How to replace carpet with tile in entryway

Question

We have an 18 year old cat who unrinates on or near doors that lead outside. I'm looking for solutions to make it easier to clean up/eliminate the odor. We do eventually plan on replacing the carpeting the room he's targeting right now, but not until he crosses the rainbow bridge. One thought I had was to install tile in front of the door, to provide an impermeable surface we can easily clean (especially if we put a rug right there that's machine washable, much easier to wash a rug than carpet).

Below are pictures of the space, including a paint outline of where the tile would go.

My questions are as follows:

1. Is this a good idea?
2. Is there a specific phrase to describe what we're trying to do that I can Google for information?
3. Assuming the floor beneath is level (and there isn't wood under the carpet), my plan was to cut the carpet away from where we intend to install the tile, then treat the subfloor directly with cleaners before sealing the area with stain-blocking primer. Would you recommend installing or treating with anything else prior to following instructions for installing tile? Removing the tainted subfloor would probably be better, right?
4. Is there a better idea for how to turn this pee zone into something I can clean up after?
5. What would be the best way to handle the curved transition zone?

My husband and I are moderately experienced DIY'ers but we haven't done tile before.

And as is required on the Internet, cat tax. The jerk in question. His face isn't blurred for his protection, it's because he was mid-meow asking why I was taking pictures.

Answer 1

It's not clear whether you'd like to keep the hard floor after your friend departs, but you might consider vinyl plank flooring. It would be much quicker and simpler and can be quite beautiful. You'd simply remove the carpet, install 1/4" underlayment plywood, and stick down the vinyl.

Modern vinyl plank flooring is quite durable and attractive. Don't let the name make you think it'll look cheap. Select a product that's self-sealing at the joints. You can cut it with a knife (straight single cuts) or a jigsaw (curved or compound cuts) and it doesn't require grouting.

If you do want to use ceramic or porcelain tile you'll probably need to add at least 1/2" to your subfloor. You need a minimum of 1-1/4" to prevent cracking of grout joints and the tile itself.

Also, I'd consider a full rectangle. You'll find that your carpet suffers less wear and soiling if you have enough room to enter and remove footwear before making contact. This is a common strategy in snowy climates. You could also do a clipped corner if it protrudes into your space too far. That would still be easier than cutting curves and fitting your carpeting to it.