[taregg (OP)]

what is the strongest nonmetal element bonder
to mix with iron instead carbon to make it more
harder metal...

[Bored chemist]

Why do you assume that carbon isn't the best?
It is , for example, very good at making strong bonds.
http://en.wikipedia.org/wiki/Diamond

[CliffordK]

Tungsten is a metal, of course, but it can be alloyed with steel or carbon to make very hard metals.

Here is a list of some common steel alloys:
http://www.onlinemetals.com/steelguide.cfm

Sulfur and phosphorous is added to some of the metals. 

There are several factors that one would be concerned with.
Hardness, brittleness...  important for things like making saw blades and metal working tools.  However, it can be easy to chip or fracture.
Strength, which can be the resilience against fracture.
Machineability, cutting keyways, splines, and etc.
Can it be hardened and tempered?

[lightarrow]

...
Sulfur and phosphorous is added to some of the metals. 

I don't think so; it's indicated the maximum percentage of them in the steel composition, as those elements are unwilled in the alloy.

[CliffordK]

...
Sulfur and phosphorous is added to some of the metals. 

I don't think so; it's indicated the maximum percentage of them in the steel composition, as those elements are unwilled in the alloy.

When you read about 1144 Stressproof steel, there are a lot of notes about sulfur and phosphorus.  While the phosphorus level ratings appear to be similar in different alloys, the sulfur levels aren't.  The sulfur is supposed to aid in the machinability of the alloy.

Looking at the original manufacture page, the 1144 Stressproof steel also has Silicon added (not listed on the onlne metals page above).
http://www.niagaralasalle.com/product-stressproof.html#chemistry

Silicon is also a used as an alloy with copper to form silicon bronze, much harder and stronger than pure copper.

My guess is that almost everything in modern (new) alloys is there because it was intentionally put in the mixture, although many of the steel alloys have been around for decades so the chemistry may imitate older metals.

[taregg (OP)]

so what is the strongest nonmetal element bonder ....some say fluorine and some say nitrogen....

[CliffordK]

Your halogens make one bond...  strong yes, but not particularly good for crosslinking.

Carbon and silicon make 4 bonds which make them ideal for crosslinking internally to a structure.

Carbon likely first entered our iron and steel production as artifacts from the smelting and manufacturing process, but it seems to have excellent strengthening properties.

Of course, alloys with other metals should not be ignored for modifying the properties of the metals such as high temperature alloys, stainless, and etc.

[damocles]

OK, I can see that two different things are being discussed here. It is important to distinguish between
(1) which non-metal can be bonded with iron to make the strongest/hardest material?
and
(2) which non-metal atom makes the strongest bonds with an iron atom?

The latter question can be subdivided into
(2a) which non-metal atom makes the strongest bonds in a diatomic molecule?
or
(2b) which non-metal makes the strongest bonds in a molecule or network (as nature would dictate)?

Most of the posts here have been in terms of (1); taregg's last post appears to be in terms of (2a), but may well be conflating and confusing all three senses.

In the sense (2a), the least practically important but best defined, there is not enough experimental data available, because most of the diatomic systems have not been sufficiently studied. However, the trend across all transition metals (but not without exception) is
 O > F > N ~ C > all other non-metals.
For example, TiO delta H of atomization is 158 kcal/mol; TiF 136 kcal/mol; TiN 111 kcal/mol.

In the sense (2b) we are looking for delta H values for the reaction
n X(gas, monatomic) + m Fe(gas, monatomic) --> Fe_mX_n (solid, network or molecular).
These values can be deduced from tables of heat of formation. They should be put on a "per iron atom" basis for fair comparison. Will update this line in another post shortly.

[damocles]

For the various iron compounds, the strongest network compounds (on a per iron atom basis) appear to be a near dead heat (the experimental error in some of the figures is quite large).

I found the result quite surprising, and would like to have my work cross checked. My league table is

FeP₂ 1209 kJ/mol of iron atoms
Fe₂O₃ 1189 kJ/mol
FeCl₃ 1173 kJ/mol
FeS₂ 1137 kJ/mol
Fe₃O₄ 1109 kJ/mol

This, or some amended form of it, is the answer for sense (2b) of the OP

[CliffordK]

I am not surprised that oxides form strong bonds with iron.  But, that doesn't mean that it necessarily makes structurally sound metal alloys and ceramics.  I.E. rusted steel often looses strength.

However, aluminum oxides can form a strong (but brittle) protective barrier over aluminum metal, and to some extent, iron oxides can also form a protective layer over steel and cast iron.

Furthermore, aluminum oxide glasses, crystals, and ceramics can be extremely strong.