Menjelaskan mengenai Energi Kisi Kristal. Terutama pada materi pengantar fisika Zat Padat. Kristal atau hablur adalah suatu padatan yaitu atom, molekul, atau ion yang penyusunnya terkemas secara teratur dan polanya berulang melebar secara tiga dimensi. Secara umum, zat cair membentuk kristal ketika mengalami proses pemadatan.

1. Energi Kisi Kristal
Disusun Oleh: Kelompok 4
1. Gloria Putri Ixora (42014200)
2. Vedtara Febriani Kurnia Sari (42014200)
3. Milkha Berliana (4201420077)

2. Vibrasi Kristal
Dwiatomik
03 ESPAÑOL

3. Persamaan gerak kristal 1D dari berbagai macam partikel diformulasikan dengan membentuk suatu
kelompok yang berisi p buah atom. Kristal dengan N kelompok memiliki Np jumlah atom. Akan ada
sejumlah p persamaan gerak untuk mencari solusi relasi dispersinya.
Persamaan-persamaan gerak suatu kelompok yang terdiri dari 2 jenis atom dengan massa
berbeda (m1 dan m2) dengan m1 > m2 dapat dinyatakan sebagai:
Gambar 1. Rantai kristal dwiatom

4. dengan us, vs, masing-masing merupakan simpangan zarah bermassa m1 dan m2. Dan
dengan mengambil penyelesaian umum gelombang yang berbentuk:
maka didapatkan harga-harga us1 dan vs1 setelah disulihkan ke persamaan (3.24) dalam
persamaan-persamaan berikut:
Kemudian persamaan (3.25) dapat disederhanakan menjadi
yang merupakan dua persamaan serba sama dengan dua peubah dan akan mempunyai
penyelesaian non trivial apabila:

5. Sehingga melalui ekspansi sederhana diperoleh:
Untuk mendapatkan hasil yang eksak, diambil harga-harga istimewa dari ka dalam syarat batas
periodik. Pada ka yang relatif kecil berlaku cos ka  1- k 2a 2/2 + ...... , sehingga kedua akarnya
berharga
sedangkan untuk ka =   kedua akarnya berharga:

6. Terlihat adanya dua lengkungan dispersi atau adanya dua cabang yaitu cabang optik dan cabang akustik.
Daerah frekuensi pada
yang artinya dalam keadaan demikian kekisi tidak dapat meneruskan gelombang (gelombang
terpadamkan). Perbedaan cabang optik dan cabang akustik dapat dijelaskan pada daerak k0 atau >>.
Hubungan dispersi kekisi dwiatom ditunjukkan pada Gambar 3.7.

7. Gambar 3.7 Grafik Relasi Dispersi Kekisi Dwiatom

8. Perluasan persamaan gerak untuk koordinat umum 3D menjadi lebih kompleks. Kita bahas
detailnya secara kualitatif dengan mengabaikan penyelesaian secara matematis. Logikanya kita
kembangkan dari solusi dalam kasus 1 dimensi.
Persamaan gerak kekisi Bravais monoatomik yang setiap sel satuannya hanya terdiri dari satu
atom dapat dirumuskan seperti halnya pada persamaan (3.5). Dengan bentuk penyelesaian umum
persamaan gelombang 3D untuk gelombang datar.
Generalisasi Untuk Kristal 3 Dimensi
dengan k merupakan arah penjalaran gelombang dan rs adalah posisi vektor atom ke-s. Vektor A
merupakan amplitudo yang mempunyai arah sama dengan arah vibrasi atom. Sehingga vektor ini bila
dipolarisasikan menjadi gelombang longitudinal untuk A sejajar dengan k, atau gelombang
transversal untuk A tegak lurus k. Jadi akan ada 1 gelombang longitudinal dan 2 gelombang
transversal dalam vibrasi kekisi 3D yang ditunjukkan pada Gambar 3.8.

9. Gambar 3.8 Cabang relasi dispersi kristal monoatom 3-D

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Mercury
It’s the closest planet to the
Sun and the smallest one in
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bit larger than the Moon
Venus
Venus has a beautiful name
and is the second planet from
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16. Mercury
It’s the closest planet to
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one in the Solar System
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Venus is the second
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Saturn
Saturn is a gas giant and
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Jupiter
Jupiter is the biggest
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Neptune
Neptune is the farthest
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Mars
Mars is actually a very
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Mercury
It’s the closest planet
to the Sun
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50%
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Mars
It’s the closest planet to
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Venus has a beautiful
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Despite being red, Mars is
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Mercury
It’s the closest planet
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Venus
Venus is the second
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Mars
Despite being red, is
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33. A Timeline Always Works Fine
Venus
It’s the second planet
from the Sun
Neptune
It’s the farthest planet
from the Sun
Mars
Mars is actually a
very cold place
Mercury
It’s the closest planet
to the Sun
Week 1 Week 2 Week 3 Week 4
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It’s the closest planet
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Venus
Venus is the second
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Mars
Despite being red, it’s
actually a cold place
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It’s the closest planet
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C
Venus
Venus is the second
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Z
Mars
Despite being red, it’s
actually a cold place
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9
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