Tungsten nitrides have attracted significant attention from scientists due to their excellent chemical, mechanical, and thermal properties. However, incorporating nitrogen into the tungsten lattice is thermodynamically unfavorable under atmospheric pressure, making the preparation of tungsten nitrides challenging and requiring relatively harsh conditions. Scientists have synthesized a series of nitrides by reacting sodium tungstate with boron nitride under high temperature and high pressure, among which M is one. M crystallizes in the hexagonal system with unit cell parameters $\ a = 2 8 9\ \mathrm { p m } , \ c = 1 5 2 9\ \mathrm { p m } $, and a tungsten-nitrogen bond length of $d=216\ \mathrm { p m }$. If A, B, C represent the close-packed layers of nitrogen atoms, and a, b, c represent the close-packed layers of tungsten atoms, with $\square$ denoting a vacant layer, then the stacking sequence of this crystal is $…AbAbA\square BaBaB\square AbAbA\square BaBaB\square …$

Based on the given information, select the correct option from the following choices.
钨的氮化物因具有优异的化学、机械和热学性能而受到科学家的重视。然而，在钨晶格中掺入氮在大气压力下是热力学不利的，因此制备钨的氮化物具有一定的困难，需要较苛刻的条件。科学家通过高温高压下由钨酸钠与氮化硼反应，得到了一系列氮化物，M就为其中之一。M属六方晶系，其晶胞参数 $\ a = 2 8 9\ \mathrm { p m } , \ c = 1 5 2 9\ \mathrm { p m } $ ，钨氮键键长$d=216\ \mathrm { p m }$,若分别用A、B、C和a、b、c代表氮原子和钨原子的密堆积层，$\square$代表空层，则该晶体堆积方式为$…AbAbA\square BaBaB\square AbAbA\square BaBaB\square …$

根据题意，从下列选项中选出正确的选项。
According to the above data, the density of M is $6.15\ \mathrm{g\cdot cm^{-3}}$
In the unit cell of M, nitrogen atoms are packed to form octahedral voids, tetrahedral voids, and trigonal prismatic voids. The numbers of these voids in one unit cell are 2, 4, and 8, respectively. Additionally, the coordination numbers of both nitrogen and tungsten atoms in M are 6.
In the chemical equation for the reaction of sodium tungstate with boron nitride to produce the product, the ratio of the sum of the coefficients on the reactant side to the sum of the coefficients on the product side is 12:11.
The interlayer spacing between the two nitrogen atom layers above and below the vacancy layer $\square$ in M crystal is 187 pm.
按照上述数据计算，M的密度为$6.15\ \mathrm{g\cdot cm^{-3}}$
在M的晶胞中，氮原子堆积形成八面体空隙、四面体空隙和三棱柱空隙。它们在一个晶胞中的数目分别为2个、4个和8个；且M中氮原子和钨原子的配位数均为6
由钨酸钠与氮化硼反应得到该产物的化学方程式中，反应物一侧系数之和与产物一侧系数之和的比例为12:11
M晶体中空层$\square$上下的两层氮原子的层间距为187 pm.
A. The structure contained within one unit cell of the M crystal is "AbAbA$\square$BaBaB$\square$", where uppercase letters represent N and lowercase letters represent W. Thus, a unit cell contains 6 N atoms and 4 W atoms, with the chemical formula $\mathrm{W_2N_3}$. The density  

$\rho=\frac{zM}{N_AV}=\frac{6\times 14.01+4\times 183.8}{6.02\times 10^{23}\times \frac{\sqrt{3}}{2}\times 289^2\times1529\times10^{-30}}\ \mathrm{g\cdot cm^{-3}}=12.3\ \mathrm{g\cdot cm^{-3}}$  

Therefore, option A is incorrect.  

<Checkpoint>[$\rho=12.3\ \mathrm{g\cdot cm^{-3}}$](1)</Checkpoint>  

B. Identical N atom layers can form trigonal prismatic voids A(b/c)A or B(a/c)B. Each such arrangement generates two such trigonal prismatic voids in the unit cell, totaling $4\times 2=8$ in one unit cell. Tetrahedral voids A(a/b)B and octahedral voids A(c)B exist between layers stacked with different letters, numbering $2\times 2=4$ and $2\times 1=2$, respectively. All W atoms are in trigonal prismatic coordination environments with a coordination number of 6. The N atoms have two coordination environments: one surrounded by W atoms in a trigonal prismatic arrangement (coordination number 6), and the other adjacent to one layer of W and one empty layer (coordination number 3). The ratio of N atoms with these two coordination numbers is 1:2. Thus, option B is incorrect.  

<Checkpoint>[Nitrogen atom stacking forms octahedral voids, tetrahedral voids, and trigonal prismatic voids, numbering 2, 4, and 8 per unit cell, respectively](1)</Checkpoint>  

<Checkpoint>[All W atoms are in trigonal prismatic coordination environments with a coordination number of 6](1)</Checkpoint>  

<Checkpoint>[N atoms have two coordination environments with coordination numbers of 6 and 3](1)</Checkpoint>  

C. Under high temperature and pressure, sodium tungstate reacts with boron nitride to produce $\mathrm{W_2N_3}$ as well as stable products corresponding to Na, O, and B, such as sodium metaborate $\mathrm{NaBO_2}$, or stable products corresponding to B and O, such as $\mathrm{B_2O_3}$. Excess nitrogen escapes as $\mathrm{N_2}$. Since the only reactant containing Na and O is sodium tungstate $\mathrm{Na_2WO_4}$, and the Na-to-O ratio is 1:2 (matching $\mathrm{NaBO_2}$), $\mathrm{B_2O_3}$ should not appear as a separate product. The balanced equation is:  

$\mathrm{4Na_2WO_4+8BN \rightarrow 2W_2N_3+8NaBO_2+N_2}$  

The sum of reactant coefficients is 12, and the sum of product coefficients is 11. Thus, option C is correct.  

<Checkpoint>[$\mathrm{4Na_2WO_4+8BN=2W_2N_3+8NaBO_2+N_2}$](2)</Checkpoint>  

D. The height of the tungsten-coordinated trigonal prism:  

$h=2×[d²-(a / \sqrt { 3 } ) ^ { 2 } ] ^ { 1 / 2 } = 2 \times [ ( 2 1 6\  \mathrm { p m } ) ^ { 2 } - ( 2 8 9\ \mathrm { p m } / \sqrt { 3 } ) ^ { 2 } ] ^ { 1 / 2}  = 274 \  \mathrm { p m }$  

<Checkpoint>[$h=274 \  \mathrm { p m }$](1)</Checkpoint>  

Thus, the interlayer spacing of nitrogen atoms:  

$d _ { \mathrm { N - N } } = \left( c - 4 h \right) / 2 = ( 1 5 2 9 \ \mathrm { p m } - 4 \times 2 7 4\ \mathrm { p m } )/2=216 \ \mathrm { p m } $  

<Checkpoint>[ $d _ { \mathrm { N - N } } = 216 \ \mathrm { p m } $](1)</Checkpoint>  

Therefore, option D is incorrect.
A. M晶体中一个晶胞中所内含的结构为“AbAbA$\square$BaBaB$\square$”，其中大写字母代表N，小写字母代表W，因此一个晶胞内有6个N原子和4个W原子，化学式为$\mathrm{W_2N_3}$，密度

$\rho=\frac{zM}{N_AV}=\frac{6\times 14.01+4\times 183.8}{6.02\times 10^{23}\times \frac{\sqrt{3}}{2}\times 289^2\times1529\times10^{-30}}\ \mathrm{g\cdot cm^{-3}}=12.3\ \mathrm{g\cdot cm^{-3}}$

因此A选项不正确。

<Checkpoint>[$\rho=12.3\ \mathrm{g\cdot cm^{-3}}$](1)</Checkpoint>

B. 相同N原子层间可以构成三棱柱空隙A(b/c)A或B(a/c)B，每存在一个这样的排列则在晶胞中生成两个这样的三棱柱空隙，一个晶胞中共$4\times 2=8$个；四面体空隙A(a/b)B和八面体空隙A(c)B则存在于不同字母所堆积的层间，数目分别为$2\times 2=4$个及$2\times 1=2$个；W原子均处于三棱柱配位环境，配位数为6. 而N原子有两种配位环境，其一周围被W原子以三棱柱形式包围，配位数为6；其二与一层W和一层空层相邻，配位数为3. 这两种配位数的N的数目之比为1:2，B选项错误。

<Checkpoint>[氮原子堆积形成八面体空隙、四面体空隙和三棱柱空隙，在一个晶胞中的数目分别为2个、4个和8个](1)</Checkpoint>

<Checkpoint>[W原子均处于三棱柱配位环境，配位数为6](1)</Checkpoint>

<Checkpoint>[N原子有两种配位环境，配位数分别为为6和3](1)</Checkpoint>

C. 高温高压下，钨酸钠与氮化硼反应，除生成该产物$\mathrm{W_2N_3}$之外，还应该生成对应于Na、O、B的稳定产物偏硼酸钠$\mathrm{NaBO_2}$或对应于B、O的稳定产物$\mathrm{B_2O_3}$，剩余的N元素以氮气形式逸出，由于反应物中含有Na和O元素的物种只有钨酸钠$\mathrm{Na_2WO_4}$，且Na与O的数目之比为1:2，与$\mathrm{NaBO_2}$相同，因此产物中不应出现单独的$\mathrm{B_2O_3}$，方程式配平后如下

$\mathrm{4Na_2WO_4+8BN \rightarrow 2W_2N_3+8NaBO_2+N_2}$

反应物系数之和为12，产物系数之和为11，C选项正确。

<Checkpoint>[$\mathrm{4Na_2WO_4+8BN=2W_2N_3+8NaBO_2+N_2}$](2)</Checkpoint>

D. 钨配位三棱柱的高度：

$h=2×[d²-(a / \sqrt { 3 } ) ^ { 2 } ] ^ { 1 / 2 } = 2 \times [ ( 2 1 6\  \mathrm { p m } ) ^ { 2 } - ( 2 8 9\ \mathrm { p m } / \sqrt { 3 } ) ^ { 2 } ] ^ { 1 / 2}  = 274 \  \mathrm { p m }$

<Checkpoint>[$h=274 \  \mathrm { p m }$](1)</Checkpoint>

因此，氮原子的层间距：

 $d _ { \mathrm { N - N } } = \left( c - 4 h \right) / 2 = ( 1 5 2 9 \ \mathrm { p m } - 4 \times 2 7 4\ \mathrm { p m } )/2=216 \ \mathrm { p m } $

<Checkpoint>[ $d _ { \mathrm { N - N } } = 216 \ \mathrm { p m } $](1)</Checkpoint>

故D选项错误。