Hi! I have information on your William Vaughan m. Francis Elizabeth Herriman, their family history is listed in the Hardeman County Historical Sketches which were published in 1979. I just ordered a used copy of the book and would be more than happy to email you scans of information on your family if you like. Here is what it says: William "Billy" Vaughan was born 1 Mar 1839 in Hardeman Co. is parents were from Tennessee and Virginia. He married 9 Feb 1865 in Hardeman Co., Francis Elizabeth Herriman, born 5 Jun 1844 in Hardeman Co., died 22 Nov 1917 and buried in Walnut Grove Baptist Church Cemetery. Her parents were Joseph and Louisa Jane Harty Herriman. The Vaughan family were early settlers in the county. William was a farmer and served in the Civil War as a private in 22nd Tenn Confederate Army.
My email is firstname.lastname@example.org and I would be more than happy to help you with your research!!