5.3. Lattice Systems There Are Multiple Ways to Classify Crystals
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I`mt`qx1/00Lhmdq`knesgdLnmsg9Rbnkdbhsd This month’s mineral, scolecite, is an uncommon zeolite from India. Our write-up explains its origin as a secondary mineral in volcanic host rocks, the difficulty of collecting this fragile mineral, the unusual properties of the zeolite-group minerals, and why mineralogists recently revised the system of zeolite classification and nomenclature. OVERVIEW PHYSICAL PROPERTIES Chemistry: Ca(Al2Si3O10)A3H2O Hydrous Calcium Aluminum Silicate (Hydrous Calcium Aluminosilicate), usually containing some potassium and sodium. Class: Silicates Subclass: Tectosilicates Group: Zeolites Crystal System: Monoclinic Crystal Habits: Usually as radiating sprays or clusters of thin, acicular crystals or Hairlike fibers; crystals are often flattened with tetragonal cross sections, lengthwise striations, and slanted terminations; also massive and fibrous. Twinning common. Color: Usually colorless, white, gray; rarely brown, pink, or yellow. Luster: Vitreous to silky Transparency: Transparent to translucent Streak: White Cleavage: Perfect in one direction Fracture: Uneven, brittle Hardness: 5.0-5.5 Specific Gravity: 2.16-2.40 (average 2.25) Figure 1. Scolecite. Luminescence: Often fluoresces yellow or brown in ultraviolet light. Refractive Index: 1.507-1.521 Distinctive Features and Tests: Best field-identification marks are acicular crystal habit; vitreous-to-silky luster; very low density; and association with other zeolite-group minerals, especially the closely- related minerals natrolite [Na2(Al2Si3O10)A2H2O] and mesolite [Na2Ca2(Al6Si9O30)A8H2O]. Laboratory tests are often needed to distinguish scolecite from other zeolite minerals. Dana Classification Number: 77.1.5.5 NAME The name “scolecite,” pronounced SKO-leh-site, is derived from the German Skolezit, which comes from the Greek sklx, meaning “worm,” an allusion to the tendency of its acicular crystals to curl when heated and dehydrated. -
Types of Lattices
Types of Lattices Types of Lattices Lattices are either: 1. Primitive (or Simple): one lattice point per unit cell. 2. Non-primitive, (or Multiple) e.g. double, triple, etc.: more than one lattice point per unit cell. Double r2 cell r1 r2 Triple r1 cell r2 r1 Primitive cell N + e 4 Ne = number of lattice points on cell edges (shared by 4 cells) •When repeated by successive translations e =edge reproduce periodic pattern. •Multiple cells are usually selected to make obvious the higher symmetry (usually rotational symmetry) that is possessed by the 1 lattice, which may not be immediately evident from primitive cell. Lattice Points- Review 2 Arrangement of Lattice Points 3 Arrangement of Lattice Points (continued) •These are known as the basis vectors, which we will come back to. •These are not translation vectors (R) since they have non- integer values. The complexity of the system depends upon the symmetry requirements (is it lost or maintained?) by applying the symmetry operations (rotation, reflection, inversion and translation). 4 The Five 2-D Bravais Lattices •From the previous definitions of the four 2-D and seven 3-D crystal systems, we know that there are four and seven primitive unit cells (with 1 lattice point/unit cell), respectively. •We can then ask: can we add additional lattice points to the primitive lattices (or nets), in such a way that we still have a lattice (net) belonging to the same crystal system (with symmetry requirements)? •First illustrate this for 2-D nets, where we know that the surroundings of each lattice point must be identical. -
Solid State Chemistry CHEM-E4155 (5 Cr)
Solid State Chemistry CHEM-E4155 (5 cr) Spring 2019 Antti Karttunen Department of Chemistry and Materials Science Aalto University Course outline • Teacher: Antti Karttunen • Lectures – 16 lectures (Mondays and Tuesdays, 12:15-14:00) – Each lecture includes a set of exercises (a MyCourses Quiz) – We start the exercises together during the lecture (deadline: Sunday 23:59) • Project work – We create content in the Aalto Solid State Chemistry Wiki – Includes both independent and collaborative work (peer review) – Lots of content has been created in the Wiki during 2017-2018. • Grading – Exercises 50% – Project work 50% • Workload (135 h) – Lectures, combined with exercises 32 h – Home problem solving 48 h – Independent project work 55 h 2 Honor code for exercises • The purpose of the exercises is to support your learning • Most of the exercises are graded automatically – Some of the more demaning exercises I will grade manually • It is perfectly OK to discuss the exercises with the other students – In fact, I encourage discussion during the exercise sessions • It is not OK to take answers directly from the other students – This also means that is not OK to give answers directly to the other students • The exercise answers and timestamps are being monitored 3 Mondays: 12.15 – 14.00 Course calendar Tuesdays: 12.15 - 14.00 Week Lect. Date Topic 1: Structure 1 25.2. Structure of crystalline materials. X-ray diffraction. Symmetry. 2 26.2. Structural databases, visualization of crystal structures. 2: Bonding 3 4.3. Bonding in solids. Description of crystal structures. 4 5.3. Band theory. Band structures. 3: Synthesis 5 11.3. -
Chapter 4, Bravais Lattice Primitive Vectors
Chapter 4, Bravais Lattice A Bravais lattice is the collection of all (and only those) points in space reachable from the origin with position vectors: n , n , n integer (+, -, or 0) r r r r 1 2 3 R = n1a1 + n2 a2 + n3a3 a1, a2, and a3 not all in same plane The three primitive vectors, a1, a2, and a3, uniquely define a Bravais lattice. However, for one Bravais lattice, there are many choices for the primitive vectors. A Bravais lattice is infinite. It is identical (in every aspect) when viewed from any of its lattice points. This is not a Bravais lattice. Honeycomb: P and Q are equivalent. R is not. A Bravais lattice can be defined as either the collection of lattice points, or the primitive translation vectors which construct the lattice. POINT Q OBJECT: Remember that a Bravais lattice has only points. Points, being dimensionless and isotropic, have full spatial symmetry (invariant under any point symmetry operation). Primitive Vectors There are many choices for the primitive vectors of a Bravais lattice. One sure way to find a set of primitive vectors (as described in Problem 4 .8) is the following: (1) a1 is the vector to a nearest neighbor lattice point. (2) a2 is the vector to a lattice points closest to, but not on, the a1 axis. (3) a3 is the vector to a lattice point nearest, but not on, the a18a2 plane. How does one prove that this is a set of primitive vectors? Hint: there should be no lattice points inside, or on the faces (lll)fhlhd(lllid)fd(parallolegrams) of, the polyhedron (parallelepiped) formed by these three vectors. -
Space Symmetry, Space Groups
Space symmetry, Space groups - Space groups are the product of possible combinations of symmetry operations including translations. - There exist 230 different space groups in 3-dimensional space - Comparing to point groups, space groups have 2 more symmetry operations (table 1). These operations include translations. Therefore they describe not only the lattice but also the crystal structure. Table 1: Additional symmetry operations in space symmetry, their description, symmetry elements and Hermann-Mauguin symbols. symmetry H-M description symmetry element operation symbol screw 1. rotation by 360°/N screw axis NM (Schraubung) 2. translation along the axis (Schraubenachse) 1. reflection across the plane glide glide plane 2. translation parallel to the a,b,c,n,d (Gleitspiegelung) (Gleitspiegelebene) glide plane Glide directions for the different gilde planes: a (b,c): translation along ½ a or ½ b or ½ c, respectively) (with ,, cba = vectors of the unit cell) n: translation e.g. along ½ (a + b) d: translation e.g. along ¼ (a + b), d from diamond, because this glide plane occurs in the diamond structure Screw axis example: 21 (N = 2, M = 1) 1) rotation by 180° (= 360°/2) 2) translation parallel to the axis by ½ unit (M/N) Only 21, (31, 32), (41, 43), 42, (61, 65) (62, 64), 63 screw axes exist in parenthesis: right, left hand screw axis Space group symbol: The space group symbol begins with a capital letter (P: primitive; A, B, C: base centred I, body centred R rhombohedral, F face centred), which represents the Bravais lattice type, followed by the short form of symmetry elements, as known from the point group symbols. -
Apophyllite-(Kf)
December 2013 Mineral of the Month APOPHYLLITE-(KF) Apophyllite-(KF) is a complex mineral with the unusual tendency to “leaf apart” when heated. It is a favorite among collectors because of its extraordinary transparency, bright luster, well- developed crystal habits, and occurrence in composite specimens with various zeolite minerals. OVERVIEW PHYSICAL PROPERTIES Chemistry: KCa4Si8O20(F,OH)·8H20 Basic Hydrous Potassium Calcium Fluorosilicate (Basic Potassium Calcium Silicate Fluoride Hydrate), often containing some sodium and trace amounts of iron and nickel. Class: Silicates Subclass: Phyllosilicates (Sheet Silicates) Group: Apophyllite Crystal System: Tetragonal Crystal Habits: Usually well-formed, cube-like or tabular crystals with rectangular, longitudinally striated prisms, square cross sections, and steep, diamond-shaped, pyramidal termination faces; pseudo-cubic prisms usually have flat terminations with beveled, distinctly triangular corners; also granular, lamellar, and compact. Color: Usually colorless or white; sometimes pale shades of green; occasionally pale shades of yellow, red, blue, or violet. Luster: Vitreous to pearly on crystal faces, pearly on cleavage surfaces with occasional iridescence. Transparency: Transparent to translucent Streak: White Cleavage: Perfect in one direction Fracture: Uneven, brittle. Hardness: 4.5-5.0 Specific Gravity: 2.3-2.4 Luminescence: Often fluoresces pale yellow-green. Refractive Index: 1.535-1.537 Distinctive Features and Tests: Pseudo-cubic crystals with pearly luster on cleavage surfaces; longitudinal striations; and occurrence as a secondary mineral in association with various zeolite minerals. Laboratory analysis is necessary to differentiate apophyllite-(KF) from closely-related apophyllite-(KOH). Can be confused with such zeolite minerals as stilbite-Ca [hydrous calcium sodium potassium aluminum silicate, Ca0.5,K,Na)9(Al9Si27O72)·28H2O], which forms tabular, wheat-sheaf-like, monoclinic crystals. -
Infrare D Transmission Spectra of Carbonate Minerals
Infrare d Transmission Spectra of Carbonate Mineral s THE NATURAL HISTORY MUSEUM Infrare d Transmission Spectra of Carbonate Mineral s G. C. Jones Department of Mineralogy The Natural History Museum London, UK and B. Jackson Department of Geology Royal Museum of Scotland Edinburgh, UK A collaborative project of The Natural History Museum and National Museums of Scotland E3 SPRINGER-SCIENCE+BUSINESS MEDIA, B.V. Firs t editio n 1 993 © 1993 Springer Science+Business Media Dordrecht Originally published by Chapman & Hall in 1993 Softcover reprint of the hardcover 1st edition 1993 Typese t at the Natura l Histor y Museu m ISBN 978-94-010-4940-5 ISBN 978-94-011-2120-0 (eBook) DOI 10.1007/978-94-011-2120-0 Apar t fro m any fair dealin g for the purpose s of researc h or privat e study , or criticis m or review , as permitte d unde r the UK Copyrigh t Design s and Patent s Act , 1988, thi s publicatio n may not be reproduced , stored , or transmitted , in any for m or by any means , withou t the prio r permissio n in writin g of the publishers , or in the case of reprographi c reproductio n onl y in accordanc e wit h the term s of the licence s issue d by the Copyrigh t Licensin g Agenc y in the UK, or in accordanc e wit h the term s of licence s issue d by the appropriat e Reproductio n Right s Organizatio n outsid e the UK. Enquirie s concernin g reproductio n outsid e the term s state d here shoul d be sent to the publisher s at the Londo n addres s printe d on thi s page. -
Crystal Systems and Example Minerals
Basics of Mineralogy Geology 200 Geology for Environmental Scientists Terms to Know: •Atom • Bonding • Molecule – ionic •Proton – covalent •Neutron – metallic • Electron • Isotope •Ion Fig. 3.3 Periodic Table of the Elements Fig 3.4A Ionic Bonding Fig 3.4B Covalent Bonding Figure 3.5 -- The effects of temperature and pressure on the physical state of matter, in this case water. The 6 Crystal Systems • All have 3 axes, except for 4 axes in Hexagonal system • Isometric -- all axes equal length, all angles 90ο • Hexagonal -- 3 of 4 axes equal length, three angles@ 90ο, three @ 120ο • Tetragonal -- two axes equal length, all angles 90ο (not common in rock forming minerals) • Orthorhombic -- all axes unequal length, all angles 90ο • Monoclinic -- all axes unequal length, only two angles are 90ο • Triclinic -- all axes unequal length, no angles @ 90ο Pyrite -- an example of the isometric crystal system: cubes Galena -- an example of the isometric crystal system: cubes Fluorite -- an example of the isometric crystal system, octahedrons, and an example of variation in color Garnet -- an example of the isometric crystal system: dodecahedrons Garnet in schist, a metamorphic rock Large masses of garnet -- a source for commercial abrasives Quartz -- an example of the hexagonal crystal system. Amethyst variety of quartz -- an example of color variation in a mineral. The purple color is caused by small amounts of iron. Agate -- appears to be a noncrystalline variety of quartz but it has microscopic fibrous crystals deposited in layers by ground water. Calcite crystals. Calcite is in the hexagonal crystal system. Tourmaline crystals grown together like this are called “twins”. -
Crystal Structure
Physics 927 E.Y.Tsymbal Section 1: Crystal Structure A solid is said to be a crystal if atoms are arranged in such a way that their positions are exactly periodic. This concept is illustrated in Fig.1 using a two-dimensional (2D) structure. y T C Fig.1 A B a x 1 A perfect crystal maintains this periodicity in both the x and y directions from -∞ to +∞. As follows from this periodicity, the atoms A, B, C, etc. are equivalent. In other words, for an observer located at any of these atomic sites, the crystal appears exactly the same. The same idea can be expressed by saying that a crystal possesses a translational symmetry. The translational symmetry means that if the crystal is translated by any vector joining two atoms, say T in Fig.1, the crystal appears exactly the same as it did before the translation. In other words the crystal remains invariant under any such translation. The structure of all crystals can be described in terms of a lattice, with a group of atoms attached to every lattice point. For example, in the case of structure shown in Fig.1, if we replace each atom by a geometrical point located at the equilibrium position of that atom, we obtain a crystal lattice. The crystal lattice has the same geometrical properties as the crystal, but it is devoid of any physical contents. There are two classes of lattices: the Bravais and the non-Bravais. In a Bravais lattice all lattice points are equivalent and hence by necessity all atoms in the crystal are of the same kind. -
Crystals the Atoms in a Crystal Are Arranged in a Periodic Pattern. A
Crystals The atoms in a crystal are arranged in a periodic pattern. A crystal is made up of unit cells that are repeated at a pattern of points, which is called the Bravais lattice (fig. (1)). The Bravais lattice is basically a three dimensional abstract lattice of points. Figure 1: Unit cell - Bravais lattice - Crystal Unit cell The unit cell is the description of the arrangement of the atoms that get repeated, and is not unique - there are a various possibilities to choose it. The primitive unit cell is the smallest possible pattern to reproduce the crystal and is also not unique. As shown in fig. (2) for 2 dimensions there is a number of options of choosing the primitive unit cell. Nevertheless all have the same area. The same is true in three dimensions (various ways to choose primitive unit cell; same volume). An example for a possible three dimensional primitive unit cell and the formula for calculating the volume can be seen in fig. (2). Figure 2: Illustration of primitive unit cells 1 The conventional unit cell is agreed upon. It is chosen in a way to display the crystal or the crystal symmetries as good as possible. Normally it is easier to imagine things when looking at the conventional unit cell. A few conventional unit cells are displayed in fig. (3). Figure 3: Illustration of conventional unit cells • sc (simple cubic): Conventional and primitive unit cell are identical • fcc (face centered cubic): The conventional unit cell consists of 4 atoms in com- parison to the primitive unit cell which consists of only 1 atom. -
INTERNATIONAL GEMMOLOGICAL CONFERENCE Nantes - France INTERNATIONAL GEMMOLOGICAL August 2019 CONFERENCE Nantes - France August 2019
IGC 2019 - Nantes IGC 2019 INTERNATIONAL GEMMOLOGICAL CONFERENCE Nantes - France INTERNATIONAL GEMMOLOGICAL August 2019 CONFERENCE Nantes - France www.igc-gemmology.org August 2019 36th IGC 2019 – Nantes, France Introduction 36th International Gemmological Conference IGC August 2019 Nantes, France Dear colleagues of IGC, It is our great pleasure and pride to welcome you to the 36th International Gemmological Conference in Nantes, France. Nantes has progressively gained a reputation in the science of gemmology since Prof. Bernard Lasnier created the Diplôme d’Université de Gemmologie (DUG) in the early 1980s. Several DUGs or PhDs have since made a name for themselves in international gemmology. In addition, the town of Nantes has been on several occasions recognized as a very attractive, green town, with a high quality of life. This regional capital is also an important hub for the industry (e.g. agriculture, aeronautics), education and high-tech. It has only recently developed tourism even if has much to offer, with its historical downtown, the beginning of the Loire river estuary, and the ocean close by. The organizers of 36th International Gemmological Conference wish you a pleasant and rewarding conference Dr. Emmanuel Fritsch, Dr. Nathalie Barreau, Féodor Blumentritt MsC. The organizers of the 36th International Gemmological Conference in Nantes, France From left to right Dr. Emmanuel Fritsch, Dr. Nathalie Barreau, Féodor Blumentritt MsC. 3 36th IGC 2019 – Nantes, France Introduction Organization of the 36th International Gemmological Conference Organizing Committee Dr. Emmanuel Fritsch (University of Nantes) Dr. Nathalie Barreau (IMN-CNRS) Feodor Blumentritt Dr. Jayshree Panjikar (IGC Executive Secretary) IGC Executive Committee Excursions Sophie Joubert, Richou, Cholet Hervé Renoux, Richou, Cholet Guest Programme Sophie Joubert, Richou, Cholet Homepage Dr. -
Properties of Minerals for Processing
2 C h a p t e r Properties of Minerals for Processing 2.1 SAMPLING Sampling is a process of obtaining a small portion from a large quantity of a similar material such that, it truly represents the composition of the whole lot. It is an important step before testing of any material in the laboratory. Sampling of homogeneous materials is easy as compared to heterogeneous materials and hence, has to be conducted carefully. It is so because unlike heterogeneous materials, homogeneous materials have a uniform composition. However, almost all metallurgical materials are heterogeneous in nature. 2.1.1 Sampling of Ores/Minerals The process of sampling is complicated because of the following reasons: (1) A large variety of constituents are present in ores and minerals. (2) There is a large variation in the distribution of these constituents throughout the material. (3) In many cases, weight of the sample may vary from, 0.5 to 5 gm or 10 gm. Small fraction from large quantity like 50 to 250 tonnes are not true representative of the entire lot. The size of the sample required for testing depends on the method of testing and the testing machine which is used. However, sampling may involve three operations, namely, crushing and/or grinding, mixing and finally cutting. These operations may be executed repeatedly wherein the quantity of sample can be reduced to a desired weight. Sampling should be based on the relation between maximum particle size and the amount of sample. The size of ore/mineral particles taken for sampling depends on uniformity of composition, i.e., if the composition is more uniform, smaller particle size of the sample is taken and vice versa.