1x1 unit cell dimensions

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Hi All,

Let's consider a Copper bulk material. This one can be reproduce (ad infinitum) by using a cubic unit cell (fcc) of lattice constant a. Let's cut this bulk along the (110) plane and expose the Cu(110) surface to the vacuum. My question is: which are the x and y dimensions of a (1x1) unit cell ? After my calculations the 1x1 unit cell, on the Cu(110) surface, will have the x and y dimensions of a and a*sqrt(2). However, according to my solid state course, the x and y dimensions of a 1x1 unit cell, on the Cu(110) surface, are of a and a*sqrt(2)/2. I simply can not understand from where it is coming the division to 2. I would expect to have only a*sqrt(2) as this is a cube face diagonal (and we cut along a cube face diagonal to get the 110 surface).

Can anyone help me with an explanation?

With all the best wishes,
Eduard
 

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