2. Introduction to GnuPlot
College of Natural Sciences Computing Laboratories
University of Northern Iowa
Cedar Falls, IA 50614
http://www.cs.uni.edu/Help/gnuplot/
Amethyst is a violet tinted gemstone consisting of crystalline quartz with iron as an added impurity. The iron impurity in amethyst acts differently from the chromium impurity in ruby which makes ruby red. In ruby the impurity is excited directly by the "visible" photon; in amethyst, it is not. Instead, the impurity in amethyst creates another unstable species in the crystal and this new species jumps to an excited state by absorbing a "visible" photon. This species is known as a color center. By absorbing a "visible" photon, it makes the crystal appear colored.
The simplest color center is found in sodium chloride or table salt, normally a colorless crystal. Sodium chloride is built from little cubes, with sodium ions Na+and chloride ions Cl- alternating at each corner. Every Na+ is surrounded by Cl- and vice versa; and the attraction between the positive and negative charges makes salt a strong crystal. When salt is bombarded by high energy radiation (cosmic rays from outer space or gamma rays from a radioactive source), a Cl- can be ejected from the crystal, creating a vacancy where the Cl- had been. Momentarily the crystal is no longer electrically neutral: it is missing a negative charge. To regain stability, it grabs an available electron close to the crystal and sticks it in the vacancy previously occupied by the ejected Cl-. The crystal then appears as in the following figure.
Figure 10.7, Tilley, p.240
With the electron replacing the ejected Cl-, there are now equal numbers of positive and negative charges in the crystal; and the electron is held firmly in its site by the surrounding positively charged NaNow the crystal has an electron in place of the original Cl-+ ions. This process turns the colorless salt crystal into an orange/brown. The trapped electron, responsible for the color, is known as a "color center." The color center produces the color exactly as the impurity does in the ruby crystal. The color center can also exist in an excited state, and the energy needed to reach that excited state is equal to the energy of a visible photon. The color center actually absorbs a "violet" photon by jumping to the excited state; and the crystal appears with the color orange/brown (the complement of violet).g
Analogous color centers occur in several minerals. In some cases, impurities are involved in forming the color centers.
An iron impurity is responsible for the violet color in amethyst by creatiing a color center. The color center, not the iron impurity, is responsible for absorbing the "yellow" photon that makes amethyst violet. In another example, topaz, a fluoroaluminosilicate with iron as an added impurity, achieves its yellow color by means of a color center, again created by the iron impurity.
Summary
Why are some crystals colorless and others colored?
In some cases (e.g. ruby), an impurity will achieve this if the impurity has an excited state of the right energy. In other cases (e.g. sapphire), an excited state of the right energy can be achieved by charge transfer (or, transfering a charge between) between two impurities. Again (e.g. in amethyst) a new species, a color center, with an excited state of the right energy, can be created within the crystal, formed using vacancies and, often, impurities.
(This page is under development, and might be completed Winter 2002).
Take a century-old glass bottle, and expose it in the desert to the ultraviolet radiation present in strong sunlight. Come back after ten years, and the glass will have acquired an attractive purple color. Heat the bottle in an oven, and the color disappears. Next expose the bottle to an intense source of energetic radiation, as in the cobalt-60 gamma ray cell of Figure 24, and within a few minutes an even deeper purple color appears, as shown in Plate XI.
The color in this "desert amethyst glass" derives from a color center, as do the colors of the natural gemstones amethyst, smoky quartz, and blue and orange topaz. Many other materials, both natural and man-made, can be irradiated to produce color centers, including irradiated blue, yellow, and green diamonds. Some of these colors, such as all the ones mentioned so far, are perfectly stable, losing their color only when heated. Other color centers are unstable and fade when exposed to light, while yet others fade even in the dark.
The term "color center" is sometimes used so loosely that even transition-metal and the band-gap colorations are included. This rare usage ignores the unique characteristics of color centers; the conventional narrow interpretation is followed here.
Consider an ionic crystal, such as the alkali halide sodium chloride NaCl (ordinary table salt), which consists of a three dimensional array of Na+ and Cl- ions. A single Cl- can be missing in two ways. If a compensating Na+ is also missing, then the crystal remains neutral and there are no consequences of interest with respect to color. If, however, a Na+ is not missing, then one way of maintaining electrical neutrality is for a free electron, designated c, to occupy the spot vacated by the Cl-. This is called an F-center, after the German "Farbe" (color), as shown at the top left of Fig. 25. One can view this electron as if it were part of a transition metal in the ligand field of the surrounding K' ions or, preferably, one can view this electron as providing a trapping energy level within the band gap of this transparent wide-band-gap semiconductor material, as shown in Fig. 26.
Some form of relatively high energy such as irradiation by ultraviolet or high-energy electrons, x-rays, or gamma rays can now promote an electron from the valence band into the trap. There are, however, excited energy levels within the trap, such as the level at Ea (at 2.7 eV for NaCI), which can absorb blue light, leading to a yellow-brown color in irradiated defect- containing NaCl; this defect is now called a color center. Note that the electron in this excited energy level is still within the trap. Only by supplying energy corresponding to Eb can the electron leave the trap and return via the conduction band directly to the valence band. This can happen if the crystal is heated, and results in bleaching of the color center. If Eb is about the same size as Eb, then bleaching can occur merely while the material is being illuminated, leading to optical bleaching. If Eb is sufficiently small, the material may even fade in the dark at room temperature. This occurs in self-darkening sun glasses, in which the ultraviolet present in sunlight produces the darkening and room temperature leads to fading as soon as there is no ultraviolet. Other centers are possible in alkali halides, some of which are also shown in Fig. 25; these may absorb in the visible, the ultraviolet, or the infrared. Some such color centers also show fluorescence and some of these can function as laser materials. As alternatives to irradiation, growth in the presence of excess metal or solid-state electrolysis can also be used to generate color centers.
The most general description of a material capable of supporting a color center is given in Fig. 27, in which the colorless state is shown above and the colored state below. Two kinds of precursors are needed: a hole precursor A which can lose an electron, e.g., when absorbing irradiation, to form a hole center A+, and an electron precursor B which can gain the electron lost from A to form the electron center B-. Either A+ or B- can be the color center itself that absorbs light, or even both can do so. On heating, the electron is released from B- and returns to A+', thus restoring the colorless state of A plus B.
A number of gemstone materials derive their beauty from color centers. Colorless "rock-crystal" quartz, shown center above in Plate XI, is composed of silicon oxide SiO2, shown schematically at A in Fig. 27. All natural and synthetic quartz contains the aluminum impurity Al3+, typically replacing one out of every 10,000 Si"; for charge neutrality a hydrogen ion H+ or a Na+ is nearby. Such quartz is colorless, but irradiation, either natural in the ground over many thousands of years or man-provided in 20 minutes in a cobalt-60 gamma source such as that of Fig. 24, now produces smoky quartz, also shown in Plate X1. As illustrated at B in Fig. 28, irradiation ejects an electron from an oxygen adjacent to the Al3+, the whole [AlO4] grouping acting as the hole precursor and converting to the hole center [AlO4]. The electron is trapped by the H+ electron precursor, converting it into the neutral H electron center. In this case it is the hole center that is the color center and provides the gray-to-brown-to-black color of smoky quartz seen in Plate XI. Also shown in this figure is yellow citrine (often erroneously called "smoky topaz"), which is quartz containing Fe3+ instead of Al3+; this produces the purple amethyst, also shown in Plate XI, by an exactly analogous irradiation process leading to the hole color center [FeO4].
The colors of both amethyst and smoky quartz are stable to light but are lost on being heated to 300 to 500"C; if not overheated, the color center and the color can be restored by another irradiation, and so on.
A century ago, glass used to be decolorized with manganese additions to remove the green color caused by iron impurities. It is the Mn2+ left from this process which loses an electron to form the purple Mn7+ shown in Plate XI in the solarization process described at the beginning of this section.
Natural yellow-to-orange-to-brown precious topaz contains a color center stable to light; any colorless topaz can be irradiated to a similar color that, however, is usually unstable and fades in a few days in light. Blue topaz also contains a color center, which can be either natural or manproduced; here both are stable. The exact nature of most of these color centers is unknown. Interestingly enough, the irradiation of colorless diamonds can produce stable yellow, blue, brown, and green colors. Although the first two of these are similar in appearance to the N-caused yellow and the B-caused blue discussed above, they represent much less valued materials, which can be distinguished by spectroscopic and other features.
FIG. 24. A sample being placed into a gamma-ray cell for irradiation by the author.
PLATE XI. Color centers. Above: century-old glass bottle irradiated to form "desert amethyst glass," colorless syntheticquartz crystal as grown, and one that has been irradiated to form smoky quartz. Below: a synthetic citrine quartz colored yellow by Fe and one that has been additionally irradiated to form amethyst.
FIG. 25. Different types of color-center defects in an ionic crystal (schematic).
FIG.26. Trapping of energy from absorbed light in a halide vacancy trap in an alkali-halide crystal.
FIG. 27. The irradiation of hole and electron precursors (a) to form hole and electron centers (b).
FIG. 28. Schematic representation of the structure of quartz (A) and the formation by irradiation of a smoky- quartz color center (B).
"현수가 일을 낼겁니다." 이에리사 선수단 총감독은 남자 1,000m와 1,500m에서 안현수(21, 한국체대)가 금메달 두 개를 따내자 이같이 예고했다. 이에리사 감독의 이러한 확신은 안현수가 당시 2관왕에 올랐기 때문이 아니었다. 그동안 안현수가 보여준 남다른 태도 때문이었다.
이에리사 감독이 전하는 안현수는 '영감'이다. 또래에 비해 매우 신중하고 사려가 깊다는 것이 이에리사 감독의 설명. 특히 승부에 대한 진지한 자세는 그동안 이름을 날려온 그 어떤 쇼트트랙 스타와도 비교가 안된다는 것이 이 감독의 말이다.
특히 안현수는 경기와 훈련시간, 식사시간이 아니면 토리노의 선수촌에서 방 밖으로 나오는 일이 없었다. 다른 선수들의 경우 인터넷을 하기 위해 촌내에 마련된 PC방을 찾거나 쇼핑센터 등에 들려 여가를 즐기곤 했다. 어린 선수들이 갑갑한 선수촌 생활을 견디기 위해서는 어쩌면 당연한 일.
그러나 안현수는 언제나 방안에 틀어박혀 머리 속으로 경기장면을 그리고 있었다. 인터넷을 멀리한 것 역시 초심을 잃지 않기 위한 하나의 방법이었다. 언론에서 연일 쏟아내는 자신에 대한 기사를 보면 자만에 빠질 수 있다고 생각한 안현수는 이를 모두 멀리했다.
안현수는 자신의 마지막 경기였던 남자 계주 결승이 끝날 때까지 좀처럼 웃는 모습도 보이지 않았다. 첫 금메달을 땄을때나, 2관왕을 달성했을 때에도 엷은 미소만을 보일뿐 흐트러진 모습은 찾아볼 수 없었다. 모든 경기를 마치고 3개의 금메달과 하나의 동메달을 목에 건 뒤에야 안현수는 동료들과 장난을 치며 또래다운 모습을 보였다.
이처럼 마지막까지 집중하고 긴장의 끈을 놓지 않은 안현수의 남다른 모습이 올림픽 최고의 별로 떠오르게 한 원동력이 아닐까.
토리노=CBS체육부 백길현 기자
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이번 동계 올림픽! 너무 인상적인 장면이 많았다~
특히 계주 마지막 바퀴에서 안현수가 역주하는 장면에서 느꼈던 전율은 아직까지도 생생하다~
마지막 역주서, 마치 부스터를 단 듯한 그의 레이스는 보는 이들을 환호하게 만들었다~
세계적인 선수들과 대결에서 그와같은 기량차를 만들어 내기까지
그 뒤 숨겨진 노력은 본인이 아니고선 모르겠지~
그리고 남다른 그 집중력 또한 그 원동력 중 하나일 것이다.
전에 고승덕 변호사의 글에도 이런 글이 있었던거 같다.
자신이 한 분야에 대해 투자한 노력에 대해서 말하는데
투자한 시간이 노력을 말해주는 것이 아니라, 집중력이라는 웨이트 펙터를 준 것이다.
뭐 수식으로 표현하자면 " 노력 = 집중력 * 시간 " 이렇게 표현이 된다.
이번 동계올림픽을 보면서 느꼈던 그 전율을, 비록 트랙에서는 아니지만 내가 만들어서 느껴보고싶다.
자! 새학기도 시작했는데 새로운 마음으로 남다른 집중력과 기복없는 노력으로 좋은 결과를 얻어보자꾸나!