The most expensive necklace materials are typically those that are rare, have high demand, and possess unique qualities. The most expensive materials include diamonds, pearls, and certain gemstones like rubies, sapphires, and emeralds. These materials are not only valued for their beauty but also for their rarity and the craftsmanship required to set them into necklaces.

Diamonds are often the most expensive necklace material due to their rarity and the difficulty in mining them. According to the Gemological Institute of America (GIA), the average price of a diamond necklace can range from $10,000 to over $100,000, depending on the carat weight, clarity, color, and cut. The most valuable diamonds are those with the highest color grades (D to F) and clarity grades (Flawless to Internally Flawless).

Pearls, particularly South Sea and Tahitian pearls, are also highly sought after for their luster and rarity. The value of a pearl necklace can vary widely, but high-quality South Sea pearls can command prices of $10,000 to $50,000 or more, depending on size, luster, and shape. The rarity of these pearls, which are cultivated in controlled environments, contributes significantly to their price.

Ruby, sapphire, and emerald necklaces are also expensive due to their rarity and the intense labor required to mine and cut them. For example, a ruby necklace with a high-quality stone can cost upwards of $20,000, while a sapphire necklace can range from $5,000 to $15,000, and an emerald necklace can be priced from $10,000 to $30,000 or more. The color, clarity, and cut of these gemstones play a crucial role in determining their value.

The high cost of these materials is also influenced by the craftsmanship involved in creating a necklace. The design, setting, and overall quality of the piece can significantly impact its price. For instance, a custom-designed necklace with a unique setting or an intricate design can cost tens of thousands of dollars or more.

In conclusion, the most expensive necklace materials are diamonds, pearls, and certain gemstones like rubies, sapphires, and emeralds, due to their rarity, demand, and the craftsmanship required to create a high-quality piece. The value of these materials is further influenced by factors such as color, clarity, and cut, as well as the design and setting of the necklace.