These are the heads of housholds in 1870 TN. Are you sure you have looked at each one?

African Americans in the 1870

Surname,Given Name,Age,Sex,Race,Birthplace,State,County,Locale,M593-Roll,Part,Page

WILLIAMS,FRANK,40,M,B,TN,TN,DAVIDSON,5-WD NASHVILLE,1523,0,293
WILLIAMS,FRANK,13,M,B,TN,TN,FAYETTE,GALLAWAY P O,1526,0,314
WILLIAMS,FRANKLIN,23,M,B,TN,TN,DECATUR,DECATURVILLE,1524,0,31
WILLIAMS,FRANK,21,M,B,TN,TN,TIPTON,BLOOMINGTON,1567,0,126
WILLIAMS,FRANKLIN,22,M,B,TN,TN,MONTGOMERY,GUTHRIE P O,1551,0,182
WILLIAMS,FRANK,16,M,B,TN,TN,MARSHALL,MOORESVILLE P O,1546,0,158
WILLIAMS,FRANK,25,M,B,TN,TN,RUTHERFORD,MURFREESBORO P O,1557,0,406
WILLIAMS,FRANK,34,M,B,TN,TN,FAYETTE,MACON P O,1526,0,376