crystallography design

What is a crystal?

If the atoms or ions that compose it are arranged in a regular way (i.e, a crystal has internal order due to the periodic arrangement of atoms in three dimensions) is called crystal.

CRYSTAL HABIT? Crystal habit is a description of the shapes and aggregates that a certain mineral is likely to form. Often this is the most important characteristic to examine when identifying a mineral. Although most minerals do have different forms, they are sometimes quite distinct and common only to one or even just a few minerals. Many collectors strive to collect mineral specimens of certain typical and abnormal habits.

Kinds The Pedion The Pinacoid The Dome The Sphenoid The Prism The Pyramid

The Pedion In a mineral with low symmetry, a pedion is a possible face. It is a flat face that is not parallel or geometrically linked to any other faces. It can be found on the top of prismatic crystals that lack a perpendicular mirror plane or a two fold rotational axes. Elbaite is a mineral known to form a pedion face. The pedion is possible only on minerals that lack symmetry operations parallel to the pedion face and lack a center. ^ The Pinacoid The pinacoid is composed of only two parallel faces.

Pinacoid

Symmetry"Symmetry" refers to sameness. Here are some examples of symmetric patterns of objects to illustrate symmetry!

symmetry

Unit cellThe Unit cell is the basic building block for a crystal. In order to understand this concept, think of the unit cell as being like a brick in a wall (if the wall is built by stacking bricks directly upon one another). The shape of the unit cell is described in terms of the lengths of the cell edges and angles between the cell edges. The unit cell contents are specified in terms of where individual atoms are located within this volume.

unit cell.The basic arrangement of atoms that describes the crystal structure is identified. This is termed the unit cell.

Minerals are classified based on their chemical composition and crystal structure.Mineral Classification

Quartz

SpinelCalcite

Introduction to CrystallographyThe study of crystals and the laws that govern their growth, external shape and internal structure is called crystallography.

A crystal may possess only certain combinations of symmetry elements. Based on their symmetry elements mineral crystals are grouped into 6 crystal systems. Every mineral belongs to one of these crystal classes.

Introduction to CrystallographyMinerals belonging to the same crystal system have the same shaped unit cell.

Introduction to CrystallographyThe Unit Cell is the basic building block for a crystal

The shape of the unit cell is described in terms of the lengths of the cell edges (a, b, c) and the angles between the cell edges (a , b , g)

Two-dimensional projection of the crystal structure for the mineral quartz (Dimensions: ~ 25 20) . The blue spheres represent Si (silicon) atoms and the red spheres represent O (oxygen) atoms. Introduction to CrystallographyThe Unit Cell

Three-dimensional projection of the crystal structure for the mineral quartz (Dimensions: ~ 25 20) . The blue spheres represent Si (silicon) atoms and the red spheres represent O (oxygen) atoms. Introduction to CrystallographyThe Unit Cell

Introduction to CrystallographyThe Unit Cell

QuartzIntroduction to CrystallographySymmetry

Introduction to CrystallographySymmetry

When the faces of a crystal can be arranged in a repetitive and regular pattern around the center of the crystal, the crystal has symmetry.

If you look at crystals closely they will show a repetition, or symmetry, of crystal faces and angles.

These operations are movements of the crystal that, when completed, the crystal will look the same as when you started.


Symmetry Axis of Rotation

1-fold, 2-fold,axis


Reflection Across a Plane

mirror plane


Symmetry Axis of Rotary Inversion

Introduction to CrystallographyThe Six Crystal Stystems

Isometric (cubic)HexagonalTetragonalOrthorhombicMononclinicTriclinic

optically isotropicoptically anisotropicuniaxialbiaxial

MINERALOGYCRYSTAL SYSTEMS

SymmetryMirror Plane = imaginary plane that divides a crystal into halves, each of which is the mirror image of the otherAxis of Rotation = imaginary line through a crystal about which the crystal may be rotated and repeat itself in appearance (1,2,3,4 or 6 times during a complete rotation)

Tips for creating modelsWrite your name on each model BEFORE folding and taping!Cut into the pattern rather than around it. Fold along each face intersection BEFORE taping into place.Have fun learning something new!

IsometricSystem909090ISOMETRIC = = = 90a = b = cc = ab = aaPyrite, Galena,Halite, Fluorite,Garnet, DiamondUnique Symmetry:Four 3-fold axes

TetragonalSystem909090TETRAGONAL = = = 90a = b cc ab = aaWulfenite, Zircon,

Chalcopyrite, RutileUnique Symmetry:One 4-fold axis

HexagonalSystem1209090HEXAGONAL = 120, = = 90a = b cc > aQuartz, Beryl (Emerald),Apatite, Graphite,Corumdum (Ruby, Sapphire)Unique Symmetry:One 6-fold axis

OrthorhombicSystem909090ORTHORHOMBIC

= = = 90a b cc ab aaSulfur, Barite,

Olivine, TopazUnique Symmetry:

Three 2-fold axes

MonoclinicSystem9090MONOCLINIC

= = 90, 90a b cc ab aaOrthoclase,Malachite, Azurite,Gypsum, Mica, TalcUnique Symmetry:One 2-fold axis90

TriclinicSystem90 90TRICLINIC 90a b cc aTurquoise, PlagioclaseKyanite, AlbiteUnique Symmetry:None90b aa

Crystal SystemsSystemAxesAnglesUnique SymmetryDiagramExamples

Isometrica=b=c===90Four 3-foldPyrite, Halite, Galena, Garnet, Diamond, Fluorite

Tetragonala=bc===90One 4-foldWulfenite, Rutile, Zircon, Chalcopyrite

Hexagonala=bc=120, ==90One 6-foldQuartz, Beryl (Emerald), Apatite, Corundum (Ruby, Sapphire)

Orthorhombicabc===90Three 2-foldSulfur, Barite, Olivine, Topaz

Monoclinicabc==90, 90One 2-foldOrthoclase, Malachite, Azurite, Mica, Gypsum, Talc

Triclinicabc90NoneTurquoise, Kyanite, Albite, Plagioclase

Crystal SystemsSystemAxesAnglesUnique SymmetryDiagramExamples

Isometric

Tetragonal

Hexagonal

Orthorhombic

Monoclinic

Triclinic

END

GRADE LEVEL: This lesson is designed for Grade 8. It is suitable for Grades 7-12.

GOAL: The purpose of this lesson is to create a set of manipulatives that will help the student apply geometry, chemistry, physics, and art to the study of minerals and to help students realize the unique aspects of crystal systems on a detailed level.

OBJECTIVE: The student will be able to: define and demonstrate principles of symmetry quantify the differences between the crystal systems recognize the crystal system by its physical characteristics visualize model properties within actual mineral specimens name representative minerals from each crystal system

DURATION: This lesson is designed for 2 class periods, being most effective when each student creates their own individual set of models.Option 1: The lesson may be completed in 1 period if groups of 6 work to create a single set, contributing 1 system model each.Option 2: The teacher may chose to create a class set of models, allowing students to reference the designs rather than create their own sets.

INSTRUCTIONAL STRATEGY: The lesson consists of an introductory presentation defining and demonstrating symmetry, followed by individual desk work to create the models and complete the summary sheet. The teacher will be available to move throughout the classroom assisting students as needed.AUTHOR: Rebekah K. NixYou can define/demonstrate the general concept of "symmetry" using an apple. Insert the skewers into the stem and base, hold with each hand, and have a student "spin" the apple to illustrate the axis of rotation. Then, cut the apple through the center, along the axis of rotation, to create two mirror halves to show a mirror plane. Note that there is an infinite number of similar planes of symmetry for this example. Finally, cut the half-apple horizontally to emphasis the lack of symmetry between the upper and lower sections.

In a similar way, mineralogists use imaginary reference lines, called crystallographic axes, to describe crystals. These are parallel to the intersection edges of major crystal faces and coincide with the symmetry axes or normals to the symmetry planes. Note that the symmetry given on the model is "unique". There may be other symmetries within a system, i.e. isometric. Also point out that the grey spots on the models indicate "finger spots" to help students identify the unique symmetry axes.

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Introduce the 6 basic crystal systems with the greatest symmetry first, gradually decreasing the degree of symmetry until there is none at all. (The "Crystal Systems" summary sheet highlights the progressive changes in degree of symmetry.)Emphasize that these general shapes describe the form, or crystal habit, typically observed in the field, however few are ever absolutely perfect. Variations of these 6 basic crystal "systems" result in 32 "classes" of crystal forms.

Tips for creating models: Be sure that each student writes his/her name on their model(s) BEFORE folding and taping!It's a lot easier to cut "into" the pattern. In other words, make more short cuts from the edge of the page inward, rather than one long cut that twists and bends the page.The model is easier to "assemble" if you fold along each face intersection BEFORE attempting to tape into place.Using a different color paper for each crystal system helps with discussion and reinforces differentiation.Be sure to "test" various paper stocks/weights. Some cardstock is hard to fold along the lines and may result in skewed models. Some paper is too thin to hold the form on taping and rotating and reviewing.

The isometric system, also called the cubic system, has three mutually perpendicular axes of equal length.

The tetragonal system is just like the isometric system, except that one axis is not equal to the other two. There are three perpendicular axes, including two of equal length and a third axis that is longer or shorter.

The hexagonal system consists of four axes. There are three equal and horizontal axes that intersect at 120 degree angles. A fourth vertical axis is perpendicular to the plane of the other three and has a different length.

The orthorhombic system also has three mutually perpendicular axes, but none of them are equal.

The monoclinic system has three unequal axes like the orthorhombic system, however, two are inclined at oblique angles - only the third is perpendicular.

The triclinic system exhibits no symmetry at all. It includes three unequal axes that all intersect at oblique angles.

The summary sheet simply presents the characteristics given on the models in a tabular format. It may be used as a follow-up assignment or completed interactively during the introduction.

crystallography design

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