You did not do anything wrong and while that may not be an answer that increases your confidence in the camera, it is the most likely cause. The failure that you described, a partially black shot with just a small part of the image visible, is an indication that the mirror was stuck and did not "flip up" in time or, at all, when the shutter fired. This can occasionally happen when taking rapid continuous shots, but, usually means that there is a possibly progressive issue with the spring mechanism that lifts the mirror. The only way to minimize the possibility of it occurring again is to have the body checked out professionally. Even if it is new, there may be a factory defect.
Please keep in mind that my diagnosis & solutions provided are directly dependent on the accuracy of your description of the problem. As with any "do it yourself" fixes, success is a "team effort", since I can't see or touch the camera, and relies on the customer's manual dexterity and ability to follow the instructions well. If the "do it yourself" approach doesn't work out for you and you need conventional repair, please let me know.
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Have you attempted to transfer the full series of photos to the computer? If so, is the result the same?
Recovery is possible if the problem was a card issue. Generally a Corrupted Photo File will look like the attached example, but this unit may be displaying black instead of the scrambled portion.
Once you have transfered all other files, you can try the Recovery suggestions below on the card.
For windows Try the Program Download at the link below. (This one will allow you to recover up to 1gb of photo files absolutely free and save them to a new folder on your hard drive.
Make sure that before you open the program, after installing it, put the card in first. When you open the program, it will try to detect it when you click on "Media Recovery".
If unsuccessful try (The ones below have a charge to save the recovered files)http://www.tech-pro.net/flash-recovery.html orhttp://www.cardrecovery.com/
For Mac Tryhttp://www.cardrescue.com/http://www.stellarinfo.com/mac-photo-recovery.htmorhttps://www.piriform.com/recuva
If the program is able to recover the photo files you will be given the option to purchase (usually around $40) the function that allows you to save and retain your photo files. Depending on how important these photos are, can determine if the cost is worth it.Also, some retail camera shops and office supply stores offer Memory card recovery services if you do not feel comfortable running the process yourself.If you require additional information, please use the Reply to Expert to contact me. Click the ratings only after our exchange is complete and you are satisfied.
If you are satisfied that my answer is accurate, please do not forget to rate my answer OK, Good or Excellent.Thank you