, each being able to contain 2 electrons, for a maximum total of 14 electrons. Only shells with principal quantum numbers of 5 or greater can contain f -orbital electrons. The Pauli Exclusion Principal states that no 2 electrons in an atom can have the same quantum numbers, thus each of the sub-orbitals described above can have a maximum of 2 electrons, and each of these will have opposite values of the spin quantum number. As the atomic number (number of protons) in an atom increases, the shells and sub-shells with lower energy are filled first. The drawing at the right illustrates qualitatively the energy relationships between the various shells and sub-shells of atoms. Thus 1s sub-shells with the lowest energy are filled first. These are followed by 2s orbitals, then 2p orbitals. As the principal quantum number increases to 3, the 3s, 3p, and 3d orbitals are filled. But, beginning with n = 4, there is overlap between the energies of s and d orbitals, and thus