Signature Redacted Signature of Author: Department of Chemical Engineering January 1976 Signature Redacted Certified By: Adel F

Total Page:16

File Type:pdf, Size:1020Kb

Signature Redacted Signature of Author: Department of Chemical Engineering January 1976 Signature Redacted Certified By: Adel F THE BEHAVIOR OF ASH IN PULVERIZED COAL UNDER SIMULATED COMBUSTION CONDITIONS by ASHOK S. PADIA B.E. (Hons.), Birla Institute of Technology and Science Pilani, India (1970) S. M., Massachusetts Institute of Technology (1971) Ch.E., Massachusetts Institute of Technology (1973) Submitted in partial fulfillment of the requirements for the degree Doctor of Science at the Massachusetts Institute of Technology January 1976 Signature Redacted Signature of Author: Department of Chemical Engineering January 1976 Signature Redacted Certified by: Adel F. Sarofim, Thesis Supervisor- Signature Redacted J~ck B. Howard, Thesis Supervisor Approved by: Signature Redacted Archives Glenn C. Williams, Thesis Supervisor Chairman, Departmental Committee on Graduate Students MAY 28 1976 2. THE BEHAVIOR OF ASH IN PULVERIZED COAL UNDER SIMULATED COMBUSTION CONDITIONS by ASHOK S. PADIA Submitted to the Department of Chemical Engineering on January 14, 1976 in partial fulfillment of the requirements for the degree of Doctor of Science. ABSTRACT A systematic study of the physical and chemical behavior of mineral matter during rapid combustion of pulverized coal particles was performed by first completely characterizing the distribution of mineral matter in the coal with respect to its composition and particle size distribution, and then oxidizing the coal particles in a preheated drop-tube furnace. Two types of coals, a Montana lignite and a Pittsburgh seam bituminous, pulverized and size graded into two fractions 38-45pm and 75-90pm, were used in the study. In order to obtain the distribution of mineral matter in the original coal, mineral matter was separated from coal samples in its essentially unaltered state by low temperature ashing. Major minerals present in the coals were identified by x-ray diffraction patterns. Examination of the mineral matter under a scanning electron microscope with simultaneous energy dispersive x-ray analysis to obtain elemental composi- tion made it possible to characterize the composition and particle size distribution of the mineral matter in coal. The major minerals in coal consisted of kaolinite [Al2 Si 0 (OH)A] ranging from 1 to 5pm platelets (2.5ym mass median Mie), carbonates and sulfates mainly of calcium of about 2pm mass median size and pyrites [FeS 2 ] about lym mass median size. The overall mass median size of low temperature ash was determined to be about 2pm. The high temperature behavior of mineral matter from both coals was studied in a drop tube furnace operated at tempera- tures up to 1830*K with an oxidizing atmosphere. The particle residence time was about 1 second and the heating rates were of the order of 10 5 *C/second. The weight loss of mineral mat- ter and the particle size distribution of ash were measured as a function of temperature, coal type and coal size. 3. Loss of about 30 percent by weight of the mineral matter at temperatures up to the ASTM ashing temperature (7500 C) can be attributed to the thermal decomposition of kaolinite and carbonates and the oxidation of pyrites. Additional loss of about 25 percent by weight of ASTM ash for lignite and about 6 percent for bituminous was observed when the ash was heated to 1830*K. This additional loss was contributed mainly by CaSO 4 decomposition and some (about 3 percent) silica vapori- zation. These results of thermal decomposition of kaolinite, carbonates and sulfates and oxidation of pyrites are supported by successive diffraction patterns obtained for each sample. Significant effects of combustion conditions (oxidizing or inert) are observed on the weight loss of ash. During heating the individual mineral particles fuse at about 1000-1200 0 K and agglomerate as the carbon burnout pro- gresses. Surface tension forces are high enough to retain the fused ash particle on the burning char surface. If all the mineral matter particles in one coal particle agglomerate without separation from char surface during combustion, this would result in the formation of 1 ash/coal particle. The experimental observationssuggest that about 3 ash particles/ coal particle for lignite and 5 ash particles per coal parti- cle for bituminous coal are produced. Combustion temperature from 1250 to 1830 0 K did not have any noticeable effect on the resulting particle size distribution. The mean particle size of ash produced was proportional to the mean particle size of parent coal particles. Physical observations of burning be- havior of lignite and bituminous coals provide evidence of fragmentation of char particles and formation of hollow spheres (cenospheres) of char in the case of bituminous coals. The formation of more than 1 ash particle per coal particle is consistent with the observed physical behavior of the char during oxidation. Ash also formed cenospheres due to evolution of gas by thermal decomposition. The formation of cenospheres resulted in a distribution of specific gravities of ash ranging from less than 1 to 3.5. The formation of cenospheres is governed by the viscous relaxation of the fused ash and the kinetics of gas evolution. The temperature range in which cenospheres were formed could be explained by use of a simple theoretical model. Some experiments performed with silica and carbon in inert atmosphere up to 2250*K temperature showed that SiC formed at high temperatures. Silica also seemed to volatilize in the form of more volatile SiO which disproportionates into SiO 2 and Si. Condensation products about 0.5pm in size, probably due to disproportionation of SiO, were observed on the cooler portions of the furnace. 4. The implications of the above findings to ash vaporization and heat transfer pertinent to MHD combustors are also outlined. Recommendations have been made for further work. Thesis Supervisors and Titles: Professor Adel F. Sarofim, Professor of Chemical Engineering Professor Jack B. Howard, Professor of Chemical Engineering Professor Glenn C. Williams, Professor of Chemical Engineering 5. Department of Chemical Engineering Massachusetts Institute of Technology Cambridge, Massachusetts 02139 January 1976 Professor Irving Kaplan Secretary of the Faculty Massachusetts Institute of Technology Cambridge, Massachusetts 02139 Dear Professor Kaplan: In accordance with the regulations of the faculty, I herewith submit a thesis entitled "The Behavior of Ash in Pulverized Coal under Simulated Combustion Conditions", in partial fulfillment of the requirements for the degree of Doctor of Science in Chemical Engineering at the Massachusetts Institute of Technology. Respectfully submitted, Signature Redacted Ashok S. Padia 6. ACKNOWLEDGEMENTS I wish to express my deepest gratitude to my thesis supervisors, Professor A.F.Sarofim, Professor J.B.Howard and Professor G.C.Williams. Their invaluable contribu- tions and continued encouragement are most appreciated. Thanks are also due to Professor J.F.Elliott and Profes- sor H.C.Hottel for their valuable comments and suggestions during committee meetings. The Office of Coal Research made funds available for this research. Their support is gratefully acknowledged. Professor J. P. Longwell first introduced me to low temperature ashing technique, for which I am extremely grateful. Thanks are due to Professor C. Hamrin of the University of Kentucky for providing me with low tempera- ture ash samples of our coals and due to LFE Corporation, Waltham, Massachusetts, for letting me use their low temperature asher. I am grateful also to Professor R.E. Ogilvie, Dr. Kaplesh Kumar and Joe Adario of the Depart- ment of Metallurgy for their assistance on x-ray diffrac- tion studies. Leonard Suddenfield and Dr. Allen Parks are acknowledged for their assistance in scanning electron microscopy and electron microprobing, respectively. Thermosystem Incorporation demonstrated their laser doppler anemometer which made it possible to measure particle velocities. Their courtesy is sincerely appreciated. 7. I am extremely grateful to my colleague Hisashi Kobayashi for his assistance and superb cooperation during the whole thesis. Group efforts with Hisashi Kobayashi, John H.Pohl and Jerry Mandel during experimental investigations were en- joyable and fruitful. Robert Sherry provided assistance in atomic absorption spectroscopy, his help is kindly noted. Discussion and associations with Dr. Benno L. Wersborg, Dr. Sanjay Amin, Dr. Parvez Wadia, Dr. J. Shukla, Franklin Wong, Dr. Reggie Mitchell et al were most helpful and rewarding. Stanley R. Mitchell is to be thanked for his many technical suggestions and his efforts in the preparation of this manuscript. Sincere thanks are extended to Mrs. Elenore D. Kehoe for the excellent typing of my thesis. I am most indebted to my parents and parents-in-law for their continuous confidence and support throughout my studies. Finally, my deepest praise is for my wife, Usha, whose patience, understanding and encouragement were an immeasurable support. Not only did she spend considerable time performing particle size analyses, but provided me the love, affection and encouragement during difficult times. 8. Dedicated to my family 9. TABLE OF CONTENTS Page CHAPTER 1 SUMMARY 23 1.1 Introduction 23 1.1.1 Background and Motivation 23 1.1.2 Previous Studies 24 1.1.3 Method of Approach 25 1.2 Apparatus and Procedure 26 1.2.1 Mineral Matter Characterization 26 1.2.2 Drop-tube Furnace 26 1.2.3 Crucible Experiments 28 1.2.4 Analysis 30 1.2.5 Coals Studied 30 1.3 Results 31 1.3.1 Characterization of Mineral Matter in Pulverized Coal 31 1.3.2 Chemical Transformations 41 1.3.3 Physical Transformations
Recommended publications
  • The Conway Space-Filling
    Symmetry: Art and Science Buenos Aires Congress, 2007 THE CONWAY SPACE-FILLING MICHAEL LONGUET-HIGGINS Name: Michael S. Longuet-Higgins, Mathematician and Oceanographer, (b. Lenham, England, 1925). Address: Institute for Nonlinear Science, University of California San Diego, 9500 Gilman Drive, La Jolla, CA 92037-0402, U.S.A. Email: [email protected] Fields of interest: Fluid dynamics, ocean waves and currents, geophysics, underwater sound, projective geometry, polyhedra, mathematical toys. Awards: Rayleigh Prize for Mathematics, Cambridge University, 1950; Hon.D. Tech., Technical University of Denmark, 1979; Hon. LL.D., University of Glasgow, Scotland, 1979; Fellow of the American Geophysical Union, 1981; Sverdrup Gold Medal of the American Meteorological Society, 1983; International Coastal Engineering Award of the American Society of Civil Engineers, 1984; Oceanography Award of the Society for Underwater Technology, 1990; Honorary Fellow of the Acoustical Society of America, 2002. Publications: “Uniform polyhedra” (with H.S.M. Coxeter and J.C.P. Miller (1954). Phil. Trans. R. Soc. Lond. A 246, 401-450. “Some Mathematical Toys” (film), (1963). British Association Meeting, Aberdeen, Scotland; “Clifford’s chain and its analogues, in relation to the higher polytopes,” (1972). Proc. R. Soc. Lond. A 330, 443-466. “Inversive properties of the plane n-line, and a symmetric figure of 2x5 points on a quadric,” (1976). J. Lond. Math. Soc. 12, 206-212; Part II (with C.F. Parry) (1979) J. Lond. Math. Soc. 19, 541-560; “Nested triacontahedral shells, or How to grow a quasi-crystal,” (2003) Math. Intelligencer 25, 25-43. Abstract: A remarkable new space-filling, with an unusual symmetry, was recently discovered by John H.
    [Show full text]
  • Mini Set 1 Activities
    Mini Set 1 Activities Geometiles® is a product of TM www.geometiles.com Welcome to Geometiles®! Your Mini Set 1 contains 20 equilateral triangles and 12 regular pentagons. This booklet contains some problems and brainteasers for you to try. The puzzles are all at different levels, so there’s something for everyone. Puzzle 1 Make an equilateral triangle that is 1/9 yellow, 1/3 green and 5/9 purple. Now make an equilateral triangle that is 1/4 purple, 1/4 green, 3/16 orange and 5/16 yellow. Notes: In these problems, the student must first realize that he needs 9 and 16 triangles, respectively, to make each figure. (A multiple of 9 or 16 would also work, but this impossible due to the size of the set) Puzzle 2 Make a closed object out of all the 12 pentagons in your box such that any two adjacent tiles have different colors. Puzzle 3 Build a closed solid having 6 rhombic faces Hints: You can make a rhombus by joining two equilateral triangles. Think “stretched out cube”. Just as a cube is made of 6 square faces, with three faces joining at each corner, so too will your solid. The difference is that in your solid, the faces will be rhombic instead of square. Puzzle 4 A solid is strictly convex if a line segment joining any two of its points is entirely contained inside the solid (not on its surface or outside it). Note that a strictly convex solid may not have any coplanar faces. Here are some examples of solids that are NOT strictly convex.
    [Show full text]
  • Rhombohedra Everywhere
    Rhombohedra Everywhere Jen‐chung Chuan [email protected] National Tsing Hua University, Taiwan Abstract A rhombohedron is a 6-face polyhedron in which all faces are rhombi. The cube is the best-known example of the rhombohedron. We intend to show that other less-known rhombohedra are also abundant. We are to show how the rhombohedra appear in the algorithm of rhombic polyhedral dissections, in designing 3D linkages and in supplying concrete examples in mathematics amusement. A tongue-twisting jargon: in case all six rhombic faces are congruent, the rhombohedron is known as a trigonal trapezohedron. 1. Minimum Covering for the Deltoidal Icositetrahedron Why choosing deltoidal icositetrahedron? It is known that every convex polyhedron is the intersection of the half spaces defined by the supporting planes. It is not straightforward to find one such 6n-face polyhedron so the supporting planes enclose n rhombohedra exactly. It turns out that the deltoidal icositetrahedron, having 24 congruent “kites” as its faces, fits such requirement. The coloring scheme below shows the possibility of painting the faces with four colors so each edge-adjacent faces shall receive distinct colors: Figures 1(a) and (b) It turns out that each fixed color, say the blue, occupies exactly three pairs of parallel faces. The six supporting planes enclosed the red-edge rhombohedron. This together with green-, yellow- red- edge rhombohedra cover all faces. The rich symmetries possessed by the deltoidal icositetrahedron enables us to visualize the interplay between the dynamic geometry and combinatorial algorithm. Figure 2 2. Minimum Covering for the Rhombic Icosahedron Unlike the deltoidal icositetrahedron, no choice for any collection of six faces of the rhombic icosahedron can have non-overlapping vertices.
    [Show full text]
  • Hexagonal-System.Pdf
    94 CRYSTALLOGRAPHY the indices of the face in question. The indices of a prism face like l(310) can be readily obtained in exactly the same manner as described under the Isometric System, Art. 84. p. 75. 111. HEXAGONAL SYSTEM 119. The HEXAGONALSYSTEM includes all the forms which are referred to four axes, three equal horizontal axes in a common plane intersecting at angles of 60") and a fourth, vertical axis, at right angles to them. Two sections are here included, each embracing a number of distinct classes related among themselves. They are called the Hexagonal Division and the Trigonal (or Rhombohedral) Division. The symmetry of the former, about the vertical axis, belongs to the hexagonal type, that of the latter to the trigonal type. Miller (1852) referred all the forms of the hexagonal system to three equal axes arallel to the faces of the fundamental rhombohedron, and hence intersecting at e ual angr)es, not 90". This method (further explained in Art. 169) had the disadvantage ofyailing to bring out the relationship between the normal hexagonal and tetragonal types, both characterized by a principal axis of symmetry, which (on the system adopted in this book) is the vertical crystallo raphic axis. It further gave different symbols to faces which are crystallo- graphic$y identical. It is more natural to employ the three rhombohedra1 axes for tri- gonal forms only, aa done by Groth (1905), who includes these groups in a Trigonal Syslem; but this also has some disadvantages. The indices commonly used in describing hexagonal forms are known as the Miller-Bravais indices, since the were adopted by Bravais for use with the four axes from the scheme used by Miller in tKe other crystal systems.
    [Show full text]
  • Crystallography J
    All Lectures Crystallography J. Crystal Mathematics 1. Introduction We are all familiar wit h the subdivision of the natural world into th e plant, animal, and mineral kingdoms. Of these the realm of mineral s is the study and resear ch area of mineralogy. A min eralogist uses the word mineral, however, in a much more restricted sense than prevails with common usage. If we examine a rock rather closely, we notiee, for example, tha t a sandstone is composed of individual quartz grains. When we examine a specimen of granite, we ean recog­ inze feldspar, dark mica, and perhaps also hornblende, in addition to quartz. From a specimen of certain ores, galena, ehalcopyrite, and sphalerite all shine forth brilliantly. Any such individual rock constituent is a min eral. Mineralogy encompasses the study of these min erals and the manner in which they oceur , and includ es the properties of all rock materials, which, in the sense used here, embra ce ore and salt deposits, as weIl as ot her useful min eral deposits. Minerals occur as eonstituents of rocks not only in assemblage , but are found also as separate individuals. Frequ ently these have the opportunity to develop without restrietion in eavities or in surrounding media which could yield to their growth. Under these conditions they often develop into polyhedra l form s called crystals. Th ese have from time immemorial attracted the attention of thoughtful natural scientists as weIl as laym en. Earlier all natural bodies with planar external boundaries were called crystals. For exa mple, A. G.
    [Show full text]
  • 10.1. CRYSTALLOGRAPHIC and NONCRYSTALLOGRAPHIC POINT GROUPS Table 10.1.1.2
    International Tables for Crystallography (2006). Vol. A, Section 10.1.2, pp. 763–795. 10.1. CRYSTALLOGRAPHIC AND NONCRYSTALLOGRAPHIC POINT GROUPS Table 10.1.1.2. The 32 three-dimensional crystallographic point groups, arranged according to crystal system (cf. Chapter 2.1) Full Hermann–Mauguin (left) and Schoenflies symbols (right). Dashed lines separate point groups with different Laue classes within one crystal system. Crystal system General Monoclinic (top) symbol Triclinic Orthorhombic (bottom) Tetragonal Trigonal Hexagonal Cubic n 1 C1 2 C2 4 C4 3 C3 6 C6 23 T n 1 Ci m 2 Cs 4 S4 3 C3i 6 3=mC3h –– n=m 2=mC2h 4=mC4h ––6=mC6h 2=m3 Th n22 222 D2 422 D4 32 D3 622 D6 432 O nmm mm2 C2v 4mm C4v 3mC3v 6mm C6v –– n2m ––42mD2d 32=mD3d 62mD3h 43mTd n=m 2=m 2=m 2=m 2=m 2=mD2h 4=m 2=m 2=mD4h ––6=m 2=m 2=mD6h 4=m 32=mOh 10.1.2. Crystallographic point groups the a axis points down the page and the b axis runs horizontally from left to right. For the five trigonal point groups, the c axis is 10.1.2.1. Description of point groups normal to the page only for the description with ‘hexagonal axes’; if In crystallography, point groups usually are described described with ‘rhombohedral axes’, the direction [111] is normal (i) by means of their Hermann–Mauguin or Schoenflies symbols; and the positive a axis slopes towards the observer. The (ii) by means of their stereographic projections; conventional coordinate systems used for the various crystal (iii) by means of the matrix representations of their symmetry systems are listed in Table 2.1.2.1 and illustrated in Figs.
    [Show full text]
  • Fall 1996 Gems & Gemology
    VOLUME XXXII FALL 1996 THE QUARTERLY JOURNAL OF THE GEMOLOGICAL INSTITUTE OF AMERICA - -' ' ii2 -.F..Ñ[. 1 . :'^ . i':..>ib,:, Q*.,:. ;: ,* ; , ,<, ; . i -..,,,, .t , ,:Ah' f I 8 ., * - + ;.<' , . *- . ' ..1 V ' ,: ' i . , : < , ''; > GEMS&'. ,' :, . , -v ,.. r , . .. + , . , ' . ... ..] . <.^ -..t.*' -( ",i ' . ' . ., ALL^ 996;. ,, -, ,GEb.OLOGy.i~.-..,,,>*- VOLUME 32 NO. 3 1 TABL CON 15 3 EDITORIAL Opening Pandora's Black Box Richard T. Liddicoat, Editor-in-Chief LETTERS FEATURE ARTICLES De Beers Natural versus Synthetic Diamon Verification Instruments Christopher M.Welbourn, Martin Cooper, and Paul M. Spear Introduction to Analyzing Internal Growth Structures: Identification of the Negative d Plane in Natural Ruby Christopher P. Smith Russian Flux-Grown Synthetic Alexandrite Karl Schmetzer, Adolf Peretti, Olaf Medenbach, and Heinz-Jvrgen Bernhardt REGULAR FEATURES pg. 176 1996 Challenge Winners Gem Trade Lab Notes Gem News Book Reviews Gemological Abstracts ABOUT THE COVER: Responding to trade concerns about the possible cominer- cia1 availability of cuttable-quality synthetic diamonds, De Beers researchers in pg. 187 Maidenhead, England, have developed two types of machines-the DiamondSure and the DiamondView-to separate natural from synthetic diamonds. These new instruments are the focus of the lead article in this issue, by Christopher Welbourn, Martin Cooper, and Paul Spear. The natural-diamond rings shown here contain round brilliants weighing a total of 5.19 ct (top), 4.38 ct (left),5.36 ct (bottom), and (right)6.78 ct with a 3.49 ct yellow emerald-cut diamond. Courtesy of Hans D. Krieger, Idar-Obatstein, Germany, Photo 0 Harold &> Erica Van Pelt-Photographers, Los Angeles, CA Color separations for Gems & Gemology are by Effective Graphics, Co~npton,CA.
    [Show full text]
  • Geometry of Crystal Lattice
    0 Geometry of Crystal Lattice 0.1 Translational Symmetry The crystalline state of substances is different from other states (gaseous, liquid, amor- phous) in that the atoms are in an ordered and symmetrical arrangement called the crystal lattice. The lattice is characterized by space periodicity or translational sym- metry. In an unbounded crystal we can define three noncoplanar vectors a1, a2, a3, such that displacement of the crystal by the length of any of these vectors brings it back on itself. The unit vectors aα, α = 1, 2, 3 are the shortest vectors by which a crystal can be displaced and be brought back into itself. The crystal lattice is thus a simple three-dimensional network of straight lines whose points of intersection are called the crystal lattice1. If the origin of the co- ordinate system coincides with a site the position vector of any other site is written as 3 = = ( )= =( ) R Rn R n ∑ nαaα, n n1, n2, n3 , (0.1.1) α=1 where nα are integers. The vector R is said to be a translational vector or a transla- tional period of the lattice. According to the definition of translational symmetry, the lattice is brought back onto itself when it is translated along the vector R. We can assign a translation operator to the translation vector R(n).Asetofall possible translations with the given vectors aα forms a discrete group of translations. Since sequential translations can be carried out arbitrarily, a group of transformations is commutative (Abelian). A group of symmetry transformations can be used to ex- plain a number of qualitative physical properties of crystals independently of their specific structure.
    [Show full text]
  • 30 Cubes on a Rhombic Triacontahedron
    Bridges 2010: Mathematics, Music, Art, Architecture, Culture 30 Cubes on a Rhombic Triacontahedron Investigation of Polyhedral Rings and Clusters with the Help of Physical Models and Wolfram Mathematica Sándor Kabai UNICONSTANT Co. 3 Honvéd Budapest HUNGARY 1203 E-mail: [email protected] Abstract A cube is placed on each face of a rhombic triacontahedron (RT). In the cluster of 30 cubes produced in this manner, the cubes are connected at their vertices. With the use of physical models and the computer software Wolfram Mathematica, we study the possible geometrical features and relationships that can be associated with this geometrical sculpture. The purpose of this article is to introduce a method which is suitable for teaching a number of concepts by association to a single object. The Golden Rhombus A method of teaching/learning spatial geometry could be based on a selected object having simple geometrical features. The objective is to associate as much knowledge as possible with the use of simple relationships. Later, the associated concepts can be recollected by thinking of the object and using the simple relationships. Here, the relationship of a golden rhombus and an inscribed square is used. If half of the large diagonal is assumed as unity, then the small diagonal of the rhombus is 2/ φ, and the cube that can be fitted into such a rhombus has an edge length of 2/ φ2, where φ is the golden ratio. The cube edges divide the sides of the golden rhombus in proportion to the golden ratio. If such a cube is placed on each of the 30 faces of a rhombic triacontahedron (RT), then a cluster of 30 cubes is produced, in which the cubes are in contact with their neighbors’ vertices.
    [Show full text]
  • Roo /, Rhombohedra Are Projected in the Same Way: All That Need Be Given Is the Angle VW/~, Which Is the Complement I /I
    62 On some twins of calcite ; and on a simple method of drawing crystals of calcite and other rhombohedral crystals, and of deducing the relations of their symbols. BY W. J. LgwIs, M.A. Professor of ~[ineralogy in the University of Cambridge. [Read January 21, 1908.J 1. Having had occasion recently to draw the twins of calcite, I noticed the advantage of the twin-axes being all placed in the plane of the paper. The representation of the rhombohedron which results from this condition is so unsatisfactory that, obvious as the idea must have been to all crystal draughtsmen, few, if any, seem to have tested the utility of the projection. I desire to point out a few of its advantages. 2. The 9"hombohedron. Fig. 1 shows a rhombohedron in two positions--the upper one being , :a /•,, a plan on the central horizontal (equa- torial) plane, and the lower one an o'o', :/ ,% elevation with the principal axis VW, the polar edge V/~, and the polar diagonal W/~ all in the paper. All roo /, rhombohedra are projected in the same way: all that need be given is the angle VW/~, which is the complement I /I . of the angle made by a face with the I I, j base. Thus, for the fundamental rhom- i ~,.V" I bohedron of calcite, shown in fig. 1 and i [, by interrupted lines in figs. 2 and 8, the angle VV'g is 45 ~ 28.4'. The figure is easily drawn. A ver- tical llne being drawn for the principal axis, three equal lengths, V't', t't, and t F, are marked off on it.
    [Show full text]
  • Another Solution to the Polyhedron in Dürer's Melencolia: a Visual
    AESTHETICS No.13 (2009) The Japanese Society for Aesthetics / 179 Another Solution to the Polyhedron in Dürer’s Melencolia: A Visual Demonstration of the Delian Problem ISHIZU Hideko Seijo University, Tokyo Introduction The engraving Melencolia (1514) (Fig. 1) by Albrecht Dürer (1471-1528) has been inter- preted in various ways, but is not yet completely solved. It is filled with marvelous instru- ments, and among them a large stone polyhedron in the left center has attracted both art historians and scientists, and the efforts to clarify the significance of the polyhedron have been made by both sides. The preliminary sketch of the polyhedron (Fig. 2), which Dürer drew in perspective, indicating the center of vision by an eye, shows all edges of the polyhedron transparently. And each vertex bears a mark. This polyhedron (Fig. 3) has been regarded as a truncated rhombohedron, which consists of 6 rhombuses. Cut off two corners along the planes perpendicular to the line AH, the solid now consists of 6 irregular pentagons and 2 equilateral triangles. One side of the upper trian- gular face and one side of the bottom triangular face are perpendicular to the picture plane. The engraving is also drawn in perspective. Lines that are perpendicular to the picture plane, such as the side cornice of the building and the arm of the balance, converge at the vanishing point on the horizon of the sea. Dürer set the mirror image of the polyhedron of the sketch in such a manner that the vanishing points and horizons of both planes correspond with each other, so that the polyhedron may be regarded as correct in perspective on the engraving.
    [Show full text]
  • A Standardized Japanese Nomenclature for Crystal Forms
    MINERALOGICAL JOURNAL, VOL. 4, No. 4, pp. 291-298, FEB., 1565 A STANDARDIZED JAPANESE NOMENCLATURE FOR CRYSTAL FORMS J. D. H. DONNAY and HIROSHI TAKEDA The Johns Hopkins University, Baltimore, Maryland, U. S. A. with the help of many Japanese crystallographers ABSTRACT The system of the crystal-form names according to the proposal of the Fedorov Institute is explained, and adequate Japanese equivalents are given. Introduction Efforts have been made in the past to standardize the names of the crystal forms. Particularly noteworthy were the proposals of the Fedorov Institute (Boldyrev 1925, 1936) and of Rogers (1935), both of which are modifications of the Groth nomenclature. Recently the Committee on Nomenclature of the French Society of Mineralogy and Crystallography have re-examined the problem (see Donnay and Curien 1959) and have essentially proposed the sys tem of the Fedorov Institute as a basis for possible international agreement. In view of these developments, it was thought that it would be useful to see if the Japanese nomenclature of crystal forms could be adapted to the Federov-Institute system. The present paper first explains the system of form names, and attempts to give adequate Japanese equivalents, for non-cubic and then for cubic forms. Then the English names are listed with syno nyms, together with the various Japanese terms that have been used. When there is more than one Japanese name, they are listed in a tentative order of preference, arrived at after many inquiries and consultations. Finally a key to the crystal forms in the 32 point 292 A Standardized Japanese Nomenclature for Crystal Forms groups is given.
    [Show full text]