Struktur kristal

1. STRUKTUR KRISTAL:
HEXAGONAL
Kelompok 2
Gema Sukmawati S
Ingriet Sintha Karel
Rahmaniah

2. (http://2012books.lardbucket.org/books/principles-of-general-chemistry-v1.0)

3. STRUKTUR HEXAGONAL

4. GALLIUM NITRIDE (GaN)
https://en.wikipedia.org/wiki/Gallium_nitride

5. STRUKTUR KRISTAL GALLIUM NITRIDE
(http://www.academicjournals.org/)
Struktur kristal hexagonal
(https://en.wikipedia.org/wiki/Wurtzite_crystal_structure)

6. Gallium Nitride (GaN) (Balkas et al., 1995)
Jumlah Puncak = 23

7. MENCARI PARAMETER KISI
1
𝑑2 =
4
3
ℎ2+ℎ𝑘+𝑘2
𝑎2 +
𝑙2
𝑐2 (1)
𝜆 = 2𝑑 𝑠𝑖𝑛𝜃 𝜆2
= 4𝑑2
𝑠𝑖𝑛2
𝜃 atau 𝑠𝑖𝑛2
𝜃 =
𝜆2
4𝑑2 (2)
𝟏
𝒅 𝟐 =
𝟒
𝟑
𝒉 𝟐+𝒉𝒌+𝒌 𝟐
𝒂 𝟐 +
𝒍 𝟐
𝒄 𝟐 =
𝟒𝒔𝒊𝒏 𝟐 𝜽
𝝀 𝟐
𝒔𝒊𝒏 𝟐
𝜽 =
𝝀 𝟐 𝒉 𝟐+𝒉𝒌+𝒌 𝟐
𝟑𝒂 𝟐 +
𝝀 𝟐 𝒍 𝟐
𝟒𝒄 𝟐
Jarak antar bidang, d:
Menurut Bragg :
Penggabungan pers.
(1) dan (2)

8. MENCARI PARAMETER KISI
Menggunakan
hubungan
sin2
𝜃 −
𝜆2
3𝑎2
ℎ2
+ ℎ𝑘 + 𝑘2
−
𝜆2
4𝑐2
𝑙2
= 𝐷sin2
2𝜃sin2
𝜃 =
𝜆2
4
∙
4
3
ℎ2
+ ℎ𝑘 + 𝑘2
𝑎2
+
𝜆2
4
∙
𝑙2
𝑐2
, dan
sin2
𝜃 = 𝐶𝛼 + 𝐵𝛾 + 𝐴𝛿,
Diperoleh
bentuk Keterangan: 𝐶 =
𝜆2
3𝑎2 ; 𝛼 = ℎ2
+ ℎ𝑘 + 𝑘2
𝐵 =
𝜆2
4𝑐2 ; 𝛾 = 𝑙2
𝐴 =
𝐷
10
; δ = 10sin2
2θ
Nilai C, B, dan A dapat diperoleh
dari 3 persamaan:
𝜮𝜶𝒔𝒊𝒏 𝟐
𝜽 = 𝑪𝚺𝜶 𝟐
+ 𝑩𝜮𝜶𝜸 + 𝑨𝜮𝜶𝜹
𝜮𝜸𝒔𝒊𝒏 𝟐
𝜽 = 𝑪𝜮𝜶𝜸 + 𝑩𝚺𝜸 𝟐
+ 𝑨𝜮𝜸𝜹
𝜮𝜹𝒔𝒊𝒏 𝟐
𝜽 = 𝑪𝜮𝜶𝜹 + 𝑩𝜮𝜸𝜹 + 𝑨𝚺𝜹 𝟐

9. Puncak 2 Radian 2 h k l  Radian   2 g g2 g sin2 (2) sin2 () d d2 d gd sin2() gsin2 () dsin2 ()
1
32.388
0.565277238 1 0 0 16.194 0.282638619 1 1 0 0 0 0.286920866 0.077779935 2.869208664 8.232358356 2.869208664 0 0.077779935 0 0.223166863
2
34.563
0.603238149 0 0 2 17.2815 0.301619075 0 0 4 16 0 0.321842983 0.088248553 3.21842983 10.35829057 0 12.87371932 0 0.352994211 0.284021775
3
36.853
0.643206189 1 0 1 18.4265 0.321603095 1 1 1 1 1 0.359716902 0.099911542 3.597169016 12.93962493 3.597169016 3.597169016 0.099911542 0.099911542 0.359398702
4
48.077
0.839101944 1 0 2 24.0385 0.419550972 1 1 4 16 4 0.553600583 0.165934356 5.536005827 30.64736052 5.536005827 22.14402331 0.165934356 0.663737425 0.918613563
5
57.776
1.008381429 1 1 0 28.888 0.504190714 3 9 0 0 0 0.71566504 0.233384659 7.156650399 51.21764493 21.4699512 0 0.700153977 0 1.670252413
6
63.449
1.107393957 1 0 3 31.7245 0.553696979 1 1 9 81 9 0.800196155 0.276502883 8.001961553 64.0313887 8.001961553 72.01765398 0.276502883 2.48852595 2.212565442
7
67.811
1.183525219 2 0 0 33.9055 0.591762610 4 16 0 0 0 0.857370639 0.311168487 8.573706392 73.5084413 34.29482557 0 1.244673949 0 2.667867248
8
69.103
1.206074873 1 1 2 34.5515 0.603037437 3 9 4 16 12 0.872772897 0.321655458 8.727728974 76.17325304 26.18318692 34.91091589 0.964966374 1.286621832 2.807321660
9
70.510
1.230631656 2 0 1 35.255 0.615315828 4 16 1 1 4 0.888682794 0.333178834 8.886827942 78.97571087 35.54731177 8.886827942 1.332715336 0.333178834 2.960902971
10
72.909
1.272502104 0 0 4 36.4545 0.636251052 0 0 16 256 0 0.913628559 0.353054907 9.136285586 83.47171431 0 146.1805694 0 5.648878512 3.225610458
11
78.413
1.368565026 2 0 2 39.2065 0.684282513 4 16 4 16 16 0.959657005 0.399572171 9.596570049 92.0941567 38.3862802 38.3862802 1.598288685 1.598288685 3.834522331
12
82.037
1.431815758 1 0 4 41.0185 0.715907879 1 1 16 256 16 0.980808446 0.430733208 9.808084459 96.19852075 9.808084459 156.9293513 0.430733208 6.891731322 4.224667680
13
91.106
1.590099668 2 0 3 45.553 0.795049834 4 16 9 81 36 0.999627427 0.509651071 9.996274273 99.92549934 39.98509709 89.96646846 2.038604286 4.586859642 5.094611893
14
95.119
1.660139731 2 1 0 47.5595 0.830069866 7 49 0 0 0 0.992038972 0.544612296 9.920389722 98.41413224 69.44272806 0 3.812286071 0 5.402766222
15
97.647
1.704261655 2 1 1 48.8235 0.852130827 7 49 1 1 7 0.982292523 0.566534722 9.822925229 96.48986006 68.76047661 9.822925229 3.965743056 0.566534722 5.565028216
16
99.953
1.744508947 1 1 4 49.9765 0.872254474 3 9 16 256 48 0.970126239 0.586420138 9.701262387 94.1144919 29.10378716 155.2201982 1.759260415 9.382722215 5.689015632
17
105.000
1.832595715 1 0 5 52.5 0.916297857 1 1 25 625 25 0.933012702 0.629409523 9.330127019 87.05127019 9.330127019 233.2531755 0.629409523 15.73523806 5.872470792
18
105.400
1.839577032 2 1 2 52.7 0.919788516 7 49 4 16 28 0.929479948 0.632778059 9.294799485 86.39329746 65.06359639 37.17919794 4.429446411 2.531112235 5.881545174
19
109.160
1.905201411 2 0 4 54.58 0.952600706 4 16 16 256 64 0.89227999 0.664103634 8.922799895 79.61635797 35.69119958 142.7647983 2.656414535 10.62565814 5.925663834
20
113.570
1.982170431 3 0 0 56.785 0.991085216 9 81 0 0 0 0.840104646 0.699934586 8.401046458 70.5775816 75.60941813 0 6.299411271 0 5.880182972
21
119.080
2.078338073 2 1 3 59.54 1.039169037 7 49 9 81 63 0.763774502 0.743015173 7.63774502 58.335149 53.46421514 68.73970518 5.201106214 6.68713656 5.674960440
22
125.200
2.185152223 3 0 2 62.6 1.092576112 9 81 4 16 36 0.667725785 0.788216158 6.677257849 44.58577238 60.09532064 26.7090314 7.093945423 3.152864632 5.263122528
23
126.030
2.199638456 0 0 6 63.015 1.099819228 0 0 36 1296 0 0.654010441 0.794104386 6.540104405 42.77296563 0 235.4437586 0 28.5877579 5.193525593
Jumlah 81 471 179 3287 369 18.13533604 10.24990474 181.3533604 1536.124843 692.239951 1495.025769 44.77728745 101.2197524 86.8318044
Perhitungan Parameter kisi GaN

10. NILAI PARAMETER KISI GaN (Berdasarkan Tabel Perhitungan)
𝛴𝛼𝑠𝑖𝑛2 𝜃 = 𝐶𝛴𝛼2 + 𝐵𝛴𝛼𝛾 + 𝐴𝛴𝛼𝛿
𝛴𝛾𝑠𝑖𝑛2
𝜃 = 𝐶𝛴𝛼𝛾 + 𝐵𝛴𝛾2
+ 𝐴𝛴𝛾𝛿
𝛴𝛿𝑠𝑖𝑛2
𝜃 = 𝐶𝛴𝛼𝛿 + 𝐵𝛴𝛾𝛿 + 𝐴𝛴𝛿2
44.77729 = 471 𝐶 + 369 𝐵 + 692.239951 𝐴
101.2198 = 369 𝐶 + 3287 𝐵 + 1495.025769 𝐴
86.831804 = 692.239951 𝐶 + 1495.026 𝐵 + 1536.124843 𝐴
Menjadi bentuk matriks A x = B
471 369 692.24
369 3287 1495.026
692.24 1495.026 1536.125
𝐶
𝐵
𝐴
=
44.77729
101.21975
86.831804

11. NILAI PARAMETER KISI GaN (Berdasarkan Tabel Perhitungan)
Mencari determinan matriks A
𝐴 =
471 369 692.24
369 3287 1495.026
692.24 1495.026 1536.125
471 369
369 3287
692.24 1495.026
𝐴 = 471 × 3287 × 1536.125 + 369 × 1495.026 × 692.24 + 692.24 × 369 × 1495.026
− 692.24 × 3287 × 692.24 + 1495.026 × 1495.026 × 471 + 1536.125 × 369 × 369
𝐴 = 2378193151 + 381884212.5 + 381884212.5 − 1575117744 + 1052733066 + 209160294.7
𝐴 = 3141961576 − 2837011105
𝐴 = 304950471.1

12. NILAI PARAMETER KISI GaN (Berdasarkan Tabel Perhitungan)
Mencari determinan matriks A1
𝐴1 =
44.77729 369 692.24
101.21975 3287 1495.026
86.831804 1495.026 1536.125
= 23714738.15
Mencari determinan matriks A2
𝐴2 =
471 44.77729 692.24
369 101.21975 1495.026
692.24 86.831804 1536.125
= 6726298.097
𝑪 =
𝑨 𝟏
𝑨
= 𝟎. 𝟎𝟕𝟕𝟕𝟔𝟓𝟖𝟕
𝑩 =
𝑨 𝟐
𝑨
= 𝟎. 𝟎𝟐𝟐𝟎𝟓𝟕𝟎𝟐

13. NILAI PARAMETER KISI GaN (Berdasarkan Tabel Perhitungan)
Nilai parameter kisi a
𝒂 =
𝝀
𝟑 ∙ 𝑪
= 𝟑. 𝟏𝟗𝟎 Å
Nilai parameter kisi c
𝒄 =
𝝀
𝟐 ∙ 𝑩
= 𝟓. 𝟏𝟖𝟕 Å
𝟓. 𝟏𝟖𝟕 Å
Perbandingan hasil perhitungan dengan data JCPDS
Parameter Kisi
Data JCPDS
(Balkas et al., 1995)
a = 3.190 Å 3.189 Å
c = 5.187 Å 5.185 Å

14. TERIMA KASIH