Check out page 8 http://students.washington.edu/zanghell/TAs/BSTR521/notes/anomalous_scattering.pdf
I thought that Friedels are reflections related by pure inversion
symmetry, while Bijvoets are reflections related by non-inversion symmetry
of the reciprocal lattice. Thanks,
Let's try this again, with definitions, and pls scream
if I am wrong:
a) Any reflection pair hR = h forms a symmetry related pair.
R is any one of G point group operators of the SG.
This is a set of reflections (S). Their amplitudes
are invariably the same. They do not even show up
as individual pairs in the asymmetric unit of the reciprocal
space.
NB: their phases are restricted but not the same.
b) a set h=-h (set F) exist where reflections may or may not
carry anomalous signal. They form the centrosymmetrically related
wedge
of the asymmetric unit of reciprocal space.
c) a centric reflection (set C) is defined as
hR=-h
and cannot carry anomalous signal. Example zone h0l in PG 2.
As Ian Tickle pointed out, the CCP4 wiki is wrong:
"Centric reflections in space group P2 and P21 are thus
those with 0,k,0." Not so; an example listing is attached
at the end.
d) therefore, some e:F exist that carry AS (F.ne.C)
and some that do not carry AS (F.el.C).
I hope we can agree on those facts.
Now for the name calling:
(S) is simply the set of symmetry related reflections, defined as hR=h.
(F) is the set of Friedel pairs, defined as h=-h.
(C) are centric reflections, defined as hR=-h.
Thus, only if (F.ne.C), anomalous signal. I thought those
are Bijvoet pairs. They are, but it may not be the definition
of a Bijvoet pair.
Try 1:
>Bijvoet pair is F(h) and any mate that is symmetry-related to F(-h),
>e.g., F(hkl) and F(-h,k,-l) in monoclinic.
hkl is not related to -hk-l via h = -h. Only h0l is, and those are (e:C).
So, I cannot quote follow that, probably try 1 is not a good definition.
Try 2:
> I've always thought that a Bijvoet pair is any pair for which an
> anomalous difference could be observed.
Good start. I subscribe to that.
> This includes Friedel pairs (h & h-bar)
Good. That's the definition of F.
> but it also includes pairs of the form h & h', where h'
> is symmetry-related to h-bar.
Ooops. That is the definition of a centric reflection.
> Thus Friedel pairs are a subset of all possible Bijvoet pairs.
Cannot see that. I still maintain that Bijvoet pairs are
a subset of Friedel pairs (which does include Pat's definition).
I fail to see anything else but Friedel pairs in my list
of reflections - some of them carry AS (F.ne.C) and some
don't (F.el.C).
B = F.ne.C.
Seems to be a necessary and sufficient condition,
in agreement with Pat's definition (though not the explanation).
But - isn't that exactly what I said from the beginning?
"A Bijvoet pair is an acentric Friedel pair..."
Or - where are any other Bijvoet pairs hiding? Where did I miss them?
(NB: Absence of anisotropic AS assumed -let's not go there)
See reflection list P2 (hkl |F| fom phi 2theta stol2)
last 3 items: centric flag, epsilon, m(h)