Aflux is still in beta development (read, it may break at any moment,
but the semantics are stable). Results are returned as JSON serialized object
arrays. Examples of summons follow...

Numerical matching:
    http://aflowlib.duke.edu/search/API/?Egap(1*,*1.01)

Will return the first 64 results from all data with a gap value greater than
or equal to 1eV AND less than or equal to 1.01eV; comma "," is an AND operator.
colon ":" is an OR operator. Multiple ranges can be selected like
    http://aflowlib.duke.edu/search/API/?Egap((1*,*1.01):(2*,*2.01)),paging(2)
Indexed to show 2nd page of 64 entries from N total results.

if you don't want to see the index use the suppression "$" operator
    http://aflowlib.duke.edu/search/API/?Egap(1*,*1.01),$paging(0)
Summoning the zeroth page returns all possible results.

NB: Be careful here, large data responses can crash your browser, I suggest
wget, curl or some other direct method for full retrieval.

Matching is possible on all the property names that are either in our schema,
Aflow REST API and Aflux papers or you can see them in the advanced search
page filters
    http://aflowlib.duke.edu/search/API/?schema
or
    http://aflowlib.org/advanced.php

multiple properties are also possible
    http://aflowlib.duke.edu/search/API/?Egap(1*,*1.01),Pearson_symbol_relax,paging(-0)
shown in reverse order

string matching works similarly
    http://aflowlib.duke.edu/search/API/?Egap(1*,*1.01),Pearson_symbol_relax(*'F'*)

Don't worry if your browser percent encodes some characters, the API will
still understand
    http://aflowlib.duke.edu/search/API/?Egap(1*,*1.01),Pearson_symbol_relax(*%27F%27*),$compound,$aurl
Suppressing two of the three default property identifiers.

We also have an inversion operator '!'
    http://aflowlib.duke.edu/search/API/?Egap(1*,*1.01),Pearson_symbol_relax(!*'F'*),$auid,$aurl,paging(0)

Aflux Reference:  http://dx.doi.org/10.1016/j.commatsci.2017.04.036
Aflow REST API: https://doi.org/10.1016/j.commatsci.2014.05.014
LICENSE.  The data included within the aflow.org repository is free for scientific, academic and non-commercial purposes.  Any other use is prohibited.