I can’t comment on exactly why your material is like it is, but here are some basic principles to help you get your mind round what slag is.
It’s the generic term for the unwanted impurities from various furnace processes. It arises both during the initial smelting of metallic ores such as producing pig-irons from iron ores and the subsequent processes to convert pig-irons to steels (of various compositions).
Usually, carbon is used as a reducing agent to convert metallic oxides to native metal, together with limestone to aid the removal of silicates from the host rock. During conversion to steel, usually quicklime and magnesium carbonate are also added together with other agents which collectively serve to remove other impurities, protect the lining of the furnace, and condition the slag into a usable material (generally as aggregate for construction purposes) rather than just being a waste product. The impurities float to the top of the liquid metal and are then poured off to remove them… like this:
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In the case of iron ores, typically around 290kg of slag is generated for every 1,000kg of pig iron produced; and up to 540kg of slag per 1,000kg of steel. The composition varies widely. It’s usually a mixture of metal oxides, metal sulphides and silicon dioxide but, since it’s poured off from the top of the molten material in the furnace, portions of it can be high in elemental metals all the way up to the same composition as the retained portion in the furnace.
The poured off slag may be air-cooled or water-cooled but water-quenching produces irregular lumps which can exhibit ropey or laminar flow lines from having been poured into the water in a molten state.
Regarding the lack of rusting, the presence of other metals (even in low quantities) can have a dramatic effect on the degree to which iron rusts. That’s how we make stainless steels for example. Stainless steel usually has at least 11% chromium as the ‘rust inhibitor’ but, these days, some stainless steels are produced using much lower levels of titanium with the added advantage of increased strength. The amount used is typically 0.25 – 0.6% which is not inconsistent with your reading of 0.27% titanium.
When titanium is added to steel, it can form small granules of titanium carbide which are stable and do not readily dissolve. They’re often present in the slag together with other particulate materials that have floated to the top.
PS: Welcome to Tnet.