It is permissible to don the Tefillin of Rabbeinu Tam, but according to Maran the Mishnah Berurah (Siman 555), one should not recite the four scriptural passages (parashiyot) because this is akin to studying the Torah. However, the common practice worldwide is to recite the four passages, in accordance with the words of the Kaf HaChaim in the name of Maran the Ben Ish Chai and the author of Batzek HaChaim (Vol. 3, Siman 87) at length. Regarding the Tefillin of Shimusha Rabba and Raavad, the Rema mi-Fano rules that they are not to be donned at all on Tisha B’Av.