Under certain conditions, a stoichiometric oxide $\mathbf{A}_xO_y$ crystal can be obtained. This crystal belongs to the cubic crystal system, and both $\mathbf{A}$ and O have only one type of coordination environment. Its structure can be described in two ways:

1. In this crystal, $\mathbf{A}$ forms a certain type of closest packing, and O orderly fills a certain proportion of a specific type of regular polyhedral voids.

2. This crystal can be regarded as a layered stacking, which is obtained by stacking $\mathbf{A}$ layers and O layers in a certain order.

The density of this crystal is $\rho = 3.22 g/cm^3$, and the shortest distance between two O atoms in the crystal is $d = 229.4 pm$.

Deduce the composition of the crystal and select the correct description from the following.
一定条件下，可得到整比氧化物$\mathbf{A}_xO_y$的晶体。该晶体为立方晶系，$\mathbf{A}$和O均只有一种配位环境，其结构有两种描述方法：

1.该晶体中$\mathbf{A}$做某种最密堆积，O有序填充一定比例的某一种正多面体空隙。

2.将该晶体视为层堆积，则其由$\mathbf{A}$层和O层按某种顺序堆叠得到。

该晶体的密度$\rho = 3.22 g/cm^3$，晶体中两个O原子之间的最短距离$d = 229.4 pm$。

推断该晶体的组成，并选择以下正确的描述。
The ratio of the number of $\mathbf{A}$ layers to O layers in the crystal is $2:1$.
Under normal temperature and pressure, $\mathbf{A}_xO_y$ is sparingly soluble in water.
The crystal has a face-centered cubic lattice.
The coordination number of $\mathbf{A}$ in this crystal is 4.
The shortest interlayer spacing between two O layers in the crystal, denoted as $h$ (pm), satisfies $75 < h < 80$.
In this crystal, the O layer is a non-close-packed layer, where the occupancy ratio <i>r</i> of O satisfies $25\%<r<75\%$.
该晶体中$\mathbf{A}$层和O层的数量比是$2:1$
常温常压下，$\mathbf{A}_xO_y$难溶于水
该晶体是面心立方点阵。
该晶体中$\mathbf{A}$的配位数为4
该晶体中两个O层之间的最短层间距$h (pm)$满足$75<h<80$
该晶体的中的O层是非密置层，其中O的占有率$r$满足$25\%<r<75\%$
Since the crystal has a cubic lattice, A must be cubic close-packed with 4 A atoms per unit cell. We can initially set $x=4$.

<Checkpoint>[A is cubic close-packed](1)</Checkpoint>

Let the unit cell parameter be $a$ (pm), and the formula weight of the entire unit cell be $M$.  

If O occupies the octahedral voids, then $d=a$ or $a/\sqrt2$.  

If O occupies the tetrahedral voids, then $d=a/2$, $a/\sqrt2$, or $\sqrt3a/2$.  

<Checkpoint>[$d$ possible values are $a,a/\sqrt2,a/2,\sqrt3a/2$](4)</Checkpoint>  

The following scenarios are discussed case by case.  

If $d = a$, then $y = 1$, $M = \rho a^3N_A=23.4 (g/mol)$, which is unreasonable.  

<Checkpoint>[$d=a$ is unreasonable](1)</Checkpoint>  

If $d = a/\sqrt2$, then $y=4$, $M=66.2(g/mol)$, which is unreasonable.  

<Checkpoint>[$d=a/\sqrt2$ is unreasonable](1)</Checkpoint>  

If $d=a/2$, then $y=8$, $M=187.3(g/mol)$, which is unreasonable.  

<Checkpoint>[$d=a/2$ is unreasonable](1)</Checkpoint>  

If $d=\sqrt3a/2$, then $y=2$, $M=36.0(g/mol)$, indicating A is H, so the crystal is $H_4O_2$, i.e., $H_2O$.  

<Checkpoint>[$d=\sqrt3a/2$ has a reasonable solution $H_2O$](2)</Checkpoint>  

In reality, this crystal adopts the $Cu_2O$ packing, with the ratio of A layers (H layers) to O layers being $1:2$, so option A is incorrect.  

<Checkpoint>[The ratio of A layers to O layers is $1:2$](3)</Checkpoint>  

$H_2O$ is not poorly soluble in water, so option B is incorrect.  

<Checkpoint>[$H_2O$ is not poorly soluble in water](1)</Checkpoint>  

This crystal has a simple cubic lattice, so option C is incorrect.  

<Checkpoint>[This crystal has a simple cubic lattice](1)</Checkpoint>  

In this crystal, the coordination number of A (H) is 2, so option D is incorrect.  

<Checkpoint>[The coordination number of A is 2](1)</Checkpoint>  

In this crystal, the interlayer spacing of O layers is $h=\sqrt3a/6=76.5pm$, so option E is correct.  

<Checkpoint>[The interlayer spacing of O layers is $h=76.5pm$](3)</Checkpoint>  

In this crystal, the occupancy rate of O layers is 25%, so option F is incorrect.  

<Checkpoint>[The occupancy rate of O layers is 25%](1)</Checkpoint>
因为晶体是立方点阵，因此$\mathbf{A}$必为立方最密堆积，一个晶胞里有4个$\mathbf{A}$，可先令$x=4$。

<Checkpoint>[A是立方最密堆积](1)</Checkpoint>

设晶胞参数为$a(pm)$，整个晶胞的式量为$M$。

若O填充八面体空隙，则$d=a或a/\sqrt2$

若O填充四面体空隙，则$d=a/2$或$a/\sqrt2$或$\sqrt3a/2$

<Checkpoint>[$d$的可能值为$a,a/\sqrt2,a/2,\sqrt3a/2$](4)</Checkpoint>

以下分类讨论。

若$d = a$，则$y = 1,M = \rho a^3N_A=23.4 (g/mol)$，无合理解。

<Checkpoint>[$d=a$不合理](1)</Checkpoint>

若$d = a/\sqrt2$，则$y=4,M=66.2(g/mol)$，无合理解。

<Checkpoint>[$d=a/\sqrt2$不合理](1)</Checkpoint>

若$d=a/2$，则$y=8,M=187.3(g/mol)$，无合理解。

<Checkpoint>[$d=a/2$不合理](1)</Checkpoint>

若$d=\sqrt3a/2$，则$y=2,M=36.0(g/mol)$，可得$\mathbf{A}$是H，因此该晶体是$H_4O_2$即$H_2O$，此时$\mathrm{a = 264.9 pm}$。

<Checkpoint>[$d=\sqrt3a/2$有合理解$H_2O$，$\mathrm{a = 264.9 pm}$](2)</Checkpoint>

该晶体实际上为$Cu_2O$堆积，$\mathbf{A}$层（即H层）和O层比例$1:2$，A错误。

<Checkpoint>[$\mathbf{A}$层与O层的比例为$1:2$](3)</Checkpoint>

$H_2O$不会难溶于水，B错误。

<Checkpoint>[$H_2O$不难溶于水](1)</Checkpoint>

该晶体为简单立方点阵，C错误。

<Checkpoint>[该晶体为简单立方点阵](1)</Checkpoint>

该晶体中$\mathbf{A}$（即H）的配位数为2，D错误。

<Checkpoint>[$\mathbf{A}$的配位数为2](1)</Checkpoint>

该晶体中O层的层间距$h=\sqrt3a/6=76.5pm$，E正确。

<Checkpoint>[O层的层间距$h=76.5pm$](3)</Checkpoint>

该晶体中O层的占有率为25%，F错误。

<Checkpoint>[O层占有率为25%](1)</Checkpoint>