材料物理导论-Chapter 2-1-企业文化-

Seven

crystal

systems

and

fourteen

Bravais

latticeCrystalsystemBravaislatticeCrystal

systemBravaislatticeTriclinicSimple

triclinicHexagonalSimple

hexagonala≠b≠c

，α≠β≠γa1=a2＝a3≠c，α=β＝90º

，

γ=120ºMonoclinica≠b≠c，

α=γ=90ºSimple

monoclinicRhombohedralSimple≠βRhombobedralBottom-centereda=b=c,α=β=γ≠90ºmonoclinicSimple

tetragonalSimple

orthorhombicBody-centeredtetragonalTetragonalOrthorhombicBottom-centeredBottom-centered

orthorhombica≠b≠c，α=

β=

γ=

90°Body-centered

orthorhombica≠b≠c，α=

β=

γ

=

90°Face-centered

orthorhombica≠b≠c，α=

β=

γ

=

90°Simple

hexagonala=b

≠

c，α=β=90°，γ

=120°Simple

rhombobedrala=b=c，α=β=γ

≠

90°Simple

tetragonala=b

≠

c，α=β=γ

=90°Body-centered

tetragonala=b

≠

c，α=β=γ

=90°Simple

cubica=b=c，α=β=γ

=90°Body-centered

cubica=b=c，α=β=γ

=90°Face-centered

cubica=b=c，α=β=γ

=90°2.

Indices

of

directions

and

Indices

of

crystal

planeCrystal

plane

:

one

of

a

set

of

parallel,

equally

spacedplanes

in

a

crystal

structure.Crystal

direction:

the

crystallographic

directions

arefictitious

lines

linking

nodes

(atoms,

ions

or

moleculesof

a

crystal).Indices

of

directions

and

indices

of

crystal

plane(Miller

indices):

a

notation

system

in

crystallographyfor

planes

and

directions

in

crystal

lattice.2.1

Foundation

of

crystallographya)

Indices

of

directions

in

the

cubic

crystal

systemsSteps

of

determining

the

indices

of

directions

[uv

w]

in

cubic

crystal

systems:Building

coordinateSolving

coordinateConverting

into

an

integerListing

square

brackets

[u

v

w],

adding

a

minus

sign

atthe

top

of

the

indices

if

the

coordinate

value

isnegative.The

coordinate

of

each

lattice

pointin

cubic

crystal

systemThe

sketch

map

of

determining

crystaldirection

[u

vw]in

the

cubic

crystal

systemCommon

crystal

directions

[u

v

w]

inthe

cubic

crystal

systemb).

Indices

of

crystal

plane

in

the

cubic

crystalsystemsSteps

of

determining

the

indices

of

crystal

plane(h

k

l)

in

cubic

crystal

systems:Building

coordinateSolving

interceptTaking

reciprocalConverting

into

an

integer

:

h,

k,

lListing

round

brackets

(h

k

l),

adding

a

minus

sign

at

the

top

of

the

indices

if

the

intercept

value

is

negative.The

sketch

map

of

crystal

plane

(h

k

l)

inthe

cubic

crystal

systemTwo

crystal

planes

(h

k

l)

in

the

cubiccrystal

systemh≠k≠

l≠0，then

there

are

24

crystal

planes 3!

×

4

=

24，

for

example：｛1

2

3｝h≠k

≠0

or

k≠

l≠0

or

h≠

l≠0,

then

there

are

12

crystal

planes3!／2!

＝

12，

for

example:

{1

1

2}h=k=l，then

there

are

4

crystal

planes 3!／3!

×

4

＝

4，

for

example:{1

1

1}h=0

or

k=0

or

l=0

，then

there

are

12

crystal

planes (3!／2)

×

4

＝

12，

foe

example:

{1

2

0}h==k=0

or

h=l=0

or

k=l=0，then

there

are

3

crystal

planes(4)

(3!／2!22)

×

4

＝

3，

for

example:{1

0

0}(5)Numbers

the

crystal

planes

in

the

family

ofcrystal

planes

{h

k

l}c).

Indices

of

crystal

direction

and

crystal

plane

inthe

hexagonal

crystal

systemThe

determining

step

is

same

as

that

of

the

cubiccrystal

system,but

we

always

choose

four

coordinatesto

denote

the

indices

of

the

crystal

direction

in

thehexagonal

crystal

system:a1、a2、a3、c,where

a1、a2、a3

locate

the

same

bottom

face

and

the

angle

betweenthem

is

120o

(the

c-axis

orientation

is

normal

to

thebottom

face).Indices

of

crystal

plan

（h

k

i

l),

where

i=-（h+k）Indices

of

crystal

direction

[u

v

t

w],

where

t=-（u+v）Miller

index

in

the

hexagonal

crystal

systemThree

axisa1，a2，cfour

axisa1，a2，a3，c120°120°120°（h

k

i

l

)[u

v

t

w]i=

-(

h+k

)t=

-(

u+v

)The

sketch

map

of

crystal

direction(plane)

in

the

hexagonal

crystal

system[h

k

i

l]

in

the

hexagonal

crystal

systemd).

ZoneZone:

azone

is

defined

as

a

group

of

crystal

facesthat

intersect

in

parallel

edges.Zone

law:

the

relationship

between

[uvw]

and

（hkl）in

the

same

zone

is：hu+kv+lw=0We

can

get

the

[uvw]

or

(h

k

l)according

to

the

zone

law.e)．Interplaner

spacingThe

perpendicular

distance

between

successive

parallelplanes

of

atoms

in

a

crystal,

it

is

denoted

with

d,h,k,l.RectangularcoordinatesCubicHexagonalThe

above

formula

is

only

for

simple

unit

cell.

For

a

complex

simple,we

should

consider

the

effect

of

the

additional

planes.Cubi

crystal

system：fcc:

when

h,

k

and

l

are

not

all

odd

or

all

evenFor

example

{100},

{110}bcc

h+k+l=odd, For

example

{100},

{111}Hexagonal

crystal

system

：When

h+2k=3n

(n=0,1,2,3,……),

I=oddFor

example

{0

0

0

1}The