为什么钻石那么硬？
Why is diamond so hard?
钻石里每个碳都以 sp³ 杂化与四个相邻碳共价相连，键能高、方向固定，整块晶体是一张三维共价网络。要让一层原子滑过另一层就得同时切断大量这种键，网络又无易滑移的弱面，所以极难被刻划，莫氏硬度 10 由此而来；同为碳的石墨靠范德华力堆层，一推就滑。但要注意硬度只指抗划伤与抗压入，不等于韧：钻石有解理面，受击会崩口。
Every carbon in diamond is sp³-bonded to four neighbours, strong links of fixed orientation making one three-dimensional covalent network. Sliding a plane of atoms means cutting many of those bonds at once, and the network offers no weak slip plane, so it resists scratching and sits at 10 on the Mohs scale; graphite, the same element stacked by van der Waals forces, shears at a push. Hardness here means resistance to scratching and indentation, not toughness: diamond has cleavage planes and chips under a blow.
难度 专业 · 适合 高中(15-18)
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
傅献彩 等,《物理化学》第5版,高等教育出版社,2005
Fu Xiancai et al., Physical Chemistry, 5th ed., Higher Education Press, 2005
独立核验依据 · Independent verification: 核验依据 2 DOUBAN ISBN 标识 9787040167696（按标识回读: 物理化学(第五版)上册）
#碳 #晶体 #硬度
在单晶X射线衍射中，什么是“系统消光”？为什么螺旋轴和滑移面会使特定类型的衍射点（如h00中h为奇数者）完全消失？这一现象又如何反过来帮助确定晶体的空间群？
In single-crystal X-ray diffraction, what are "systematic absences"? Why do screw axes and glide planes cause certain classes of reflections (for example h00 with h odd) to vanish entirely, and how does this observation help determine a crystal's space group?
螺旋轴和滑移面均含平移分量：被它们联系的一对等效原子所散射的波，相位差为2πh·t。当该相位差恰为π的奇数倍时，两列波完全相消，相应类型反射的结构因子恒等于零，与原子的种类和坐标无关。因此，只需查明哪些hkl类型的衍射系统性地缺失，就能确定各对称元素中的平移成分，从而锁定空间群。
Screw axes and glide planes carry translational components: waves scattered by two atoms related by such a translation t differ in phase by 2πht. When this phase difference equals an odd multiple of π, the waves cancel exactly and the structure factor of that reflection class is zero no matter where the atoms lie. Identifying which hkl classes are systematically absent therefore fixes the translational part of each symmetry element and pins down the space group.
难度 专业 · 适合 高中(15-18)
CC BY 4.0 · 来源待核验 · Source pending review
来源 · Source
出处备注：著录含书名，但缺版次 / 出版社 / 年份中的一部分，需编辑补全后才能做独立比对。
《国际晶体学表》A卷：空间群对称性，M. I. Aroyo主编，第6版，国际晶体学联合会（IUCr），2016年。
International Tables for Crystallography, Vol. A: Space-Group Symmetry, ed. M. I. Aroyo, 6th ed., International Union of Crystallography, 2016.
#晶体学 #系统消光 #空间群
钙钛矿结构的“容忍因子”是什么？
What is the perovskite tolerance factor?
Goldschmidt 容忍因子 t=(rA+rX)/(√2(rB+rX)) 衡量 A、B、X 三种离子半径是否匹配；t≈1 时立方钙钛矿最稳定。
The Goldschmidt tolerance factor t=(rA+rX)/(√2(rB+rX)) checks whether A, B, X ionic radii fit; t≈1 gives the most stable cubic perovskite.
难度 进阶 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-08-23
来源 · Source
Brown, LeMay 等,《Chemistry: The Central Science》第14版,Pearson,2017
T. L. Brown et al., Chemistry: The Central Science, 14th ed., Pearson, 2017
#钙钛矿 #容忍因子 #晶体结构
从过饱和溶液怎么长出大晶体？
How do you grow large crystals from a supersaturated solution?
溶液过饱和后，缓慢降温或蒸发让溶质在晶种上有序沉积，长成规则的单晶。
After supersaturation, slow cooling or evaporation lets solute deposit orderly onto a seed, growing a regular single crystal.
难度 进阶 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-08-23
来源 · Source
Brown, LeMay 等,《Chemistry: The Central Science》第14版,Pearson,2017
T. L. Brown et al., Chemistry: The Central Science, 14th ed., Pearson, 2017
#晶体生长 #过饱和 #晶种
为什么观测晶体衍射必须使用X射线，而可见光不行？
Why must X-rays, rather than visible light, be used to observe diffraction from crystals?
衍射要求入射波长与散射体间距相当。晶体中原子间距约为0.1 nm，正落在X射线波长范围内，相邻晶面的散射波相干叠加，才能产生符合布拉格方程 nλ = 2d·sinθ 的衍射峰。可见光波长约500 nm，比原子间距大数千倍，遇晶体只发生反射与折射，无法感知内部周期排列，故测定晶体结构须用X射线或电子、中子束。
Diffraction requires a wavelength comparable to the spacing between scatterers. Atoms in a crystal lie roughly 0.1 nm apart, exactly the X-ray range, so waves scattered from neighboring atoms or planes interfere coherently to give peaks obeying Bragg's law, nλ = 2d sinθ. Visible light, at about 500 nm, is thousands of times longer than the atomic spacing; it is merely reflected and refracted by a crystal and senses none of the internal periodicity. Structure determination therefore relies on X-rays, or on shorter-wavelength electron and neutron beams.
难度 进阶 · 适合 初中(12-15)
CC BY 4.0 · 已核验 · Verified 2026-10-04
来源 · Source
C. Giacovazzo 主编《Fundamentals of Crystallography》第3版, Oxford University Press (IUCr), 2011
C. Giacovazzo (ed.), Fundamentals of Crystallography, 3rd ed., Oxford University Press (IUCr Texts on Crystallography), 2011
独立核验依据 · Independent verification: 核验依据 1 ISBN 978-0-19-957366-0 (2011, OUP)
#X射线衍射 #布拉格定律 #晶面间距 #晶体结构
为什么冰糖透明大块而红糖发暗？
Why is rock sugar clear and large while brown sugar is dark?
冰糖是蔗糖溶液缓慢重结晶得到的纯净大晶体，故透明；红糖保留了糖蜜，含色素和矿物质，未充分精制，故色深。
Rock sugar is pure sucrose grown as large slow crystals, hence clear; brown sugar keeps molasses with pigments and minerals, so it is dark.
难度 进阶 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
傅献彩 等,《物理化学》第5版,高等教育出版社,2005
Fu Xiancai et al., Physical Chemistry, 5th ed., Higher Education Press, 2005
独立核验依据 · Independent verification: 核验依据 2 DOUBAN ISBN 标识 9787040167696（按标识回读: 物理化学(第五版)上册）
#制糖 #结晶 #重结晶
为什么晶体常有规则外形？
Why do crystals have regular shapes?
内部粒子按重复的规律排列，长成有棱角的外形。
Particles repeat in a regular pattern, growing faceted shapes.
难度 入门 · 适合 小学低段(6-8)
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
傅献彩 等,《物理化学》第5版,高等教育出版社,2005
Fu Xiancai et al., Physical Chemistry, 5th ed., Higher Education Press, 2005
独立核验依据 · Independent verification: 核验依据 2 DOUBAN ISBN 标识 9787040167696（按标识回读: 物理化学(第五版)上册）
#晶体 #晶格 #外形
石英晶体为什么能当时钟？
Why can a quartz crystal act as a clock?
压电效应使晶片在电场下精确机械振动，频率极稳，用作振荡基准。
The piezoelectric effect makes the wafer vibrate mechanically at a very stable frequency under electric field, used as an oscillator reference.
难度 入门 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-08-23
来源 · Source
Brown, LeMay 等,《Chemistry: The Central Science》第14版,Pearson,2017
T. L. Brown et al., Chemistry: The Central Science, 14th ed., Pearson, 2017
#石英 #压电 #频率
冰糖（rock candy）是怎么长出来的？
How does rock candy grow?
热糖浆冷却后变得过饱和，糖分子沿棉线一根根有序堆积，长成大方晶。
Cooled syrup becomes supersaturated and sugar molecules stack orderly along a string, growing big square crystals.
难度 入门 · 适合 幼儿(3-6)
CC BY 4.0 · 已核验 · Verified 2026-08-23
来源 · Source
Brown, LeMay 等,《Chemistry: The Central Science》第14版,Pearson,2017
T. L. Brown et al., Chemistry: The Central Science, 14th ed., Pearson, 2017
#冰糖 #结晶 #过饱和
雪花为什么大多是六角的？
Why are snowflakes mostly six-sided?
冰的六方晶格让水分子按六重对称排列，分支也沿六个方向生长。
Ice's hexagonal lattice arranges water molecules with six-fold symmetry, so branches grow along six directions.
难度 入门 · 适合 幼儿(3-6)
CC BY 4.0 · 已核验 · Verified 2026-08-23
来源 · Source
Brown, LeMay 等,《Chemistry: The Central Science》第14版,Pearson,2017
T. L. Brown et al., Chemistry: The Central Science, 14th ed., Pearson, 2017
#雪花 #六方 #冰