Question

ʜᴏᴡ ᴛᴏ ᴄᴀʟᴄᴜʟᴀᴛᴇ ᴅɪsᴛᴀɴᴄᴇ ɪɴ ғᴄᴄ ᴀɴᴅ ʙᴄᴄ ᴄʀʏsᴛᴀʟ sᴛʀᴜᴄᴛᴜʀᴇs?

ᴘʟᴢ ʜᴇʟᴘ.

ᴄʟᴀss 12ᴛʜ​

Answer 1

Answer:

for a reciprocal lattice vector G→" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-style: normal; font-variant: inherit; font-weight: normal; font-stretch: inherit; line-height: normal; font-family: inherit; font-size: 15px; vertical-align: baseline; display: inline; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">G⃗ G→ to the case of a cubic lattice. For FCC and BCC lattices you can express the reciprocal lattice vectors (usually written in terms of the Miller indices (h,k,l)" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-style: normal; font-variant: inherit; font-weight: normal; font-stretch: inherit; line-height: normal; font-family: inherit; font-size: 15px; vertical-align: baseline; display: inline; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">(h,k,l)(h,k,l)) in terms of the reciprocal lattice vectors for a SC system BUT this is not quite correct!

In fact, the Miller index (1,0,0)" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-style: normal; font-variant: inherit; font-weight: normal; font-stretch: inherit; line-height: normal; font-family: inherit; font-size: 15px; vertical-align: baseline; display: inline; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">(1,0,0)(1,0,0) for a BCC lattice does not describe a family of lattice planes, because if you look at a BCC lattice, there are extra atoms at the centre of each SC cube. This means that the the correct lattice vector is in fact (2,0,0)" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-style: normal; font-variant: inherit; font-weight: normal; font-stretch: inherit; line-height: normal; font-family: inherit; font-size: 15px; vertical-align: baseline; display: inline; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">(2,0,0)(2,0,0).

Explanation:

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