A binary compound $M_xN_y$ crystal has the same lattice structure as NaCl crystal. If M is the vertex, then the coordinates of one N atom are $(1/2,2/3,2/3)$. Let the cell parameter be $a(pm)$, and the shortest distance between M and N be $d(pm)$.

Select the correct description below.
一种二元化合物$M_xN_y$的晶体，其点阵形式与NaCl晶体相同。若以M为顶点，则其中一个N原子的坐标是$(1/2,2/3,2/3)$。设晶胞参数为$a(pm)$，M和N之间的最短距离为$d(pm)$。

选择以下正确的描述。
There are 24 N atoms in one unit cell of this crystal
The coordination number of M in this crystal is 12
In this crystal, M is situated in a coordination environment of a regular polyhedron.
$d$ and $a$ satisfy the relation $d=\sqrt5/6a$
The shortest distance between N and N in the crystal is $a/3$
In a unit cell with M as the vertex, the body diagonal passes through 4 atoms within the unit cell (excluding the vertices).
该晶体的一个晶胞中有24个N原子
该晶体中M的配位数为12
该晶体中M位于一个正多面体的配位环境中
$d$与$a$满足关系$d=\sqrt5/6a$
该晶体中N与N之间的最短距离为$a/3$
在以M为顶点的晶胞中，体对角线在一个晶胞内（不包括顶点）穿过4个原子
This is a face-centered cubic crystal.

$(1/2,2/3,2/3)$ undergoes $C_3$ axis and mirror operations to yield 12 points, namely $(1/2,\pm2/3,\pm2/3),(\pm2/3,1/2,\pm2/3),(\pm2/3,\pm2/3,1/2)$. Considering the three translation operations in the face-centered cubic lattice, a total of $12\times(3+1)=48$ points can be generated, i.e., $y=48$. Therefore, option A is incorrect.

<Checkpoint>[There are 48 N atoms in a unit cell](3)</Checkpoint>

In this crystal, N forms a truncated octahedron around M, which is not a regular polyhedron, with a coordination number of 24. Therefore, options B and C are incorrect.

<Checkpoint>[The coordination polyhedron of N around M is a truncated octahedron](2)</Checkpoint>

<Checkpoint>[The coordination number of N around M is 24](2)</Checkpoint>

The shortest distance between M and N in this crystal is the distance from $(0,0,0)$ to $(0,1/6,1/3)$, i.e., $d=\sqrt5/6a$, so option D is correct.

<Checkpoint>[$d=\sqrt5/6a$](2)</Checkpoint>

The shortest distance between N and N in this crystal is the distance from $(0,1/6,1/3)$ to $(0,1/3,1/6)$, which is $\sqrt2/6a$, so option E is incorrect.

<Checkpoint>[The shortest N-N distance is $\sqrt2/6a$](2)</Checkpoint>

In this crystal, apart from the vertices, no other atoms lie along the body diagonal, so option F is incorrect.

<Checkpoint>[No atoms lie on the body diagonal except at the vertices](1)</Checkpoint>
这是面心立方晶体。

$(1/2,2/3,2/3)$经$C_3$轴和镜面操作能得到12个点即$(1/2,\pm2/3,\pm2/3),(\pm2/3,1/2,\pm2/3),(\pm2/3,\pm2/3,1/2)$。再考虑面心立方中的三种平移操作，总共能生成$12\times(3+1)=48$个点，即$y=48$。因此选项A错误。

<Checkpoint>[一个晶胞里有48个N](3)</Checkpoint>

该晶体中N对M形成了切角八面体，不是正多面体，配位数为24。因此选项B和C错误。

<Checkpoint>[N对M的配位多面体是切角八面体](2)</Checkpoint>

<Checkpoint>[N对M的配位数为24](2)</Checkpoint>

该晶体中M和N之间最短距离是$(0,0,0)$到$(0,1/6,1/3)$之间的距离，即$d=\sqrt5/6a$，选项D正确。

<Checkpoint>[$d=\sqrt5/6a$](2)</Checkpoint>

该晶体中N和N之间的最短距离是$(0,1/6,1/3)$到$(0,1/3,1/6)$之间的距离，为$\sqrt2/6a$，选项E错误。

<Checkpoint>[N与N间最短距离为$\sqrt2/6a$](2)</Checkpoint>

该晶体除顶点外在体对角线上不存在其他原子，选项F错误。

<Checkpoint>[除顶点外体对角线不穿过原子](1)</Checkpoint>