In the crystal of metal fluoride ${ \mathrm { \mathbf{M} F } } _ { n }$, ${ \mathrm { \mathbf{M} F } } _ { 4 }$ quadrilaterals are vertex-sharing connected to form a helical structure, where each helix is independent, and a $6 _ { 1 }$ screw axis passes through the unit cell point $( 0 , 0 , 0 )$.  

The coordinates of one $\mathbf{M}$ are known to be $(0.4812, 0.2406, 0.0833)$, and the coordinates of an F atom shared by two $\mathbf{M}$ atoms are $(0.1673, 0.1673, 0.1667)$.  

Around the $\mathbf{M}$ atom at coordinates $(0.4812, 0.2406, 0.0833)$ (denoted as ${\mathbf { M } } _ { 1 }$), there are two distinct $\mathbf{M}-\mathrm{F}$ bond lengths (with a ratio of 1:1, measuring $205.2 \ \mathrm {pm}$ and $193.3 \ \mathrm {pm}$, respectively).  

Which of the following statements is correct?
在金属氟化物 ${ \mathrm { \mathbf{M} F } } _ { n }$ 的晶体中， ${ \mathrm { \mathbf{M} F } } _ { 4 }$ 四边形共顶点连接形成螺旋结构，各个螺旋之间相互独立，过晶胞 $( 0 , 0 , 0 )$ 点有 $6 _ { 1 }$ 螺旋轴。  
已知一个 $\mathbf{M}$ 的坐标为$（0.4812.0.2406.0.0833)$，且一个被$2$个$\mathbf{M}$共用的$F$原子坐标为$（0.1673,0.1673,0.1667)$。

坐标为$(0.4812,0.2406,0.0833)$的 $\mathbf{M}$ 原子(记为 ${\mathbf { M } } _ { 1 } )$ 周围有两种长度的$\mathbf{M}-F$键(数目比为$1：1$，键长分别为 $2 0 5 . 2 \ \mathrm { p m }$ 和 $1 9 3 . 3 \ \mathrm { p m } )$ 。

下面的说法中正确的是？
The bond length between the F atom at coordinates $(0.1673, 0.1673, 0.1667)$ and $\mathbf{M}_1$ is $\mathrm{193.3 pm}$.
Crystal coordinate parameters: $\mathrm{a=b=534.5\ pm,\ c=1652.6\ pm}$
There is an $\mathbf{M}$ atom at $(0, 0.1673, 0.3333)$.
There is an $\mathbf{M}$ atom at $(0.7594, 0.2496, 0.4167)$
If the density of the crystal is $6.189 \mathrm{g} / \mathrm{cm}^{3}$, then $\mathbf{M}$ is most likely $Re$.
None of the above statements are correct.
The above statements are multiple correct
坐标为$(0.1673,0.1673,0.1667)$的$F$原子与 $\mathbf{M}_1$ 所成键的键长$\mathrm{193.3 pm}$
晶体的坐标参数:$\mathrm{a=b=534.5 pm，c=1652.6 pm}$
在$(0, 0.1673, 0.3333)$处有一个$\mathbf{M}$原子
在$(0.7594, 0.2496, 0.4167)$有一个$\mathbf{M}$原子
若晶体的密度为$6 . 1 8 9 \mathrm { g } / \mathrm { c m } ^ { 3 }$，则$\mathbf{M}$最可能是$Re$。
以上说法均不正确
以上说法有多个是正确的
According to the question, the chemical formula of the crystal is $\mathrm{\mathbf{M}F}_{3}$, which belongs to the hexagonal crystal system.

<Checkpoint>[The chemical formula of the crystal is $\mathrm{\mathbf{M}F}_{3}$](1)</Checkpoint>

According to the information in the question, some coordinates of $M$ and $F$ can be deduced:

$ \mathbf{M}(0.4812, 0.2406,0.0833) (0.2406,0.7594,0.9167) (0.7594,0.5188,0.7500) (0.5188, 0.7594, 0.5833)(0.7594, 0.2406, 0.4167)(0.2406, 0.4812, 0.2500) $

<Checkpoint>[$ \mathbf{M}(0.4812, 0.2406,0.0833) (0.2406,0.7594,0.9167) (0.7594,0.5188,0.7500) (0.5188, 0.7594, 0.5833)(0.7594, 0.2406, 0.4167)(0.2406, 0.4812, 0.2500) $](1)</Checkpoint>

$F (0.1673, 0.1673, 0.1667) (0, 0.1673, 0.3333)(0.8327,0, 0.5000) (0.8327,0.8327,0.6667)(0,0.8327,0.8333) (0.1673, 0, 0)$

<Checkpoint>[$F (0.1673, 0.1673, 0.1667) (0, 0.1673, 0.3333)(0.8327,0, 0.5000) (0.8327,0.8327,0.6667)(0,0.8327,0.8333) (0.1673, 0, 0)$](1)</Checkpoint>

Therefore, $C D$ is incorrect.

The $F$ atom with coordinates $(0.1673,0.1673,0.1667)$ is a bridging atom, and its bond length corresponds to $\mathrm{205.2pm}$

<Checkpoint>[The $F$ atom with coordinates $(0.1673,0.1673,0.1667)$ is a bridging atom, and its bond length corresponds to $\mathrm{205.2pm}$](1)</Checkpoint>

Therefore, $A$ is incorrect.

 $\mathrm { 205.2 pm } = [ ( 0 . 0834 c ) ^ { 2 } + ( 0 . 3139 a ) ^ { 2 } + ( 0 . 0733 a ) ^ { 2 } - 0 . 3139 a \times 0.0733a]^{0.5}$

 $\mathrm { 193.3 pm }  = [ ( 0 . 0791 c ) ^ { 2 } + ( 0 . 2949 a ) ^ { 2 } + ( 0 . 223 3 a ) ^ { 2 } - 0 . 294 9 a \times 0.2233a]^{0.5}$

Solving for $a=534.5 pm，c=1652.6 pm$

<Checkpoint>[$a=534.5 pm，c=1652.6 pm$](1)</Checkpoint>

Therefore, $B$ is correct.

According to the density, $M$ should be $Au$, $E$ is incorrect.

<Checkpoint>[$\mathbf{M}$ should be $Au$](1)</Checkpoint>

In summary, choose $B$.
由题意，该晶体的化学式为$\mathrm{\mathbf{M}F}_{3}$ ，属于六方晶系。

<Checkpoint>[该晶体的化学式为$\mathrm{\mathbf{M}F}_{3}$ ](1)</Checkpoint>

根据题目的信息可以推出部分$M$和$F$的坐标：

$ \mathbf{M}(0.4812, 0.2406,0.0833) (0.2406,0.7594,0.9167) (0.7594,0.5188,0.7500) (0.5188, 0.7594, 0.5833)(0.7594, 0.2406, 0.4167)(0.2406, 0.4812, 0.2500) $

<Checkpoint>[$ \mathbf{M}(0.4812, 0.2406,0.0833) (0.2406,0.7594,0.9167) (0.7594,0.5188,0.7500) (0.5188, 0.7594, 0.5833)(0.7594, 0.2406, 0.4167)(0.2406, 0.4812, 0.2500) $](1)</Checkpoint>

$F (0.1673, 0.1673, 0.1667) (0, 0.1673, 0.3333)(0.8327,0, 0.5000) (0.8327,0.8327,0.6667)(0,0.8327,0.8333) (0.1673, 0, 0)$

<Checkpoint>[$F (0.1673, 0.1673, 0.1667) (0, 0.1673, 0.3333)(0.8327,0, 0.5000) (0.8327,0.8327,0.6667)(0,0.8327,0.8333) (0.1673, 0, 0)$](1)</Checkpoint>

因此$C D$错误。

坐标为$(0.1673,0.1673,0.1667)$的$F$原子为桥连原子，其键长对应 $\mathrm{205.2pm}$

<Checkpoint>[坐标为$(0.1673,0.1673,0.1667)$的$F$原子为桥连原子，其键长对应 $\mathrm{205.2pm}$](1)</Checkpoint>

因此$A$错误

 $\mathrm { 205.2 pm } = [ ( 0 . 0 8 3 4 c ) ^ { 2 } + ( 0 . 3 1 3 9 a ) ^ { 2 } + ( 0 . 0 7 3 3 a ) ^ { 2 } - 0 . 3 1 3 9 a \times 0.0733a]^{0.5}$

 $\mathrm { 193.3 pm }  = [ ( 0 . 0 7 9 1 c ) ^ { 2 } + ( 0 . 2 9 4 9 a ) ^ { 2 } + ( 0 . 2 2 3 3 a ) ^ { 2 } - 0 . 2 9 4 9 a \times 0.2233a]^{0.5}$

解得$a=534.5 pm，c=1652.6 pm$

<Checkpoint>[$a=534.5 pm，c=1652.6 pm$](1)</Checkpoint>

因此$B$正确

根据密度可以求出，$M$应为$Au$，$E$错误

<Checkpoint>[$\mathbf{M}$应为$Au$](1)</Checkpoint>

综上选$B$。