It is possible to do the analysis using HCl extract and then Iron and Al oxides may be estimated by using Ammonium Hydroxide, boil and filter. With these they will get precipitated and can be quantified
There are several methods for determining soil iron oxides, depending on what you want to analyse: total, “free”, “active”, … iron oxides. You can have a look to the following chapter:
Loeppert, R. H., W. P. Inskeep 1996. Iron. In: D.L. Sparks, A.L. Page, P.A. Helmke, R.H. Loeppert, editors, Methods of Soil Analysis Part 3—Chemical Methods, SSSA Book Ser. 5.3. SSSA, ASA, Madison, WI. p. 639-664. doi:10.2136/sssabookser5.3.c23.
I can send you privately a copy, if you want.
If you look for a particular mineral, you can look in:
ULERY, A. L. & DREES, L. R., editors. 2008. Methods of Soil Analysis Part 5—Mineralogical Methods. SSSA Book Ser. 5.5. SSSA, Madison, WI. doi:10.2136/sssabookser5.5
In soils you have a lot of forms of sesquioxides. Please to be sure what form you is interested for (e. g., organic one or 'free' one). After your aim is clarified, you can choose one method, according the Dr. FERNANDEZ-MARCOS's indications.
Pete Birkeland's Soil Geomorphology textbook has a really nice description of what oxides the different methods are thought to extract. My recent paper in CATENA compares oxalate with dithionite methods to determine approximate ages.
An alternative approach for determination of Fe oxides derives from the third step of sequential extraction of Tessier method:
Samples extracted with 40 ml of 0.04 M NH2OH.HCl in 25 % acetic acid (v/v) for 5 h at
96 ± 3 under intermittent agitation.
However the extractability of Fe oxides with hydroxylamine hydrochloride extraction depends on the properties of the samples, especially their Fe oxide content and crystallinity (Sado et al 2013).
The Fe analysis methods are very dependent on the aim of your study. There are plant available Fe methods, total Fe by strong acids with HF, pseudo total with aqua-regia, alkaline fusion method etc. You can find the details of these methods in most of reference books for chemical analysis of soils.