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[Matt_Zukowski]

I the first chapter of Apatite-The Great Pretender (Lithographie No. 7), on page 9, Rakovan and Hughes describe triangular growth hillocks on the prism faces of apatite.

My understanding was that prism faces of (most?) hexagonal minerals display 2-fold symmetry and that this is why the growth and etch features on beryl prism faces are rectangular. Is this wrong? Doesn't apatite also show the same 2-fold symmetry through the prism faces? Is there something unique about the way the apatite structure intersects the prism faces that causes this?

I looked online for the reference (Rakovan 2002) but could not find it to read more.

Thanks.

[John Rakovan]

Hi Matt,

The triangular growth hillocks on the {100} crystal faces are made up of three vicinal faces with steps that are oriented in different directions, [001], [011] and [01-1]. See the attached figure. The answer to why steps on the {100} take the orientations that they do is a bit involved but it can be understood through a concept called Hartman-Perdok Theory.

As for the relationship of the hillocks to symmetry, you are correct that they are constrained to follow the symmetry of the (100) face. The point group symmetry of apatite is 6/m; a six-fold axis of rotation oriented parallel to the c crystallographic axis and a mirror plane perpendicular to the c-axis . Thus, the only symmetry in the (100) of apatite is a mirror plane. There is no 2-fold symmetry as in beryl. That being said, etch pits on the (100) of apatite often exhibit pseudo 2-fold symmetry as well as mirror symmetry. Anyway, the shape of the triangular hillocks is constrained by the mirror, and two vicinal faces of the hillock, [011] and [01-1] are related by the mirror. The [001] vicinal face is not related by symmetry to the other two. This by the way can lead to beautiful examples of intrasectoral zoning in apatite.

Cheers

John

[Matt_Zukowski]

Wow...interesting...and thanks for the quick reply. I need to expand my understanding of hexagonal minerals to take in the range of point groups. I certainly see how the triangular growth features obey the mirror plane, and thus the symmetry.

[Gerhard Niklasch]

A somewhat related observation:

While Quartz has 2-fold rotations which exchange the two ends of the c axis, its 'm' prism faces have no such 2-fold symmetry individually. (In an ideal crystal, the 2-fold axes pass through the edges between adjacent prism faces.)

And indeed there's sometimes a noticeable difference in surface texture (striations, hills, pits…) between the two ends of one and the same 'm' face, the one adjacent to an 'r' pyramid face and the one adjacent to 'z' - and when enough of the crystal is visible, you can see these features alternating in orientation as you move around the prism.

Enjoy,
Gerhard

[John Rakovan]

Matt,

If you are interested in diving into Hartman & Perdok theory and periodic bond chains in apatite I suggest the following papers. I tried copying both references into google and found copies of each available online.

Hartman, P. and Perdok, W.G. (1953) On the relations between structure and morphology of crystals I. Acta Crystallogrphica, 8, 49 52.

Terpstra, R.A., Bennema, P., Hartman, P., Woensdregt, C.F., Perdok, W.G., and Senechal, M.L. (1986) F faces of apatite and its morphology: Theory and observation. Journal of Crystal Growth, 78, 468 478.

Cheers,

John

[Pete Richards]

[Peter]

Thank you gentlemen for your insight and for sharing
Peter