Playing on home soil has helped many an American player break through in the past.  The indoor tournament in Memphis, an ATP 500 event, offers valuable prize money and ranking points to the host of home hopes who enter it.  Three Americans reached the quarterfinals in Memphis this week:  Michael Russel, Alex Kuznetsov, and Jack Sock.  Here's a look at what lies behind and ahead of them.

Michael Russell:  At just 5 feet 8 inches, Russell doesn't fit the mold of the huge server whom one might expect to excel on an indoor hard court.  The 35-year-old veteran uses his experience to compensate for his lack of size, and he upset seventh seed Michal Przysiezny in the first round.  Rallying after he lost the first set in that match, Russell advanced more routinely over younger compatriot Tim Smyczek.  He will face a much stiffer test in the quarterfinals against two-time major champion Lleyton Hewitt or fierce but mercurial ball-striker Marcos Baghdatis.  This is Russell's second straight quarterfinal in Memphis.  He has not won a main-draw match outside the United States since Wimbledon 2012.

Alex Kuznetsov:  Born in Kiev, the capital of Ukraine, Kuznetsov now divides his time between Pennsylvania and Florida.  He never has cracked the top 100 and ranks currently at No. 141, which meant that he needed to qualify for the Memphis main draw.  Not dropping a set through three qualifying rounds, Kuznetsov eased past David Goffin in his opener.  He won his fifth straight match in Memphis by mounting a comeback from a poor first set to upset eighth seed Mikhail Kukushkin.  This match ended in a third-set tiebreak, which Kuznetsov dominated by mastering the moment more effectively than Kukushkin did.  Up next for him is fourth seed Yen-Hsun Lu, another player who rebounded from losing the first set on Thursday. 

Jack Sock:  Whereas Russell is in the twilight of his career and the 27-year-old Kuznetsov well into his prime, Sock still has his best tennis several years ahead of him.  Fans may remember him best so far for winning the 2011 US Open mixed doubles title with Melanie Oudin.  The 21-year-old American can wield the massive weapons that wreak havoc in Memphis, relying on a serve-forehand combination that recalls former champion Andy Roddick.  He'll need to fire those weapons as fearlessly as he can in a matchup against one of two formidable servers, Croatian giant Ivo Karlovic or Spanish second seed Feliciano Lopez.  Sock survived a third-set tiebreak in his first match before dominating his second opponent.

While the quarterfinals involving Russell and Kuznetsov will unfold during the afternoon session on Friday, Sock will face Karlovic or Lopez during the evening session.