Recall, gentle reader, that we were in the midst of a discussion about Celestial Spheres, with the intimation that they would somehow be related to the use of crystal balls as a scrying medium. In this post, the saga continues...
Aristotle, in his Metaphysics, added more spheres to the Celestial model to correct for observations of the outer planets, and postulates that the spheres themselves are made of an unchanging fifth element, the aether. According to Aristotle, the motion of each sphere is motivated by its own god, who inspires the movement simple by being loved by it.
"The final cause, then, produces motion by being loved, but all other things move by being moved." 
Possible links between the model of the heavens and the use of a crystal globe for scrying may well originate in Persia. The first use of the Ptolemaic system to calculate the distances between planets was undertaken by al-Farghani, who was also involved in making one of the first calculations of the diameter of the Earth. During the years of al-Farghani’s life, philosophers were developing a more spiritual take on the nature and purpose of the celestial spheres. Like Plotinus, it is documented that Persian philosophers al-Farabi and Avicenna (8th BCE) envisioned the movers of the planets coming into being through a series of emanations of God. Each sphere moved continually by virtue of its soul, which was attempting to attain to the perfection of the intelligence, because the intelligences were the direct emanation, and the soul the secondary one. The idea of the Empyrean heaven was later added by Christian and Muslim philosophers as the dwelling place of god. An outer sphere, wherein dwelt the angels, was added in some cases.
All this history has been presented for the sole fact that it supports the idea of the sphere as being the perfect solid, and also a type of early philosophical orrery, in that it could serve as a model to explain the actions of God upon the Universe. Later orreries were complicated machines that described the motions of the planetary bodies, of course. The model of the Celestial Spheres describes more about their origin and God’s impact on humanity. The sphere could have been the way for the scryer to essentially take the observational place of God in the system. This notion is supported by the description of a medieval Islamic scrying tool, the Cup of Jamshid, which was purportedly filled with an elixir of Immortality. Historians have stated that the seven heavens of the universe could be observed by looking into it. Others have said that the whole world was reflected within. At least one English translation of the text describing it refers to the Cup as a crystal globe. 
Of course, it is a matter of common knowledge that the ancients were fond of scrying with water. Early Greeks considered crystals to be condensed water, so instead of my elaborate argument here regarding the history of crystal gazing, you could come to the conclusion that some Greek diviner thought, “Oh, look! Water that I can put in my pocket! How convenient!”
Keeping in mind that the Lemegeton advocates the use of a circle for the protection of the magician and a triangle for the holding of spirits called, to me, the most interesting aspect of the question “why a crystal” is the use of this material for the attraction and interaction of spirits. The first use of the crystal to actually contain a spirit may have been described by pseudo-Trithemius (that is “Trithemius of Spanheim” reported in Francis Barrett’s, “The Magus” 1801). In this document, the use of a small crystal (“the size of a small orange,” maybe 1.5” in diameter) covered with a plate of gold to make a hemispherical mirror and embedded in a paddle of ebony wood or ivory. A ritual for calling an archangel is then documented:
"In the name of the blessed and holy Trinity, I do desire thee, thou strong and mighty angel, Michæl (or any other spirit or angel), that if it be the divine will of him who is called Tetragrammaton, &c. the Holy God, the Father, that thou take upon thee some shape as best becometh thy celestial nature, and appear to us visibly here in this crystal…” 
This document also broaches a subject of intense interest to me: that of the seer’s preparations prior to the attempt to aid a magician in the contact and conversation with a spirit. As a teaser for the next post: “It is necessary therefore that the invocant religiously dispose himself for the space of many days to such a mystery, and to conserve himself during the time chaste, abstinent, and to abstract himself as much as he can from all manner of foreign and secular business; likewise he should observe fasting, as much as shall seem convenient to him, and let him daily, between sun-rising and setting, being clothed in pure white linen, seven times call upon God, and make a deprecation to the angels to be called and invocated, according to the rule which we have before taught. Now the number of days of fasting and preparation is commonly one month, i. e. the time of a whole lunation. Now, in the Cabala, we generally prepare ourselves forty days before.” 
N.B. I am grateful for many discussions about this material with R.O., my love, my brother and my magus.
Be thou blessed.
 Aristotle Metaphysics 1072b4.
Graphics are J. W. Waterhouse's "Circe Invidiosa" and "The Crystal Ball." The orrery is housed at the Mariner's Museum, Newport News, VA.