BO MON VAT LY CHAT RAN

BAI GIANG MON BO MON VAT LY CHAT RANC S VAT LY CHAT RANAI HOC QUOC GIA THANH PHO HO CH MINHTRNG AI HOC KHOA HOC T NHIENCAN BO GIANG DAY: Ths. Vu Th Phat MinhGIAO TRNH S DUNG CHO MON HOC: VAT LY CHAT RANCUA TAC GIA: LE KHAC BNH NGUYEN NHAT KHANH3 TN CH (45TIET: 30 TIET LY THUYET + 15 TIET BAI TAP)NOI DUNG MON HOCTINH THE CHAT RAN.LIEN KET TRONG TINH THE CHAT RAN.DAO ONG MANG TINH THE.TNH CHAT NHIET CUA CHAT RAN.KH IEN T T DO TRONG KIM LOAI.NANG LNG CUA IEN T TRONG TINH THE CHAT RAN.CAC CHAT BAN DAN IEN.CHNG I. TINH THE CHAT RANA.LY THUYETPhan I. AI CNG VE TINH THE CAC TRANG THAI C BAN CUA VAT CHAT TRONG T NHIEN. MANG TINH THE

Phan II. PHAN TCH CAU TRUC TINH THE BANG PHNG PHAP NHIEU XA TIA X. CONG THC NHIEU XA CUA VULF BRAGG CAU PHAN XA CUA EWALD CAC PHNG PHAP CHUP TINH THE BANG TIA X

B.BAI TAP

CAC TRANG THAI C BAN CUA VAT CHAT TRONG T NHIEN.II. MANG TINH THE.Chng I- TINH THE CHAT RANPHAN I - AI CNG VE TINH THE

I. CAC TRANG THAI C BAN CUA VAT CHAT TRONG T NHIENTrong t nhien vat chat ton tai di 3 trang thai c ban (cac trang thai ngng tu cua vat chat): RAN - LONG - KHRan = Tinh the + vo nh hnh

Cau truc :Tinh the : cau truc co o trat t cao nhat.Kh : cau truc hoan toan mat trat t.Long: phan tch cau truc bang tia X, tia e- va ntron vi phng phap chu yeu cua Debye va Laue cau truc long gan vi tinh the hn kh.

The RANThe LONGThe KHCac trang thai cua vat chat

The PLASMAChat luTinh theVo nh hnho mat trat t

Pyrite ng Kim cngThach anh

MOT SO TINH THE TRONG T NHIEN

Ban danSieu danLaserMan hien th

MOT SO NG DUNG

II. MANG TINH THEMang tinh the dung mo ta cau truc tinh the. Cau truc tinh the = mang tinh the + c s

A. CAU TRUC TINH THETinh the l tng = s sap xep eu an trong khong gian cac n v cau truc giong het nhau.n v cau truc = c s = mot nguyen t, mot nhom nguyen t hay cac phan t (co the ti hang tram nguyen t hay phan t. VD: chat hu c)

Tinh the NaClGiai phong NaClMANG TINH THE NaCl

C s + Mng tinh the = Cau truc tinh the

B- BIU DIN MANG TINH THE1. TNH TUAN HOAN MANGMoi nut cua mang eu suy c t mot nut goc bang nhng phep tnh tien :

la vect n v.la 3 vect tnh tien khong ong phang = Vec t tnh tien c s.= vect tnh tien bao toan mang tinh the.n1, n2, n3 la nhng so nguyen hay phan so nao o. Neu n1, n2, n3 = so nguyen thla vect nguyen to (hay vect c s).

Neu n1, n2, n3 = phan so thMang tinh the 2DVECT NGUYEN TO (VECT C S)

n1 = 2; n2 = 4

Mang tinh the 2DVECT N VN1 = 2/3; n2 = 3/2

VECT TNH TIEN BAO TOAN MANG TINH THE

Vect tnh tien c s(3D)

Mang tinh the 2D 2. O MANG TINH THEQua ba vect khong ong phang hoan toan xac nh mot mang, o la mot he thong vo han cac nut. Chung chiem v tr nh cua cac hnh hop nho xac nh bi ba canh a1, a2, a3.Cac hnh hop chong kht len nhau va keo dai vo han trong khong gian O mang.

Co rat nhieu cach chon a1; a2; a3 nhieu cach chon o mang khac nhau. O n v la o c xac nh t 3 vect n v a1, a2, a3.The tch cua o n v: V

O nguyen to la o c xac nh t 3 vect nguyen to a1, a2, a3. O nguyen to ch cha 1 nut mang. O N VO n v co the cha nhieu hn mot nut.O NGUYEN TOABEDFCMot so cach chon O n vABEDFCMot so cach chon o nguyen toCung he vi he cua toan mang (tc he tinh the).So canh bang nhau va so goc (gia cac canh) bang nhau cua o mang phai nhieu nhat.Neu co goc vuong gia cac canh th so goc o phai nhieu nhat.Sau khi thoa man cac ieu kien tren, th phai thoa man ieu kien the tch o mang la nho nhat.O C S (O BRAVAIS)La o nguyen to thoa man cac ieu kien : O WIGNER SEITZ

O Wigner Seitz la mot o nguyen to c ve sao cho nut mang nam tam o.Cach ve o Wigner Seitz 2 chieu:Chon mot nut mang bat k lam goc O. Noi O vi cac nut lan can gan nhat ta c mot so oan thang bang nhau. Ve cac mat phang trung trc cua cac oan thang o ta thu c h mt th nht to mot mien khong gian kn bao quanh O.Tng t, t O noi vi cac nut lan can tiep theo va ve cac mat phang trung trc cua cac oan thang o ta thu c h mt th hai. Neu h mt th hai nam ngoai mien khong gian bao bi ho th nhat, tc ho th nhat xac nh mien the tch nho nhat va o la o Wigner Seitz. Ngc lai th o Wigner Seitz c xac nh ong thi ca hai loai mat sao cho o co the tch nho nhat. CACH VE O WIGNER SEITZ CHO MANG 2 CHIEU

O Wigner-Seitz cua mang lap phng

O Wigner-Seitz cua mang lap phng tam khoiO Wigner-Seitz cua mang lap phng tam mat

3. S OI XNG CUA MANG TINH THEa. YEU TO OI XNGPhep bien oi khong gian lam cho mang tinh the trung lai vi chnh no goi la yeu to oi xng.

b. CAC LOAI YEU TO OI XNG

Phep tnh tien bao toan mang T. Mat phang oi xng P (m). Tam oi xng C. Truc oi xng LnPPP, P: mat oi xng gng. QQ : khong phai mat oi xng gng. Mat phang chia tinh the lam hai phan bang nhau vi ieu kien phan nay nh anh cua phan kia qua mat gng at tai P. PHEP TNH TIEN BAO TOAN MANG

th tinh the trung lai vi chnh no.Khi tnh tien tinh the i mot vect MAT OI XNG GNG P (m)La mot iem C nam ben trong tinh the co ac tnh mot phan t bat ky trong tinh the qua no cung co iem oi xng vi no qua C. CTAM OI XNG C =

CCCo tam oi xng.CCo tam oi xngKhong tam oi xng TRUC OI XNG XOAY Lnvi n bac cua truc.Nguyen t hay phan t khi rieng le n = 1,2, 3 bat k. Trong tinh the n = 1, 2, 3, 4, 6.L1 : 1 = 360oL2 : 2 = 360o/ 2 =180oL3 : 3 = 360o/ 3 =120o L4 : 4 = 360o/ 4 =90oL6 : 6 = 360o/ 6 =60o

Truc oi xng la mot ng thang khi quay quanh no tinh the tr lai trung vi chnh no.Goc be nhat e tinh the tr lai trung vi chnh no goi la goc xoay c s cua truc. Cac truc oi xng Truc bac 1 (360o)Truc bac 4 (90o)Truc bac 6 (60o)Truc bac 2(180o)Truc bac 3(120o)NH LY Trong tinh the ch co cac truc oi xng bac 1, 2, 3, 4, 6 (do tnh chat tnh tien tuan hoan cua mang khong gian)

A1A2A3A4aaannHnh 1.3CHNG MINHXet mot nut mang A1, qua phep tnh tien mot oan a ta suy c nut A2. Sau o ap dung phep quay quanh mot truc oi xng Ln, ta suy c 2 nut A3 va A4 nh hnh 1.3.V A3, A4 la 2 nut mang tinh the nen khoang cach gia chung phai bang:A3A4 = k.a, vi k Z(2)T (1) va (2) suy ra:1 - 2 cosn = kSuy ra: -1 cosn = (1 - k)/2 1 -1 k 3k = -1, 0, 1, 2, 3Do o:Khi k = -1: cosn = 1 n = 1 = 360o Truc oi xng L1 Khi k = 0: cosn = 1/2 n = 6 = 60o Truc oi xng L6Khi k = 1: cosn = 0 n = 4 = 90o Truc oi xng L4Khi k = 2: cosn = -1/2 n = 3 = 120o Truc oi xng L3Khi k = 3: cosn = -1 n = 2 = 180o Truc oi xng L2A3 A4 = a + 2 asin ( n - /2)sin (n - /2) = - cosn A3A4 = a (1 - 2 cosn)(1)A1A2A3A4aaannHnh 1.3TRUC OI XNG NGHCH AO Lino la mot ng thang ma tinh the sau khi quay quanh no mot goc n roi cho oi xng iem chnh gia cua tinh the th tinh the tr lai v tr tng t vi v tr ban au.Lin = Ln * CCac loai truc nghch ao : Li1 = C, Li2 = P, Li3 = L3C, Li6 = L3P va Li4.Tom lai, trong tinh the v mo co the thay cac yeu to oi xng sau : C, P, L1, L2, L3, L4, L6, Li4, Li6 .

Truc oi xng nghch ao (truc nghch ao) Lin = Phep oi xng qua tam oi xng C tng ng vi phep quay mot goc 3600 quanh mot truc i qua C + phep oi xng qua C Tam nghch ao.

C12Li1 = C

TAM NGHCH AOa1O2Pa11a2Li2 = PC513264Li3 = L3CPO4213Li4O642315Li6 = L3PP4. HANG HE TINH THE 7 HE 3 HANG TINH THE He ba nghieng- He mot nghieng - He trc thoi He ba phng - He bon phng - He sau phng - He lap phng. Hang thap: he ba nghieng, he mot nghieng, he trc thoi.Hang trung: he ba phng, he bon phng, he sau phng. Hang cao: he lap phng.NHOM IEM Tap hp cac yeu to oi xng gom tam oi xng, mat phang oi xng va cac truc oi xng co c trong mot tinh the nhom oi xng iem. Co 32 nhom iemNeu ket hp them phep tnh tien bao toan mang th ta c nhom oi xng khong gian. Co 230 nhom khong gian.5. CAC LOAI MANG C BAN (MANG BRAVAIS)

a. O MANG BRAVAISMoi he tinh the se co mot o c s 7 c s cua cac mang thuoc bay he tinh the khac nhau O Bravais.3 ieu kien e chon o Bravais:O phai mang tnh oi xng cao nhat cua he tinh the.O co so goc vuong ln nhat hoac so canh bang nhau va so goc bang nhau phai nhieu nhat.O co the tch nho nhat. Neu khong ong thi thoa man 3 ieu kien tren th viec chon O Bravais theo th t u tien 1, 2, 3. KIEU O MANG BRAVAISTrng hp 3 chieu 14 kieu o mang Bravais. Trng hp 2 chieu 5 kieu o mang Bravais. Cac loai o mang BravaisLoai nguyen thuy (ky hieu P). Nut mang ch phan bo nh cua o mang. Loai tam ay (A, B, hay C). Nut mang phan bo v tr nh + tam cua hai ay nao o cua o mang. Loai tam khoi I. Nut mang phan bo v tr nh + tam cua tam cua o c s.Loai tam mat F Nut mang phan bo v tr nh + tam cua cac mat. 5 KIEU MANG BRAVAIS 2 CHIEU

Mangac iem cua o mangMang nghieng (1)a1 a2, 900Mang luc giac (2)a1 = a2, = 1200Mang vuong (3)a1 = a2, = 900Mang ch nhat (4)Mang ch nhat tam mat (5)a1 a2, = 900Mang vuonga1 = a2, = 900

= 900(3)

Mang nghienga1 a2, 900

900(1)

Mang luc giaca1 = a2, = 1200 = 1200(2)

Mang ch nhata1 a2, = 900 = 900(4)

= 900(5)

Mang ch nhat tam mata1 a2, = 90014 KIEU MANG BRAVAIS 3 CHIEU

He tinh the Truc oi xngKieu mang Bravaisac iem cua o mang BravaisBa nghiengL1Pa1 a2 a3, Mot nghiengL2 P,Ca1 a2 a3, = = 900 Trc thoi3L2P, C, I, Fa1 a2 a3, = = = 900Ba phngL3Pa1 = a2 = a3, = = 900Bon phngL4P, Ia1 = a2 a3, = = = 900Sau phngL6Pa1 = a2 a3, = = 900, = 1200Lap phng4L3P, F, Ia1 = a2 = a3, = = = 900

HE LAP PHNGHE BON PHNGHE TRC THOIHE SAU PHNGHE N TAHE TAM TAHE BA PHNG4 KIEU O N VP : NGUYEN TOI : TAM KHOIF : TAM MATC : TAM 2 MAT OI+7 HE TINH THE 14 LOAI MANG BRAVAIS SO NUT CHA TRONG MOT O MANGMang nguyen thuy : 8 nut 1/8 = 1 nut

Mang tam khoi : 8 nut 1/8 + 1 nut = 2 nut

Tam mat : 8 nut 1/8 + 6 nut 1/2 = 4 nut

Tam ay : 8 nut 1/8 + 2 nut 1/2 = 2 nutMANG NGUYEN THUY 8 nut = 1 nut

MANG TAM KHOI 8 nut + 1 nut = 2 nut

Tam mat : 8 nut + 6 nut = 4 nut

L = 0,52

HE SO LAP AY TRNG HP HE LP THUY PVO mang = a3

He so lap ay =

L =

V vat chat = V 1 nguyen t = = =

TRNG HP HE LAP PHNG TAM KHOI IV O mang = a3

V vat chat = V 2 nguyen t = 2.

Vi R =

V vt cht = =

He so lap ay = = 0,68

ky hieu nut o la [[ ]].BIEU DIEN CAC NUT - CHUOI - MAT TINH THE CH SO MILLER

a. Ky hieu mot nutMot nut bat ky cua mang lien he vi goc bang mot vect tnh tien :Toa o cua nut o tren ba truc toa o la : n1a1, n2a2, n3a3. Neu a1, a2, a3 la o dai n v tren ba truc th toa o cua nut la n1, n2, n3 ky hieu nut o la [[n1 n2 n3]] hay n1n2n3.

Neu ni < 0 ky hieu , vi i = 1, 2, 3.

V du: Mot nut mang co toa o thoa:MOT SO NUT C BAN TRONG TINH THE LAP PHNG xyZ 00010000

001 01

11

011 10

[[ 011]][[000]][[100]][[110]][[010]][[001]][[101]]xyz[[111]] b. Ky hieu mot chuoi (chieu) trong tinh the Qua goc ke ng thang song song vi chuoi noi tren. Ngoai goc ra, nut gan goc nhat nam tren ng thang co ky hieu [[uvw]] th chuoi mang nay co ky hieu [uvw].MOT SO CHIEU C BAN TRONG TINH THE LAP PHNG[001]z[010][001][100]xy000[100][010]zxy[101][011][011][110][101]000zxy[111][111][111][111]000c. Ky hieu mot mat mange ky hieu cho mot mat mang hay mot ho mat mang song song nhau, ta chon mat nao o nam trong ho nay gan goc nhat. Gia s mat nay cat ba truc toa o theo thong so n1a1, n2a2, n3a3.Ta lap t so kep : at h : k : l = n2n3 : n1n3 : n1n2 ch so Miller (do Miller e xuat): (h k l)

Mot ho mat mang song song nhau co mat mang gan truc toa o nhat cat truc toa o tai: x = 2a1, y = a2, z = 3a3Ta lap t so kep : at h : k : l = 3:6:2 ch so Miller = (362)V DU

Cac mat c ban trong tinh the lap phng

(111)

(210)

(110)(001)(002)zxy - Trong mot ho mat mang, khoang cach gia hai mat lan can nhau c goi la thong so mat mang va c ky hieu d. Ho mat mang co ky hieu (h k l) th thong so mang la dhkl.- Ky hieu mat mang the hien:V tr tng oi cua mat mang oi vi cac truc cua tinh the. So mat song song cat truc trong pham vi cua moi n v dai tren truc Y NGHA CUA K HIEU MAT MANGOa1a2ya1/hza3a3/lHna2/kxCONG THC LIEN HE GIA dhkl VI hkl VA a1, a2, a3dhkl la ai lng quan trong trong cac phep tnh toan cau truc.Xet trng hp Ox Oy Oz; thong so cua ho mat hkl la dhkl.hkl cat ba truc toa o theo o dai a1/h, a2/k, a3/l ke t O.a1, a2, a3 : o dai n v.Phng trnh cua mat phang (h k l) :

hayAx + By + Cz = 1Phng trnh cua ng thang ke t Omat phang (h k l)

x = mA, y = mB, z = mCH va H mp hkl thoa ca hai phng trnh : toa o H(xH, yH, zH) : AxH + ByH + CzH = 1xH = mA, yH = mB, zH = mC mA2 + mB2 + mC2 = 1

Trng hp he lap phng: a1 = a2 = a3 = a

dhkl =

Trng hp he bon phng:a1 = a2 a3

dhkl =

Trng hp he ba phng va sau phng: a1 = a2 a3; = = 900, = 1200

dhkl =

Mang Bravais: mang lap phng tam mat F (cfc)C s cua o mang gom:mot ion Na+ [[000]] va mot ion Cl- [[00]] cach nhau canh cua o mang hnh lap phng.Hay: ion Na+ [[000]] va ion Cl- [[ , , ]].

7. CAU TRUC TINH THE CUA MOT SO TINH THE N GIAN a. Cau truc cua NaClMng Bravais: Thuoc mang lap phng nguyen thuy P vi moi o mang co hai nguyen t c s.C s cua o mang gom:Cs : [[000]]; Cl : [[ , , ]]

b. Cau truc cua CsCl: - Lp th nhat: Moi qua cau c bao xung quanh bi 6 qua cau khac v tr A.co sau v tr hom vao cua lp th nhat thuoc hai loai B va C. c. Cau truc luc giac xep chat AAAAAAAAAAALp th hai: Co the at cac qua cau lp th hai vao v tr B hay C sao cho moi qua cau lp th 2 tiep xuc vi 3 qua cau cua lp th nhat. Gia s lp th hai chiem cac v tr B.BBBCCCBBBLp th 3: co 2 cach xep:+ Cach 1: at cac qua cau len v tr A, roi lp tiep theo la B va c the tao thanh cac lp lien tiep ABABAB Cau truc luc giac xep chat.AAAAAAABBBAAAAAAABBBAAAAAAABBBAAAAAAABBB+ Cach 2: at cac qua cau len v tr C, roi lp tiep theo la A va c the tao thanh cac lp lien tiep ABCABC Cau truc lap phng tam mat. AAAAAAABBBCCCAAAAAAABBBCCCCAU TRUC LUC GIAC XEP CHAT

AAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBBBCau truc luc giac xep chat ABABABAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBBBAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBBBMang luc giac xep chat co o mang Bravais luc giac loai P.CAU TRUC XEP CHAT KIEU LP TAM MATAAAAAAABBBCCCAAAAAAABBBCCCCau truc xep chat ABCABCCau truc xep chat dan en mang lap phng tam mat

Mang lap phng tam mat vi mat xep chat la (111).

Cau truc luc giac xep chat (Mg)

Cau truc xep chat dan en mang lap phng tam mat (Ca)CAC CHAT KET TINH THEO MANG LUC GIAC- Mang Bravais: Lap phng tam mat F.- C s: hai nguyen t carbon v tr nut [[000]] va [[1/4 1/4 1/4]]. - O n v cha 8 nguyen t. Cau truc kim cng co the c mo ta bang hai mang lap phng tam mat, dch chuyen vi nhau theo ng cheo chnh mot oan bang 1/4 ng cheo o.- He so lap ay: 0,34. Khong thuoc mang xep chat.

d. Cau truc cua kim cng

O MANG TINH THE KIM CNG DI CAC GOC NHN KHAC NHAU8. MANG AO (MANG NGC)Ta bieu dien ho mat mang song song mat ( ) tc ho mat (100) bang mot vect vuong goc mat phang ( ) va a1* = 2/d100.

a. NH NGHA

Cho mot mat thuan co ba vect c sO

a1

Goi Oa1la hnh chieu cua tren phap tuyen cua mat (100) tc Oa1 = d100, ta co:

a1*. Oa1 = 2(100)Tat ca cac ieu kien tren cho phep ta co :

Tng t ta thanh lap cac vect sao cho:

O

a1

1 neu i = j ij = 0 neu i j Mang c xay dng tren ba vect c goi la mang ngc cua mang thuan a cho.

Cac nut cua mang ngc co the xac nh bi vect:

MOT SO TNH CHAT CUA MANG AO (MANG NGC)1. Goi V la the tch cua o mang thuan; V* the tch cua o mang ngc, ta co:

Suy ra: V.V* = (2)3

co the bieu dien mot ho mang thuan bang mot nut cua mang ngc.moi nut cua mang ngc co the bieu dien cho mot ho mang thuan (tc mang tinh the) ve hng va thong so mat mang.

phai vuong goc mat mang (h k l) cua mang thuan va co o dai :

3. ch li cua mang ngc : neu noi goc toa o vi mot nut (h k l) cua mang ngc c bieu dien bang vect tc la : V DUNut [[312]] cua mang ngc bieu dien ho mat mang (312) cua mang thuan. Ho (312) co hng vuong goc vi la hng cua vect noi t goc O en nut [[312]] cua mang ngc va co thong so:

4. Mang ngc cua mot mang ngc la mang thuan.

V DU Nut [[111]] c bieu dien bi vec t G111 trong mang ngc se bieu dien cho ho mang (111) co thong so d111 trong mang thuan.Nut [[222]] c bieu dien bi vec t G222 trong mang ngc se bieu dien cho ho mang (222) co thong so d222 trong mang thuan.

5. Nut cua mang ngc ma ky hieu la [nh, nk, nl] tng ng vi mot ho mang thuan (nh, nk, nl) va co thong so n lan nho hn thong so cua ho (h k l) .

Ta co: G222 = 2G111