An infix is a simple affix that is inserted into a morpheme (cf. Helmbrecht & Lehmann 2008, section 3). is a stock example from Latin conjugation: a present stem is formed by infixation:

The above definition requires the following comments:

• Taken literally, an affix (ad-fix) should be attached at the periphery of its host, so that an infix could by definition not be an affix. This is, however, not meant by the term ‘affix’; it means just any bound non-root.
• A simple affix is distinguished from a discontinuous affix. There are also discontinuous counterparts to infixes; but they are called transfixes.
• An infix is by definition inserted into a morpheme. The host morpheme is generally a root. However, an infix in an affix is not excluded by the definition; examples are mentioned below.
• An infix disrupts its host, making it discontinuous. An affix that follows the root, e.g. the -ly in lone-ly-ness, is by definition not an infix, but a suffix. (There are non-peripheral suffixes!) This is so despite the fact that non-peripheral suffixes are again and again called infixes.¹
• Available definitions² often call the host of the infix a stem. This is multiply misleading:
  • A stem that is not a root consists by definition of more than one morpheme. How would the infixation work then? If it were inserted between these morphemes, it would not be an infix.
  • Apart from the exceptions mentioned below, the far majority of infixes are, in fact, inserted in the root, not in any other morpheme of a derived stem.
  • If an infix is inserted in the root of a complex stem, this presupposes that it also works on the bare root. For instance, the Latin compound verb rescindere ‘cut off’ contains the -n- infix; but it inherits this process from the root verb scindere ‘tear’ ().

Diachronically, an infix can originate in two ways, either by metathesis or by entrapment.

• In metathesis, an outer affix crosses the syllable boundary of its host and becomes its infix. For instance, the Latin -n- of was a suffix prehistorically.
• In entrapment, an affix that is flanked by two other morphemes becomes their infix in the moment that these two are united into one morpheme.

In 99% percent of the cases, the host morpheme of the infix is a root. However, it is even possible to get an infix into an affix. It happened by entrapment in Gedeo (Highland East Cushitic, Gragg 2008):

What appear synchronically to be monomorphemic 1^st and 2^nd singular suffixes were originally composed of two morphemes, the first marking person and the second marking aspect. The negative suffix attached to the first of these, and then followed the aspect suffix. Later the person and aspect complex was monomorphemicized so that the negative suffix got entrapped and became an infix. A similar case is reported from Hocank in Helmbrecht & Lehmann 2008. Infixation in a suffix by metathesis is posited for Yucatec Maya.

¹ Spurious infixes are alleged (27.09.26) for Akkadian (Buccellati 1997:77), Esperanto and Latin. Earlier on, Celticists used to work with infixes which are not even affixes, but proclitics.

² e.g. in the English and German Wikipedia articles on the infix (27.09.26)

References

Buccellati, Giorgio 1997, "Akkadian." Hetzron, Robert (ed.), The Semitic languages. London: Routledge (Routledge Language Family Descriptions); 69-99.

Gragg, Gene 2008, "Morphological expression of verbal negation in Cushitic". 3^rd Meeting of the International Association of Comparative Semitics, Turin, 2 - 5 october 2008.

Helmbrecht, Johannes & Lehmann, Christian 2008, "Hocank's challenge to morphological theory." Harrison, David & Rood, David & Dwyer, Arienne (eds.), Lessons from documented endangered languages. Amsterdam & Philadelphia: J. Benjamins (Typological Studies in Language, 78); 271-315. [ download ]