Officially at least—which is to say, on Facebook—Greenpeace International and Facebook are friends. But there are signs they’re not getting along. There are those unflattering photos of Facebook that Greenpeace posted, for instance. And that snarky quiz about Facebook’s bad habits —that wasn’t very nice. And then there’s all that stuff Greenpeace has on its own Web site.

What has come between them? And can this relationship be saved? An answer may come as soon as Tuesday, when representatives from the two organizations are scheduled to meet at Facebook headquarters in Palo Alto, Calif. Greenpeace says it’s all about Facebook’s relationship with coal. But the issue may go deeper than that: Facebook is just way more popular than Greenpeace, and Greenpeace may just be picking a fight to get attention.

It all began in January 2010, when Facebook announced plans to build its first data center in Prineville, Ore., which is expected to begin operating in a few months. Facebook boasted that its new data center would be one of the most energy efficient in the IT industry, with a PUE rating of 1.15. (A PUE is an energy efficiency measurement; most IT companies aim for a PUE between 2 and 1.5.) What’s more, Facebook explained, the chilly weather of Prineville would reduce its cooling costs.

Greenpeace was not impressed. Shortly after Facebook’s announcement, Greenpeace released a report called, “Make IT Green.” In 2007, it said, server farms and data centers emitted 14 percent of global emissions in the information communications technology sector. * In 2020, that number will rise to 18 percent. Greenpeace’s report condemned Facebook’s choice of data center location, and the utility company that would power its operation: PacifiCorp, a utility company that, like most utility companies in the United States, gets most of its energy from coal. *

Facebook’s emphasis on efficiency, the report noted, missed a central tenet in the climate change debate: “Efficiency by itself is not green if you are simply working to maximize output from the cheapest and dirtiest energy source available,” Greenpeace explained. The organization began its “Facebook: Unfriend Coal” campaign last spring by creating—what else?—a Facebook page. With the page and subsequent media attention, Greenpeace’s team quickly garnered 500,000 supporters. Now it has more than 600,000.

When Facebook responded by announcing that it planned to double the size of its Prineville facility, the dispute got more serious. Foregoing Facebook altogether, Greenpeace International Executive Director Kumi Naidoo wrote Facebook Chief Executive Mark Zuckerberg a letter. “Facebook appears to be on a path that will make breaking our addiction to dirty coal-fired electricity even more difficult,” Naidoo wrote. He asked Zuckerberg to commit to phasing out the use of coal-fired electricity in its data centers, build data centers in locations that are served by majority renewable energy utility centers, disclose greenhouse gas emissions, and, of course, share the plan with the world.

In January, Naidoo set a deadline for this commitment: April 22, 2011, or Earth Day.

I sat down with Naidoo in Greenpeace’s Washington office recently and asked him why Greenpeace chose Facebook as a target. It was all about the timing, he told me. Facebook hasn’t signed and sealed all of their contracts with PacifiCorp and other energy providers, so there’s still a chance for it to choose a different direction.

But there may be more to it than that. Could Greenpeace’s campaign be a cheap marketing ploy—a desperate publicity bid by Greenpeace? Or is Facebook really the ExxonMobil of the IT industry, and the Prineville data center its Valdez?

Unlike ExxonMobil, Facebook is not the largest company in its industry. That title goes to Google, the acknowledged industry leader in renewable energy investment and energy efficiency. It built a massive solar panel on the roof of its headquarters in Mountain View, Calif., which releases 1.6 megawatts of energy. It is also an equity investor in several North Dakota wind farms and has a long-term power purchase agreement with a wind farm in Iowa. All the same, according to Greenpeace’s report, Google still gets a lot of its power from coal—50.5 percent at its data center in Lenoir, N.C., for example, about the same as Facebook’s proposed Prineville center.

Amazon, the second-largest Internet company, is notoriously tight-lipped about its data center locations and emissions numbers. According to Rich Miller, the founder and editor of the Web site Data Center Knowledge, Amazon has a data center in Northern Virginia and one on the West Coast—no one knows for sure. Amazon’s Northern Virginia data center, located in Ashburn, is powered by Dominion. In 2010, Dominion reported an energy mix of 43 percent coal, 40 percent nuclear, 13 percent natural gas, 2 percent oil and 2 percent renewables.

Facebook also argues that it is doing what it can to minimize its environmental impact, but that its options are limited. “Long-term, we believe in a strategy of adopting more renewable energy, but ultimately that’s up to the utility providers we work with,” says Jonathan Heiliger, vice president of technical operations at Facebook.

Greenpeace says that a company like Facebook could invest in renewable energy projects, like windfarms or solar panels, or choose to locate its data center near a utility company that relies on renewables. But the area must also have superior network connectivity and be easily accessible to its workers. *

So what is Facebook doing? So far, it has decided to join two environmental organizations—neither of which has anything to do with the matter at hand.

One, the Alliance To Save Energy, is “fuel neutral,” says Monique O’Grady, the alliance’s vice president of communications. “We don’t really talk about renewables.” The other, the Digital Energy Solutions Campaign, focuses “on innovation and smart technologies as vital to clean energy,” says Chris Hankin, its executive director. “That’s our fixation. Demonizing coal isn’t.”

Greenpeace, for its part, acknowledges the P.R. benefits of getting into a fight with Facebook. “I’ve been at Greenpeace for 15 months now, and I’ve done lots of media work,” Naidoo says. “But that letter to Mark Zuckerberg and the amount of media pickup there was globally, nothing [has come] close to it. The reach and power of Facebook is unique.”

Greenpeace also says it’s used a softer approach with Facebook than it uses with, say, the Japanese whaling industry. “We love Facebook, it has helped revolutionize how we do our campaign work,” says Casey Harrell, a Greenpeace analyst. In fact, Greenpeace is the largest nonprofit on Facebook, with more than six million members on its pages. Greenpeace’s kinder, gentler campaign against Facebook is reminiscent of its 2006 campaign against Apple, which helped convince Apple to stop using certain chemicals in its manufacturing process.

It is a strategy Facebook fails to appreciate. “It’s an interesting campaign, but I wish that Greenpeace would dive perhaps into the details of what actually goes into data center selection, and how data centers are designed and used,” says Facebook’s Heiliger. “We continue to be surprised by Greenpeace’s actions, and even confused on their motivations,” he says.

For Naidoo, the issue is as simple as Spider-Man’s credo: “With increasing influence, power, and profile also come the burden of increased public responsibility,” he says. “To be quite blunt about it, it’s not a very big ask we’re making of Facebook.”

Tuesday’s meeting, Naidoo says, is crucial. “Depending on what comes out of it, then we’ll up the ante, or continue as is.”

And what exactly does “upping the ante” mean?

Naidoo can’t tell me. “Some of it, the element of surprise is important,” he says.