$\bf A$ atoms and $\bf B$ atoms form a cubic crystal. In this crystal, $\bf A$ atoms occupy all positions of the proper unit cell vertices, body center, edge center, and face center; $\bf B$ atoms only form $\bf B_4$ quadrilaterals and fill some $\bf A_8$ cubic voids formed by A atoms. One way to fill the $\bf B_4$ quadrilateral into the cubic void is as follows:

<MultiModal>![This is a way to fill the $\bf B_4$ quadrilateral into the cubic void, a cube representing the crystal structure, $\mathsf A$ atoms occupy the vertices of the cube, and 4 $\mathsf B$ atoms are inside the cube, forming a planar quadrilateral and the plane where the quadrilateral is located is parallel to one face of the cube.](/media/uploads/acd33bca-002c-475e-9258-ba9b6e45a18f.png)</MultiModal>

Regarding this crystal, the following conclusions are drawn:

Conclusion 1: There are three types of cubic voids with different chemical environments or spatial environments in the crystal.

Conclusion 2: The chemical formula of the crystal is $\mathbf{AB}_2$.

Conclusion 3: If the $\bf A-B$ bond length is 230 pm and the $\bf B-B$ bond length is 180 pm, then the lattice parameter of the crystal is a = 820 pm.

Conclusion 4: The proper unit cell of the crystal can be regarded as being composed of 64 cubes formed by $\bf A$ atoms as described above.

Conclusion 5: The crystal is a face-centered cubic lattice type.

Select the option corresponding to the correct conclusion.
$\bf A$ 原子和 $\bf B$ 原子形成了一种立方晶体。在该晶体中，$\bf A$ 原子占据正当晶胞顶点、体心、棱心、面心的所有位置；$\bf B$ 原子仅形成 $\bf B_4$ 四边形，并填入A原子形成的部分 $\bf A_8$ 立方体空隙中。 $\bf B_4$ 四边形填入立方体空隙的一种方式如下：

<MultiModal>![这是 $\bf B_4$ 四边形填入立方体空隙的一种方式，一个代表晶体结构的立方体，$\mathsf A$ 原子占据了立方体的顶点，4个 $ \mathsf B$ 原子处于立方体内，形成平面四边形且该四边形所在平面平行于立方体的一个面。](/media/uploads/acd33bca-002c-475e-9258-ba9b6e45a18f.png)</MultiModal>

关于这个晶体，有以下结论：

结论一：该晶体中存在三种化学环境或空间环境不同的立方体空隙。

结论二：该晶体的化学式为 $\mathbf{AB}_2$。

结论三：若 $\bf A-B$ 键长为230 pm，$\bf B-B$ 键长为180 pm，则该晶体的晶胞参数为a = 820 pm。

结论四：该晶体正当晶胞可看作由64个由 $\bf A$ 原子形成的上述立方体构成。

结论五：该晶体为面心立方点阵型式。

选择对应正确结论的选项。
All of the above conclusions are incorrect.
Conclusion 1
Conclusion 2
Conclusion 3
Conclusion 4
Conclusion 5
以上结论均不正确
结论一
结论二
结论三
结论四
结论五
The characteristic symmetry elements of a cubic crystal are 4 threefold axes parallel to the body diagonals, but the cube given in the problem does not have threefold axes, so there must be 4 types of cubes, and conclusion one is incorrect.

<Checkpoint>[Cubic symmetry requires 4 threefold axes parallel to the body diagonals, but the cube given in the problem does not have threefold axes, so there should be 4 types of cubes. Conclusion one is incorrect](1)</Checkpoint>

Three of the 4 types of cubes constitute threefold axis symmetry with the given cube, plus one cube without B located on the threefold axis to form a cubic unit cell. Their ratio is 1:1:1:1.

<Checkpoint>[There are 4 types of cubes in the crystal, with a ratio of 1:1:1:1](1)</Checkpoint>

Each cube contains 1 $\bf A$ atom; one type of cube does not contain $\bf B$ atoms, and three types of cubes contain 4 $\bf B$ atoms, where the $\bf B_4$ quadrilateral planes have different directions. Therefore, the ratio of $\bf A$ to $\bf B$ is 4:12 = 1:3. Therefore, the chemical formula of the crystal is $\bf{AB}\mathrm{_3}$. Conclusion two is incorrect.

<Checkpoint>[The chemical formula of the crystal is $\mathbf {AB}_3$. Conclusion two is incorrect](1)</Checkpoint>

The proper unit cell of this crystal can be regarded as being composed of 8 of the above cubes formed by $\mathbf A$ atoms, with two of each of the 4 types of cubes. From the threefold rotation axis, it can be inferred that the two cubes of the same type satisfy body-centered translational symmetry, and the crystal is a body-centered cubic lattice. Conclusion four and conclusion five are incorrect.

<Checkpoint>[The proper unit cell of this crystal can be regarded as being composed of 8 of the above cubes formed by $\mathbf A$ atoms. Conclusion four is incorrect](1)</Checkpoint>

<Checkpoint>[This crystal is a body-centered cubic lattice. Conclusion five is incorrect](1)</Checkpoint>

Let the side length of the cube be $x$, then the following equation can be listed:

$$
(\frac{x-180}{2})^2+(\frac{x-180}{2})^2+(\frac{x}{2})^2 = 230^2
$$

Solving for: $x=372\rm{~ pm}$

<Checkpoint>[The side length of the cube is$~x=372\rm{~ pm}$](1)</Checkpoint>

From the previous conclusion, it can be obtained that the unit cell parameter of the crystal is twice the side length of the cube: $a = 2x = 744\rm{~ pm}$, which is not equal to $\mathrm{820 ~pm}$. Conclusion three is incorrect.

<Checkpoint>[The unit cell parameter of the crystal: $a= 744  \mathrm {~pm} \neq 820 \rm{~pm}$, Conclusion three is incorrect.](1)</Checkpoint>

There is no correct conclusion, choose option A.
立方晶体的特征对称元素为4个平行于体对角线的3次轴，而题目给出的立方体不具有3次轴，因此必然存在4种立方体，结论一错误。

<Checkpoint>[立方对称性要求4个平行于体对角线的3次轴，题目给出的立方体不具有3次轴，因此应该存在4种立方体。结论一错误](1)</Checkpoint>

4种立方体中3种与题给立方体构成3次轴对称性的立方体，再加上一个不含B的位于三次轴上的立方体来形成立方晶胞。它们的比例为1:1:1:1。

<Checkpoint>[晶体存在4种立方体，比例为1:1:1:1](1)</Checkpoint>

每个立方体都含有1个 $\bf  A$ 原子；有1种立方体不含 $\bf B$ 原子，有3种立方体含4个 $\bf B$ 原子，其中 $\bf B_4$ 四边形平面方向互不相同。因此 $\bf A$ 和 $\bf B$ 的比例为 4:12 = 1:3。因此晶体的化学式为 $\bf{AB}\mathrm{_3}$。结论二错误。

<Checkpoint>[晶体的化学式为 $\mathbf {AB}_3$。结论二错误](1)</Checkpoint>

该晶体的正当晶胞可看作由8个由 $\mathbf A$ 原子形成的上述立方体构成，4种立方体各两个。由3次旋转轴可以推断出同种的两个立方体满足体心平移对称性，该晶体为体心立方点阵。结论四、结论五错误。

<Checkpoint>[该晶体的正当晶胞可看作由8个由$\mathbf A$原子形成的上述立方体构成。结论四错误](1)</Checkpoint>

<Checkpoint>[该晶体为体心立方点阵。结论五错误](1)</Checkpoint>

设立方体的边长为 $x$，则可列出以下方程：

$$
(\frac{x-180}{2})^2+(\frac{x-180}{2})^2+(\frac{x}{2})^2 = 230^2
$$

解得：$x=372\rm{~ pm}$

<Checkpoint>[立方体的边长$~x=372\rm{~ pm}$](1)</Checkpoint>

由之前结论可得到晶体的晶胞参数为立方体边长的两倍：$a = 2x = 744\rm{~ pm}$，不等于 $\mathrm{820 ~pm}$。结论三错误。

<Checkpoint>[晶体的晶胞参数：$a= 744  \mathrm {~pm} \neq 820 \rm{~pm}$，结论三错误。](1)</Checkpoint>


没有正确结论，选择A选项。