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Question
Does a FCC Tetragonal unit cell exist?
Does a FCC Tetragonal unit cell exist?
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Solution
No it doesn't.
It is because face centered tetragonal lattice is redundant. To be recognized as unique lattice it should be unique and it should be in line with symmetry requirements of the crystal system.Violation of either disqualifies the given array of points as a unique lattice. Answer to the question asked above gives the reasoning as to how redundancy effects the no of lattices. To understand how the notion of redundancy fits this case, visualize a face centered tetragonal unit cell. By definition, this unit cell when repeated endlessly in all direction gives the required space lattice. In this thought process consider two immediate face centered tetragonal unit cells. You can see that a body centered tetragonal can be delineated from two face centered tetragonal lattice. This is another way of saying that given face centered tetragonal unit cell can be comfortably represented by a body centered tetragonal unit cell, and is not unique.
It is because face centered tetragonal lattice is redundant. To be recognized as unique lattice it should be unique and it should be in line with symmetry requirements of the crystal system.Violation of either disqualifies the given array of points as a unique lattice. Answer to the question asked above gives the reasoning as to how redundancy effects the no of lattices. To understand how the notion of redundancy fits this case, visualize a face centered tetragonal unit cell. By definition, this unit cell when repeated endlessly in all direction gives the required space lattice. In this thought process consider two immediate face centered tetragonal unit cells. You can see that a body centered tetragonal can be delineated from two face centered tetragonal lattice. This is another way of saying that given face centered tetragonal unit cell can be comfortably represented by a body centered tetragonal unit cell, and is not unique.
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