fizica cristalelor

54
FIZICA CRISTALELOR - Conf.dr.ing. Mircea Ionu Petrescu 1 !" # " " $ % " " " & " ( ) * " & * # " !+$ , - . " ’

Upload: vladuttz24

Post on 23-Nov-2015

76 views

Category:

Documents


4 download

DESCRIPTION

cristalografie

TRANSCRIPT

  • FIZICA CRISTALELOR - Conf.dr.ing. Mircea Ionu Petrescu

    1

    !"#

    " " $ % " " " & ' " ()

    * " & * # " '

    !+$,-.

    "'

  • FIZICA CRISTALELOR - Conf.dr.ing. Mircea Ionu Petrescu

    2

    !/$ 0

    1"""2 " " -3

    1 " " - " 1 3 " ,"! $ &"3"3 * ! !" $0

    4 2 3 " 1 "3 4 !#$ ) +'/"" 4$%!$!$& !#&$""

  • FIZICA CRISTALELOR - Conf.dr.ing. Mircea Ionu Petrescu

    3

    1 "3 "

    #'( )*+*+

    ),

    +

    -.+&* + &+ * * *. ), + ( & /*

    0&),+(&

    4 1

    ! 3 $ "3 (2(2(3!#$

    #41 . ! 2! 2!3+

    (* *

    5

  • FIZICA CRISTALELOR - Conf.dr.ing. Mircea Ionu Petrescu

    4

    4 &!!2!2!3'

    !6!2!2!37 !5$ !*!8*( & "3"3!$ 9 !!#3$

    9,$! !6$ " 2

    " 4 $ * % '

    9,$! 9,$! 93,$!3 !7$ 9

    !

    #3 ), * ) * *

    !).(90& ),* ), * * * ) * *

    9 ! !#3&$ -:"'

  • FIZICA CRISTALELOR - Conf.dr.ing. Mircea Ionu Petrescu

    5

    9,$!,$!,$3!39,$!,$!,$3!393,$3!,$3!,$33!3 !8$ $ $ ! $% $ %

    $! - 9$%!$,"3"";

    [[[[ ]]]]

    ====

    333231

    232221

    131211

    ij

    kkk

    kkk

    kkk

    k !:$

    1 * "

    #3& 1 /$% % 2

  • FIZICA CRISTALELOR - Conf.dr.ing. Mircea Ionu Petrescu

    6

    !.

    **1

    " !$ !$ 1 "#= 223 " >2>2>3"

  • FIZICA CRISTALELOR - Conf.dr.ing. Mircea Ionu Petrescu

    7

    "#=(>3 &9&@

    >!$ ?!,$+ / 5

    @+ ++ +/ +5@/ /+ // /5@5 5+ 5/ 55

    "@&

    =

    3

    2

    1

    333231

    232221

    131211

    ,3

    ,2

    ,1

    x

    x

    x

    aaa

    aaa

    aaa

    x

    x

    x

    !+A$

    @(>B%(% 2%223 !+A$

    ! + A

    A

    3 $ & 223

    3>2>2>3"'

    >AA33>AA33>33A3A333>%% !"$ !++$

    %>% !"$ !++$('

    >%% !"$ !++$

    '

    %>%!"$ !++$- /

    % ! $ B *$'

    >$$B$$$$%>% !+/$!++$!9$!++$!$

  • FIZICA CRISTALELOR - Conf.dr.ing. Mircea Ionu Petrescu

    8

    >>%>% !+/$

    !$4

    '>%$%$ !+5$0,C+5&+5

    '>%%A%A%33A%A%A%33A3%3A3%3A3%333 !+5$

    &>"

    ; & ! 913/&!3 " $ $%$% 3'

    332313

    232212

    131211

    kkk

    kkk

    kkk

    !+6$

    ! $$$3$3$3$3$1

    /3"('

    3

    2

    1

    k00

    0k0

    00k

    !+7$

    $$$31/4 ! "=$

  • FIZICA CRISTALELOR - Conf.dr.ing. Mircea Ionu Petrescu

    9

    3.+-

    3 1 " 1 " 2'

    %((%C !+8$%(""%"

  • FIZICA CRISTALELOR - Conf.dr.ing. Mircea Ionu Petrescu

    10

    #:4**D2DE2D5(*

    %

    "

  • FIZICA CRISTALELOR - Conf.dr.ing. Mircea Ionu Petrescu

    11

    =5*+

    * - 3-" %(> !+9;7$ - " * " * (2(2(3 " (> 2(> 2(>3 3 @ ! " " ""$'

    (>(A(A3(3(>(A(A3(3(>33(A3(A33(3 !+;$

    *',

    333231

    232221

    131211

    sss

    sss

    sss

    i !+9$

    '

    100

    010

    001

    100

    010

    001

    100

    010

    001

    !/A$ !/A$ !/A$

  • FIZICA CRISTALELOR - Conf.dr.ing. Mircea Ionu Petrescu

    12

    /+;A 69A

    100

    010

    001

    100

    001

    010

    !/A$ !/A$ 1@33( (>F&6(2(2(3 @ '

    3

    2

    1

    3

    1

    2

    3

    2

    1

    x

    x

    x

    100

    001

    010

    x

    x

    x

    100

    001

    010

    x

    x

    x

    !/+$ !/+$

    3

    2

    1

    3

    1

    2

    x

    x

    x

    100

    001

    010

    x

    x

    x

    100

    001

    010

    !/+$ !/+$

    & " " ?6(2(2(37 " 3

    6G7 ?$4 6

    lkh

    lhk

    lkh

    hlk #

  • FIZICA CRISTALELOR - Conf.dr.ing. Mircea Ionu Petrescu

    13

    #% >%$%$ !//$ / " , B5 3&'

    =

    =

    332313

    232212

    131211

    332313

    232212

    131211

    ,ij

    ppp

    ppp

    ppp

    ppp

    ppp

    ppp

    100

    010

    001

    )j(

    100

    010

    001

    )i(p !/5$

    & 4$>%'

    33

    2212

    1211

    p00

    0pp

    0pp

    /

  • FIZICA CRISTALELOR - Conf.dr.ing. Mircea Ionu Petrescu

    14

    2 6 !@$

  • FIZICA CRISTALELOR - Conf.dr.ing. Mircea Ionu Petrescu

    15

    33

    11

    11

    p00

    0p0

    00p

    6

    # " 1 / 6 !& /

    #;

    +

    (*+.-0&0&0*&*((2I2

    J

    +*((>2(>2(>3

  • FIZICA CRISTALELOR - Conf.dr.ing. Mircea Ionu Petrescu

    16

    -3 "3 1 "#; " (2I2 (>2I>2> - / !#;$ -3 / !I !#;&$- !#;$ - 568 3 !#;*$ - "3 !#;$ -3 " / *

    + * + . . *.* +

    * + )

    +

    2 .(

    2

    &.)+

  • FIZICA CRISTALELOR - Conf.dr.ing. Mircea Ionu Petrescu

    17

    :!**. - "/ 1 /9!B5/$&" / ?+ "5!B5+$3"32!$3!B5A$("&%$6 !$ !$ ;+ !B56$ 1 ) ) "! $ ! $ ) " ! $ / ! $ & / ! $ 36!$ -/""!&"

  • FIZICA CRISTALELOR - Conf.dr.ing. Mircea Ionu Petrescu

    18

    !&!+

    !$ 2!$ )!$

    &!A$ !A$ ?!A$

    4!A$ 0!A$ !A$

    !+$ 0!A$ 4!+$

    4!/$ 4!+$ &!+$

    !/$ 4!+$ -!+$

    0!/$ 4!+$ &!+$

    2!/$ 4!+$ -!+$

    4!/$ #!+$ %!+$

    &!/$ 0!A$ &!/$

    !5$ 4!+$ &!/$

    1!6$ 0!/$ &!/$

    )!6$ &!/$ 0!/$

  • FIZICA CRISTALELOR - Conf.dr.ing. Mircea Ionu Petrescu

    19

    5. .

    "

  • FIZICA CRISTALELOR - Conf.dr.ing. Mircea Ionu Petrescu

    20

    &. '3

    !" $J

    3 . *

    ! , $

    *!.$ " !F$&" . " """3 ! $ 1 " ! $ !$ ! $ " !$ !$ "" , - " 3 !$ !$J ! $J , , ! $J J!$

  • FIZICA CRISTALELOR - Conf.dr.ing. Mircea Ionu Petrescu

    21

    ( " ! $ " " !$4-3" ! $ ! $ ! $ " " " " " " " " """"G" 4 " !$!$"" " " ! " $ & !$ - G G " " J ""

  • FIZICA CRISTALELOR - Conf.dr.ing. Mircea Ionu Petrescu

    22

    & 1 & "" "3 " ! $ ! $ G G & " "!$!$ * ) & 2 2 K * .. & * * *.K ) 2 ) *. . * * J * ( " " " "

  • FIZICA CRISTALELOR - Conf.dr.ing. Mircea Ionu Petrescu

    23

    3JK*

    3J & !/7$ "K5(""!!&3$( " -(

    !&3J83

    )*

    *K&

    #F/* A9/ #451/!2*6$5 5/A2L4 +99 *(Mg,Fe)2SiO4 5//#4 /+7 &(Mg,Fe)CaSi2O6 55AF>4 /+8 &4 57A#42*6/F/* /55 41/*5 6AA*L251*; /78 )0*/ 6/A2(Mg, Fe)3Si2O5(OH)4 /8A EE2*6 67A1>251*; /8+ MM2*6 68;42*/ /87 %2/ 7A/0 526*+A!*F$/ /:A %5*6 7+;444*5 /:+ F%/*5 7/7142/1/*; /:: %% :5A KAl2(Si3AlO10)(F,OH)2 /;A #2 :7;&4 !4*5$/ /9A 4F2 ;+;(MgSiO3 5+A 44 ;97%4%/ 5+; 11 +95A*L

    " 64 ! A9999:5K5$ -# N= !#F$ "M"MG LM8M,MG !/8$

  • FIZICA CRISTALELOR - Conf.dr.ing. Mircea Ionu Petrescu

    24

    & ! O$ 2 !>4$ B78591!+B+A;1$>P43" !$8A/5+A/5>P /543577- >P 5;/+A3/5 43 7;9+A3/5' .BK?B6!5;/P7;9$+A3/5K!7859+A3;$5B/+:K5 !/:$

    #F &+ NI2 *+

    .-

    M&)0&MG&)

  • FIZICA CRISTALELOR - Conf.dr.ing. Mircea Ionu Petrescu

    25

    - 5 ? ? " !11F4%M$"J

    - " " J

    - L* *

    1 " " " " 1

    - 5*

    * * K ," -

    Q!1F1 4$ " 6 G :7K5"/357K5

    &"

    '- Q J

    - .1 1

  • FIZICA CRISTALELOR - Conf.dr.ing. Mircea Ionu Petrescu

    26

    3*&

    " ' "3

    4"'

    t

    t

    0t 2nn

    ==== !/;$

    '- @ ! $

    - !$- "- R ", 3,0 ", "

    ",

  • FIZICA CRISTALELOR - Conf.dr.ing. Mircea Ionu Petrescu

    27

    ++) /35 Q+A3+7 Q ! $)

    &'- J#3 UJ

    - "- ,

    D "'- & / 6

    - &+ D "3 (' !+

    5F$ G 3 "!/

    5F$",+/68( G G

  • FIZICA CRISTALELOR - Conf.dr.ing. Mircea Ionu Petrescu

    28

    " " 9//56

  • FIZICA CRISTALELOR - Conf.dr.ing. Mircea Ionu Petrescu

    29

    =

    =5*& "

    - "!+=$9,$!( " , - ( "!& :1

    !&:+

    2)*

    2

    2

    0!L$

    4C!NKL$

    &!+A38L3+$

    4!NKL$

    # 5+A 5+8 585 +8 6/ /9 +;8% ) 5AA 7;6 55; 7A8 88 99 9; ++:9( ) 5AA 5/: /:/ 65+ +86 +67 +8; ;/+4 0 5AA 57/ B 6+; 35/ B +55 ;574 0 5AA 87A B ++5 +6 B 9 668# F 5AA 577 B ;9 3+// B /8: ;761 4 5AA /A; B B /5 B B /6574 4 /:5 6+A B B +8: B B /665& 4 /:5 +5; B B A;9 B B 8++F 4 5AA 7;A B B 6A B B 7A7 4 5AA 5+; B B +99 B B 5/77 -" # " - ! $"""-

  • FIZICA CRISTALELOR - Conf.dr.ing. Mircea Ionu Petrescu

    30

    HAA+I&" ! $ E J 1

    =J & % / "

    O! ! $ P% ! /$' P%%O! !/9$

    #BJ*

    .**) ) + * * ) * ) *+

    0 & )

    * * * * ( " * ) *+ * ( " '. (, )*+

    *@@@@Q

    & " !AO!$ !AO!$!A3O!$ - " "!%9$4"" " 4

  • FIZICA CRISTALELOR - Conf.dr.ing. Mircea Ionu Petrescu

    31

    "" Q" " 4 -& O

    1'- & " J

    - & " " " +6AA4" '

    =35 4 ! $ 5

    !C$ 3 3 "N8$Q(' O58!O! !5A$ OO!!

  • FIZICA CRISTALELOR - Conf.dr.ing. Mircea Ionu Petrescu

    32

    :+

    :'-

    /1"/!R$!P$36 0R%*#"3*% R%*#8*% !5+$ * "3 " ",!#@$

    #@D

    ).,*

    *

    ** ),* *.

    ) * *+

    & '**

    (R2R2R3 - '

  • FIZICA CRISTALELOR - Conf.dr.ing. Mircea Ionu Petrescu

    33

    1xxx

    23

    23

    22

    22

    21

    21 =

    +

    +

    !5/$

    4 RRR3 RSRSR30'

    33

    22

    11

    00

    00

    00

    !5/$

    '

    332313

    232212

    131211

    !5/$

    # J

    .

    *. */* . * . * *.+ ( T2T2T3 & 5 &*2 *.)*J+

    *)***+ & (T2T2T3!#$1

  • FIZICA CRISTALELOR - Conf.dr.ing. Mircea Ionu Petrescu

    34

    " 2 ! " $ "#&!3$ * FC 1"3"R% P$ ! 4=$-3 = 1 " ' R%%$P$ !55$ "' P%%$R$ !55$ 06%$%$

  • FIZICA CRISTALELOR - Conf.dr.ing. Mircea Ionu Petrescu

    35

    !&

  • FIZICA CRISTALELOR - Conf.dr.ing. Mircea Ionu Petrescu

    36

    #3 * ),

    H ) *+ * J * + ' * * * * * * & *J?2BBB

    4, "&3 !#3$ 13"!" $ 3#3& 3 2 = /7V " !H+AAI$!HA+AI$2"#=&&"" "3 !LC/AAA$2"3" " !2+998$

  • FIZICA CRISTALELOR - Conf.dr.ing. Mircea Ionu Petrescu

    37

    #=* ),

    * ?+

    * ) *+

    0 .*.+*&X.+*) & " FY +AV"!#:$

    #: + *

    * **.+)XG

    1 " " & " Z/AAAK " [7AAAK

  • FIZICA CRISTALELOR - Conf.dr.ing. Mircea Ionu Petrescu

    38

    :&

    3

    &' & " - -" "

  • FIZICA CRISTALELOR - Conf.dr.ing. Mircea Ionu Petrescu

    39

    & 1 "3 4 !$ Q " !#

  • FIZICA CRISTALELOR - Conf.dr.ing. Mircea Ionu Petrescu

    40

    , " - #

    1 " 4 !$ " "!$"3

    0

    "& " !+++$ H++AI H+A+IHA++I4

    # * K 1

    !$""

    " !G>4$ !++A$ " !AA+$ " 1 !#F$, - !+++$ " !#F&$ "

  • FIZICA CRISTALELOR - Conf.dr.ing. Mircea Ionu Petrescu

    41

    #F#*

    *?-. *&@@0&. **

    2 "

    !AAA+$"!#B$

    #B#*

    &**-. *&*@,0&

    &@@@

    :35%4,

    " 4 , %, " 0 , " " ,,

    D . * % " " Q

  • FIZICA CRISTALELOR - Conf.dr.ing. Mircea Ionu Petrescu

    42

    ,

    5. *%, &,'- 4,!$,4"J

    - 4, ! $ ,J

    - 4,!$,J

    - 4,!$,3J

    - 4, ! $ ""

    :=J & " " " & " Q !?C E )CY$& ?C & ! N\$ +AAA & !)Y$ &

  • FIZICA CRISTALELOR - Conf.dr.ing. Mircea Ionu Petrescu

    43

    ' & " " 1 3"++A"'+3/353637383:3;3 93 +A3 # " Q 2C! 4 , " ) "1"& ! $!3G$

  • FIZICA CRISTALELOR - Conf.dr.ing. Mircea Ionu Petrescu

    44

  • FIZICA CRISTALELOR - Conf.dr.ing. Mircea Ionu Petrescu

    45

    ( " " N] 4 "+;;A2"2*6

    63"-85-5"#

  • FIZICA CRISTALELOR - Conf.dr.ing. Mircea Ionu Petrescu

    46

    "3 ( & , % "+A7 3+4 "-

  • FIZICA CRISTALELOR - Conf.dr.ing. Mircea Ionu Petrescu

    47

    #F ) * . )

    ))*(**&

    4

    +A38"

  • FIZICA CRISTALELOR - Conf.dr.ing. Mircea Ionu Petrescu

    48

  • FIZICA CRISTALELOR - Conf.dr.ing. Mircea Ionu Petrescu

    49

    4"!$+!!&F$

    !&F5*

    2

    4!$

    E ) :87 +/8A ::A4 0 ;A/ ;7; 4 0 68A 656 & 4 7;: # 4 +;AA F 4 7::

    2 " 4 " J

  • FIZICA CRISTALELOR - Conf.dr.ing. Mircea Ionu Petrescu

    50

    ;+

    &XH'

    HX !58$/ "

    ! " $ & & & " " 26P */3 1 - &ZA4

    1" 5 %5P /P 5"%/P"",'

    + / / 5 5 5%/P %5P /P

    4

    "

  • FIZICA CRISTALELOR - Conf.dr.ing. Mircea Ionu Petrescu

    51

    1 O O 0 "

    #B(**HD*++ ) *+ 6@7 * .*W50D=F )+

    *

  • FIZICA CRISTALELOR - Conf.dr.ing. Mircea Ionu Petrescu

    52

    !$ - . . 3 * - !4?4$ " " *"-" 0 "

  • FIZICA CRISTALELOR - Conf.dr.ing. Mircea Ionu Petrescu

    53

    -3 " " J 1 # @& "!#@$-!#@&$ " - " !E$4" 1 " # " - 4?4 " H+AAIH++AIH+++I

    # * *

    & ), &+ * . * &?( E#DB *. /

    @D0&:@D23@F@DD@38pipipipi8H

    > & "3 2 (

  • FIZICA CRISTALELOR - Conf.dr.ing. Mircea Ionu Petrescu

    54

    & " D4" - ::A4J7:;4

    "

    .41%/*6 1 4>4%/P%3!+A/3+A8 $ " "-24 """& J

    !&B

    !&BH+

    2

    2!2-+A37$ 0

    4!4$

    1 ) 3+66 3+6/ 3+85 4 0 3+7+ 3+7/ 4 0 3+/6 3+5; F 4 3+58 J ) 0 +A7 ++/ # 4 5AA7 7:;F 0 +5+ 8:7