You can kill areas of unwanted grass without poisoning the soil, and all you'll need is cardboard and straw. There are even some fancy names for this earth-friendly "technique" of clearing a spot of its current vegetation. Some refer to it as solarization or sheet mulching, while informal enthusiasts call it lasagna gardening, due to the layers of materials being used. The concept is simple: Deprive grass of the elements it requires, and it will die. .
Mow or trim the grass as low as possible. Don't rake the clippings away. They'll contribute to the natural decomposition process and enrich the soil. Soak the area deeply with water.
Top the area with a single layer of cardboard, overlapping edges where necessary to cover the ground. Drench the cardboard with water. Add another layer of cardboard and soak it well. Repeat until you have a 1-inch-thick pile of wet cardboard.
Pack a layer of straw over the cardboard 2 to 5 inches thick. Wet it thoroughly.
Top the straw with another ½- to 1-inch-thick pile of wet cardboard. This will help to hold everything in place for the next 4 to 8 weeks, as the pile smothers and kills the grass underneath.
Cultivate the decomposed grass, cardboard and straw into the soil below.