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第88行：
第88行： − 固体中秩序的最严格形式是'''晶格周期性''': 某种模式( '''<font color="#ff8000">单元格 Unit Cell</font>''' 中原子的排列)一次又一次地重复，形成一个平移不变的空间'''<font color="#ff8000">平铺 Tiling</font>'''。这就是'''<font color="#ff8000">晶体 Crystal</font>'''的定义属性。可能的对称性已在14个'''<font color="#ff8000">布拉维斯晶格 Bravais Lattice</font>'''和230个'''<font color="#ff8000">空间群 Space Group</font>'''中分类。+ 第98行：
第98行： − + 第128行：
第128行： − 长程有序+ 第138行：
第138行： − + 第178行：
第178行： − + − − − −
→Characterizing order
The strictest form of order in a solid is lattice periodicity: a certain pattern (the arrangement of atoms in a unit cell) is repeated again and again to form a translationally invariant tiling of space. This is the defining property of a crystal. Possible symmetries have been classified in 14 Bravais lattices and 230 space groups.
The strictest form of order in a solid is lattice periodicity: a certain pattern (the arrangement of atoms in a unit cell) is repeated again and again to form a translationally invariant tiling of space. This is the defining property of a crystal. Possible symmetries have been classified in 14 Bravais lattices and 230 space groups.
固体中最严格的秩序形式是'''晶格周期性''': 某种模式( '''<font color="#ff8000">即单元格 Unit Cell</font>''' 中原子的排列)一次又一次地重复，通过平移形成一个不变的空间'''<font color="#ff8000">平铺 Tiling</font>'''。这就是'''<font color="#ff8000">晶体 Crystal</font>'''的定义属性。可能的对称性已在14个'''<font color="#ff8000">布拉维斯晶格 Bravais Lattice</font>'''和230个'''<font color="#ff8000">空间群 Space Group</font>'''中进行了分类。
Lattice periodicity implies long-range order: if only one unit cell is known, then by virtue of the translational symmetry it is possible to accurately predict all atomic positions at arbitrary distances. During much of the 20th century, the converse was also taken for granted – until the discovery of quasicrystals in 1982 showed that there are perfectly deterministic tilings that do not possess lattice periodicity.
Lattice periodicity implies long-range order: if only one unit cell is known, then by virtue of the translational symmetry it is possible to accurately predict all atomic positions at arbitrary distances. During much of the 20th century, the converse was also taken for granted – until the discovery of quasicrystals in 1982 showed that there are perfectly deterministic tilings that do not possess lattice periodicity.
格点周期性意味着'''长程有序''': 如果只知道一个单位单元，那么借助于平移对称性，就有可能在任意距离上精确地预测所有原子的位置。在20世纪的大部分时间里，相反的情况也被认为是合理的——直到1982年'''<font color="#ff8000">准晶体 Quasicrystal</font>'''的发现表明，完全确定性的倾斜并不具有晶格周期性。
格点周期性意味着'''长程有序''': 如果我们只知道一个单位单元，那么借助于平移对称性，就有可能在任意距离上精确地预测所有原子的位置。在20世纪的大部分时间里，相反的情况也被认为是合理的——但直到1982年'''<font color="#ff8000">准晶体 Quasicrystal</font>'''的发现表明，完全确定性的倾斜并不具有晶格周期性。
===Long-range order===
===Long-range order===
远程有序
Long-range order characterizes physical systems in which remote portions of the same sample exhibit correlated behavior.
Long-range order characterizes physical systems in which remote portions of the same sample exhibit correlated behavior.
'''长程有序'''描述了同一样本的远程部分表现出'''<font color="#ff8000">相关 correlated</font>'''行为的物理'''<font color="#ff8000">系统 System</font>'''。
'''远程有序'''描述了同一样本的远程部分表现出'''<font color="#ff8000">相关 correlated</font>'''行为的物理'''<font color="#ff8000">系统 System</font>'''。
This function is equal to unity when <math>x=x'</math> and decreases as the distance <math>|x-x'|</math> increases. Typically, it decays exponentially to zero at large distances, and the system is considered to be disordered. But if the correlation function decays to a constant value at large <math>|x-x'|</math> then the system is said to possess long-range order. If it decays to zero as a power of the distance then it is called quasi-long-range order (for details see Chapter 11 in the textbook cited below. See also Berezinskii–Kosterlitz–Thouless transition). Note that what constitutes a large value of <math>|x-x'|</math> is understood in the sense of asymptotics.
This function is equal to unity when <math>x=x'</math> and decreases as the distance <math>|x-x'|</math> increases. Typically, it decays exponentially to zero at large distances, and the system is considered to be disordered. But if the correlation function decays to a constant value at large <math>|x-x'|</math> then the system is said to possess long-range order. If it decays to zero as a power of the distance then it is called quasi-long-range order (for details see Chapter 11 in the textbook cited below. See also Berezinskii–Kosterlitz–Thouless transition). Note that what constitutes a large value of <math>|x-x'|</math> is understood in the sense of asymptotics.
当<math>x=x'</math>时，这个函数等于单位数，当距离<math>|x-x'|</math>增加时，这个函数减少。通常情况下，它在很大距离上'''<font color="#ff8000">呈指数衰减 Decays Exponentially</font>'''为零，系统被认为是无序的。但是如果相关函数(量子场论)衰变为一个常数值，那么这个系统就被认为具有长程序。如果它衰变为零作为距离的幂，那么它被称为准长程序(详见下面引用的教科书第11章)。参见'''<font color="#ff8000">Berezinskii–Kosterlitz–Thouless过渡 Berezinskii–Kosterlitz–Thouless Transition</font>''')。请注意，构成较大的<math>|x-x'|</math>的值可以理解为渐近性。
当<math>x=x'</math>时，这个函数等于单位数量，当距离<math>|x-x'|</math>增加时，函数值减少。通常情况下，它在很大距离上'''<font color="#ff8000">呈指数衰减 Decays Exponentially</font>'''为零，系统被认为是无序的。但是如果相关函数(量子场论)衰变为一个常数值，那么这个系统就被认为具有远程有序。如果它衰变成为零以作为距离的幂，那么它被称为准远程有序(详见下面引用的教科书第11章)。参见'''<font color="#ff8000">Berezinskii–Kosterlitz–Thouless过渡 Berezinskii–Kosterlitz–Thouless Transition</font>''')。请注意，构成较大的<math>|x-x'|</math>的值可以理解为渐近性。
==Quenched disorder==
==Quenched disorder==