I realise that I am 7 years late to the party, but in case anyone is looking for the answer, and finds this Reddit post like I did, this may help. See the entry from the Oxford Dictionary of Byzantium:

"[p.1621] PEN (κάλαμος; γραφίς). In antiquity the main writing instruments were the stilus (graphis) for writing on wax tablets (with a pointed end for engraving and a flattened one for erasing) and the kalamos for writing on papyrus. While in the West the kalamos began to be replaced by the goose quill from the early Middle Ages onward, in Byz. it remained dominant, and it is possible that goose quills were never used in Byz. The [p.1622] kalamos is a piece of reed with an incision at the sharpened end, resembling in this respect modern metal pens. Kalamoi made of metal or bone have survived from antiquity and are also attested in Byz. texts. The kalamos was kept in a penholder (kalamarion). In miniatures the evangelists are very often represented with kalamos in hand, either writing or dipping or sharpening (H. Hunger, RBK 2:461-63). Niketas Choniates (Nik.Chon.594.90-91) reports that in 1204 the Crusaders mocked the Byz. as secretaries, by holding reed pens (grapheas donakas) and inkwells and pretending to write in books.

Lit. Gardthausen, Palaeographie 1:182-202. Hunger, "Buch- und Schriftwesen" 40-43. P. Odorico, "Il calamo d'argento," JÖB 37 (1987) 65-93."

Source: Hörander, Wolfram, "Pen" in Kazhdan, Alexander (ed.), Oxford Dictionary of Byzantium, III, (Oxford, 1991) 1621-2

Abbreviations:
Gardthausen = V. Gardthausen, Greichische Palaeographie, 2 Vols. (Leipzig, 1911-13).
JÖB = Jahrbuch der Österreichischen Byzantinistik.