Recently I've been getting Trinity Force on Riven. Should I get a Frozen Mallet instead, or stay with the Tri-force?
Usually on Riven, you shouldn't get either one of them.
You can get Frozen Mallet against enemies with true damage (Irelia/Olaf), or if the enemy is really mobile (Ezreal, Corki, Ahri et al.) so you can slow them and chase them down.
Triforce on Riven is a snowball item (get ahead, buy Triforce, get ahead even more) but Brutalizer and Bloodthirster do this even better. So instead of getting Triforce, try to get Brutalizer (if ahead) or just get BT, and after that get Guardian's Angel. You will do way more damage with BT, have more sustain (life leech), be tankier (shield stronger cause you got more AD) and if you get GA soon afterwards, you wont even get focused.
Frozen Mallet gives you very little over Trinity Force. Trinity force you are getting way more damage, and the bonus hp from Frozen Mallet is not worth much without armor and magic resist to back it up. There are many better items to go for than Frozen Mallet; you are paying 3250 gold for an item that gives 20 AD, which is not a smart choice given Riven scales extremely well with AD. You can get that AD for less than 1k gold with double Doran's or something else.
In case you think that Frozen Mallet buffs Atma's Impaler nicely, Frozen Mallet only provides a bonus 10.5 AD with Atma's, which is pitiful at best. Trinity matches that 10 AD inherently.
So maybe you want to pay for the reliable slow. That is reasonable, although with Trinity Force Riven has a ~58% chance of triggering the slow in 3 attacks factoring in attack speed. This means that every 2.5 seconds you have a ~58% chance of applying the slow again before the previous slow wears off. Those chances aren't that bad, and in practice if your target gets away it's likely not only because you didn't slow them. Dashes, knockback, and flashing all will render slows less than effective for chasing.
Having said all that, even choosing Trinity Force is not the best move. Although the stats are amazing for one item slot, you are sinking at lot of gold into Sheen, which remains next to useless until finally built into Trinity Force (you have no mana or AP scaling, and base damage bonus is low before Trinity Force). There are many better items for early-mid game you should be considering, like The Brutalizer or Wriggle's Lantern. You are typically in the jungle or top lane as Riven, so both of those items will help you do better in lane then a Phage, Sheen, or Zeal will by providing a larger damage boost and in the case of Wriggle's a lot of needed sustain.
Please refer to this astounding build guide for Riven. It helps me out quite a lot! I currently have won nearly every single game as Riven thanks to Goldfather8.
After the beginning buy, I usually go TriDorans, then sell one Dorans for a Wriggles, and then get a Bloodthirster if its an AD champ, or a Hexdrinker if its an AP champ in my lane. If its Double AP, I get GA then FoN. If its just one AP I get GA then Thornmail.
My end build:
Defensive Lv 2 boots Wriggles Bloodthirster GA FoN / Thornmail / Warmogs
if you get really fed and dominate the game:
If your team has very little CC:
If both are true, Sell the Wriggles and buy both.
That's just me though.
Trinity force is pretty useless on Riven. She doesn't need the attack speed very much, and Sheen is not useful on her compared to other champions. The only useful item is Phage, which should be built into the Frozen Mallet.
Riven is a tanky DPS, and Frozen Mallet suits that role well, providing amazing health, a little bit of damage, and a very useful slow that works well with her kit.
Personally though, I prefer Warmog's over all three.
trin force is just useless cause you normaly attack just 1x or 2x with the effect. frozen mallet can be usefull cause riven is after she used spells kill able if she didnt got a good position/hp/armor ... but i think bloodthirster shild > hp from frozen mallet in the end but its just my personal way to play i pref to play shoes+blood+maw+ga+lastw+blood/frozenheart/omen
Get frozen mallet and Atma's impaler; you don't want AS on Riven and the sheen doesn't help much.
I would recommend going Frozen mallet if you want a safe lane/team fight, frozen mallet gives a lot of utility since all your attacks slows by 40%, and since you wont get any Attack speed items as riven you wont proc Trinitys slow very often which is bad. So I would definitely go for Frozen Mallet unless you totally dominate and just stomp them in teamfights.
I agree with Peter, frozen mallet is almost necessary on a lot of AD bruisers right now as the slow, health, and damage it gives is really really good. trinity force would be good for her if the cost wasn't so astronomical. instead you could get a bloodthirster and frozen mallet for just a bit more than a trinity force and get more out of it in the long run. so my money goes to frozen mallet.
You shouldn't really ever purchase these items on Riven. Bloodthirster x 3 - Merc - LW - GA. If you're getting bursted, Replace a Bloodthirster lategame with a Warmogs.