Solid-State Relation Cross Scans

Band Occupancy Three-Row Scan

Empty, partial, and filled rows keep slot accounting visible. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Zero electrons is the empty boundary row

The band has 4 sites times 2 states per site, so total slots are 8. Electron count 0 gives filled slots 0 and empty slots 8.

slots=4⋅2=8,filled=0,empty=8slots=4\cdot 2=8,\quad filled=0,\quad empty=8
Band row emptyOccupancy is finite slot accounting only.sites=4statesPerSite=2electrons=0slots=8filled=0empty=8occupancy=empty

Five electrons leave destination slots

The band has 4 sites times 2 states per site, so total slots are 8. Electron count 5 gives filled slots 5 and empty slots 3.

slots=4⋅2=8,filled=5,empty=3slots=4\cdot 2=8,\quad filled=5,\quad empty=3
Band row partialOccupancy is finite slot accounting only.sites=4statesPerSite=2electrons=5slots=8filled=5empty=3occupancy=partial

Eight electrons fill every toy slot

The band has 4 sites times 2 states per site, so total slots are 8. Electron count 8 gives filled slots 8 and empty slots 0.

slots=4⋅2=8,filled=8,empty=0slots=4\cdot 2=8,\quad filled=8,\quad empty=0
Band row filledOccupancy is finite slot accounting only.sites=4statesPerSite=2electrons=8slots=8filled=8empty=0occupancy=filled