I'm laying slate tile over linoleum that was installed about 6 months ago....the linoleum is in very good condition, very smooth with no rips or lifting. I've done some research and figured I could put down cement board and then lay the tile on that. The floor under the linoleum is cement. Is there a special drill/special screw necessary to attach the cement board to the cement foundation?
You will have to scrape off the linoleum cover and the adhesive as well which was used for laying the linoleum sheet in order to ensure that the laying of slate tiles however laid gets a bonding with the original floor without which the money you spend to get the best value of it will never be guaranteed.
Here's how a tile contractor would do it. First off you need to look how the tile floor will finish to the other floorings it will tie into. Ideally you want the same level when finished. It is common though to have a slight offset (up to 1/4 is acceptible). So remove whatever you need to be 1 lower then the other floor, before you install 1/2 hardibacker and the tile. What you listed above is a waste of time and money. You don't need plywood and hardibacker. You use one or the other. The industry has gotten away from tile directly on plywood, so don't consider that. Use the hardibacker. My guess is when you remove the vinyl and hardwood, you will be about 1 down. Screw the subfloor down then attach the hardibacker with 1 5/8 screws and lay the tile. If it is within the tolerance I noted above (1/4), you can buy a transition strip to apply at the change from tile to existing flooring. If your floor is up and down, do this, use a level as a straight edge on the floor, marking the high and low spots. The high spots need to be feathered out and the low spots need to be filled in. You should do this before you install the hardibacker. You can listen to a kid that worked with his dad or a listen to guesses from people that tiled a floor or two. You can even listen to a woman on here that claims to have been a remodel contractor, master electrician, building inspector and everything else she claims to have been, or you just take free advice from a guy that does tile floors. Your call.
You would be a lot better off removing the linoleum. You wouldn't need the expense/hassle of installing cement board, since you would be tiling directly on concrete. If you really don't want to do that, you will need to use a hammer drill and Tapcons. Use 3/16 x 1-3/4 screws. with a 5/32 masonry bit. Remember that you are adding height to the floor as well, and will need to make transitions to other surfaces. If there are any doors that open into the kitchen, they may need to be cut. Hope this helps.
Your best to remove the vinyl but it is a LOT of hard work and truly not needed if it is down tight and no air pockets etc.. No cement board is needed at all . A wasted expense.You really can rough up the vinyl w/ belt sander, and tile over the vinyl w/ proper thin set.. Allow an extra day or two to let the thin set dry since moisture has no where to go.. Make sure your use a damp sponge to wipe off back of slate since the way its cut it leaves a residue on the back ( dusty) that will not let thin set bond properly.. A gauged slate is easy to set just like any tile its the ungauged slate you ll have to be more carefull with.. Seal the slate at LEAST once before installing or thinset and grout may stain or be almost impossible to remove GL
I really like Woodtick's answer, and i want to encourage you to not bother with trying to install concrete board on top of a concrete floor. Not only is it very redundant, and expensive, and timely, but you also run the risk of seeing your concrete board crack under the tile, which would cause uneven surfaces and even tile breaks after installation. Concrete board is not very flexible, and is designed to go over soft, water damage prone materials such as wooden studs and joists. It would be a more structurally sound idea, and easier, and cheaper to buy a heat gun to remove the linoleum and adhesive with a scraper and lay tile on that.