3. Crystallography تار ا
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ارات Crystallography .3 The study of crystalline solids and the principles that govern their growth, external shape, and internal structure تاار د ا اﺏار اةا ( ر أاو تار) ،ا ﺏ داائ ﺕ : ا – ا را – اﺥاآا . Crystal – a solid bounded by geometrically-arranged smooth faces ف اة ر وأ د ( ر ء ان ) و ا ذ اااي ر ﺱ. ا ار ن اة ددو أورا :Perfection of crystal face development ﻡ ر ﺏوأEuhedral – perfect crystal faces ﺕﻡا نو رةد ﺏ وأSubhedral – imperfectly developed crystal faces او ( ﺕان ر )ﺏووأ أ Anhedral – no crystal faces •External Crystal Form (Morphology) وه ﺕف ﺏ لﺵﺏ نﻥا ار اي ا وﺵ اأرة راأو ا ودﻡةﺏ رةﻡا، .ودة وا (Faces): رة ا ﺕرياو ة اﺕ رار ا راااا ﺕوﻥ ﺥ (crystallization) ﻡ ﻡ ﺏ ﺕآات ﺹ ﻡ و وف ﻡ (ﺥودرة واطرتﺡ ﻡ). اﺡف (Edge): ه ﺡا راا وء ﻥ ﺕ اا رة .اف واا ا (Interfacial Angles): ه اوا ﺏاﺥ ارة راا ء وﺕ انﻥ ا . و و س او ف أوﻡس ا اﺏمﻡ ﺏ ا ا ﻥﻡ ﺏ(Contact Goniometer) ا وا ا(Interfacial Angles): و ا ا ويأ ر واا اه ور، ور ا دا رةو ااا آ ارة ا واا و أ، ا ااو ا .ارة س ااو ﺏ ا ﺏام ﻡ اس (Contact Goniometer) Steno’s Law of Interfacial Angles اا وﺏن ﻥ • Angles between adjacent crystal faces will be constant, regardless of crystal shape and size. • ﺕن اوا اﺏ ،ﺏﺹ ا راﺏا و أو ﺡرة اﺵ . أﻥ ﻡل ﻡن اارﺕ: Internal Atomic Arrangement اﺕ اري ا ﺡا د ﺵﺕاﺏ وﺥف اا ا (X-ray diffraction-XRD) وا ﺕ ادن ﺏ ا. ﺥته ﻥ وا ١٤ ﻥع ﻡ ا ار ( وه اﻥذج ﺹات اد ) رذﺕاو ٣٢ ، وﻥ ﻡ ذ٢٣٠ ﻡ ا. - determined from X-ray diffraction - 14 lattice types (Bravais lattices) - Combination of 32 point groups and 14 lattice types yields 230 space groups the general external : ا ار Crystal Habit shape of a crystal (e.g., prismatic, cubic, bladed...) refers to a group of : ا اري Crystal Form faces which have the same relation to the elements of symmetry. open closed form form Note: Crystals with higher degrees of symmetry .tend to generate more form faces ( ا ) ا ار وﻥ ارة Crystal Habit and Crystal Growth را : ا انﻡ ادات ﺏ رﻥﻥ ( فﺏ ﻡ ه و ريا )ةل ﺵداﻡ هور الﺵ ا،ﺕ . ﺵ ﺡ و واتاا ر: Geode – A rock with a hollow, roughly spherical, interior with concentric bands of mineral (usually agate) on the wall and possibly crystals on the interior surface, pointing inwards. Geode, with quartz and calcite crystals, 8cm across, Mexico Blocky or Equant – Roughly box-like or ball-like, as in pyrite and garnet. Rhodolite garnet, 8 cm across, Brazil Tabular - Shaped like a pad of paper (thin tabular) or a deck of playing cards (thick tabular). Barite 4cm across, Bolivia Prismatic – Elongated with opposite faces parallel to one another, in which case they may be short and stout, or long and thin. Includes minerals such as quartz and tourmaline crystals Tourmaline (elbaite) 9 cm tall, California Bladed - Long thin crystals may be flattened like the blade of a knife. Stibnite, 5cm across, Romania Acicular – Needle-like Millerite, 1.5cm. long, Wisconsin Filiform or Capillary – Like hair or thread Pyrite filament 0.2 mm long, New Mexico Divergent or Radiating - Growing outward from a point in sprays or starbursts, such as some hemimorphite exhibits. Adamite 3.5 cm across,Mexico Reticulated – Interconnected like a lattice or trellis, such as rutile and cerussite. Cerussite, Tsumeb, Namibia 2 cm across Dendritic or Arborescent - Slender divergent branch- or fern-like clusters, such as some native silver and native copper crystals Copper, Michigan, 4cm tall Botryoidal – Globular or ball-like clusters – like a bunch of grapes. Hematite, 2cm across, Wisconsin Mammillary – Large rounded masses resembling human breasts. Quartz variety chalcedony, 4cm across, Nebraska Reniform – Radiating compact clusters of crystals ending in rounded, kidney-like, surfaces, such as hematite often exhibits. Hematite 6 cm across, Wisconsin Plumose – Feather-like sprays of fine scales, similar to dendritic but with a much finer structure, such as one form of native silver. Manganese oxide dendrites, New Mexico 6 cm across Oolitic – Masses of small round spheres about the size of fish eggs (0.25-2.0mm). Larger is called “pisolitic” Manganese oxide, 3cm across, Australia Banded – Showing different bands or layers of color or texture, as in some agates or some fluorite. Goethite, 8 cm tall, Wisconsin Fibrous – Aggregates of parallel or radiating slender fibers, such as chrysotile. Chrysotile External Symmetry Elements ﺹ اس ار Rotation Reflection Center of Symmetry Rotation with Inversion Reflection Rotation Center of Symmetry Rotation with _ Inversion note 2 = m اﺵل ار Crystal Forms Anthophyllite Quartz Pyrite NaCl Closed forms & open forms اﺵل ا واﺵل اﺡ Any group of crystal faces related by the same symmetry is called a form . There are 47 or 48 crystal forms depending on the classification used. Closed forms are those groups of faces all related by symmetry that completely enclose a volume of space. It is possible for a crystal to have entirely faces of one closed form. Open forms are those groups of faces all related by symmetry that do not completely enclose a volume of space. A crystal with open form faces requires additional faces as well. There are 17 or 18 open forms and 30 closed forms. Closed forms from the Cubic system _____________________________ Closed forms from the Tetragonal, Trigonal & Hexagonal systems Low Symmetry Forms Pyramids and Dipyramids Prisms Trapezohedron, Scalehedron, Rhombehedron, Disphenoid Isometric Forms Isometric Crystal System • Axes equal length, 90º • If first number is four 3 4-fold axes (432, 43m, 4/m32/m) || axes • If first number 2, three 2-fold axes (23, 2/m3) || axes Hexagonal Crystal System • 1 long or short axis (c), 90º to 3 axes of equal length (a1, a 2, a3), 120º to each other • c aligned with A 6 or A 3; a1, a 2, a 3 are aligned parallel to A2 or m planes or arbitrary (3, 3, 6, 6) Tetragonal Crystal System • 1 long or short axis (c), two axes of equal length ( a1, a 2); all axes 90º to each other • c aligned with A 4; a1 and a 2 are aligned parallel to A2 or m planes or arbitrary (4, 4) Orthorhombic Crystal System • three axes of unequal length ( a, b, c ); all axes 90º to each other • axes aligned parallel to A 2; for mm2, c aligned parallel with A 2, a & b normal to m planes Monoclinic Crystal System • three axes of unequal length ( a, b, c ); β ≠ 90º, α=γ= 90º, • b axis is parallel to A 2 (2, 2/m) or normal to mirror (m); a and c axes normal to b and normal to crystal faces or edges Triclinic Crystal System • three axes of unequal length ( a, b, c ); α ≠ β ≠ γ ≠ 90º • a, b, & c axes normal to crystal faces or edges Numerical Notation for Crystal Planes and Faces •relative values, not absolute distances •units defined by largest face cutting all three axes – Unit Face Unit Face Crystal Face Intercepts 1c UNIT FACE 2/3 c 1/3 c 1b 2b 3b Miller Indices Invert intercept values and clear fractions Law of Rational Indices – common faces have simple whole numbers for Miller Indices Negative Indices Crystal Face Intercepts 1c UNIT FACE 2/3 c 1/3 c Miller Indices 1b 2b 3b (1/1,1/1,1/1) = 111 (1/2,1/2,3/2) = 113 or 1a, 1b, 1/3c or 3a, 3b, 1c (1/1,1/1,3/1) = 113 (1/3,1/3,1/1) = 113 Miller Indices in Hexagonal System Crystal Zone and Zone Axis ZoneZone [100][100] ZoneZone [001][001] Zone [100] axis Zone [001] axis Faces m’,a,m and b intersect in lines parallel to [001], normal to (001) face c.