In an X-ray diffraction experiment, a sample is placed into the center of an instrument and illuminated with a beam of X-rays.

樣品放置在儀器的中心，受到一束 X 光照射。

The X-ray tube and detector move in a synchronized motion.

X 光光管和探測器同步的移動，

The signal coming from the sample is recorded and graphed,

記錄了從樣品散射出來的訊號並做成圖譜。

where peaks are observed related to the atomic structure of the sample.

圖譜中的繞射峰提供了樣品原子結構的訊息。

Most materials are made up of many small crystals like sand on a beach.

大多數的材料都是由許多小晶體組成的， 這就像沙灘上的沙一樣。

Each of these crystals is composed of a regular arrangement of atoms,

這些小晶體裏面都有許多整齊排列的原子，

and each atom is composed of a nucleus surrounded by a cloud of electrons.

而每個原子裏面包含了一個原子核和圍繞在周圍的電子雲，

It's at this scale that the story of X-ray diffraction begins.

X 光繞射就是在這個原子尺度下發生的。

X-rays are high-energy light with a repeating period called the wavelength.

X 光是一種周期性高能光束線,它的周期稱爲波長。

Since the wavelength of an X-ray is similar to the distance between atoms in a crystal,

由於 X 光的波長與晶體中的原子間距接近,

a special interference effect called "diffraction" can be used to measure the distance between the atoms.

形成了一種可以利用來量測原子間距的特殊干涉現象， 稱爲繞射。

Interference occurs when X-rays interact with each other.

當X射線相遇發生交互作用時，就會產生干涉現象。

If the waves are in alignment, the signal is amplified. This is called "constructive interference".

如果相位相同，訊號會被加强，稱爲建設性干涉。

If the waves are out of alignment, the signal is destroyed. This is called "destructive interference".

相反的，如果相位相反，則會消弱，稱爲破壞性干涉。

When an X-ray encounters an atom, its energy is absorbed by the electrons.

當X光擊中電子時，它的能量會被電子吸收。

Electrons occupy special energy states around an atom. Since this is not enough energy for the electron to be released,

電子在原子的周圍占據了特定能態的軌道。由於能量不足以讓電子脫離，

the energy must be re-emitted in the form of a new X-ray, but the same energy as the original.

這些能量會以二次 X 光的形式釋放，能量大小與原始 X 光相同。

This process is called "elastic scattering".

這個過程稱爲彈性散射。

In a crystal, the repeating arrangement of atoms form distinct planes separated by well-defined distances.

在晶體中，周期性排列的原子形成了等間距的晶面。

When the atomic planes are exposed to an X-ray beam, X-rays are scattered by the regularly spaced atoms.

當 X 光照射到晶面，就會被規則排列的原子散射。

Strong amplification of the emitted signal occurs at very specific angles

散射 X 光會在特定的角度產生非常强烈的建設性干涉訊號。

where the scattered waves constructively interfere. This effect is called "diffraction".

這個效應，就稱爲繞射現象。

The angle between the incident and the scattered beam is called 2-theta.

入射光和散射光之間的夾角稱爲 2theta 角。

In order for constructive interference to occur, the scattered waves must be in alignment,

要形成建設性干涉，散射光必須與入射光同相。

meaning that the second wave must travel a whole number of wavelengths.

也就是説第二條光線必須比第一條光線多走一個波長的距離。

In this case, one half of a wavelength is traveled on the incident side,

這時，半個波長會在入射側，而另外半個波長會在散射側，這樣可以凑成額外一個波長。

and one half on the scattered side, yielding one additional wavelength.

到了下一條光線，入射側和散射側各多一個波長，

In the case of the next X-ray, one wavelength has traveled on

這樣就有兩個波長的光程差。 這樣的叠加現象會在整個晶體裏出現，

both the incident and the scattered side resulting in two wavelengths.

繞射現象發生的角度位置是由紅色的三角形決定。

This reinforcement occurs throughout the crystal.

三角形上方的角度稱爲 theta 角， 是入射光跟散射光之間夾角的一半。

The exact angle at which diffraction occurs will be determined from the red triangle.

三角形的長邊是晶面間距，而短邊就是半波長的距離。

The angle at the top is theta, half the angle between the incident and scattered beams.

繞射角的晶面間距正好形成正弦函數的關係。

The long side is the distance between the atomic planes and the short side we know is one half of a wavelength.

如果我們把等式移項就能得到布拉格定律（Bragg's Law)。

The relationship between the diffraction angle,

這個定律是以 Sir William Henry Bragg 和 William Lawrence Bragg 這對父子檔命名的。

and the spacing between the atoms can be determined by applying the sine function.

他們在 1915 年因爲X光繞射在晶體結構分析的成就， 得到諾貝爾獎。

Rearranging this equation yields an equation commonly known as "Bragg's Law",

如今，X光繞射分析技術被廣汎的應用在各種材料，

named after Sir William Henry and William Lawrence Bragg, the father-son team who won the Nobel Prize in 1915

包括單晶磊晶薄膜、多晶粉末混合物，

for their work analyzing crystal structures with X-ray diffraction.

甚至是無序的非晶質材料。

This technique of X-ray diffraction is used today for a wide variety of materials, ranging from

X光繞射幫助科學家研發新藥品，

single crystal epitaxial thin films, to polycrystalline mixtures of powders, and even randomly oriented amorphous materials.

根據礦物組成鑒定岩石種類，

X-ray diffraction helps scientists to develop new pharmaceuticals, classify rock formations

瞭解原子排列對儲能材料的影響。

based on their mineral components and understand how the arrangement of atoms

當科學家把材料工程推向原子層次時，X光繞射分析也成爲越來越重要的工具。

affects the behavior of energy storage materials.

先進的儀器設計讓X光繞射分析更易於使用， 功能也越來越强大。

As scientists push their ability to engineer materials on the atomic level,

X-ray diffraction becomes an increasingly important tool in their toolbox.

Advances in equipment design have made X-ray diffraction easier to use, and more powerful than ever.