Isometric tetragonal system

isometric system tetragonal system cubic system Crystallography

1. Isometric & tetragonal system - Ujjaval Patel DEPARTMENT OF EARTH SCIENCE GEL 407

2. outline Introduction about crystal system Introduction of Isometric system Introduction of Isometric division Classes of Isometric division Form of each classes 2 ISOMETRIC SYSTEM & TETRAGONAL SYSTEM Introduction of Tetragonal system Introduction of Tetragonal division Classes of Tetragonal division Form of each classes

3. Definition of Crystal A Crystal is the regular polyhedral form bounded by smooth surfaces which is assumed by a chemical compound under the action of its internal atomic forces when passing under suitable conditions from the state of the liquid or gas to that of a solid. There are mainly six system in the crystallography which are as follow- Isometric System Tetragonal System Hexagonal System Orthorhombic System Trigonal system Monoclinic System Triclinic System 3 ISOMETRIC SYSTEM & TETRAGONAL SYSTEM

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5. Introduction of isometric system Isometric system includes all the crystals which are referred to three equal and mutually perpendicular axes. As the axes are equal, they are interchangeable and hence designated by a 1 , a 2 and a 3 . a 1 is front to back, a 2 is right to left and a 3 is top to bottom axes. 5 a 1 = a 2 = a 3 α = β = γ = 90 o ISOMETRIC SYSTEM & TETRAGONAL SYSTEM

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7. 7 All crystals of the isometric system possess four 3-fold axes of symmetry . Crystals of the isometric system may also demonstrate up to three separate 4-fold axes of rotational symmetry . Furthermore crystals of the isometric system may possess six 2-fold axes of symmetry . Minerals of this system may demonstrate up to nine different mirror planes . There are five crystal classes found in this system: Tetroidal , Diploidal , Hextetrahedral , Gyroidal and Hexoctahedral . Examples of minerals which crystallize in the isometric system are halite, magnetite, and garnet . Tetartohedral Pyritohedral Tetrahedral Plagiohedral Normal ISOMETRIC SYSTEM & TETRAGONAL SYSTEM

8. (1) Normalclass: Galena type Symmetry: 4/m  2/m 3 xl. Ax. 4, 4diagonal Ax. 3, 6 diag. Ax. 2. 3 xl. P, 6 diag. P. Centre Present Seven distinct forms occur in this class. (1) Cube or Hexahedron (100). (2) Dodecahedron or Rhombic dodecahedron (110). (3) Octahedron(111). (4) Tetrahexahedron (210) (310) (410) (hk0). (5) Trapezohedron or Tetragonal trisoctahedron (211) (311) (322) (hll). (6) Trisoctahedron or Trigonaltrisoctahedron (221) (331) (332) (hhl). (7) Hexoctahedron (321) (421) (432) (hkl). Fluorite , Halite, Magnetite, Garnet, Analcite, Spinel, Galena etc. are the minerals crystallizing in this class. 8 ISOMETRIC SYSTEM & TETRAGONAL SYSTEM

9. 2) Pyritohedral class: Pyrite type Symmetry:2/m  3 xl. Ax. 2, 4 diag. Ax. 3. 3 xl. P. Centre Present Seven forms occur of which two are unique. ( 1) Cube (100). ( 2) Dodecahedron (110). ( 3) Octahedron(111). ( 4) Pyritohedron - pentagonal dodecahedron (210) (hk0) (Developed from the alternate faces of Tetrahexahedron, so +ve and –ve). ( 5) Trapezohedron (211) (hll). ( 6) Trisoctahedron (221) (hhl). ( 7) Diploid (321) (231) (hkl) (Developed from the alternate faces of hexoctahedron, so +ve and –ve). Pyrite is a mineral crystallizing in this class. 9 ISOMETRIC SYSTEM & TETRAGONAL SYSTEM

10. (3) Tetrahedral class: Tetrahedrite type Symmetry:  3 m 3 xl. Ax. 2, 4 diagonal Ax. 3. 6 diagonal P. Forms : (1) Cube (100). (2) Dodecahedron (110). (3) Tetrahedron (111) (1 ī 1) (hhh) (Developed from the alternate octants of Octahedron, so +ve and –ve). (4) Tetrahexahedron (210). (5) Tristetrahedron or Trigonaltristetrahedron (211) (2 ī 1) (hll). (6) Deltoiddodecahedron or Tetragonal tristetrahedron (221) (221) (hhl). (7) Hexatetrahedron (321) (321) (hkl). Tetrahedrite, Sphellerite and Boracite are the minerals crystallizing in this class. 10 ISOMETRIC SYSTEM & TETRAGONAL SYSTEM

11. (4) Plagiohedral or Gyroidal class: Cuprite type (4) Plagiohedral or Gyroidal class: Cuprite type: Symmetry: 4 3 2 3 xl. Ax. 4, 4 diagonal Ax. 3, 6 diag. Ax. 2. Seven distinct forms occur in this class. (1) Cube or Hexahedron (100). (2) Dodecahedron or Rhombic dodecahedron (110). (3) Octahedron(111). (4) Tetrahexahedron (210) (310) (410) (hk0). (5) Trapezohedron or Tetragonal trisoctahedron (211) (311) (322) (hll). (6) Trisoctahedron or Trigonaltrisoctahedron (221) (331) (332) (hhl). (7) Pentagonal icositetrahedron ( Icosi means 20). Right handed (312) and Left handed (321). This class is rare among the minerals. It is represented by cuprite and Sal ammoniac. 11 ISOMETRIC SYSTEM & TETRAGONAL SYSTEM

12. (5) Tetartohedral Class: Ullamannite type Symmetry : 2 3 3 xl. Ax. 2, 4 diag. Ax. 3 . Forms: (1) Cube (100). (2) Rhombdodecahedron (110). (3) Tetrahedron (111). (4) Pyritohedron (210) (hk0) (Developed from the alternate faces of Tetrahexahedron, so +ve and –ve). (5) Tristetrahedron (211) (hll). (6) Deltoiddodecahedron (221) (hhl). (7) Tetrahedral pentagonal dodecahedron (321) derived from hexoctahedron, one quarter of the faces and hence four types, Right handed +ve& -ve. Left handed +ve&-ve. 12 ISOMETRIC SYSTEM & TETRAGONAL SYSTEM

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14. 14 Introduction of tetragonal system ● Tetragonal system includes all crystals which are referred to three mutually perpendicular axes. Two horizontal planes are equal and interchangeable. They are called a1 and a2. The third is the vertical or C axis and it may be shorter or longer than the horizontal axes. Length of a C axis is referred to the unit length of axes. ISOMETRIC SYSTEM & TETRAGONAL SYSTEM

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16. 16 Minerals of the Tetragonal System all possess a single 4-fold symmetry axis . They may possess up to four 2-fold axes of rotation , a center of inversion , and up to five mirror planes . There are seven crystal classes found in this system: Disphenoidal , Pyramidal, Dipyramidal , Scalenohedral , Ditetragonal pyramidal , T rapezohedral and Ditetragonal-Dipyramidal . Some examples of minerals that crystallize in this system include Common minerals that occur with this symmetry are anatase, cassiterite, apophyllite, zircon, and vesuvianite. Tetartohedral Pyramidal hemimorphic Tripyramidal Sphenoidal Hemimorphic Trapezohedral Normal ISOMETRIC SYSTEM & TETRAGONAL SYSTEM

17. (1) Normal class: Zircon type: Symmetry : 4/m 2/m 2/m 1 verti. Ax. 4, 4 hori. Ax. 2. 1 hori. P, 4 verti . P. C. Forms: Various possible forms under the normal class of this system are as follows: (1) Base or Basal pinacoid (001). (2) 1 st order prism (110). (3) 2 nd order prism (100). (4) Ditetragonal prism (210) (310) (320) (hk0). (5) 1 st order bipyramid (111) (221) (223) (hhl). (6) 2 nd order bipyramid (101) (201) (203) (h0l). (7) Ditetragonalbipyramid (321) (421) (122) (hkl). Minerals crystallizing in normal class are Zircon, Rutile, Vesuvianite, Cassiterite, Apophyllite, Octahedrite. 17 ISOMETRIC SYSTEM & TETRAGONAL SYSTEM

18. (2) Hemimorphic class: Iodosuccinimide type: Symmetry : 4 mm 1 verti . Ax. 4, 4 verti . P . This class differs from the normal class in having no horizontal axes or plane of symmetry hence the forms are hemimorphic. It is not known to be represented among minerals but it shown on the crystal of Iodosuccinimide. Forms: (1) Basal plane or pedion (001) & (00 ī). (2) 1 st order prism (110). (3) 2 nd order prism (100). (4) Ditetragonal prism (210) (310) (320) (hk0). (5) 1 st order pyramid upp . (111), Lr . (11 ī). (6) 2 nd order pyramid upp . (101), Lr . (10 ī). (7) Ditetragonal pyramid upp . (321), Lr . (32 ī). 18 ISOMETRIC SYSTEM & TETRAGONAL SYSTEM

19. (4) Tripyramidal hemimorphic class: Wulfenite type: Symmetry: 4 1 verti . Ax. 4.   This class is similar to tripyramidal class having the same symmetry axis but no horizontal plane of symmetry hence the forms are hemimorphic. Forms: (1) Basal plane or Pedion (001) or (00 ī). (2) 1 st order prism (110). (3) 2 nd order prism (100). (4) 3 rd order prism Rh. (120), Lt. (210). (5) 1 st order pyramid upp . (111), Lr . (11 ī). (6) 2 nd order pyramid upp . (101), Lr . (10 ī). (7) 3 rd order pyramid upp . Rh. (122), upp . Lt. (212), Lr . Rh. (122), Lr . Lt. (212). Wulfenite is the mineral crystallizing in this class. 19 ISOMETRIC SYSTEM & TETRAGONAL SYSTEM

20. (5) Sphenoidal class: Chalcopyrite type: Symmetry:  2 m 3 xl. Ax. 2 2 verti . Diag. P.   The typical forms of this are sphenoid and the tetragonal scalenohedron. FORMS: (1) Basal pinacoid (001). (2) 1 st order prism (110). (3) 2 nd order prism (100). (4) Ditetragonal prism (210). (5) Tetragonal sphenoid +ve (111), -ve (1 ī 1). (6) Bipyramid of 2 nd order (101). (7) Tetragonal scalenohedron +ve (212), –ve (2 ī 2). Chalcopyrite is a mineral crystallizing in this class. 20 ISOMETRIC SYSTEM & TETRAGONAL SYSTEM

21. (6) Trapezohedral class: Nickel sulphate type: Symmetry : 4 2 2 1 verti . Ax. 4, 4 hori . Ax. 2.   Characteristic form Tetragonal Trapezohedron is derived from the ditetragonal bipyramid of the normal class by the extension of the alternate faces. Therefore two types + ve or right handed and –ve or left handed. FORMS: Tetragonal Trapezohedron +ve or Rh. (212) and –ve or Lh . (122). Nickel Sulphate and few other artificial salts belong to this class. 21 ISOMETRIC SYSTEM & TETRAGONAL SYSTEM

22. (7) Tetartohedral class: 2CaOAl 2 O 3 SiO 2 type: Symmetry:  1 verti . Ax. 2 .   Forms: (1) Basal pinacoid (001). (2) 1 st order prism (110). (3) 2 nd order prism (100). (4) 3 rd order prism Rh. (120), Lt. (210). (5) 1 st order sphenoid +ve (111), -ve (1 ī 1). (6) 2 nd order sphenoid Rh. or +ve, Lt. or -ve. (7) 3 rd order sphenoid Rh. +ve (122), Rh. –ve (ī 22), Lt. +ve (212), Lt. –ve (2 ī 2). 22 ISOMETRIC SYSTEM & TETRAGONAL SYSTEM

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27. reference A TEXTBOOK OF MINERALOGY BY: EDWARD SALISBURY DANA ISOMETRIC SYSTEM & TETRAGONAL SYSTEM 27

28. ISOMETRIC SYSTEM & TETRAGONAL SYSTEM 28 #FRIDAY_FUN_FACTS