200x年国家司法考试试卷一真题解析Tit

QuasicrystalsAlCuLi

QCRhombic

triacontrahedral

grainTypical

decagonal

QCdiffraction

pattern

(TEM)•精品课件•1QuasicrystalsDiffraction

patternfor

8-fold

QCDiffraction

patternfor

12-fold

QC•精品课件•2QuasicrystalsPrincipal

types

of

QCs:icosahedraldecagonal•精品课件•3QuasicrystalsPrincipal

types

of

QCs:icosahedraldecagonalmetastable

(rapidsolidifcation)stable

(conventionalsolidification)•精品课件•4QuasicrystalsPrincipal

types

of

QCs:icosahedraldecagonalmetastable

(rapidsolidifcation)stable

(conventionalsolidification)QCs

usually

havecompositions

close

tocrystalline

phases

-

the"crystalline

approximants"•精品课件•5QuasicrystalsWhile

pentagons

(108°

angles)

cannot

tile

tofill

2=D

space,

two

rhombs

w/

72°

&

36°angles

can

-

if

matching

rules

are

followed•6N.B.-see

definitive

&

comprehensive

book

ontiling

by

Grünbaum

•a精nd品S课h件epherdQuasicrystalsWhile

pentagons

(108°

angles)

cannot

tile

tofill

2=D

space,

two

rhombs

w/

72°

&

36°angles

can

-

if

matching

rules

are

followed•精品课件•7QuasicrystalsFourier

transform

of

this

Penrose

tiling

gives

apattern

which

exhibits

5

(10)

-

fold

symmetry

–very

similar

to

diffraction

patterns

foricosahedral

QCs•精品课件•8Quasicrystals•精品课件•9Quasicrystals•精品课件•10QuasicrystalsDiffraction

pattern

(in

reciprocal

space)

of

icosahedral

QCcan

be

indexed

w/

6

six

integers

-

axes

along

6icosahedron

directions

qi

(referred

to

Cartesian

qx,

qy,

qz)•精品课件•11t1QuasicrystalsDiffraction

pattern

(in

reciprocal

space)

of

icosahedral

QCcan

be

indexed

w/

6

six

integers

-

axes

along

6icosahedron

directions

qi

(referred

to

Cartesian

qx,

qy,

qz)q1

=

(1

t

0)q4

=

(0

1

t)q3

=

(t

0

1)q6

=

(0

t

1)t1•12q2

=

(t

0

1)精q5品=课(件1

t

0)Quasicrystalstt

=

(1

+

5)2t

=

1.618…Diffraction

pattern

(in

reciprocal

space)

of

icosahedral

QCcan

be

indexed

w/

6

six

integers

-

axes

along

6icosahedron

directions

qi

(referred

to

Cartesian

qx,

qy,

qz)q1

=

(1

t

0)

q2

=

(t

0

1)

q3

=

(t

0

1)q6

=

(0

t

1)t1•13q4

=(0

1

t)•精品课q5件=(1

t

0)QuasicrystalsDiffraction

pattern

(in

reciprocal

space)

of

icosahedral

QCcan

be

indexed

w/

6

six

integers

-

axes

along

6icosahedron

directions

qi

(referred

to

Cartesian

qx,

qy,

qz)q1

=

(1

t

0)q4

=

(0

1

t)q2

=

(t

0

1)

q3

=

(t

0

1)q5

=

(1

t

0)

q6

=

(0

t

1)Thus,

icosahedral

QC

is

periodic

in

6D•精品课件•14QuasicrystalsAlso

consider:to

periodically

tile

in

2-D

–need

three

translation

vectorsif

5-fold,

reasonable

cell

is

pentagon

–need

additional

dimension

tofill

space

(tile)

–

more

translationvectors•精品课件•15QuasicrystalsDiffraction

pattern

(in

reciprocal

space)

of

icosahedral

QCcan

be

indexed

w/

6

six

integers

-

axes

along

6icosahedron

directions

qi

(referred

to

Cartesian

qx,

qy,

qz)q1

=

(1

t

0)q4

=

(1

t

0)q2

=

(t

0

1)q5

=

(t

0

1)q3

=

(0

1

t)q6

=

(0

1

t)Thus,

icosahedral

QC

is

periodic

in

6DBut

not

in

3DTo

understand

this,

consider

periodic

2D

crystal:•精品课件•16QuasicrystalsTo

understand

this,

consider

periodic

2D

crystal:The

2D

crystal

is

not

in

our

observable

world

-

what

ISseen

is

the

cut

along

EBut

cut

along

E

may

or

may

not

pass

through

latticenodesCut

shown

has

slope

1/

t

-

does

not

pass

through

latticenodes

except

origin•精品课件•17QuasicrystalsTo

understand

this,

consider

periodic

2D

crystal:But

can

observe

both

real

structure

and

diffraction

patternfor

this

1D

quasiperiodic

crystalMust

be

some

kind

of

structure

in

the

extended

space

(the•精品课件•182nddimension)

-

shown

here

as

lines

through

the

2Dlattice

nodesQuasicrystalsTo

understand

this,

consider

periodic

2D

crystal:Must

be

some

kind

of

structure

in

the

extended

space

(the•精品课件•192nddimension)

-

shown

here

as

lines

through

the

2Dlattice

nodesSome

of

the

lines

intersect

"the

real

world"

cut

E,

therebyallowing

observation

of

the

real

quasiperiodic

structureQuasicrystalsTo

understand

this,

consider

periodic

2D

crystal:Note

short

&

long

segments

in

real

real

world

cut

-

form"Fibonacci

sequence":s

l

sl

lsl

sllsl

lslsllsl

sllsllslsllsl……..if

s

=

1,

l

=

t•精品课件•20QuasicrystalsTo

understand

this,

consider

periodic

2D

crystal:Think

of

2

spaces•精品课件•21-

"parallel"

(real)

&

"perp"

(extended)QuasicrystalsConsider

incommensurate

crystals:Need

additional

dimension

to

completely

describe

structure•精品课件•22QuasicrystalsConsider

incommensurate

crystals:Similar

to

quasiperiodic

case•精品课件•23QuasicrystalsThere

are

16

space

groups

for

the

6-D

point

group

532

w/P,

I,

F

6-d

cubic

latticesThe

6-D

structure

&

the

parallel

&

perpendicular

subspacesare

all

invariant

under

the

operations

of

532•精品课件•24QuasicrystalsThere

are

16

space

groups

for

the

6-D

point

group

532

w/P,

I,

F

6-d

cubic

latticesThe

6-D

structure

&

the

parallel

&

perpendicular

subspacesare

all

invariant

under

the

operations

of

532•精品课件•25To

visualize

6-D

structure,

must

make

2-D

cuts

whichnecessarily

must

show

both

parallel

&

perp

spacesQuasicrystalsThere

are

16

space

groups

for

the

6-D

point

group

532

w/P,

I,

F

6-d

cubic

latticesThe

6-D

structure

&

the

pa