'My_Files\Placed_Calls.txt'
First thing comes to my mind, you should use pathdelim to propely specify a sub-directory in a cross-platform (and a safe) way:
'My_Files'+pathdelim+'Placed_Calls.txt'
Second, when you Rewrite file, you open it too.
//empty it.
Rewrite(Placed); // <------ this is absolutely enough
//Open it.
Append(Placed); <----- I can hardly tell, why aren't you getting an IO error here.
And don't forget to CloseFile(Placed) after you've processed it, or you'll get data not written completely or an IO error.
(UPD) One more thing to check:
You may get a strange behaviour of CreateDir('My_Files'); in case the directory already exists. You should either delete it first or check if it exists and not create it again in such case.