A complex oxide $\mathrm{ABO}_{2}$ can form multiple crystal polymorphs. In the crystal structures involved in this problem, the same type of metal ions occupy identical interstitial sites, with the same coordination number and coordination polyhedra.

For the cubic phase $\alpha-\mathrm{ABO}_{2}$, X-ray diffraction measurements revealed several characteristic interplanar spacings of the crystal as 239.9, 207.7, 146.9, 125.3, and 103.9 $\mathrm{pm}$. The density of this crystal is known to be 4.389 $\mathrm{g\cdot cm^{-3}}$ with an error margin below 0.08%.

For $\gamma-\mathrm{ABO}_{2}$, the unit cell parameters were measured as $a=b=405.7 \mathrm{pm}, c=875.9 \mathrm{pm}$, with $\gamma$ unknown. This crystal can be described as: $\mathrm{A}$ and $\mathrm{B}$ alternately filling interstitial sites within layers to form polyhedral layers, where all polyhedral layers share identical chemical environments.

For another $\mathrm{ABO}_{2}$ structure, the unit cell parameters were measured as $a=b=296.3 \mathrm{pm}, c=1463.6 \mathrm{pm}$, with $\gamma$ unknown. This crystal can be viewed as having $\mathrm{A}$ and $\mathrm{B}$ arranged in alternating layers, where atoms of the same type share identical chemical environments.

Determine the identities of $\mathrm{A}$ and $\mathrm{B}$ before answering.
某复合氧化物 $\mathrm{ABO}_{2}$ 可以形成多种晶型, 在本题所涉及的晶体结构中, 同种金属离子填入了相同类型的空隙, 配位数和配位多面体相同。

对于立方晶系的 $\alpha-\mathrm{ABO}_{2}$, 通过 X-射线衍射测得该晶体中若干特征的晶面间距分别为 239.9、207.7、146.9、125.3 与 103.9 $\mathrm{pm}$。已知该晶体密度为 4.389 $\mathrm{g\cdot cm^{-3}}$ , 误差小于0.08%。

对于 $\gamma-\mathrm{ABO}_{2}$, 测得其晶胞参数 $a=b=405.7 \mathrm{pm}, c=875.9 \mathrm{pm}$, $\gamma$ 未知。该晶体可以描述为: $\mathrm{A}$ 与 $\mathrm{B}$
交替填充层内空隙构成多面体层, 所有的多面体层化学环境相同。

对于另一种 $\mathrm{ABO}_{2}$ 结构, 测得其晶胞参数 $a=b=296.3 \mathrm{pm} ,  c=1463.6 \mathrm{pm}$, $\gamma$未知。该晶体可以看作A、B分层排布,同种原子化学环境相同。

请确定$\mathrm{A}$ 和 $\mathrm{B}$ 是何元素后回答.
$\mathrm{ABO_2}$ dissolves in hydrochloric acid under certain conditions, resulting in a light pink solution.
$\gamma-\mathrm{ABO_2}$ has the same crystal structure as chalcopyrite.
$\alpha-\mathrm{ABO_2}$ belongs to the simple cubic lattice.
From the ratio of the unit cell volumes of different crystal forms, it can be concluded that both $\gamma-\mathrm{ABO_2}$ and the third $\mathrm{ABO_2}$ belong to the tetragonal crystal system.
Based on the unit cell volume and lattice parameters, in both $\alpha$-$\mathrm{ABO_2}$ and $\gamma$-$\mathrm{ABO_2}$, the $\mathrm{O}$ atoms adopt either exact or approximate face-centered cubic close packing.
At the same temperature and pressure, the standard entropy of $\alpha-\mathrm{ABO_2}$ is lower than that of $\gamma-\mathrm{ABO_2}$.
All other options are incorrect
$\mathrm{ABO_2}$在一定条件下溶于盐酸, 得到的溶液为浅粉色. 
$\gamma-\mathrm{ABO_2}$ 具有与黄铜矿相同的晶体结构
$\alpha-\mathrm{ABO_2}$属于简单立方点阵
从不同晶型的晶胞体积之比可以得到, $\gamma-\mathrm{ABO_2}$ 与第三种 $\mathrm{ABO_2}$均属于四方晶系
根据晶胞体积和晶胞参数判断, $\alpha-\mathrm{ABO_2}$和$\gamma-\mathrm{ABO_2}$ 中, $\mathrm{O}$ 均采取准确的或近似的面心立方最密堆积
相同温度, 压力下, $\alpha-\mathrm{ABO_2}$ 的标准熵比 $\gamma-\mathrm{ABO_2}$ 的更低. 
其他选项均不正确
Analysis of the crystal structure of $\alpha - \mathrm { A B O _ { 2 } }$ and elements A, B  

$\alpha - \mathrm { A B O _ { 2 } }$ belongs to the cubic crystal system, with given interplanar spacing $d$ values: 239.9 pm, 207.7 pm, 146.9 pm, 125.3 pm, and 103.9 pm.  

For the cubic crystal system, the relationship between interplanar spacing and lattice parameter $a$ is:  

$$
{ \frac { 1 } { d ^ { 2 } } } = { \frac { h ^ { 2 } + k ^ { 2 } + l ^ { 2 } } { a ^ { 2 } } }
$$  

Based on the proportions, the $d$ values of the interplanar spacings correspond to $a/\sqrt{3}$, $a/\sqrt{4}$, $a/\sqrt{8}$, $a/\sqrt{11}$, and $a/\sqrt{16}$.  
The lattice parameter is determined as $a=415.5 ~\mathrm{pm}$.  

<Checkpoint>[$a_\alpha=415.5 ~\mathrm{pm}$ ](1)</Checkpoint>  

Moreover, the observed $h^2+k^2+l^2$ values follow the rules of a face-centered cubic (FCC) lattice (i.e., no extinction when $h$, $k$, and $l$ are all odd or all even). Thus, the $\alpha$ phase adopts a face-centered cubic lattice.  

<Checkpoint>[The $\alpha$ phase has a face-centered cubic lattice](1)</Checkpoint>  

From the density formula:  

$$
\rho=\frac{ZM}{N_Aa^3}
$$  

By enumerating the possible $M$ values for different $Z$, the smallest error occurs when $Z=2$, with $\mathrm{A}$ and $\mathrm{B}$ being $\mathrm{Li}$ and $\mathrm{Fe}$, respectively.  

<Checkpoint>[$\mathrm{A, B=Li, Fe}$](3)</Checkpoint>  

Given that $a_\gamma\approx a_\alpha$ and $c_\gamma\approx 2a_\alpha$, the $\gamma$ phase can be considered as a combination of two cubic unit cells. Therefore, the $\gamma$ phase adopts a tetragonal unit cell.  

<Checkpoint>[$\gamma-\mathrm{LiFeO_2}$ belongs to the tetragonal crystal system](1)</Checkpoint>  

The reduction in symmetry indicates that the occupancy of $\mathrm{Li}$ and $\mathrm{Fe}$ sites transitions from disordered to ordered.  

<Checkpoint>[$\alpha-\mathrm{LiFeO_2}$ is a disordered structure, while $\gamma-\mathrm{LiFeO_2}$ is an ordered structure](2)</Checkpoint>  

For the other structure, $a\approx \frac{1}{\sqrt{2}}a_\alpha$ and $c\approx 2\sqrt{3}a_\alpha$. The proportionality coefficients suggest that this structure adopts a hexagonal unit cell, with one $\mathrm{O}$ atom per layer and a total of six layers. It likely corresponds to a face-centered cubic close-packed arrangement, where $\mathrm{Li}$ and $\mathrm{Fe}$ occupy octahedral voids in different layers. The positional arrangement can be represented as $Ac_\mathrm{Li}Ba_\mathrm{Fe}Cb_\mathrm{Li}Ac_\mathrm{Fe}Ba_\mathrm{Li}Cb_\mathrm{Fe}A$.  

<Checkpoint>[The third layered structure belongs to the trigonal crystal system with an $hR$ lattice](2)</Checkpoint>  

Analysis of the options:  
A. $\mathrm{FeCl_3}$ is yellow, not light pink;  
B. $\mathrm{LiFeO_2}$ fills octahedral voids, whereas chalcopyrite $\mathrm{CuFeS_2}$ fills tetrahedral voids;  
C. $\alpha-\mathrm{ABO_2}$ adopts a face-centered cubic lattice;  
D. The third layered $\mathrm{ABO_2}$ belongs to the trigonal crystal system;  
E. Correct;  
F. $\alpha-\mathrm{ABO_2}$ is a disordered phase, while $\gamma-\mathrm{ABO_2}$ is an ordered phase. Under the same conditions, $\alpha-\mathrm{ABO_2}$ has higher entropy.
分析 $\alpha - \mathrm { A B O _ { 2 } }$ 的晶体结构和元素A、B

$\alpha - \mathrm { A B O _ { 2 } }$ 为立方晶系，给定晶面间距 $d$ 值: 239.9 pm、207.7 pm、146.9 pm、125.3 pm 和 103.9 pm。

对于立方晶系，晶面间距与晶格参数 $a$ 的关系为：

$$
{ \frac { 1 } { d ^ { 2 } } } = { \frac { h ^ { 2 } + k ^ { 2 } + l ^ { 2 } } { a ^ { 2 } } }
$$

根据比例，各晶面间距的$d$值分别是$a/\sqrt{3}$、$a/\sqrt{4}$、$a/\sqrt{8}$、$a/\sqrt{11}$、$a/\sqrt{16}$。
得到 $a=415.5 ~\mathrm{pm}$ 

<Checkpoint>[$a_\alpha=415.5 ~\mathrm{pm}$ ](1)</Checkpoint>

并且, 出现的$h^2+k^2+l^2$ 符合面心立方的规律（即$h$、$k$、$l$全奇或全偶时不消光）, 因此$\alpha$相为面心立方点阵. 

<Checkpoint>[$\alpha$相为面心立方点阵](1)</Checkpoint>

由密度公式: 

$$
\rho=\frac{ZM}{N_Aa^3}
$$

列举各个 $Z$ 对应的 $M$ , $Z=2$ 时, $\mathrm{A, B}$ 分别为 $\mathrm{Li, Fe}$ 误差最小. 

<Checkpoint>[$\mathrm{A, B=Li, Fe}$](3)</Checkpoint>

$a_\gamma\approx a_\alpha$, $c_\gamma\approx 2a_\alpha$, 可以认为$\gamma$相由2倍的立方晶胞组合得到. 因此$\gamma$相为四方晶胞. 

<Checkpoint>[$\gamma-\mathrm{LiFeO_2}$属于四方晶系](1)</Checkpoint>

对称性降低意味着$\mathrm{Li, Fe}$占据位点从无序变为有序. 

<Checkpoint>[$\alpha-\mathrm{LiFeO_2}$是无序结构, $\gamma-\mathrm{LiFeO_2}$是有序结构](2)</Checkpoint>

对于另外的结构, $a\approx \frac{1}{\sqrt{2}}a_\alpha, c\approx 2\sqrt{3}a_\alpha$, 从比例系数可以看出该结构取六方晶胞, 每层1个$\mathrm{O}$ 原子, 共6层, 应当是面心立方最密堆积, Li和Fe填充不同层的八面体空隙, 位置可以表示为$Ac_\mathrm{Li}Ba_\mathrm{Fe}Cb_\mathrm{Li}Ac_\mathrm{Fe}Ba_\mathrm{Li}Cb_\mathrm{Fe}A$. 

<Checkpoint>[第三种层状结构为三方晶系$hR$点阵](2)</Checkpoint>

分析选项: A. $\mathrm{FeCl_3}$为黄色, 并非浅粉色; B. $\mathrm{LiFeO_2}$均填充八面体空隙, 而黄铜矿$\mathrm{CuFeS_2}$ 填充四面体空隙; C. $\alpha-\mathrm{ABO_2}$属于面心立方点阵; D. 第三种层状 $\mathrm{ABO_2}$属于三方晶系; E. 正确; F. $\alpha-\mathrm{ABO_2}$ 是无序相,  $\gamma-\mathrm{ABO_2}$ 是有序相, 相同条件下, $\alpha-\mathrm{ABO_2}$ 的熵更高.