Crystal Morphology Growth of crystal is affected by the conditions and matrix from which they grow That one face grows quicker than another is generally determined by differences in atomic density along a crystal face Internal order the same here however Why did we go through all this Lattice types and space groups are important in describing the arrangement of atoms in space These arrangements result in planes of atoms which are spaced at defined intervals controlled by the mineral structure which is described by crystallography They describe possible planes in crystalline structures where ions are aligned Light and high energy particles interact with those planes which yield powerful diagnostic tools How does that translate to what we see Internal order creates changes in planar spacings for different atomic arrangements What can we use to see these planar spacings X rays Another part of the electromagnetic spectrum between 100 and 0 2 Planck s law E h hc Where is frequency is wavelength h is Planck s constant and c is the speed of light X ray generation X rays are generated by striking a target material with an accelerated e which causes an excitation When his excitation relaxes or goes back down to standard state an X ray is emitted Usually given in terms of the energy levels those ecome from and go to different levels yield X rays of different energies all dependent on the material K L M shells of a material from that those shells have different transitions and characteristic relaxations Cu K is the most intense peak and most commonly used though others are possible and have a different wavelength which can be useful X Ray interaction Scattering oscillation of incoming X rays transfer energy to electrons in material emitting secondary radiation at about the same frequency and energy as the incoming beam Interaction of X rays with same material causes some electrons to go into an excited state which upon relaxation emits radiation characteristic of the atom it excited basis for XRF used to identify chemical makeup of materials As with other interactions with minerals there can also be reflection and transmission of X rays depending on thickness but we don t typically use that information Interference Constructive and destructive interference wave properties interact to either cancel out or amplify each other When 2 centers are emitting energy at some wavelength they will interfere with each other Plane view Experiment Relationship between light as particles vs light as waves Light scattered by mesh as it travels and interacts some waves compliment each other while different waves cancel each other Diffraction Combine elements of interference with striking the x ray at an angle to the material Relationship between wavelength atomic spacing and angle of diffraction for 3 D structures derived by von Laue Bragg s determined that you could simplify this and treat it as a reflection off of the planes within an atom Bragg s Law n 2dsin Where n is the order of diffraction always an integer is the wavelength of incident radiation d is the spacing between planes and is the angle of incidence or angle of reflection they are equal Diffraction Relationship between diffraction and wavelength The smaller the diffracting object the greater the angular spacing of the diffraction pattern i e the smaller the separation between planes the wider the spacing between diffraction lines What then is diffraction The failure of light to travel in straight lines much to Newton s dismay Young s 2 slit experiment proved light could bend scattered and affected by constructive and destructive interference Bright red constructive dark destructive Bragg s Law n 2dsin Where n is the order of diffraction always an integer is the wavelength of incident radiation d is the spacing between planes and is the angle of incidence or angle of reflection they are equal Diffraction here is between parallel planes of atoms the space between them d determines the angle of diffraction Looking at the laser pattern again where is Bragg s Law satisfied and how many orders of diffraction do we see Red Laser analogue We see orders of diffraction resulting from light coming between grid spacing 2 3 4 5 etc apart In a mineral multiple parallel planes yields similar patterns at higher orders of diffraction theoretically the angle keeps increasing what do we notice about the intensity though These 2 constructively Interfere good signal d Bragg s Law These 2 destructively Interfere bad signal d n 2dsin Just needs some satisfaction
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