Solid State Physics

FISIKA ZAT PADAT

UK II PERTEMUAN KE-1

Anif Jamaluddin1

1Prodi P.Fisika, PMIPA, FKIP, Universitas Sebelas Maret, Surakarta

Solid State Physics

• Review Bidang Kristal, Jarak Antar Bidang• Non Destruktif Test (NDT)• XRD Komponen

X-Ray SampleDetektor

• Prinsip Kerja XRD Bragg’s Law Faktor Intensitas Sinar-X

• Analisa Hasil (Kualitatif) Intensitas Vs Sudut 2θ Menentukan Struktur Kristal Sudut 2 θStudi Kasus

OutlineOutline

Solid State Physics

Index MillerIndex Miller

DirectionDirection

• [hkl] represents a direction • <hkl> represents a family of directions • (hkl) represents a plane • {hkl} represents a family of planes

Solid State Physics

Bidang KristalBidang Kristal

Solid State Physics

Bidang KristalBidang Kristal

Intercepts → 1 Plane → (100)Family → {100} → 3

Intercepts → 1 1 Plane → (110)Family → {110} → 6

Intercepts → 1 1 1Plane → (111)Family → {111} → 8(Octahedral plane)

Solid State Physics

Atomic Packing Factor (APF)

APF = Volume of atoms in unit cell*

Volume of unit cell

*assume hard spheres

a=2(r Na)+ 2 (r Cl)V=a^3

Solid State Physics

Pengujian Karakterisasi tanpa merusak sample/bahan

• XRD (X-Ray Diffraction) • XRF (X-Ray Florosence)• SEM (Scanning Electron

Microscopy)• dll

Mengetahui Struktur Mikro BahanMengetahui Unsur Penyusun BahanMengetahui Topografi dari Bahan (Secara Visual)

Goal Menetukan Struktur Kristal (XRD)X-Ray λ = +- nmStruktur atom = +- nm

Solid State Physics

Skema alat XRDSkema alat XRD

Analisa Hasil

Sample (Powder)

Detektor

PC (Hasil)

Source Of X-Ray

Bragg’s Law Faktor StrukturLatihan

Solid State Physics

Solid State Physics

Source Of X-RaySource Of X-Ray

Electron (Katoda)

Anoda (Cu,Fe Co dll)

X-Ray

Solid State Physics

Jenis Sinar-XJenis Sinar-X

lmin

Bremsstrahlung

Characteristic Spectrum

(target dependent)

Solid State Physics

Bragg LawBragg Law

( )2222

2

222

4sin

sin2

lkha

N

a

lkh

ad

nd

hkl

nhkl

++=

=++

=

=

lq

lq

Solid State Physics

Skema Deteksi Sinar-XSkema Deteksi Sinar-X

2q

q

Sample

DetectorSource

Solid State Physics

• A perfect crystal contains single planes (delta function for I(q))

• An imperfect crystal will show broadened peaks.

• Liquid or amorphous materials will give a continuous function

2q Vs Intensitas2q Vs Intensitas

Solid State Physics

Faktor StrukturFaktor Struktur

• Faktor Hamburan

• Faktor Struktur Kisi

• Faktor Geometri

F(h k l)=f

Solid State Physics

Faktor StrukturFaktor Struktur

Contoh :BCC, terdapat 2 atom dalam stuan kubus, dengan basis koordinat (0 0 0)dan (½ ½ ½ ) maka

Sehingga :S (hkl)= 0 jika (h+k+l)= ganjilDan Fhkl maksimal = 2 F, jika (h+k+l)= genap

F(h k l)=f

Solid State Physics

Faktor StrukturFaktor Struktur

Table of possible diffractionsB.C.C. F.C.C. Simple Cubic h2+k2+l2

----- ----- 100 1

110 ----- 110 2

----- 111 111 3

200 200 200 4

----- ----- 210 5

211 ----- 211 6

----- ----- ----- 7

220 220 220 8

----- ----- 221 / 300 9

310 ----- 310 10

----- 311 311 11

222 222 222 12

----- ----- 320 13

321 ----- 321 14

----- ----- ----- 15

400 400 400 16

Solid State Physics

Hasil XRDHasil XRD

Solid State Physics

Studi KasusStudi Kasus

2θ θ radian sin(θ) sin^2(θ) sin^2(θ)/ sin^2(θ)min sin^2(θ)/2 sin^2(θ)/3 sin^2(θ)/4 sin^2(θ)/5 sin^2(θ)/

0,1444

44,67300 22,33650 0,38985 0,38005 0,14443 1,00000 0,07222 0,04814 0,03611 0,02889 0,99996

65,02100 32,51050 0,56742 0,53745 0,28886 1,99992 0,14443 0,09629 0,07221 0,05777 1,99984

82,33300 41,16650 0,71849 0,65825 0,43329 2,99992 0,21665 0,14443 0,10832 0,08666 2,99981

98,94500 49,47250 0,86346 0,76009 0,57774 4,00003 0,28887 0,19258 0,14444 0,11555 3,99988

116,38000 58,19000 1,01561 0,84980 0,72216 4,99992 0,36108 0,24072 0,18054 0,14443 4,99973

137,13000 68,56500 1,19669 0,93083 0,86645 5,99891 0,43322 0,28882 0,21661 0,17329 5,99868

Sinar X yang dihasilkan oleh XRD berasal dari anoda Cu dengan panjang gelombang sinar-X 1,54056 0A. Hasil XRD diperoleh puncak-puncak intensitas sinar-x pada sudut 2θ = 44,6730; 65,0210; 82,3330; 98,9450; 116,380; 137,130 , Tentukan struktur kirstal dari bahan yg diamati?Jawab :Berdasarkan deret pada table. (1,2,3,4,5dst) maka Struktur bahan tersebut adalah simple kubik

Solid State Physics

Studi KasusStudi Kasus

( )2222

2

4sin lkh

a++=

lq

Untuk h2+ k2 +l2 =1a2= l(h2+ k2 +l2 )/sin2(q)a2= 1,54056 0A(1)/ 0,38005a=2,0268A

Solid State Physics

PustakaPustakaBurn Gerald, Glazer A.M, “Space Groups for solid State Scientists”, Second Edition, Academic Press New York,1990Cullity B.D, “Element of X-Ray Diffraction” Second edition, Addison-Wesley Publishing, 1977Ducan McKey, Christine Mckie, “Essentials Of Crystallography”, Black Well Scientific Publication, 1986http://database.iem.ac.ru/mincryst/http://webmineral.com/crystal/trigonal+hexagonalscalenohedral.shtml http://rockhounds.com/rockshop/xtal/part6.html ……,PDF-ICDD(Powder Diffraction File, International Center for Diffraction Data) Database,1998 (CD-ROM)Suryanarayana, Norton Grant, “X-Ray Diffraction Practical Approach”, Plenum Press New York, 1998Verma A.R, Srivastava O.N “Crystallography Applied to Solid State Physics”, Second Edition, New Age International Publishers India, 1991