TUCSON — In February, during one of the annual gem shows here, Ray Zajicek displayed a stone that was not for sale: a 32-carat hexagonal crystal of red beryl — or “red emerald,” as the emerald dealer prefers to call it.

“It’s probably 10 times rarer than green emerald,” Mr. Zajicek said.

For an industry that creates sales allure from notions of value, wealth and scarcity, rare can be a loaded word.

But in this case, it’s an accurate one.

Unlike the classic green emeralds found in Colombia, Brazil, Zambia, Afghanistan, Ethiopia and elsewhere, red beryl is the result of such a rare geological occurrence that it has been found in only one location: a mine, closed since 2001, in the remote Wah Wah Mountains of Utah.

How does that happen?

“These seemingly unique situations are related to very specific geologic conditions,” said Christopher P. Smith, president and chief gemologist at American Gemological Laboratories in New York.

As for red beryl, he said, the presence of a specific manganese compound produces its distinctive cherry-red color.

And the one thing possibly more surprising than nature’s creation of these one-source gems?

The fact that they are discovered at all.

It almost always happens by accident. “Someone kicks over a rock and finds a pretty stone,” said Shane McClure, global director of colored stone services at the Gemological Institute of America.

That’s more or less what happened near Milas, a town in the Anatolian mountains of Turkey, about an eight-hour drive south of Istanbul. In the 1970s, bauxite miners discovered large, gem-quality specimens of a color-changing mineral called diaspore embedded in some of the ore.

“Bauxite used to sell for $20 a ton and they thought the crystals were lowering the quality of the bauxite so they put them aside,” said Murat Akgun, who was a jeweler in Istanbul’s Grand Bazaar in 1998 when he fell in love with the gem and embarked on a mission to sell it internationally.

“I was fascinated by the colors and variety and how they formed,” he said.

Diaspore, which blushes from a kiwi green under fluorescent lighting to a raspberry pink in candlelight, now is marketed under the brand names Csarite and Zultanite (Mr. Akgun owns the trademark for Csarite).

At the current pace of mining, Mr. Akgun said, there probably is a 30-year supply of the mineral. So enough of it is available to sustain demand, underscoring one of the truisms of the gem trade: Rarity is a double-edged sword.

“You need a stone to be rare enough to attract interest but not so rare that you cannot develop a market for it,” said Stuart Robertson, vice president of Gemworld International, publishers of a popular gem pricing guide.

John Bradshaw, owner of Coast to Coast Rare Stones International in New Hampshire, is well versed in the challenge. A specialist in single-source gems, he sells his inventory of esoteric finds during the Tucson gem shows. And benitoite, a bright blue stone found only in San Benito County in central California, has ranked as one of his most sought-after gems.

“People line up on opening day and at 10 a.m., when the show opens, they literally race to our booth,” Mr. Bradshaw said. “By noon this year, we had sold 187 stones between 25 points and 3 carats, mostly to Japanese dealers.”

(The Japanese also are Mr. Zajicek’s biggest customers for red beryl, a fact that the Dallas-based dealer speculated has something to do with the appeal of its American provenance.)

Mr. Bradshaw was hesitant to reveal his wholesale prices but said that a faceted benitoite of 1 to 2 carats could sell for $3,600 to $5,000 per carat, with a 10 to 15 percent premium for round stones. That is only slightly less than the cost of a one-carat round diamond, which sells for $4,000 to $7,000, depending on its color, clarity and cut.

In the case of grandidierite, a green single-mine gem from southern Madagascar that is named after the French explorer Alfred Grandidier, “asking prices are all over the board,” Mr. Bradshaw said. “A lot of people are afraid of selling it too inexpensively.”

While dealers have trouble pricing gems that lack true comparisons, the average man or woman shopping for a piece of jewelry probably doesn’t even know such gems exist. They usually aren’t found at a local jeweler, unless the store serves gem and mineral collectors, and are unlikely to be found in finished pieces of jewelry.

Anyone with a taste for such offbeat adornment probably has to find a retailer whose supplier sources stones on the secondary market. That’s where many single-mine gems end up, after deposits have been exhausted or mines stop operations. An example: pezzottaite, a pink gem discovered in central Madagascar in 2002 that now is available only secondhand.

“It was super-popular for about a year,” said Tom Cushman, a gem dealer who splits his time between Sun Valley, Idaho, and Madagascar. “But there was not enough to hit critical mass. I had an oil man from Oklahoma and he wanted something nobody else had. He bought a suite of four stones — and that’s it.”

Cultivating a get-it-before-it’s-gone mentality is part of the playbook for dealers of tanzanite, a blue-violet variety of the mineral zoisite that was found in the foothills of Mount Kilimanjaro.

Famously introduced to the world in 1968 by Tiffany & Company, whose advertisements touted its singular origin, the stone continues to be widely available, despite many marketing claims that supplies have been running out.

“For a long time, they said there are only 10 years left,” said Ian Harebottle, a former chief executive of the mining company Tanzanite One, which holds the concession on the government-controlled mine. “But that’s if we were only mining in a small-scale way. As long as you improve your efficiencies, increase demand and pricing goes up, then you can afford to keep getting deeper.”

Regardless of how the marketers spin it, playing the single-source angle can be crucial to making the sale, said the British jewelry designer Stephen Webster, who has worked extensively with both tanzanite and the color-changing diaspore from Turkey.

“It’s probably more engaging,” he said, “than saying, ‘This is whatever-nite and they find it all over Asia.’”

6 to Know

Creating a list of single-source gems is not as easy as it might seem. Each gem dealer has guidelines, and some are stricter than others. But here are six gems commonly considered to be from single sources.

Ametrine

A bicolor variety of quartz that is purple amethyst on one side and orange citrine on the other, ametrine occurs naturally only at the Anahí Mine in the Sandoval Province of eastern Bolivia.

But because there is a lot of synthetic or artificially induced ametrine on the market, the material is neither rare nor expensive. It is, however, fashionable — the Italian jewelry company Faraone Mennella used the gem for its Arcobaleno necklace.

At an average size of 20 carats in polished form, the gem lends itself to striking settings, matched only by the drama of its history: A 17th-century Spanish conquistador received the mine as a dowry when he married a native princess named Anahí, of the Ayoreos tribe, according to the authors of a 1994 article in the journal Gems & Gemology.

The article included a caveat about ametrine’s formation, a helpful reminder of the mysterious circumstances that create all single-source gems: “The unusual color patterns probably result from the uncommon geologic conditions under which these quartz crystals formed,” the authors wrote, “although the crystal chemical properties controlling the sector color zoning still elude explanation.”

Benitoite

In the early 1900s, prospectors looking for copper and cinnabar discovered benitoite near the southern edge of San Benito County, about halfway between San Francisco and Los Angeles. It became a collector darling not only for its single-mine origin but also for its beguiling blue hue.

“No gemstone in the world has the same composition as this stone,” said Dave Bindra of B&B Fine Gems in Los Angeles. “The physical beauty is outstanding.”

Benitoite’s color is created by the presence of iron and titanium impurities, and their transfer of an electron — the same subatomic process thought to give a blue sapphire its color. The gem also has a dispersion rate similar to that of a diamond; when white light enters the stone, it bounces back in a display of rainbow colors, an effect known in the industry as “fire.”

Even though benitoite was named the California state gemstone in 1985, “most people have never heard of it,” said John Bradshaw, a rare-stone dealer from New Hampshire. Each year, he sells it at one of the Tucson gem shows, drawing from stock that he and his business partner have accumulated over the past three decades (the mine closed in 2004).

“We’ve parceled the rough into different bags and boxes, and each calendar year, we bring one out,” Mr. Bradshaw said.

Diaspore

A vein of bauxite, or aluminum ore, runs through the hills and pine forests of Turkey’s Anatolian Mountains. In the 1970s, miners discovered that the ore included a mineral called diaspore, which can appear to be pink, green, yellow, champagne or even ginger under different lighting conditions.

“When you first see it, you go, ‘It’s kind of brown,’” said Rudi Wobito, the Toronto-based cutter and distributor of Csarite, one of the mineral’s two trademarked names. “But it isn’t really. You need to look at it in your living room, in your backyard, in the shopping mall. Everywhere you go, it will look a little different.”

Diaspore itself is not uncommon. What is unique about the find in Turkey is that “this deposit produces large, transparent, gem-quality crystals,” said Christopher P. Smith, president and chief gemologist at American Gemological Laboratories in New York.

Many designers have worked with the gem, including the Los Angeles-based Erica Courtney and Nak Armstrong, the Texas jeweler whose Csarite pieces are sold at Barneys New York.

Grandidierite

The gem-rich island nation of Madagascar is the only known source of gem-quality grandidierite, a translucent bluish-green stone discovered in 1902 and named for the 19th-centuryFrench explorer Alfred Grandidier.

With a ranking of 7.5 on the Mohs scale — which determines hardness based on the ability of one mineral to scratch another, and is named for its inventor, the 19th-century German mineralogist Friedrich Mohs — the gem is durable enough to be used in jewelry, although it is so scarce that faceted gems tend to end up in gem and mineral collections rather than jewelry. After all, no designer wants to create a collection based on a gem that is all but impossible to get.

On a recent buying trip to Sri Lanka, a trading hub for gems from Madagascar, Mr. Bradshaw saw a 4.43-carat grandidierite that, he said, caused his “jaw to hit the desk.” He posted a short video of it on his Instagram feed and soon heard from a retailer in New York City, who had a client who was, Mr. Bradshaw said, “dying for a great stone.” Apparently, the client had seen a 6-carat grandidierite the month before but, after deciding not to buy it, changed her mind two days later and found that the stone had been sold.

Yet she declined to buy the 4-carat gem. “She said, ‘It can’t be that rare because you found another great one too fast,’” Mr. Bradshaw recalled the retailer’s telling him.

“Just because a 6-carat stone and a 4-carat stone happened across her desk in a month doesn’t mean you could find one for another 10 years,” he said.

Red beryl

Also known as red emerald or bixbite, this unusual gem has much the same composition as a typical beryl — beryllium, for starters — but also a specific manganese compound that produces its bright red hue.

As with most mineral deposits, the mine, known as the Ruby-Violet Claim, was discovered in 1958, when miners searching for uranium in the Wah Wah Mountains of Beaver County, Utah, stumbled upon the red crystals. In 1976, the Harris family purchased mining rights to the property and spent the next two decades digging more aggressively. A deal to sell the mine to Gemstone Mining Inc. of Utah collapsed in 2001, and production came to a standstill.

Ray Zajicek, a gem dealer in Dallas, said, “I believe there are no greater than 30,000 cut stones, and probably less than 300 carat-size stones, in the world, produced between 1976 and 2002.”

At the Tucson gem shows in February, Mr. Zajicek held a 2-carat emerald-cut red beryl to the light: “A man offered me $30,000 per carat, and I said, ‘No, there’s nothing like it.’”

Tanzanite

The blue-violet variety of the mineral zoisite, tanzanite is found only in the shadow of Mount Kilimanjaro in Tanzania. But unlike many of the stones in this rarefied category, “there is no lack of material,” Mr. Bradshaw said.

A set of very specific geological conditions in East Africa transformed zoisite into tanzanite.

“One, you needed a source of vanadium,” an element found in many minerals, Mr. Smith said. “And then there were two different types of folding which took place in this region — stacked or isoclinicfolding in a horizontal direction and the other in a vertical direction — and it was this combination that created the right environment for this color variety of zoisite. In areas where there was only one type of this folding, they don’t find gem-quality crystals.”

In the mid-1960s, Tiffany & Company trumpeted the gem’s discovery and it became a designer sensation, first among high-end jewelers such as Donald Claflin and Jean Schlumberger, and then, as time passed, among mass-market manufacturers with ties to the cruise ship industry. It continues to be promoted as a gem with a finite supply, bound to run out one day.

Is it really that rare?

“Rarity is a context you have to wrap your head around,” said a diplomatic Mr. Smith. “It doesn’t have a singular definition.”