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Talk:Corundum

Untitled
Aren't emeralds a type of corundum too? Chadloder 20:47 Jan 25, 2003 (UTC)

 * Don't think so. Emerald is a type of beryl (beryllium aluminum silicate) while corundum is aluminum oxide.  Perhaps you were thinking of ruby and sapphire, which are types of corundum. -- Heron

 * Yup, you're right. Sorry. :) Chadloder 20:40 Jan 26, 2003 (UTC)

The Emery article says its mohs hardness is 8, but this article says "Emery is an impure and less abrasive variety, with a Mohs hardness of 9.0." Shouldn't this be changed to 8.0? The hardness of pure corundum is 9.0.
 * Emery is a rock, a mixture of corundum, hematite and magnetite. --Chris.urs-o (talk) 09:29, 2 November 2012 (UTC)

Merge suggestion
No! This is a mineralogy article about the naturally occurring mineral, aluminium oxide is a chemistry article about the chemical. Vsmith 15:28, 8 January 2006 (UTC)

Oppose merger I agree with the above poster. Would an article about diamond or charcoal be merged with one about carbon?--24.217.183.224 08:23, 9 January 2006 (UTC)
 * Oppose merge: there is (potentially) more than enough material to justify two articles; minerals and chemical compounds are usually treated seperately on WP. Physchim62 (talk) 09:14, 9 January 2006 (UTC)

New Merge Section
(To reduce confusion with above, which is different.)

 * Support as nom. { Slash -|- Talk } 07:32, 21 February 2007 (UTC)
 * Oppose the merger for the same reasons as the posters in 2006. One is chemistry the other a mineral. It would be more appropriate to merge Transparent alumina into the article on aluminum oxide.Dcmacnut 20:05, 2 March 2007 (UTC)

 * Support If you mean combine the transparent alumina article into this, then I'm in favour
 * Oppose for the same reasons as those of the former merger, Corundum is a Mineral article, and transparent alumina is a chemical article and so are to be treated separately Kevmin 11:08, 6 March 2007 (UTC)
 * Question to you mineral/chemical guys. Is Transparent alumina a variety of corundum? If not then I Oppose a merge. If it is, then I am Neutral but I would then state that somewhere in both articles it should at least state so. right now the only hint is that it is like "sapphire" and "ruby". As a gemstone guy, this is inaccurate. SauliH 11:28, 6 March 2007 (UTC)
 * No, transparent alumina is not a variety of corundum. Corundum is by definition a naturally occurring mineral species as defined by the International Mineralogical Association.  Transparent alumina is a artificially created chemical substance and so does not qualify for the term corundum. Kevmin 11:36, 6 March 2007 (UTC)
 * But it could be correctly termed synthetic corundum? SauliH 18:54, 6 March 2007 (UTC)
 * Oppose, there is already a section in corundum on synthetic stuff. This transparent alumina would better be merged with the aluminium oxide chemical article for its ceramic and industrial usages. Info on synthetic ruby and sapphire should (and already is I think) be in those gemstone articles. The article transparent alumina seems rather an odd term - should be redirected to aluminium oxide and pertinent material merged wherever it best fits, if not already there. Vsmith 01:08, 7 March 2007 (UTC)
 * I am still trying to get to grips with what this material is. Does it have the same crystal structure as corundum crystal? If it is a synthetic production of corundum with like crystal structure and chemical makeup then this should be made clear in the article. SauliH 05:27, 8 March 2007 (UTC)

 * From what I can find this is a man made Al2Os Glass. This means that I is not the same substance chemically as naturally crystalline Corundum, Al2O s, and not classifiable as a mineral under the IMA rules, that it is not anthropogenic in origin and that it has a definable crystal structure Kevmin 10:06, 8 March 2007 (UTC)

Transparent alumina redirect not logical, Jim
Transparent Alumina is an invention (2004, 3M, a glass; according to the Aluminium oxide article) where as Corundum seems to be about the basic mineral from which Alumina and such can be derived (and associated gems). I would have expected a reference to Star Trek (which had something of that order in one or two of it's films) and the chemical process (assuming a trade secret does not exist that stops us knowing or telling), "rare earth elements" used and industrial uses of said Transparent Alumina. As such arriving on the Corundum page is both confusing and misleading. --Lord Matt (talk) 22:00, 23 November 2007 (UTC)

To mention
could there be a note somewhere in here saying about the fact it is sometimes used as a callibration material for some X-ray diffraction equipment? —Preceding unsigned comment added by 148.168.40.4 (talk) 09:23, 5 February 2008 (UTC)

Isn't corundum the second hardest mineral (diamond being the first... roughly four times harder than corundum)? Gingermint (talk) 05:08, 16 November 2009 (UTC)

Streaks
"Due to corundum's hardness (pure corundum is defined to have 9.0 Mohs), it can scratch almost every other mineral, leaving behind a streak of white on the other mineral."

Surely it only leaves a streak on the things it can not scratch? Is the quoted sentence just poorly worded? 86.139.146.127 (talk) 12:20, 24 October 2008 (UTC)

 * yes, and in any case the other mineral may not always streak to white - eg galena, graphite, hematite, etc. Plantsurfer (talk) 12:39, 24 October 2008 (UTC)

Corundum
Would it be important to add in that corundum gets dirty easily since microscopic bits flake off most minerals but it doesn't because of hardness so dirt gets stuck easily? Scientific Alan (talk) 01:11, 4 February 2012 (UTC)

corundum vs sapphire??
Hi, i cant find the difference between corundum and sapphire. (Im personally interested in the physical perspective, not the jewellers one, is there any physical difference? i.e. is a sapphire laser a corundum laser and vice versa?) — Preceding unsigned comment added by 83.134.145.21 (talk) 00:55, 22 February 2012 (UTC)
 * Vsmith can answer this better. As far as I know, these are just different terms for the same solid - corundum is used in geology literature to refer to a mineral and sapphire is used in gemology/physics to refer to a gem or crystal (as in titanium-sapphire laser). Lattice is the same, impurities might be different, but it's impossible to tell that difference from the name only. Materialscientist (talk) 01:04, 22 February 2012 (UTC)
 * Better? nah. Seems sapphire is corundum (Al2O3) that has small amounts of Fe and Ti substituting in the Al site - which depending on the ratios and amounts (along with other impurities) makes the pretty colors that get gem people turned on. The sapphire laser is synthetic corundum with controlled amounts of titanium doping - to make it work. Disclaimer, don't know much about lasers ... cheers, Vsmith (talk) 02:07, 22 February 2012 (UTC)

Corundum is polycrystalline form of alumina （Al2O3), while sapphire or ruby is the single crystal of alumina, often with very small amount of doping to have different colors.  — Preceding unsigned comment added by 99.29.18.17 (talk) 01:03, 29 January 2013 (UTC)

Requirement of impurities
The opening section "Corundum is a crystalline form of aluminium oxide (Al2O3) with traces of iron, titanium and chromium" indicates that iron, titanium and chromium must be present in order for it to be corundum. I have found other sources which make no mention of these elements, one of which lists the essential components as just aluminium and oxygen. As far as I can tell, in scientific circles, corundum refers to a phase of Al2O3 just like diamond is a phase of carbon.

The same reference for corundum requiring traces of iron, titanium and chromium also state that diamond is "nearly pure carbon", meaning (if the references is taken to mean corundum must contain traces of these elements) it would need something else to be diamond and pure carbon can't be diamond; it states that quartz is "SiO2 with traces of other elements", again indicating pure silicon dioxide can't be quartz. It also lists 2 contradictory compositions for anatase which would make it impossible for anything to be anatase. It appears to be stating the composition of particular samples rather than the composition of corundum in general.

Are there any objections to removing the implicit requirement of it containing these trace elements and instead saying it commonly has these traces? Black.jeff (talk) 10:58, 29 September 2015 (UTC)
 * Rejiggered a bit as impurities per Mindat. Vsmith (talk) 20:15, 29 September 2015 (UTC)

Deltalumite
Deltalumite is another natural polymorph of Al2O3. And there are more (see https://www.mindat.org/min-1136.html) Eudialytos (talk) 12:37, 18 June 2017 (UTC)

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Crystal system
Corundum belongs to the R$\overline{3}$c (No. 167) space group, per these sources. This is a trigonal space group, not hexagonal, per this source and Wikipedia's own page and sources cited therein. Corundum is identified as trigonal in this reference also:

There is a lot of confusion about this even in standard references; for example, Nesse (2000) lists corundum as "Hexagonal (trigonal)" which only adds to the confusion. But perhaps the final word is:

"In corundum, every third octahedral hole is vacant, but in the ideal structure, all holes are equivalent. This results in a loweringt of the space group symmetry to R$\overline{3}$c. Thus, corundum is trigonal, while in NiAs, the symmetry of the hexagonal closest packing (P63/mmc) is retained."

--Kent G. Budge (talk) 00:55, 20 September 2021 (UTC)

title: Talk:Corundum


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Račak massacre

The Račak massacre (Masakra e Reçakut) or Račak operation (Акција Рачак/Akcija Račak) was the massacre of 45 Kosovo Albanians that took place in the village of Račak (Reçak) in central Kosovo in January 1999. The massacre was perpetrated by Serbian security forces in response to Albanian separatist activity in the region. The Serbian government refused to let a war crimes prosecutor visit the site, and maintained that the casualties were all members of the rebel Kosovo Liberation Army (KLA) killed in combat with state security forces.

The killings were investigated by two separate forensic teams, the first a joint Yugoslav–Belarusian team and the second an external Finnish team representing the EU. The first team's report, which was commissioned by the Yugoslav government, concluded that those killed, who included a woman and 12-year-old child, were all separatist guerrillas and not civilians. The findings of the second team sharply contradicted the Yugoslav investigation's report, determining that the deaths constituted killings of unarmed civilians. The lead Finnish investigator, anthropology expert Dr. Helena Ranta, called it a "crime against humanity", though refusing as a scientist to directly label it a massacre or assign blame to any specific party. Details of the Finnish team's findings were left undisclosed for two years. At the time, reporting of the incident varied from publication to publication and country to country. Media outlets covering it more definitively described the event at Račak as a gruesome terrorist atrocity by a repressive Serbian government.

Bill Clinton, then president of the United States, condemned the massacre as a deliberate and indiscriminate act of murder, and the administration sought to convince the American people that intervention in Yugoslavia was necessary. Public support for intervention among Americans remained at only about 50%, even after the extensive media attention on Račak, suggesting that war with Yugoslavia would be less popular than previous conflicts and interventions the US had undertaken in its recent history.

Regardless, the actions taken and bloodshed at Račak represented a "turning point in the war", drawing sympathy from several nations worldwide, and ultimately played a role in NATO's decision to mount an organized military operation known as Operation Noble Anvil against the Federal Republic of Yugoslavia. NATO's involvement in the Kosovo conflict in the months following the Račak incident altogether lasted 78 days and consisted of a series of tactical airstrikes.

A memorial exists to the victims of the massacre at Račak. Kosovo annually holds a ceremony to honour the victims of the massacre.

Background
Račak is a small Albanian-inhabited village in the Štimlje municipality of southern Kosovo. By 1998 it had become the scene of activity by the Albanian separatist organization the Kosovo Liberation Army (KLA). It had a population of around 2,000 people prior to the displacement of most of its inhabitants during Yugoslav military activity in the summer of 1998. By January 1999, around 350 people were reported by the Organization for Security and Co-operation in Europe (OSCE) to be living in the village. The KLA was highly active in the region and almost certainly had a presence in Račak itself, with a base near a local power plant.

On 8 January 1999, the KLA mounted an ambush on Serbian police units near the city of Suva Reka, resulting in the deaths of three Serbian policemen. The ambush was followed by a further attack on Serbian police units near the city of Uroševac two days later on 10 January, killing one policeman. The village of Račak had served as a staging area for these ambushes and in response, Yugoslav security forces established a security cordon in the area of Račak and the neighboring communities of Dulje and Caraljevo. At 06:30 on 15 January, the assault on the village of Račak began when Serbian police and KLA units began to exchange fire. Some residents of Račak were able to escape to the nearby village of Petrovo, while KLA units fought their way out to positions outside the village. KLA resistance lasted a number of hours with Serbian police units finally securing the village in the morning, later departing the village at 16:30.

Reports
On 15 January, reports were received by the Kosovo Verification Mission (KVM), an unarmed observer force from the OSCE, of civilians being killed in Račak. KVM monitors attempted to gain access to the area but were refused permission by security forces despite strong protests. Instead, they watched the fighting from a nearby hill. They later gained access to the village, where they found one dead man and a number of injured people and received reports of other deaths and of people being taken away by the Serbian security forces. They were denied permission to interview the villagers or explore the area around the village.

The monitors finally gained access to the surrounding area on 16 January. Accompanied by a number of foreign journalists and members of the European Union's Kosovo Diplomatic Observer Mission (KDOM), they found a total of 40 bodies in and around the village. Another five bodies had allegedly been removed by family members. In all, 45 were reported killed, including a 12-year-old boy and three women. All had been shot and the KVM team reported that it found several bodies decapitated. KVM head William Walker later described what he had seen:

 * "In a gully above the village, I saw the first body. It was covered with a blanket, and when it was pulled back, I saw there was no head on the corpse — just an incredibly bloody mess on the neck. Someone told me that the skull was on the other side of the gully and asked if I wanted to see that. But I said, "No, I've pretty much got this story." [Three more bodies were found.] They looked like older men, with gray hair or white hair ... They had wounds on their heads, and there was blood on their clothes. [Then a larger group of bodies.] I didn't count them. I just looked and saw a lot of holes in the head - in the top of the head and the back of the head. A couple had what appeared to be bullet wounds knocking out their eyes. I was told there were other bodies further up and over the crest of the hill, and I was asked by journalists and inspectors if I was going to go up and see the rest. I said, 'I've seen enough.'"

Walker immediately condemned what he labelled "an unspeakable atrocity" which was "a crime very much against humanity". He told the party of journalists accompanying him: "I do not hesitate to accuse the (Serb) government security forces. We want to know who gave the orders, and who carried them out. I will insist that justice will be done. They certainly didn't deserve to die in circumstances like this."

The journalists also provided first-hand accounts of the discovery of the bodies. One of them, the BBC's reporter Jacky Rowland, reported that the dead "were all ordinary men; farmers, labourers, villagers. They had all been shot in the head." The dead were aged from 14 to 99 years old. ITN's correspondent Bill Neely was also present and described how other KVM monitors reacted at the scene: "A Swedish monitor notes that the dead are all in civilian clothes and unarmed and that there are no signs of a battle... After working for two hours one monitor, a London police officer, tells me he believes many of the victims have been shot at close range."

Two days later, on 18 January, the Chief Prosecutor of the International Criminal Tribunal for the Former Yugoslavia (ICTY), Louise Arbour, attempted to enter Kosovo to investigate the killings but was refused access by Serbian authorities. On the same day, heavily armed Serbian police entered Račak under fire from the KLA, and removed the bodies, taking them to a morgue in Pristina to await a forensic examination.

A joint Yugoslavian-Belarusian team of pathologists conducted post-mortems at the end of January. A Finnish forensic team working for the European Union subsequently conducted a second post-mortem, which was more detailed but less contemporaneous than the first. The bodies were finally released to the families and buried on 10 February 1999.

Investigations
The killings at Račak became the focus of an investigation by the International Criminal Tribunal for the Former Yugoslavia. In its indictment of Slobodan Milošević and four other senior Yugoslav and Serbian officials, the ICTY's Chief Prosecutor stated that:

"On or about 15 January 1999, in the early morning hours, the village of Račak was attacked by forces of the FRY [Yugoslavia] and Serbia. After shelling by VJ [Yugoslav Army] units, the Serbian police entered the village later in the morning and began conducting house-to-house searches. Villagers, who attempted to flee from the Serbian police, were shot throughout the village. A group of approximately 25 men attempted to hide in a building, but were discovered by the Serbian police. They were beaten and then were removed to a nearby hill, where the policemen shot and killed them. Altogether, the forces of the FRY and Serbia killed approximately 45 Kosovo Albanians in and around Racak."

Eyewitness reports from the surviving villagers unanimously supported the account of a massacre. The British journalist Julius Strauss, writing for The Daily Telegraph, described how he had "spent more than a week collecting evidence on the Račak massacre from Albanian witnesses, Western monitors and diplomats and a few Serbian sources who spoke privately and at some risk." According to the survivors that he interviewed, "a small group of men dressed all in black and wearing gloves and balaclavas ... co-ordinated the attack on the village and the subsequent executions." Men had been separated from women and children before being led away to be executed. One survivor told him that "some of the Serbs were in blue, some in black. The men in black appeared to be in control and wore balaclavas over their heads. Some had uniforms with insignia which included a Serbian flag; some had none. They carried automatic guns and, as we were led up the hill, both units started shooting us." Strauss speculated that the men had been from the Specijalna Antiteroristička Jedinica, the Serbian Interior Ministry's elite anti-terrorist unit. Some eyewitnesses told reporters that "Serb troops shot and mutilated their victims, and the six-hour orgy of violence ended with a nationalist song."

The Serbian government rejected this version of events. On the day after the killings, the Serbian Interior Ministry issued a statement asserting that its police units had come under fire from "ethnic Albanian terrorist groups ... on routes leading to Račak village in the Stimlje municipality." In the subsequent counter-attack "several dozen terrorists were killed in the clashes with the police. Most of them were in uniforms bearing the insignia of the ethnic Albanian terrorist organization calling itself the Kosovo Liberation Army (KLA)."

They received some support from the French newspapers Le Figaro and Le Monde, which suggested that the KLA could have fabricated evidence. A film crew working for the Associated Press accompanied the Serbian forces in Račak for part of 15 January. Two French journalists from the Agence France Press and Le Figaro interviewed the cameramen and saw at least some of the footage, from which they concluded that it was possible that the KLA could have staged the massacre, and that "only a credible international inquiry would make it possible to resolve those doubts." According to the paper,

 * "It was in fact an empty village that the police entered in the morning, sticking close to the walls. The shooting was intense, as they were fired on from KLA trenches dug into the hillside. The fighting intensified sharply on the hilltops above the village. Watching from below, next to the mosque, the AP journalists understood that the KLA guerrillas, encircled, were trying desperately to break out. A score of them in fact succeeded, as the police themselves admitted."

Another French journalist writing for Le Monde, Christophe Chatelot, gave an account from the perspective of the two AP journalists:

 * "When at 10 a.m. they entered the village in the wake of a police armored vehicle, the village was nearly deserted. They advanced through the streets under the fire of the Kosovo Liberation Army (UCK) fighters lying in ambush in the woods above the village. The exchange of fire continued throughout the operation, with more or less intensity. The main fighting took place in the woods. The Albanians who had fled the village when the first Serb shells were fired at dawn tried to escape. There they ran into Serbian police who had surrounded the village. The UCK was trapped in between. The object of the violent police attack on Friday was a stronghold of UCK Albanian independence fighters. Virtually all the inhabitants had fled Račak during the frightful Serb offensive of the summer of 1998. With few exceptions, they had not come back. 'Smoke came from only two chimneys,' noted one of the two AP TV reporters."

The Serbian President, Milan Milutinović, accused the KVM head William Walker of fabricating the killings "by securing the co-operation of his protegés in the Kosovo Liberation Army". The Serbian media took a similar line, arguing that the Albanians had removed the KLA uniforms from the bodies and replaced them with civilian clothes. Unnamed French diplomats also criticised Walker for publicly blaming the Serbs for the killings, arguing that he should have waited for a more thorough investigation. The Yugoslav government declared Walker to be persona non grata and demanded that he leave the territory of Yugoslavia within 48 hours.

At the end of January 1999, the United States was reported to have leaked telephone intercepts that were said to prove the role of the Serb government in the killings. According to The Washington Post, the intercepts showed that the Serb government had ordered security forces to "go in hard" to the Račak area. Deputy Prime Minister Nikola Šainović and Interior Ministry General Sreten Lukić reportedly expressed concern about reaction to the Račak assault and discussed how to make the killings at Račak appear to be the result of combat between government troops and KLA rebels. On the day of the attack on Račak, Sainović was aware that the assault was underway and asked how many people had been killed. Lukić replied that as of that moment the tally stood at 22. Following the international uproar about the killings, Sainović told Lukić to re-enter Račak and retrieve the bodies. He also told Lukić that the ICTY prosecutor Louise Arbour was not to be allowed into the country.

Forensic reports
Three forensic examinations were carried out on the bodies, by separate teams from FR Yugoslavia, Belarus (at the time an ally of Serbia) and Finland (under the auspices of the European Union). All three examinations took place in controversial circumstances; the Yugoslav and Belarusian forensic teams carried out their autopsies against the opposition of the KVM and ICTY, which had demanded that the outside experts from Finland should be the first to carry out post-mortems on the dead. The Yugoslav and Belarusian autopsies were conducted on 19 January under the auspices of the Pristina Forensic Medical Institute. Its director, Professor Saša Dobričanin, stated that "Not a single body bears any sign of execution. The bodies were not massacred." He told the media that he suspected that the bodies had been mutilated posthumously to fabricate the appearance of an execution.

The Finnish (EU) team, headed by pathologist Helena Ranta, began its own autopsy on 21 January and released its initial findings on 17 March. The introduction to the report stressed that it was Ranta's personal view, and not the position of the team. The report concluded that "there was no evidence that the victims had been anything other than unarmed civilians and that they had probably been killed where they were later found by the international monitors." Addressing the claims that the dead had been killed wearing KLA uniforms which had then been replaced with civilian clothes, the report states that "...the clothing [of the dead] bore no badges or insignia of any military unit. No indication of removal of badges of rank or insignia was evident. Based on autopsy findings (e.g. bullet holes, coagulated blood) and photographs of the scenes, it is highly unlikely that clothes could have been changed or removed." Ranta testified at the subsequent ICTY trial of Slobodan Milošević, stating that retrieved bullets, bullet casings and entry and exit wounds indicated that the victims were killed where their bodies were found and at approximately the same time. A later Finnish report indicated that only one victim had provably been shot at close range.

The report from the Finnish team, however, was kept confidential by the EU until long after the war, and the team leader, Helena Ranta, issued a press release at the time containing her "personal opinion" and indicating different findings. Ranta stated that "...medicolegal investigations [such as scientific analysis of bodies] cannot give a conclusive answer to the question whether there was [in fact] a battle [between the police and insurgents]...", but she leaned towards the victims being non-combatants in part because "...no ammunition was found in the pockets" of the bodies she investigated. The report was widely understood as saying that the Finnish team had disproved the finding released by the Yugoslav and Belarusian pathologists, whose tests had shown a positive for gunshot residue on the hands of 37 out of the 40 bodies.

Criticism was levelled against the paraffin method used by the Yugoslavs and Belarusians to test for powder residue on the victims' hands, since it regularly gives false positives for many other substances, including fertilizers, tobacco, urine and cosmetics, and sometimes provides false negatives. The test is still used by the police of many countries who cannot afford more modern methods, but has been described since as early as 1967 as 'of no use scientifically.'

The international reaction to the Yugoslav and Belarusian report on one hand, (which supported the view that those killed were KLA fighters, not civilians as claimed by the Kosovo-Albanians and NATO) and that of the EU expert team on the other (which did not find any evidence to suggest that the dead were combatants) differed considerably, not least in the NATO-countries who were preparing to intervene to stop widespread human rights violations in Kosovo. The former was ignored or dismissed as propaganda, and the latter was accepted as evidence of a massacre against civilians. Several pro-war activists and writers wrote about, and quoted, the Finnish team's press-release. Both reports were used as evidence by the prosecution and also by the defence of Slobodan Milošević at his trial, until the Račak case was dropped from the indictment because of lack of evidence.

The full report of the EU team was handed over to the ICTY at the end of June 2000. An executive summary was published in 2001, but the full report has never been released.

In October 2008 Helena Ranta stated that she had been asked to modify the contents of her report, both by the Finnish Ministry of Foreign Affairs, and by William Walker, the head of the Organization for Security and Co-operation in Europe (OSCE) Kosovo Verification Mission, in order to make it more explicit, she had refused to do so, saying this was "a task for the war crimes tribunal”. According to Ranta, in the winter of 1999 William Walker, the head of the OSCE Kosovo monitoring mission, broke a pencil in two and threw the pieces at her when she was not willing to use sufficiently strong language about the Serbs.

Consequences
Many western governments, human rights groups and international organisations insisted that the Račak operation was a deliberate massacre, conducted in defiance of earlier Serbian agreements to end the violence in Kosovo. The OSCE, Council of Europe, EU, NATO and the UN Security Council all issued strongly worded statements condemning the killings. On January 22, the Contact Group of countries with an interest in Yugoslavia (Britain, France, Germany, Italy, Russia and the United States) issued a joint statement condemning "the massacre of Kosovo Albanians in Račak on 15 January. All members expressed their revulsion at this act of mass murder. No amount of provocation could justify it. The Contact Group condemns UCK [KLA] provocations which can only contribute to rising tensions and further violence... The Contact Group also condemns the decisions by the FRY authorities to refuse entry into Kosovo by ICTY Chief Prosecutor Judge Arbour." The Contact Group also called for Yugoslav authorities to "work with the International Tribunal to ensure that those responsible for Račak are brought to justice [and] suspend those VJ and MUP officers operating in Račak on 15 January pending the results of this investigation becoming available".

According to Edward S. Herman, media collaboration assisted the Račak massacre in serving as a casus belli for the NATO bombing of Yugoslavia. Ranta's news conference on 17 March 1999 during the final days of the Rambouillet Agreement talks, coupled with media outlets failing to mention the circumstances of the Serbian offensive in the area, helped to justify NATO involvement in Kosovo.

The UN Security Council and Secretary General on January 31 described the event as a massacre perpetrated by Yugoslav security forces.

ICTY indictment
The ICTY issued a sealed indictment on 27 May 1999 for crimes against humanity and violations of the laws and customs of war against a number of senior Yugoslav officials. These were Slobodan Milošević (President of Yugoslavia), Milan Milutinović (President of Serbia), Nikola Šainović (Yugoslav Deputy Prime Minister), Dragoljub Ojdanić (Chief of the General Staff of the Yugoslav Army) and Vlajko Stojiljković (Serbian Interior Minister). The Račak massacre was added by the ICTY prosecutors in an amended indictment, but was subsequently dropped from the case, to "improve the expeditiousness of the proceedings while ensuring that they remain fair".

Aftermath
On June 18, 2001, a court in Pristina sentenced Zoran Stojanović, a 32-year-old police officer, to 15 years' imprisonment for murder and attempted murder in Račak. Stojanović, a Kosovo Serb, was convicted by a joint UN-Kosovo Albanian panel of judges (two United Nations magistrates and one ethnic Albanian). Stojanović's trial was highly controversial. It was speedy, one of the first trials by a hastily organized new court. Stojanović was alleged to have killed one man and wounded two more by firing one bullet. During the trial, according to one UN legal officer, both the international judges and the Albanian judge had considered dismissing the case, but did not do so, allegedly for political reasons. During the trial, some witnesses allegedly presented testimonies that contradicted the forensic evidence.

The reconstruction of events in Račak for the trial was prevented by two men, who chased off court officials, telling them, "we don't want any Serbs in our village." The second reconstruction was prevented by an angry mob of Albanians. A subsequent reconstruction was held without the presence of either the defendant or his lawyer. The prosecutor, Tome Gashe, told the court during the trial that unless Stojanović were found guilty, the people would "take justice in their own hands". The trial and sentencing of Stojanović was criticised by the United Nations and Amnesty International.

Zoran Stojanović was pardoned in 2007 and released from custody. In late 2009, President of Serbia Boris Tadić pardoned Zoran Stojanović, declaring that the trial was unjust, which opened the question as to whether he had jurisdiction because Stojanović was sentenced by an international High court.

Denial of the massacre
Kosovo Serb politician Ivan Todosijević denied the massacre took place and said that the story was made up by "Albanian terrorists". In 2019, he was convicted of incitement to ethnic, racial, or religious intolerance and was sentenced to two years in prison by a court in Pristina for making the claims. The Serbian president, Aleksandar Vučić, supported Todosijevic, claiming that the massacre was indeed made up. This was met with stark reaction from Kosovo Albanian politicians and the civil society. The president of Kosovo, Hashim Thaçi, said that peace in the Balkans would only be established when Serbia expressed shame, and not pride, when discussing war crimes. There were reactions by the former prime minister of Kosovo Ramush Haradinaj, former Kosovar minister of foreign affairs Behgjet Pacolli, and the European Commission. The European Commission stated that “Denial and revisionism are contrary to the values of the European Union and are contrary to the project of integration of the Western Balkans into the European Union. Sentencing has to be proportionate and take into account all elements of the case”.

In October 2022, Todosijević's conviction was upheld at his retrial. Kosovo's Court of Appeals upheld the verdict in March 2023, but the Supreme Court of Kosovo overturned it in July 2023, acquitting Todosijević of inciting hate.

Documentaries

 * The Road to Racak, 29 March 2000, Canada, CBC, documentary.
 * Račak, istine i laži (Truths and Lies of Račak), 2009, Serbia, documentary, by Slaven Kranjc
 * Dosije Kosovo-Račak (Kosovo Dossier - Racak), Serbia, documentary.
 * Dosije Kosovo-Račak (Kosovo Dossier - Racak), Serbia, documentary.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Račak massacre


text:
Armillary sphere

An armillary sphere (variations are known as spherical astrolabe, armilla, or armil) is a model of objects in the sky (on the celestial sphere), consisting of a spherical framework of rings, centered on Earth or the Sun, that represent lines of celestial longitude and latitude and other astronomically important features, such as the ecliptic. As such, it differs from a celestial globe, which is a smooth sphere whose principal purpose is to map the constellations. It was invented separately, in ancient China possibly as early as the 4th century BC and ancient Greece during the 3rd century BC, with later uses in the Islamic world and Medieval Europe.

With the Earth as center, an armillary sphere is known as Ptolemaic. With the Sun as center, it is known as Copernican.

The flag of Portugal features an armillary sphere. The armillary sphere is also featured in Portuguese heraldry, associated with the Portuguese discoveries during the Age of Exploration. Manuel I of Portugal, for example, took it as one of his symbols where it appeared on his standard, and on early Chinese export ceramics made for the Portuguese court. In the flag of the Empire of Brazil, the armillary sphere is also featured.

The Beijing Capital International Airport Terminal 3 features a large armillary sphere metal sculpture as an exhibit of Chinese inventions for international and domestic visitors.

Description and use

The exterior parts of this machine are a compages [or framework] of brass rings, which represent the principal circles of the heavens.

 * 1) The equinoctial A, which is divided into 360 degrees (beginning at its intersection with the ecliptic in Aries) for showing the sun's right ascension in degrees; and also into 24 hours, for showing its right ascension in time.
 * 2) The ecliptic B, which is divided into 12 signs, and each sign into 30 degrees, and also into the months and days of the year; in such a manner, that the degree or point of the ecliptic in which the sun is, on any given day, stands over that day in the circle of months.
 * 3) The tropic of Cancer C, touching the ecliptic at the beginning of Cancer in e, and the tropic of Capricorn D, touching the ecliptic at the beginning of Capricorn in f; each 23$1/2$ degrees from the equinoctial circle.
 * 4) The Arctic Circle E, and the Antarctic Circle F, each 23$1/2$ degrees from its respective pole at N and S.
 * 5) The equinoctial colure G, passing through the north and south poles of the heaven at N and S, and through the equinoctial points Aries and Libra, in the ecliptic.
 * 6) The solstitial colure H, passing through the poles of the heaven, and through the solstitial points Cancer and Capricorn, in the ecliptic.  Each quarter of the former of these colures is divided into 90 degrees, from the equinoctial to the poles of the world, for showing the declination of the sun, moon, and stars; and each quarter of the latter, from the ecliptic as e and f, to its poles b and d, for showing the latitude of the stars.

In the north pole of the ecliptic is a nut b, to which is fixed one end of the quadrantal wire, and to the other end a small sun Y, which is carried round the ecliptic B—B, by turning the nut : and in the south pole of the ecliptic is a pin d, on which is another quadrantal wire, with a small moon Ζ upon it, which may be moved round by hand : but there is a particular contrivance for causing the moon to move in an orbit which crosses the ecliptic at an angle of 5$1/3$ degrees, to opposite points called the moon's nodes; and also for shifting these points backward in the ecliptic, as the moon's nodes shift in the heaven.

Within these circular rings is a small terrestrial globe I, fixed on an axis K, which extends from the north and south poles of the globe at n and s, to those of the celestial sphere at N and S. On this axis is fixed the flat celestial meridian L L, which may be set directly over the meridian of any place on the globe, so as to keep over the same meridian upon it. This flat meridian is graduated the same way as the brass meridian of the common globe, and its use is much the same. To this globe is fitted the movable horizon M, so as to turn upon the two strong wires proceeding from its east and west points to the globe, and entering the globe at the opposite points off its equator, which is a movable brass ring set into the globe in a groove all around its equator. The globe may be turned by hand within this ring, so as to place any given meridian upon it, directly under the celestial meridian L. The horizon is divided into 360 degrees all around its outermost edge, within which are the points of the compass, for showing the amplitude of the sun and the moon, both in degrees and points. The celestial meridian L passes through two notches in the north and south points of the horizon, as in a common globe: both here, if the globe be turned round, the horizon and meridian turn with it. At the south pole of the sphere is a circle of 25 hours, fixed to the rings, and on the axis is an index which goes round that circle, if the globe be turned round its axis.

The whole fabric is supported on a pedestal N, and may be elevated or depressed upon the joint O, to any number of degrees from 0 to 90, by means of the arc P, which is fixed in the strong brass arm Q, and slides in the upright piece R, in which is a screw at r, to fix it at any proper elevation.

In the box T are two wheels (as in Dr Long's sphere) and two pinions, whose axes come out at V and U; either of which may be turned by the small winch W. When the winch is put upon the axis V, and turn backward, the terrestrial globe, with its horizon and celestial meridian, keep at rest; and the whole sphere of circles turns round from east, by south, to west, carrying the sun Y, and moon Z, round the same way, and causing them to rise above and set below the horizon. But when the winch is put upon the axis U, and turned forward, the sphere with the sun and moon keep at rest; and the earth, with its horizon and meridian, turn round from horizon to the sun and moon, to which these bodies came when the earth kept at rest, and they were carried round it; showing that they rise and set in the same points of the horizon, and at the same times in the hour circle, whether the motion be in the earth or in the heaven. If the earthly globe be turned, the hour-index goes round its hour-circle; but if the sphere be turned, the hour-circle goes round below the index.

And so, by this construction, the machine is equally fitted to show either the real motion of the earth, or the apparent motion of the heavens.

To rectify the sphere for use, first slacken the screw r in the upright stem R, and taking hold of the arm Q, move it up or down until the given degree of latitude for any place be at the side of the stem R; and then the axis of the sphere will be properly elevated, so as to stand parallel to the axis of the world, if the machine be set north and south by a small compass: this done, count the latitude from the north pole, upon the celestial meridian L, down towards the north notch of the horizon, and set the horizon to that latitude; then, turn the nut b until the sun Y comes to the given day of the year in the ecliptic, and the sun will be at its proper place for that day: find the place of the moon's ascending node, and also the place of the moon, by an Ephemeris, and set them right accordingly: lastly, turn the winch W, until either the sun comes to the meridian L, or until the meridian comes to the sun (according as you want the sphere or earth to move) and set the hour-index to the XII, marked noon, and the whole machine will be rectified. — Then turn the winch, and observe when the sun or moon rise and set in the horizon, and the hour-index will show the times thereof for the given day.

China

Throughout Chinese history, astronomers have created celestial globes to assist the observation of the stars. The Chinese also used the armillary sphere in aiding calendrical computations and calculations.

According to Joseph Needham, the earliest development of the armillary sphere in China goes back to the astronomers Shi Shen and Gan De in the 4th century BC, as they were equipped with a primitive single-ring armillary instrument. This would have allowed them to measure the north polar distance (declination) a measurement that gave the position in a xiu (right ascension). Needham's 4th century BC dating, however, is rejected by British sinologist Christopher Cullen, who traces the beginnings of these devices to the 1st century BC.

During the Western Han dynasty (202 BC – 9 AD) additional developments made by the astronomers Luoxia Hong (落下閎), Xiangyu Wangren, and Geng Shouchang (耿壽昌) advanced the use of the armillary in its early stage of evolution. In 52 BC, it was the astronomer Geng Shouchang who introduced the first permanently fixed equatorial ring of the armillary sphere. In the subsequent Eastern Han dynasty (23–220 AD) period, the astronomers Fu An and Jia Kui added the ecliptic ring by 84 AD. With the famous statesman, astronomer, and inventor Zhang Heng (張衡, 78–139 AD), the sphere was totally complete in 125 AD, with horizon and meridian rings. The world's first water-powered celestial globe was created by Zhang Heng, who operated his armillary sphere by use of an inflow clepsydra clock.

Subsequent developments were made after the Han dynasty that improved the use of the armillary sphere. In 323 AD the Chinese astronomer Kong Ting was able to reorganize the arrangement of rings on the armillary sphere so that the ecliptic ring could be pegged on to the equator at any point desired. The Chinese astronomer and mathematician Li Chunfeng (李淳風) of the Tang dynasty created one in 633 AD with three spherical layers to calibrate multiple aspects of astronomical observations, calling them 'nests' (chhung). He was also responsible for proposing a plan of having a sighting tube mounted ecliptically in order for the better observation of celestial latitudes. However, it was the Tang Chinese astronomer, mathematician, and monk Yi Xing in the next century who would accomplish this addition to the model of the armillary sphere. Ecliptical mountings of this sort were found on the armillary instruments of Zhou Cong and Shu Yijian in 1050, as well as Shen Kuo's armillary sphere of the later 11th century, but after that point they were no longer employed on Chinese armillary instruments until the arrival of the European Jesuits.

In 723 AD, Yi Xing (一行) and government official Liang Ling-zan (梁令瓚) combined Zhang Heng's water powered celestial globe with an escapement device. With drums hit every quarter-hour and bells rung automatically every full hour, the device was also a striking clock. The famous clock tower that the Chinese polymath Su Song built by 1094 during the Song dynasty would employ Yi Xing's escapement with waterwheel scoops filled by clepsydra drip, and powered a crowning armillary sphere, a central celestial globe, and mechanically operated manikins that would exit mechanically opened doors of the clock tower at specific times to ring bells and gongs to announce the time, or to hold plaques announcing special times of the day. There was also the scientist and statesman Shen Kuo (1031–1095). Being the head official for the Bureau of Astronomy, Shen Kuo was an avid scholar of astronomy, and improved the designs of several astronomical instruments: the gnomon, armillary sphere, clepsydra clock, and sighting tube fixed to observe the pole star indefinitely. When Jamal al-Din of Bukhara was asked to set up an 'Islamic Astronomical Institution' in Khubilai Khan's new capital during the Yuan dynasty, he commissioned a number of astronomical instruments, including an armillary sphere. It was noted that "Chinese astronomers had been building [them] since at least 1092".

Indian Subcontinent
The armillary sphere was used for observation in India since early times, and finds mention in the works of Āryabhata (476 CE). The Goladīpikā—a detailed treatise dealing with globes and the armillary sphere was composed between 1380 and 1460 CE by Parameśvara. On the subject of the usage of the armillary sphere in India, Ōhashi (2008) writes: "The Indian armillary sphere (gola-yantra) was based on equatorial coordinates, unlike the Greek armillary sphere, which was based on ecliptical coordinates, although the Indian armillary sphere also had an ecliptical hoop. Probably, the celestial coordinates of the junction stars of the lunar mansions were determined by the armillary sphere since the seventh century or so."

Hellenistic world and ancient Rome
The Greek astronomer Hipparchus (c. 190) credited Eratosthenes (276 – 194 BC) as the inventor of the armillary sphere. Names of this device in Greek include ἀστρολάβος astrolabos and κρικωτὴ σφαῖρα krikōtē sphaira "ringed sphere". The English name of this device comes ultimately from the Latin armilla (circle, bracelet), since it has a skeleton made of graduated metal circles linking the poles and representing the equator, the ecliptic, meridians and parallels. Usually a ball representing the Earth or, later, the Sun is placed in its center. It is used to demonstrate the motion of the stars around the Earth. Before the advent of the European telescope in the 17th century, the armillary sphere was the prime instrument of all astronomers in determining celestial positions.

In its simplest form, consisting of a ring fixed in the plane of the equator, the armilla is one of the most ancient of astronomical instruments. Slightly developed, it was crossed by another ring fixed in the plane of the meridian. The first was an equinoctial, the second a solstitial armilla. Shadows were used as indices of the sun's positions, in combinations with angular divisions. When several rings or circles were combined representing the great circles of the heavens, the instrument became an armillary sphere.

Armillary spheres were developed by the Hellenistic Greeks and were used as teaching tools already in the 3rd century BC. In larger and more precise forms they were also used as observational instruments. However, the fully developed armillary sphere with nine circles perhaps did not exist until the mid-2nd century AD, during the Roman Empire. Eratosthenes most probably used a solstitial armilla for measuring the obliquity of the ecliptic. Hipparchus probably used an armillary sphere of four rings. The Greco-Roman geographer and astronomer Ptolemy (c. 100) describes his instrument, the astrolabon, in his Almagest. It consisted of at least three rings, with a graduated circle inside of which another could slide, carrying two small tubes positioned opposite each other and supported by a vertical plumb-line.

Medieval Middle East and Europe

Persian and Arab astronomers such as Ibrahim al-Fazari and Abbas Ibn Firnas continued to build and improve on armillary spheres. The spherical astrolabe, a variation of both the astrolabe and the armillary sphere, was likely invented during the Middle Ages in the Middle East. About 550 AD, Christian philosopher John Philoponus wrote a treatise on the astrolabe in Greek, which is the earliest extant treatise on the instrument. The earliest description of the spherical astrolabe dates back to the Persian astronomer Nayrizi (fl. 892–902). Pope Sylvester II applied the use of sighting tubes with his armillary sphere in order to fix the position of the pole star and record measurements for the tropics and equator, and used armillary spheres as a teaching device.

Korea
Chinese ideas of astronomy and astronomical instruments were introduced to Korea, where further advancements were also made. Jang Yeong-sil, a Korean inventor, was ordered by King Sejong the Great of Joseon to build an armillary sphere. The sphere, built in 1433 was named Honcheonui (혼천의,渾天儀).

The Honcheonsigye, an armillary sphere activated by a working clock mechanism was built by the Korean astronomer Song Iyeong in 1669. It is the only remaining astronomical clock from the Joseon dynasty. The mechanism of the armillary sphere succeeded that of Sejong era's armillary sphere (Honŭi 渾儀, 1435) and celestial sphere (Honsang 渾象, 1435), and the Jade Clepsydra (Ongnu 玉漏, 1438)'s sun-carriage apparatus. Such mechanisms are similar to Ch'oe Yu-ji (崔攸之, 1603~1673)'s armillary sphere(1657). The structure of time going train and the mechanism of striking-release in the part of clock is influenced by the crown escapement which has been developed from 14th century, and is applied to gear system which had been improved until the middle of 17th century in Western-style clockwork. In particular, timing device of Song I-yŏng's Armillary Clock adopts the early 17th century pendulum clock system which could remarkably improve the accuracy of a clock.

Renaissance
Further advances in this instrument were made by Danish astronomer Tycho Brahe (1546–1601), who constructed three large armillary spheres which he used for highly precise measurements of the positions of the stars and planets. They were described in his Astronomiae Instauratae Mechanica.

Armillary spheres were among the first complex mechanical devices. Their development led to many improvements in techniques and design of all mechanical devices. Renaissance scientists and public figures often had their portraits painted showing them with one hand on an armillary sphere, which represented the zenith of wisdom and knowledge.

The armillary sphere survives as useful for teaching, and may be described as a skeleton celestial globe, the series of rings representing the great circles of the heavens, and revolving on an axis within a horizon. With the earth as center such a sphere is known as Ptolemaic; with the sun as center, as Copernican.

A representation of an armillary sphere is present in the modern flag of Portugal and has been a national symbol since the reign of Manuel I.

Paralympic Games
An artwork-based model of an Armillary sphere has been used since the March 1, 2014 to light the Paralympic heritage flame at Stoke Mandeville Stadium, United Kingdom. The sphere includes a wheelchair that the user can rotate to spark the flame as part of a ceremony to celebrate the past, present and future of the Paralympic Movement in the UK. The Armillary Sphere was created by artist Jon Bausor and will be used for future Heritage Flame events. The flame in the first-ever ceremony was lit by London 2012 gold medallist Hannah Cockroft.

Heraldry and vexillology
The armillary sphere is commonly used in heraldry and vexillology, being mainly known as a symbol associated with Portugal, the Portuguese Empire and the Portuguese discoveries.

In the end of the 15th century, the armillary sphere became the personal heraldic badge of the future King Manuel I of Portugal, when he was still a Prince. The intense use of this badge in documents, monuments, flags and other supports, during the reign of Manuel I, transformed the armillary sphere from a simple personal symbol to a national one that represented the Kingdom of Portugal and in particular its Overseas Empire. As a national symbol, the armillary sphere continued in use after the death of Manuel I.

In the 17th century, it became associated with the Portuguese dominion of Brazil. In 1815, when Brazil gained the status of kingdom united with that of Portugal, its coat of arms was formalized as a golden armillary sphere in a blue field. Representing Brazil, the armillary sphere became also present in the arms and the flag of the United Kingdom of Portugal, Brazil and the Algarves. When Brazil became independent as an empire in 1822, the armillary sphere continued to be present in its national arms and in its national flag. The celestial sphere of the present Flag of Brazil replaced the armillary sphere in 1889.

The armillary sphere was reintroduced in the national arms and in the national Flag of Portugal in 1911.

title: Armillary sphere


text:
Birefringence

Birefringence is the optical property of a material having a refractive index that depends on the polarization and propagation direction of light. These optically anisotropic materials are described as birefringent or birefractive. The birefringence is often quantified as the maximum difference between refractive indices exhibited by the material. Crystals with non-cubic crystal structures are often birefringent, as are plastics under mechanical stress.

Birefringence is responsible for the phenomenon of double refraction whereby a ray of light, when incident upon a birefringent material, is split by polarization into two rays taking slightly different paths. This effect was first described by Danish scientist Rasmus Bartholin in 1669, who observed it in Iceland spar (calcite) crystals which have one of the strongest birefringences. In the 19th century Augustin-Jean Fresnel described the phenomenon in terms of polarization, understanding light as a wave with field components in transverse polarization (perpendicular to the direction of the wave vector).

Explanation

A mathematical description of wave propagation in a birefringent medium is presented below. Following is a qualitative explanation of the phenomenon.

Uniaxial materials
The simplest type of birefringence is described as uniaxial, meaning that there is a single direction governing the optical anisotropy whereas all directions perpendicular to it (or at a given angle to it) are optically equivalent. Thus rotating the material around this axis does not change its optical behaviour. This special direction is known as the optic axis of the material. Light propagating parallel to the optic axis (whose polarization is always perpendicular to the optic axis) is governed by a refractive index $n_{o}$ (for "ordinary") regardless of its specific polarization. For rays with any other propagation direction, there is one linear polarization that is perpendicular to the optic axis, and a ray with that polarization is called an ordinary ray and is governed by the same refractive index value $n_{o}$. For a ray propagating in the same direction but with a polarization perpendicular to that of the ordinary ray, the polarization direction will be partly in the direction of (parallel to) the optic axis, and this extraordinary ray will be governed by a different, direction-dependent refractive index. Because the index of refraction depends on the polarization when unpolarized light enters a uniaxial birefringent material, it is split into two beams travelling in different directions, one having the polarization of the ordinary ray and the other the polarization of the extraordinary ray. The ordinary ray will always experience a refractive index of $n_{o}$, whereas the refractive index of the extraordinary ray will be in between $n_{o}$ and $n_{e}$, depending on the ray direction as described by the index ellipsoid. The magnitude of the difference is quantified by the birefringence

 * $$\Delta n=n_\mathrm{e}-n_\mathrm{o}\,.$$

The propagation (as well as reflection coefficient) of the ordinary ray is simply described by $n_{o}$ as if there were no birefringence involved. The extraordinary ray, as its name suggests, propagates unlike any wave in an isotropic optical material. Its refraction (and reflection) at a surface can be understood using the effective refractive index (a value in between $n_{o}$ and $n_{e}$). Its power flow (given by the Poynting vector) is not exactly in the direction of the wave vector. This causes an additional shift in that beam, even when launched at normal incidence, as is popularly observed using a crystal of calcite as photographed above. Rotating the calcite crystal will cause one of the two images, that of the extraordinary ray, to rotate slightly around that of the ordinary ray, which remains fixed.

When the light propagates either along or orthogonal to the optic axis, such a lateral shift does not occur. In the first case, both polarizations are perpendicular to the optic axis and see the same effective refractive index, so there is no extraordinary ray. In the second case the extraordinary ray propagates at a different phase velocity (corresponding to $n_{e}$) but still has the power flow in the direction of the wave vector. A crystal with its optic axis in this orientation, parallel to the optical surface, may be used to create a waveplate, in which there is no distortion of the image but an intentional modification of the state of polarization of the incident wave. For instance, a quarter-wave plate is commonly used to create circular polarization from a linearly polarized source.

Biaxial materials
The case of so-called biaxial crystals is substantially more complex. These are characterized by three refractive indices corresponding to three principal axes of the crystal. For most ray directions, both polarizations would be classified as extraordinary rays but with different effective refractive indices. Being extraordinary waves, the direction of power flow is not identical to the direction of the wave vector in either case.

The two refractive indices can be determined using the index ellipsoids for given directions of the polarization. Note that for biaxial crystals the index ellipsoid will not be an ellipsoid of revolution ("spheroid") but is described by three unequal principle refractive indices $n_{α}$, $n_{β}$ and $n_{γ}$. Thus there is no axis around which a rotation leaves the optical properties invariant (as there is with uniaxial crystals whose index ellipsoid is a spheroid).

Although there is no axis of symmetry, there are two optical axes or binormals which are defined as directions along which light may propagate without birefringence, i.e., directions along which the wavelength is independent of polarization. For this reason, birefringent materials with three distinct refractive indices are called biaxial. Additionally, there are two distinct axes known as optical ray axes or biradials along which the group velocity of the light is independent of polarization.

Double refraction
When an arbitrary beam of light strikes the surface of a birefringent material at non-normal incidence, the polarization component normal to the optic axis (ordinary ray) and the other linear polarization (extraordinary ray) will be refracted toward somewhat different paths. Natural light, so-called unpolarized light, consists of equal amounts of energy in any two orthogonal polarizations. Even linearly polarized light has some energy in both polarizations, unless aligned along one of the two axes of birefringence. According to Snell's law of refraction, the two angles of refraction are governed by the effective refractive index of each of these two polarizations. This is clearly seen, for instance, in the Wollaston prism which separates incoming light into two linear polarizations using prisms composed of a birefringent material such as calcite.

The different angles of refraction for the two polarization components are shown in the figure at the top of this page, with the optic axis along the surface (and perpendicular to the plane of incidence), so that the angle of refraction is different for the $s$ polarization (the "ordinary ray" in this case, having its electric vector perpendicular to the optic axis) and the $p$ polarization (the "extraordinary ray" in this case, whose electric field polarization includes a component in the direction of the optic axis). In addition, a distinct form of double refraction occurs, even with normal incidence, in cases where the optic axis is not along the refracting surface (nor exactly normal to it); in this case, the dielectric polarization of the birefringent material is not exactly in the direction of the wave's electric field for the extraordinary ray. The direction of power flow (given by the Poynting vector) for this inhomogenous wave is at a finite angle from the direction of the wave vector resulting in an additional separation between these beams. So even in the case of normal incidence, where one would compute the angle of refraction as zero (according to Snell's law, regardless of the effective index of refraction), the energy of the extraordinary ray is propagated at an angle. If exiting the crystal through a face parallel to the incoming face, the direction of both rays will be restored, but leaving a shift between the two beams. This is commonly observed using a piece of calcite cut along its natural cleavage, placed above a paper with writing, as in the above photographs. On the contrary, waveplates specifically have their optic axis along the surface of the plate, so that with (approximately) normal incidence there will be no shift in the image from light of either polarization, simply a relative phase shift between the two light waves.

Terminology
Much of the work involving polarization preceded the understanding of light as a transverse electromagnetic wave, and this has affected some terminology in use. Isotropic materials have symmetry in all directions and the refractive index is the same for any polarization direction. An anisotropic material is called "birefringent" because it will generally refract a single incoming ray in two directions, which we now understand correspond to the two different polarizations. This is true of either a uniaxial or biaxial material.

In a uniaxial material, one ray behaves according to the normal law of refraction (corresponding to the ordinary refractive index), so an incoming ray at normal incidence remains normal to the refracting surface. As explained above, the other polarization can deviate from normal incidence, which cannot be described using the law of refraction. This thus became known as the extraordinary ray. The terms "ordinary" and "extraordinary" are still applied to the polarization components perpendicular to and not perpendicular to the optic axis respectively, even in cases where no double refraction is involved.

A material is termed uniaxial when it has a single direction of symmetry in its optical behavior, which we term the optic axis. It also happens to be the axis of symmetry of the index ellipsoid (a spheroid in this case). The index ellipsoid could still be described according to the refractive indices, $n_{α}$, $n_{β}$ and $n_{γ}$, along three coordinate axes; in this case two are equal. So if $n_{α} = n_{β}$ corresponding to the $s$ and $p$ axes, then the extraordinary index is $n_{γ}$ corresponding to the $s$ axis, which is also called the optic axis in this case.

Materials in which all three refractive indices are different are termed biaxial and the origin of this term is more complicated and frequently misunderstood. In a uniaxial crystal, different polarization components of a beam will travel at different phase velocities, except for rays in the direction of what we call the optic axis. Thus the optic axis has the particular property that rays in that direction do not exhibit birefringence, with all polarizations in such a beam experiencing the same index of refraction. It is very different when the three principal refractive indices are all different; then an incoming ray in any of those principal directions will still encounter two different refractive indices. But it turns out that there are two special directions (at an angle to all of the 3 axes) where the refractive indices for different polarizations are again equal. For this reason, these crystals were designated as biaxial, with the two "axes" in this case referring to ray directions in which propagation does not experience birefringence.

Fast and slow rays
In a birefringent material, a wave consists of two polarization components which generally are governed by different effective refractive indices. The so-called slow ray is the component for which the material has the higher effective refractive index (slower phase velocity), while the fast ray is the one with a lower effective refractive index. When a beam is incident on such a material from air (or any material with a lower refractive index), the slow ray is thus refracted more towards the normal than the fast ray. In the example figure at top of this page, it can be seen that refracted ray with s polarization (with its electric vibration along the direction of the optic axis, thus called the extraordinary ray ) is the slow ray in given scenario.

Using a thin slab of that material at normal incidence, one would implement a waveplate. In this case, there is essentially no spatial separation between the polarizations, the phase of the wave in the parallel polarization (the slow ray) will be retarded with respect to the perpendicular polarization. These directions are thus known as the slow axis and fast axis of the waveplate.

Positive or negative
Uniaxial birefringence is classified as positive when the extraordinary index of refraction $n_{e}$ is greater than the ordinary index $n_{o}$. Negative birefringence means that $Δn = n_{e} − n_{o}$ is less than zero. In other words, the polarization of the fast (or slow) wave is perpendicular to the optic axis when the birefringence of the crystal is positive (or negative, respectively). In the case of biaxial crystals, all three of the principal axes have different refractive indices, so this designation does not apply. But for any defined ray direction one can just as well designate the fast and slow ray polarizations.

Sources of optical birefringence
While the best known source of birefringence is the entrance of light into an anisotropic crystal, it can result in otherwise optically isotropic materials in a few ways:
 * Stress birefringence results when a normally isotropic solid is stressed and deformed (i.e., stretched or bent) causing a loss of physical isotropy and consequently a loss of isotropy in the material's permittivity tensor;
 * Form birefringence, whereby structure elements such as rods, having one refractive index, are suspended in a medium with a different refractive index. When the lattice spacing is much smaller than a wavelength, such a structure is described as a metamaterial;
 * By the Pockels or Kerr effect, whereby an applied electric field induces birefringence due to nonlinear optics;
 * By the self or forced alignment into thin films of amphiphilic molecules such as lipids, some surfactants or liquid crystals;
 * Circular birefringence takes place generally not in materials which are anisotropic but rather ones which are chiral. This can include liquids where there is an enantiomeric excess of a chiral molecule, that is, one that has stereo isomers;
 * By the Faraday effect, where a longitudinal magnetic field causes some materials to become circularly birefringent (having slightly different indices of refraction for left- and right-handed circular polarizations), similar to optical activity while the field is applied.

Common birefringent materials

The best characterized birefringent materials are crystals. Due to their specific crystal structures their refractive indices are well defined. Depending on the symmetry of a crystal structure (as determined by one of the 32 possible crystallographic point groups), crystals in that group may be forced to be isotropic (not birefringent), to have uniaxial symmetry, or neither in which case it is a biaxial crystal. The crystal structures permitting uniaxial and biaxial birefringence are noted in the two tables, below, listing the two or three principal refractive indices (at wavelength 590 nm) of some better-known crystals.

In addition to induced birefringence while under stress, many plastics obtain permanent birefringence during manufacture due to stresses which are "frozen in" due to mechanical forces present when the plastic is molded or extruded. For example, ordinary cellophane is birefringent. Polarizers are routinely used to detect stress, either applied or frozen-in, in plastics such as polystyrene and polycarbonate.

Cotton fiber is birefringent because of high levels of cellulosic material in the fibre's secondary cell wall which is directionally aligned with the cotton fibers.

Polarized light microscopy is commonly used in biological tissue, as many biological materials are linearly or circularly birefringent. Collagen, found in cartilage, tendon, bone, corneas, and several other areas in the body, is birefringent and commonly studied with polarized light microscopy. Some proteins are also birefringent, exhibiting form birefringence.

Inevitable manufacturing imperfections in optical fiber leads to birefringence, which is one cause of pulse broadening in fiber-optic communications. Such imperfections can be geometrical (lack of circular symmetry), or due to unequal lateral stress applied to the optical fibre. Birefringence is intentionally introduced (for instance, by making the cross-section elliptical) in order to produce polarization-maintaining optical fibers. Birefringence can be induced (or corrected) in optical fibers through bending them which causes anisotropy in form and stress given the axis around which it is bent and radius of curvature.

In addition to anisotropy in the electric polarizability that we have been discussing, anisotropy in the magnetic permeability could be a source of birefringence. At optical frequencies, there is no measurable magnetic polarizability of natural materials, so this is not an actual source of birefringence.

Measurement
Birefringence and other polarization-based optical effects (such as optical rotation and linear or circular dichroism) can be observed by measuring any change in the polarization of light passing through the material. These measurements are known as polarimetry. Polarized light microscopes, which contain two polarizers that are at 90° to each other on either side of the sample, are used to visualize birefringence, since light that has not been affected by birefringence remains in a polarization that is totally rejected by the second polarizer ("analyzer"). The addition of quarter-wave plates permits examination using circularly polarized light. Determination of the change in polarization state using such an apparatus is the basis of ellipsometry, by which the optical properties of specular surfaces can be gauged through reflection.

Birefringence measurements have been made with phase-modulated systems for examining the transient flow behaviour of fluids. Birefringence of lipid bilayers can be measured using dual-polarization interferometry. This provides a measure of the degree of order within these fluid layers and how this order is disrupted when the layer interacts with other biomolecules.

For the 3D measurement of birefringence, a technique based on holographic tomography can be used.

Optical devices
Birefringence is used in many optical devices. Liquid-crystal displays, the most common sort of flat-panel display, cause their pixels to become lighter or darker through rotation of the polarization (circular birefringence) of linearly polarized light as viewed through a sheet polarizer at the screen's surface. Similarly, light modulators modulate the intensity of light through electrically induced birefringence of polarized light followed by a polarizer. The Lyot filter is a specialized narrowband spectral filter employing the wavelength dependence of birefringence. Waveplates are thin birefringent sheets widely used in certain optical equipment for modifying the polarization state of light passing through it.

To manufacture polarizers with high transmittance, birefringent crystals are used in devices such as the Glan–Thompson prism, Glan–Taylor prism and other variants. Layered birefringent polymer sheets can also be used for this purpose.

Birefringence also plays an important role in second-harmonic generation and other nonlinear optical processes. The crystals used for these purposes are almost always birefringent. By adjusting the angle of incidence, the effective refractive index of the extraordinary ray can be tuned in order to achieve phase matching, which is required for the efficient operation of these devices.

Medicine
Birefringence is utilized in medical diagnostics. One powerful accessory used with optical microscopes is a pair of crossed polarizing filters. Light from the source is polarized in the $x$ direction after passing through the first polarizer, but above the specimen is a polarizer (a so-called analyzer) oriented in the $y$ direction. Therefore, no light from the source will be accepted by the analyzer, and the field will appear dark. Areas of the sample possessing birefringence will generally couple some of the $z$-polarized light into the $x$ polarization; these areas will then appear bright against the dark background. Modifications to this basic principle can differentiate between positive and negative birefringence.

For instance, needle aspiration of fluid from a gouty joint will reveal negatively birefringent monosodium urate crystals. Calcium pyrophosphate crystals, in contrast, show weak positive birefringence. Urate crystals appear yellow, and calcium pyrophosphate crystals appear blue when their long axes are aligned parallel to that of a red compensator filter, or a crystal of known birefringence is added to the sample for comparison.

The birefringence of tissue inside a living human thigh was measured using polarization-sensitive optical coherence tomography at 1310 nm and a single mode fiber in a needle. Skeletal muscle birefringence was Δn = 1.79 × 10−3 ± 0.18×10−3, adipose Δn = 0.07 × 10−3 ± 0.50 × 10−3, superficial aponeurosis Δn = 5.08 × 10−3 ± 0.73 × 10−3 and interstitial tissue Δn = 0.65 × 10−3 ±0.39 × 10−3. These measurements may be important for the development of a less invasive method to diagnose Duchenne muscular dystrophy.

Birefringence can be observed in amyloid plaques such as are found in the brains of Alzheimer's patients when stained with a dye such as Congo Red. Modified proteins such as immunoglobulin light chains abnormally accumulate between cells, forming fibrils. Multiple folds of these fibers line up and take on a beta-pleated sheet conformation. Congo red dye intercalates between the folds and, when observed under polarized light, causes birefringence.

In ophthalmology, binocular retinal birefringence screening of the Henle fibers (photoreceptor axons that go radially outward from the fovea) provides a reliable detection of strabismus and possibly also of anisometropic amblyopia. In healthy subjects, the maximum retardation induced by the Henle fiber layer is approximately 22 degrees at 840 nm. Furthermore, scanning laser polarimetry uses the birefringence of the optic nerve fiber layer to indirectly quantify its thickness, which is of use in the assessment and monitoring of glaucoma. Polarization-sensitive optical coherence tomography measurements obtained from healthy human subjects have demonstrated a change in birefringence of the retinal nerve fiber layer as a function of location around the optic nerve head. The same technology was recently applied in the living human retina to quantify the polarization properties of vessel walls near the optic nerve. While retinal vessel walls become thicker and less birefringent in patients who suffer from hypertension, hinting at a decrease in vessel wall condition, the vessel walls of diabetic patients do not experience a change in thickness, but do see an increase in birefringence, presumably due to fibrosis or inflammation.

Birefringence characteristics in sperm heads allow the selection of spermatozoa for intracytoplasmic sperm injection. Likewise, zona imaging uses birefringence on oocytes to select the ones with highest chances of successful pregnancy. Birefringence of particles biopsied from pulmonary nodules indicates silicosis.

Dermatologists use dermatoscopes to view skin lesions. Dermoscopes use polarized light, allowing the user to view crystalline structures corresponding to dermal collagen in the skin. These structures may appear as shiny white lines or rosette shapes and are only visible under polarized dermoscopy.

Stress-induced birefringence
Isotropic solids do not exhibit birefringence. When they are under mechanical stress, birefringence results. The stress can be applied externally or is "frozen in" after a birefringent plastic ware is cooled after it is manufactured using injection molding. When such a sample is placed between two crossed polarizers, colour patterns can be observed, because polarization of a light ray is rotated after passing through a birefringent material and the amount of rotation is dependent on wavelength. The experimental method called photoelasticity used for analyzing stress distribution in solids is based on the same principle. There has been recent research on using stress-induced birefringence in a glass plate to generate an optical vortex and full Poincare beams (optical beams that have every possible polarization state across a cross-section).

Other cases of birefringence
Birefringence is observed in anisotropic elastic materials. In these materials, the two polarizations split according to their effective refractive indices, which are also sensitive to stress.

The study of birefringence in shear waves traveling through the solid Earth (the Earth's liquid core does not support shear waves) is widely used in seismology.

Birefringence is widely used in mineralogy to identify rocks, minerals, and gemstones.

Theory
In an isotropic medium (including free space) the so-called electric displacement ($n_{o}$) is just proportional to the electric field ($n_{e}$) according to $Δn$ where the material's permittivity $n_{α}$ is just a scalar (and equal to $n_{β}$ where $n_{γ}$ is the index of refraction). In an anisotropic material exhibiting birefringence, the relationship between $D$ and $E$ must now be described using a tensor equation:

where $D = ɛE$ is now a 3 × 3 permittivity tensor. We assume linearity and no magnetic permeability in the medium: $ε$. The electric field of a plane wave of angular frequency $n^{2}ε_{0}$ can be written in the general form:

where $n$ is the position vector, $D$ is time, and $E$ is a vector describing the electric field at $ε$, $μ = μ_{0}$. Then we shall find the possible wave vectors $ω$. By combining Maxwell's equations for $r$ and $t$, we can eliminate $E_{0}$ to obtain:

With no free charges, Maxwell's equation for the divergence of $r = 0$ vanishes:

We can apply the vector identity $t = 0$ to the left hand side of $y$, and use the spatial dependence in which each differentiation in $k$ (for instance) results in multiplication by $∇ × E$ to find:

The right hand side of $x$ can be expressed in terms of $∇ × H$ through application of the permittivity tensor $H = 1⁄μ_{0}B$ and noting that differentiation in time results in multiplication by $D$, $y$ then becomes:

Applying the differentiation rule to $$ we find:

$$ indicates that $∇ × (∇ × A) = ∇(∇ ⋅ A) − ∇^{2}A$ is orthogonal to the direction of the wavevector $x$, even though that is no longer generally true for $ik_{x}$ as would be the case in an isotropic medium. $$ will not be needed for the further steps in the following derivation.

Finding the allowed values of $E$ for a given $ε$ is easiest done by using Cartesian coordinates with the $−iω$, $D$ and $k$ axes chosen in the directions of the symmetry axes of the crystal (or simply choosing $E$ in the direction of the optic axis of a uniaxial crystal), resulting in a diagonal matrix for the permittivity tensor $k$:

where the diagonal values are squares of the refractive indices for polarizations along the three principal axes $ω$, $x$ and $y$. With $z$ in this form, and substituting in the speed of light $z$ using $ε$, the $x$ component of the vector equation $$ becomes

where $y$, $z$, $ε$ are the components of $c$ (at any given position in space and time) and $c^{2} = 1⁄μ_{0}ε_{0}$, $x$, $E_{x}$ are the components of $E_{y}$. Rearranging, we can write (and similarly for the $E_{z}$ and $E$ components of $$)

This is a set of linear equations in $k_{x}$, $k_{y}$, $k_{z}$, so it can have a nontrivial solution (that is, one other than $k$) as long as the following determinant is zero:

Evaluating the determinant of $$, and rearranging the terms according to the powers of $$\frac{\omega^2}{c^2}$$, the constant terms cancel. After eliminating the common factor $$\frac{\omega^2}{c^2}$$ from the remaining terms, we obtain

In the case of a uniaxial material, choosing the optic axis to be in the $y$ direction so that $z$ and $E_{x}$, this expression can be factored into

Setting either of the factors in $$ to zero will define an ellipsoidal surface in the space of wavevectors $E_{y}$ that are allowed for a given $E_{z}$. The first factor being zero defines a sphere; this is the solution for so-called ordinary rays, in which the effective refractive index is exactly $E = 0$ regardless of the direction of $z$. The second defines a spheroid symmetric about the $n_{x} = n_{y} = n_{o}$ axis. This solution corresponds to the so-called extraordinary rays in which the effective refractive index is in between $n_{z} = n_{e}$ and $k$, depending on the direction of $ω$. Therefore, for any arbitrary direction of propagation (other than in the direction of the optic axis), two distinct wavevectors $n_{o}$ are allowed corresponding to the polarizations of the ordinary and extraordinary rays.

For a biaxial material a similar but more complicated condition on the two waves can be described; the locus of allowed $k$ vectors (the wavevector surface) is a 4th-degree two-sheeted surface, so that in a given direction there are generally two permitted $z$ vectors (and their opposites). By inspection one can see that $$ is generally satisfied for two positive values of $n_{o}$. Or, for a specified optical frequency $n_{e}$ and direction normal to the wavefronts $k$, it is satisfied for two wavenumbers (or propagation constants) $k$ (and thus effective refractive indices) corresponding to the propagation of two linear polarizations in that direction.

When those two propagation constants are equal then the effective refractive index is independent of polarization, and there is consequently no birefringence encountered by a wave traveling in that particular direction. For a uniaxial crystal, this is the optic axis, the ±z direction according to the above construction. But when all three refractive indices (or permittivities), $k$, $k$ and $ω$ are distinct, it can be shown that there are exactly two such directions, where the two sheets of the wave-vector surface touch; these directions are not at all obvious and do not lie along any of the three principal axes ($ω$, $k⁄|k|$, $|k|$ according to the above convention). Historically that accounts for the use of the term "biaxial" for such crystals, as the existence of exactly two such special directions (considered "axes") was discovered well before polarization and birefringence were understood physically. These two special directions are generally not of particular interest; biaxial crystals are rather specified by their three refractive indices corresponding to the three axes of symmetry.

A general state of polarization launched into the medium can always be decomposed into two waves, one in each of those two polarizations, which will then propagate with different wavenumbers $n_{x}$. Applying the different phase of propagation to those two waves over a specified propagation distance will result in a generally different net polarization state at that point; this is the principle of the waveplate for instance. With a waveplate, there is no spatial displacement between the two rays as their $n_{y}$ vectors are still in the same direction. That is true when each of the two polarizations is either normal to the optic axis (the ordinary ray) or parallel to it (the extraordinary ray).

In the more general case, there is a difference not only in the magnitude but the direction of the two rays. For instance, the photograph through a calcite crystal (top of page) shows a shifted image in the two polarizations; this is due to the optic axis being neither parallel nor normal to the crystal surface. And even when the optic axis is parallel to the surface, this will occur for waves launched at non-normal incidence (as depicted in the explanatory figure). In these cases the two $n_{z}$ vectors can be found by solving $$ constrained by the boundary condition which requires that the components of the two transmitted waves' $x$ vectors, and the $y$ vector of the incident wave, as projected onto the surface of the interface, must all be identical. For a uniaxial crystal it will be found that there is not a spatial shift for the ordinary ray (hence its name) which will refract as if the material were non-birefringent with an index the same as the two axes which are not the optic axis. For a biaxial crystal neither ray is deemed "ordinary" nor would generally be refracted according to a refractive index equal to one of the principal axes.

title: Birefringence


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Steve Lewis (musician)

Steve Lewis (March 19, 1896 - c. 1941?) was an American jazz pianist and composer.

Lewis was born in New Orleans, Louisiana. In 1910, he began his career as a member of the Silver Leaf Orchestra. He joined the Olympia Orchestra and toured with Bill and Mary Mack in 1917. When he returned to New Orleans, he spent the next ten years in bands with Armand J. Piron. During the 1920s, he taught piano to such students as Luis Russell. He worked as a bandleader and a freelance musician. His last days were spent in a mental institution in Louisiana.

Lewis was an eccentric character. He drove a Ford Model T which he had custom painted in bright multicolored polka-dots. He played the piano without using either of his middle fingers; these he kept extended straight while playing (in the manner of the rude gesture known as Shooting the Bird).

Lewis was influenced by the piano stylings of Tony Jackson and Jelly Roll Morton, and became the premier pianist in Storyville after those two older musicians left town.

title: Steve Lewis (musician)