Penurunan Persamaan d(hkl) pada kristal

d_hkl =

- jarak interplanar diantara bidang (hkl) berturut-turut

- jarak antara titik asal dan bidang (hkl) terdekat

d_hkl dari kristal dengan sumbu orthogonal (α = β = r = 90°)

Orthogonal menunjukkan bahwa 2 vektor saling tegak lurus satu sama lain (dalam hal ini 3 vektor yaitu x,y,z)

kebalikan atau reciprocal dari titik potong hkl adalah bidang xyz

Titik potong di titik A adalah h, sehingga OA bernilai a/h dengan a adalah besar vektor OA

Titik potong di titik B adalah k, sehingga OB bernilai b/h dengan b adalah besar vektor OB

Titik potong di titik C adalah l, sehingga OC bernilai c/h dengan c adalah besar vektor OC

Untuk pembuktian variasi aturan cosinus dapat dilihat disini

d_hkl pada kubus (a=b=c)

d_hkl pada tetragonal (a=b≠c)

d_hkl pada orthorhombic (a≠b≠c)

Dari Penurunan Persamaan Hukum Bragg :

2d sin θ = n λ

keterangan : 

d = d_hkl = jarak antar bidang atau celah (m)

n = 1,2,3, ..... = menunjukkan orde pertama, kedua, ketiga, dan seterusnya ...

λ = panjang gelombang (m)

θ = sudut sinar datang atau sudut sinar pantul (hamburan/ difraksi)

dapat disubstitusikan ke persamaan d_hkl, misalnya d_hkl pada kubus :

Sumber https://www.hajarfisika.com/
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