2110Crystal_Oct2015

7/24/2019 2110Crystal_Oct2015

1/40

Copyright The McGraw-Hill Companies, Inc. Permission required or reproduction or display.

CRYSTAL STRUCTURE AND

CRYSTAL GEOMETRY

7/24/2019 2110Crystal_Oct2015

2/40


!pace lattice and unit cell

"Physical structure of solid materials depend on the arrangement

of atoms, ions or molecules and the bonding forces between

them.

" If the arrangements in a pattern that itself crystal structure(crystalline solid or crystalline materials) most metals,

alloys

and some ceramic.

" Atomic arrangement can be described in network space

lattice

" Each space lattice can be described by specifying ite atom

position in a repeating unit cell.

"he si!e and shape of unit cell can be described by " lattice

#ectors (a, b, c) and intera$ial angels , and are the latticeconstantof the unit cell.

7/24/2019 2110Crystal_Oct2015

3/40


Figure 3.1

7/24/2019 2110Crystal_Oct2015

4/40


Crystal systems and #ra$ais %attices

" %nly se#en different types of unit cell create all point lattices" &ra#ais showed that ' standard unit cell to describe all

possible lattice network.

" basic types of unit cells simple, body-centred, face-centred

and base-centred.

"he si!e and shape of unit cell can be described by " lattice#ectors (a, b, c) and intera$ial angels , and are the latticeconstantof the unit cell.

7/24/2019 2110Crystal_Oct2015

5/40


Figure 3.2

7/24/2019 2110Crystal_Oct2015

6/40


Metallic crystal structures

" *+ elemental metal crystallise when solidified" " form of packed crystal structure are

- &ody-centred cubic, face-centred cubic and he$agonal

closed packed

" nit cell are #ery small, e.g &// iron has a 0 +.123 nm.

if unit cells of pure irons are line up side by side in ' mm,there will be ".2 $ '+4 unit cell ('mm /+.123 $'+-4 mm)

7/24/2019 2110Crystal_Oct2015

7/40


Figure 3.3

7/24/2019 2110Crystal_Oct2015

8/40


#ody-centred cu&ic '#CC( structure

" he central atom is surrounded by 2 nearest neighbours 2coordination number" Each unit cells has the e5ui#alent of two atoms per-unit

cell.

" 6elationship between the lattice constant, a and atomic radius,

6

ry e.g. ".' pg "

"

Ra=

7/24/2019 2110Crystal_Oct2015

9/40


Figure 3.4

7/24/2019 2110Crystal_Oct2015

10/40


Figure 3.5

7/24/2019 2110Crystal_Oct2015

11/40


)tomic pac*ing actor ')P+(

cellunitofvol

cellunitinatomsofvolAPF

.

.=

ry e.g. ".1 pg

C G C

7/24/2019 2110Crystal_Oct2015

12/40


+ace-centred cu&ic '+CC( structure

" Each atom is surrounded by '1 nearest neighbours '1coordination number

" Each unit cells has the e5ui#alent of four atoms per-unit

cell.

" 6elationship between the lattice constant, a and atomic radius,

6

1

Ra=

ry AP7 for 7// (+.3)

C i ht Th M G Hill C i I P i i i d d ti di l

7/24/2019 2110Crystal_Oct2015

13/40


Figure 3.6

C i ht Th M G Hill C i I P i i i d d ti di l

7/24/2019 2110Crystal_Oct2015

14/40


Figure 3.7

Copyright The McGraw Hill Companies Inc Permission required or reproduction or display

7/24/2019 2110Crystal_Oct2015

15/40


Heaganol closed-pac*ed 'HCP( structure" Each atom is surrounded by '1 nearest neighbours '1

coordination number

" Each unit cells has the e5ui#alent of 4 atoms per-unit

cell (2 $ 8 9 1 (4 $ ':4) 0 4) .

ry e.g ".", pg


7/24/2019 2110Crystal_Oct2015

16/40


Figure 3.8


7/24/2019 2110Crystal_Oct2015

17/40


Figure 3.9

Copyright The McGraw-Hill Companies Inc Permission required or reproduction or display

7/24/2019 2110Crystal_Oct2015

18/40


Atomic Positions in cubic unit cells

"o locate the atom position in unit cells, $,y,! a$es are

used

7or e.g. the position of atom in in &// are as shown in

7igure ".'+.

ry with 7//;


7/24/2019 2110Crystal_Oct2015

19/40

Copyright The McGraw Hill Companies, Inc. Permission required or reproduction or display.

Figure 3.10


7/24/2019 2110Crystal_Oct2015

20/40


7/24/2019 2110Crystal_Oct2015

21/40


Figure 3.11

ry e.g. "., ". and ".4


7/24/2019 2110Crystal_Oct2015

22/40

py g p , q p p y

++'?,

=

indices of a family or form

?+''>

?'++>

++'


7/24/2019 2110Crystal_Oct2015

23/40

py g p , q p p y

Example 3.4


7/24/2019 2110Crystal_Oct2015

24/40

py g p q p p y

Example 3.5


7/24/2019 2110Crystal_Oct2015

25/40

Example 3.6


7/24/2019 2110Crystal_Oct2015

26/40

=iller Indices for crystallographic planes in unit cubic cells

" =iller indices is used to identify crystal planes in a cubic

crystal structure.

"he procedures to obtain miller indices for cubic crystal plane

- /hoose the plane that does not pass through the origin at

(+,+,+).

-

7/24/2019 2110Crystal_Oct2015

27/40

Figure 3.13


7/24/2019 2110Crystal_Oct2015

28/40

Figure 3.14


7/24/2019 2110Crystal_Oct2015

29/40

Example 3.7


7/24/2019 2110Crystal_Oct2015

30/40

Interplanar spacing

" he direction indices of a direction perpendicular to the

crystal plane as the same as the miller indices of that plane

(applied only for cubic system).

7or e.g. >'++? direction is perpendicular to the ('++) crystal

plane.

" Interplanar spacing (dhkl) is the distance between two closestparallel planes with the same miller indices

111

lkh

ad lkh

++

=

ry /u has an 7// crystal structure and a unit cell with the a0 +."4'nm.

Chat is the interplanar spacing d11+D (pg 3)


7/24/2019 2110Crystal_Oct2015

31/40

Figure 3.15


7/24/2019 2110Crystal_Oct2015

32/40

Figure 3.16

/P unit cell are

identified using indices,

(hkil) which based on

/oordinate system with a$es, a', a1, a"and c


7/24/2019 2110Crystal_Oct2015

33/40

Folume, planar and linear density of unit cell

sing hard sphere atomic model

" #0 (mass:unit cell)/(#olume:unit cell)

" p 0 (e5ui#. no. of atoms whose center are intersected by selected area)/

(selected area)

" l 0 (no. of atomic diameter intersected by selected length of linein the direction of interest)/(selected length of line)

ry E$ample page '+, '-"


7/24/2019 2110Crystal_Oct2015

34/40

Figure 3.17


7/24/2019 2110Crystal_Oct2015

35/40

Figure 3.23


7/24/2019 2110Crystal_Oct2015

36/40

Crystal structure analysis

Analysis of crystal structure can be obtained using $-rays

diffraction techni5ues ($-ray diffractometer).&y referring to 7igure ".12,

n0 =P 9 P@ (n 0 ',1,",G.%rder of the diffraction)

&oth =P and P@ e5ual to dhklsin ,

n = 2 dhklsin (Braggs law)

Hi#es the relationship between the $-ray radiation and

interplanar spacings dhkl of the crystal plane. In most case thefirst order of diffraction is used (n0'), &raggBs law become

= 2 dhklsin

Tr e. . 10 no.4


7/24/2019 2110Crystal_Oct2015

37/40

Figure 3.28


7/24/2019 2110Crystal_Oct2015

38/40

Figure 3.29


7/24/2019 2110Crystal_Oct2015

39/40

Polymorphism or allotropy

ame element can e$ist in more than one crystallineform. 7or e.g. iron e$ist in both &// and 7// crystal

structures o#er a temperature range from room

temperature to its melting point.


7/24/2019 2110Crystal_Oct2015

40/40

LEARNING OUTCOMES: At the end of this chapter youshould e ale to:

J Identify what signify the crystalline material

J E$plain space lattice and identify some important crystal system todescribe certain elements

J Identify main crystal systems for metallic crystal structures

J /alculate the lattice constant (a) and atomic packing factor (AP7)for different type of crystal systems

J

2110Crystal_Oct2015

Documents

Transcript of 2110Crystal_Oct2015