材料科学基础英文版课件

Cleaving a crystal of rocksalt
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• The external appearance of crystals are all characterized by flat bounding planes which intersect at characteristic angles.
♪ Lattice Points do not necessarily lie at the centre of atoms
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Differences of Lattice and Crystal Structure
Lattice
An array of points in space
Crystal Structure
•面网密度：dot number in unit area •面网间距：distance between two nets.
• 面网密度大的面网其面 网间距也大
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（4）Space Lattice 空间格子
联结分布在三维空间内的结点—— Space Lattice 空间格子
• 由三个不共面的行列就可决定一个空间格子
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3) Symmetry Operations & Symmetry Elements
(1) Symmetry operations
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（2）Symmetry elements
Symmetry elements— Point, line, plane
Rotation axis Mirror plane Corresponding Symmetry elements ———————— Symmetry operations
The arrangement of atoms or molecules which actually exists in a crystal • Objective
• Contrived, abstract geometrical array • Geometrical point
• Physical obj源自文库ct
晶体是内部质点在三 维空间呈周期性重复 排列的固体；或者说， 晶体是具有格子构造 的固体。
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2) Space Lattice and Equivalent Points
Equivalent Point: Identical Surroundings the grouping of lattice points about any given point is identical to the grouping about any other point in the lattice.
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Symmetry
Snowflake
flowers
Imagine an axis passing through the center of the snowflake, if the snowflake is rotated through 1/6 of a revolution, then the new position is indistinguishable from the old.
• Space lattice with 3D period repeating pattern
is built by abstraction equivalent point in crystal structure, which shows .
periodic array of points in three dimension —— Space Lattice
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（3）Nets 面网
The intersections of one dimension array build a space lattice.
• 空间点阵中不在同一行列上 的任意3个结点就可联成一 个平面 • 任意2个相交的行列就可决 定一个面网
• 相互平行的面网的面网 密度和面网间距相等
Centre of Symmetry
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② Mirror Plane (P/m) —— Reflect
Two halves of a molecule can be interconverted by carrying out the imaginary process of reflection across the mirror plane.
Quartz
• The crystal firstly found was quartz with regular shape.
• Quartz with geometrical polyhedron shape was called as crystal.
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• Later, all solids with geometrical polyhedron shape were defined crystal, such as salt, calcite, magnetite.
(mirror plane)
Chirality Object
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③ Rotation Axis (Ln / n) —— Rotate
Rotation about the axis by 360/n degrees give an identical orientation and the operation is repeated n times before the original configuration is regained.
= 360/n, n: fold of axis
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n=2, twofold rotation axis
n=4, fourfold rotation axis
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Equivalent Points, Space Lattice
Equivalent Point: Identical position and identical surrounding i.e. Cl- center、Na+ center、between Cl- & Na+
• Geometric point，No weight and size
2) Point Symmetry
Character:
• The external appearance of crystals is the confining geometry with flat bounding planes which intersect at characteristic angles. • Macroscopic symmetry of crystals reflects the symmetry of space lattice.
Salt Calcite
magnetite
Zircon
Ruby / Corundum
Diamond
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Quartz
Salt
Beryl
Red Beryl
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Crystal Structure
The building blocks of these two are identical, but different crystal faces are developed
Chapter 1
Fundamental Concepts of Crystal
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1-1. Basic Concepts of Crystal
1) Definition of Crystal
• What is Crystal？ • Crystal and Amorphous
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• People realized that there are two kinds of mineral in nature: Crystal and Amorphous. • Are there some commonness for crystals? • Regular external shapes, flatgeometric face
Question: • Why many rounded stones and man-made cast solid objects with no external evidence are observed?
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Definition of crystal
Crystals are built up of regular arrangements of atoms, molecules or ions in three dimensions.
• atoms or ions
A space lattice is a geometrical abstraction which is a reference in describing and correlating symmetry of actual crystals.
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3) Lattice Elements 空间点阵的要素
空间格子由一系列 平行重叠的平行六 面体构成
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4) Properties of Crystals
Crystallizing Uniformity Anisotropy Confining Geometry Symmetry Lowest Energy
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1-2.Symmetry of Crystals
(1) Lattice point (dot) 结点 (2) One dimension array 行列 在空间点阵中，分布在同一直线上的结点构成一个行列。 空间点阵中，任意两个结点连接起来就是一条行列方向。 行列中两个相邻结点间的距离 ——distance between lattice points 结点间距 • 在同一行列中结点间距是相等的； • 在平行的行列上结点间距是相等的； • 不同的行列，其结点间距一般是不等的（某些方向的行 列结点分布较密；另一些方向行列结点的分布较疏。）
1) Symmetry
the regular repeating of equivalence, or identity among constituents of an entity.
R & L Hand： Minor Electric Fan: 120°
Rotor
Symmetric condition ① equivalent or identical parts of an entity ② recurrence through a specific action 19
• Crystal Structure = The periodic arrangement of atoms in the crystal.
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Lattice: Periodic repeating array
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Lattice, Basis, Crystal Structure
♪ Don't mix up atoms with lattice points ♪ Lattice points are infinitesimal points in space ♪ Atoms are physical objects
Lattice Points
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Lattice
• Lattice = An infinite array of points in space, in which each point has identical surroundings to all others. • It can be described by associating with each lattice point a group of atoms called the Motif (Basis)
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4) Symmetry Elements of Crystals
¯ ① Centre of Symmetry (C/1) reflect / inverse
A point, an identical arrangement found on the other side. Any part of a structure can be reflected through this centre of symmetry.