Silica (SiO$_{2}$) and Aluminum Phosphate (AlPO$_{4}$)

Silica (SiO$_{2}$), aluminum phosphate (AlPO$_{4}$) and related compounds all consist of nearly regular M-O$_{4}$ tetrahedra (Fig. 1) with the “metallic” atom at the center, and each vertex of the tetrahedron connected to another tetrahedron. In aluminum phosphates the AlO$_{4}$ tetrahedra are all connected to PO$_{4}$ tetrahedra, and visa versa (Fig.2). The tetrahedra are relatively rigid, with the M-O and O-O bond distances approximately equal, and the O-M-O bond angle near the ideal value of 109.47°. The tetrahedra can be tilted relative to one another. The amount of tilting can be described by the angle M₁-O-M₂, where M₁ and M₂ are the metallic atoms in the two tetrahedra connected by the oxygen atom. In β-cristobalite (C9) this angle is 180°, but it can range from 132° to 180° in AlPO$_{4}$-8.

         

Because of the nearly-perfect nature of the SiO$_{4}$ tetrahedra many silica crystal structures are more or less compact, as in the ideal β-cristobalite (Strukturbericht $C9$) structure (Wyckoff, 1925; Peacor, 1973) shown on the left in Fig. 2. The mismatched SiO$_{4}$/AlPO$_{4}$ tetrahedra, on the other hand, can lead to extremely open structures, perhaps most dramatically illustrated by the structure known as AlPO$_{4}$-5 (Klap, 2000), which has open channels formed by Al-O-P-O rings about 9.9Å in diameter, as shown in Figure 3. These wide channels allow AlPO$_{4}$ structures to be used as molecular sieves (Wilson, 1982).

      

Here we will look at all of the SiO$_{2}$, AlPO$_{4}$ and related structures listed in the Encyclopedia. This is an ongoing project, so the tables below will be updated as we add structures.

SiO$_{2}$ and Related Compounds

Silica (SiO$_{2}$) consists of joined SiO$_{4}$ tetrahedra as shown in Figure 1. This gives it a remarkable flexibility in finding crystal structures. These have been divided into several groups, which we'll list here.

Quartz

Quartz is the most stable silica, commonly found as sand. Other silica forms are heated or pressurized forms and are given other names. Commonly only the two structures listed in Table 1 are called quartz. α-quartz is the ground state, which transitions to β-quartz at 573°C (Wright, 1981). There is a 10% contraction of the quartz as the β form cools to α, so cracking will occur.

Interestingly, both forms of quartz are in Sohncke Class II chiral space groups, so the mirror image of $P3_{1}21$ α-quartz is in space group $P3_{2}21$, and the mirror image of $P6_{2}22$ β-quartz is in space group $P6_{4}22$. Both forms of α-quartz (or β-quartz) have the same density, bond lengths and bond angles, so the have identical formation energies. In a given sample the structure that occurs is determined by the chirality of its surrounding environment during formation.

The crystal structures of quartz. Both structures are chiral and can exist in either of the two space groups listed. Densities are determined from the lattice constants given on the structure's Encyclopedia page and the standard atomic weights of the elements involved. The stability range is taken from (Wright, 1981).

Structure	AFLOW Label	Space Group	Density (gm/cm3)	Stability
α-quartz	A2B_hP9_152_c_a-001	$P3_{1}21$ #152/$P3_{2}21$ #154	2.83	< 806 K
β-quartz	A2B_hP9_180_i_d-001	$P6_{2}22$ #180/$P6_{4}22$ #181	2.53	> 806 K

Tridymite

In tridymite the SiO$_{4}$ tetrahedra are packed into a two-layer structure (Gutiérrez-Castorena, 2010). It is found in volcanic rocks, including limestone, and has been found in meteorites. Although Wikipedia lists seven known structures, the Encyclopedia currently only has four noted by (Kihara, 1978) and listed in Table 2.

The crystal structures of tridymite currently in the Encyclopedia. Stability ranges are from (Kihara, 1978).

Structure	AFLOW Label	Space Group	Density (gm/cm3)	Stability
low tridymite	A2B_mC144_9_24a_12a-001	$Cc$ # 9	2.26	< 373 K
Orthorhombic tridymite	A2B_oP72_19_12a_6a-001	$P2_{1}2_{1}2_{1}$ #19	2.24	373 K - 433 K
high (α-) tridymite	A2B_oC24_20_abc_c-001	$C222_{1}$ #20	2.20	433 K - 693 K
high (β-) tridymite	A2B_hP12_194_cg_f-001	$P6_{3}/mmc$ #194	2.18	> 693 K

Cristobalite

Cristobalite contains a three-layer structure of SiO$_{4}$ tetrahedra, and is mostly found in volcanic rock (Gutiérrez-Castorena, 2010). We have only found reference to two forms, shown in Table 3. Like quartz, low (α) cristobalite can be in either of two chiral space groups.

Cristobalite has two known forms. The stability range is from (Pluth, 1985).

Structure	AFLOW Label	Space Group	Density (gm/cm3)	Stability
α cristobalite	A2B_tP12_92_b_a-001	$P4_{1}2_{1}2$ #92/$P4_{3}2_{1}2$ #96	2.34	< 530 K
β cristobalite	A2B_cF24_227_c_a-001	$Fd\overline{3}m$ #227	2.20	> 530 K

Coesite

Coesite (A2B_mC48_15_ae3f_2f-001) was first synthesized by Loring Coes, Jr. in 1953 (Coes, 1953) and was later named for him (Hazen, 1999). It has since been found in meteor craters and metamorphic rocks. With a density of 2.92 gm/cm³ it is the densest form of silica known.

Keatite

Keatite (A2B_tP36_96_3b_ab-001) was originally discovered by Paul P. Keat (Keat, 1954). It has since been found in nature. It has a typical silica density of 2.52 gm/cm³. As with some other silicas, the structure is chiral, Sohncke Class II, in space groups $P4_{1}2_{1}2$ #92 or $P4_{3}2_{1}2$ #96.

Stishovite

Stishovite is a non-silica form of SiO$_{2}$ in the rutile ($C4$) structure. Each silicon atom is surrounded by six oxygen atoms, allowing for a much higher density, 4.29 gm/cm³.

Theoretical forms of silica

Over the years computer simulations have produced several hypothetical stable phases of SiO$_{2}$. The ones include in the Encyclopedia are listed in Table 4. We note that WN$_{2}$ was not originally proposed as a silica phase. Instead it is produced by placing ordered vacancies in a supercell of WN in the rock salt structure.

Theoretical structures of silica-like compounds. As noted in the text, WN$_{2}$ was not originally proposed as a silica structure, but it is obviously related to silica. Density is take from the published lattice constants of the materials.

Structure	AFLOW Label	Space Group	Density (gm/cm3)
Monoclinic	A2B_mP12_3_ab3e_2e-001	$P2$ #3	3.19
Hexagonal	A2B_hP36_177_j2lm_n-001	$P622$ #177	2.27
Cubic	A2B_cI72_211_hi_i-001	$I432$ #211	2.63
WN$_{2}$	A2B_cI36_229_h_d-001	$Im\overline{3}m$ #229	2.07

AlPO$_{4}$ Structures

Since the basic building blocks of SiO$_{2}$ and AlPO$_{4}$ (or AlO$_{2}$PO$_{2}$) are similar, we can expect similar structures to appear in both cases. This is demonstrated in Fig. 3 which shows the ground states of both systems, α-quartz and berlinite, looking down the z-axis of both crystals. The structures look remarkably similar, with berlinite having alternating aluminum and phosphorus atoms replacing the silicon atoms in quartz. Indeed, both structures appear in the same pair of enantiomorphic space groups, $P3_{1}21$ #152 and $P3_{2}21$ #154. The major difference is that the berlinite unit cell is doubled in the z-direction compared to the quartz cell, although the stacking along the z-direction is slightly different.

SiO$_{2}$-like AlPO$_{4}$ Structures

There are indeed many AlPO$_{4}$ structures analogous to the SiO$_{2}$ structures discussed above. Here we list the ones we have in the Encyclopedia. As always, we will update this as more structures are added.

Berlinite

As noted above, α-berlinite (Onac, 2007) is the ground state of AlPO$_{4}$ and it is the analog of α-quartz. As with quartz, there is a temperature driven transaction to β-berlinite, which corresponds to β-quartz. Table 5 gives more details.

The crystal structures of berlinite. As with quartz, both forms are chiral and can exist in either of the two space groups listed. Stability information is from (Ng, 1976).

Structure	AFLOW Label	Space Group	Density (gm/cm3)	Stability
α-berlinite	ABC4_hP18_152_a_b_2c-001 (prototype Alarsite, AlAsO$_{4}$)	$P3_{1}21$ #152/$P3_{2}21$ #154	2.62	< 853 K
β-berlinite	AB4C_hP18_181_c_k_d-001	$P6_{2}22$ #180/$P6_{4}22$ #181	2.62	> 853 K

Tridymite

As with silica tridymite, AlPO$_{4}$ tridymite undergoes several phase transitions as the temperature increases. Unlike in the quartz/berlinite case, the substitution of aluminum and phosphorous for silicon changes the space group, not just the cell size. Table 6 links to the structures we have in the Encyclopedia, with phase transition temperatures taken from (Graetsch, 2002).

The crystal structures of the AlPO$_{4}$ forms of tridymite currently listed in the Encyclopedia. Phase ordering is from (Graetsch, 2002), transition temperatures are approximate. We have not been able to find any crystallographic information about the orthorhombic $P2_{1}2_{1}2_{1}$ #19 structure. There is an incommensurate structure with space group $P2_{1}$ between the orthorhombic and monoclinic II structures. Unless we find an averaged version of this structure it will not appear in the Encyclopedia.

Structure	AFLOW Label	Space Group	Density (gm/cm3)	Stability
Triclinic	AB4C_aP240_1_40a_160a_40a-001	$P1$ #1	2.26	< 293 K
Monoclinic I	AB4C_aP240_1_40a_160a_40a-001	$Pc$ #7	2.22	≈ 295 K
Orthorhombic		$P2_{1}2_{1}2_{1}$ #19		> 295 K
Monoclinic II	AB4C_mP12_4_a_4a_a-001	$P2_{1}$ #4	2.18	460 K - 590 K
Hexagonal	AB4C_hP12_186_b_bc_b-001	$P6_{3}mc$ #186	1.87	> 590 K

Cristobalite

Like quartz/berlinite, AlPO$_{4}$ cristobalite is a one-to-one match with silica cristobalite. There are two forms, with a transition temperature of about 500 K (Hatch, 1994). The structures are described in Table 7.

The crystal structures of the AlPO$_{4}$ forms of cristobalite (Hatch, 1994).

Structure	AFLOW Label	Space Group	Density (gm/cm3)	Stability
α	AB4C_oC24_20_a_2c_b-001	$C222_{1}$ #20	2.29	< 500 K
β	AB12C_cF56_216_a_h_c-001	$F\overline{4}3m$ #216	2.17	> 500 K

Open AlPO$_{4}$ Structures

Many AlPO$_{4}$ structures, such as AlPO$_{4}$-5 (shown in Fig. 2), have an “open framework” (Zheng, 2020). Some related to zeolites, while others have even larger micropores. These pores allow the structures to function as molecular sieves (Szostak, 1989).

These microporous structures are usually labeled AlPO$_{4}$-n, where n is an integer. This practice seems to have begun with (Wilson, 1982), who list nine structures, with n = 9, 11, 14, 16, 17, 18, 20, 31, 33, stating only that “The suffix n denotes a specific structure type,” and not giving a reference to the complete list. Later (Szostak, 1989, p. 256) lists additional structures with n ≤ 47, again with no reference for the complete list. (Withers, 2005) served as our reference for AlPO$_{4}$-54, of course with no further reference. At this time n = 54 is the largest value for these structures. To make things even more confusing, AlPO$_{4}$-5 is reported in two different space groups: $P6$ #168 and $P6cc$ #184.

(Zheng, 2020) have released a database of 313 AlPO$_{4}$ structures. Most of these include molecules or metallic atoms “caught” in the AlPO$_{4}$ micropores. We will discuss such systems later.

AlPO$_{4}$ Framework Structures

Since open AlPO$_{4}$ structures have large pores, it is unsurprising that they most often include other atoms or molecules in their structures. At the moment, however, we only wish to discuss the framework structures, those consisting purely of Al/P-O$_{4}$ tetrahedra. These are difficult to obtain. Usually a sample must be heated to near its melting point in a low oxygen environment, a process called calcination. The cooled calcined structures may then need to be reheated to drive off any remaining water molecules.

Table 8 lists the framework AlPO$_{4}$ structures found in the Encyclopedia. In addition to the information we presented for previous structures, here we will include information about the largest ring. The ring size will be determined by the number of aluminum and phosphorous atoms, or, alternatively, the number of oxygen atoms. The poor size, which controls the size of molecules which can pass through the pores, is estimated by finding the smallest distance between atoms on opposite sides of the ring. As an example, the AlPO$_{4}$-5 structure shown in Fig. 2 is a 12-member ring with a pore size of 9.9Å.

Open framework AlPO$_{4}$ structures currently listed in the Encyclopedia, using the notation of (Wilson, 1982) and others when possible. There can be multiple entries for each structure, such as for AlPO$_{4}$-5. Structures with disordered aluminum and phosphorous atoms are listed as (Al,P)O$_{4}$-n. Ring and pore sizes are defined in the text. We do not have good temperature ranges for the stability of these structures, so we eliminated that column.

Framework	AFLOW Label	Space Group	Density (gm/cm3)	Ring Size	Pore Size (Å)
AlPO$_{4}$-5 (Theory)	AB4C_hP72_168_2d_8d_2d-001	$P6$ #168	1.77	12	9.98
AlPO$_{4}$-5 (Orthohombic)	AB4C_oP144_27_6e_24e_6e-001	$Pcc2$ #27	1.75	12	10.01
AlPO$_{4}$-5	AB4C_hP72_184_d_4d_d-001	$P6cc$ #184	1.76	12	9.98
(Al,P)O$_{4}$-5	AB2_hP72_192_m_j2kl-001	$P6/mcc$ #192	1.77	12	10.04
(Al,P)O$_{4}$-8	AB2_oC216_63_f4h_ac3e4g5h-001	$Cmcm$ #63	1.75	24	10.01
AlPO$_{4}$-11	AB4C_oI120_46_b2c_2b9c_b2c-001	$Ima2$ #46	1.93	10	6.73
(Al,P)O$_{4}$-11	AB2_oI120_74_h2j_aef2i3j-001	$Imma$ #74	1.93	10	6.65
AlPO$_{4}$-18	AB4C_mC144_15_3f_12f_3f-001	$C2/c$ #15	1.50	8	6.46
(Al,P)O$_{4}$-25 (High Temperature)	AB2_oC72_67_mo_cgilno-001	$Cmme$ #67	2.01	8	5.70
AlPO$_{4}$-35	AB4C_hR36_148_f_4f_f-001	$R\overline{3}$ #148	2.77	8	6.53
AlPO$_{4}$-41	AB4C_mP60_4_5a_20a_5a-001	$P2_{1}$ #4	1.93	10	7.06
AlPO$_{4}$-53 (B)	AB4C_oP144_61_3c_12c_3c-001	$Pbca$ #61	2.01	8	6.62
AlPO$_{4}$-53 (C)	AB4C_mC72_5_3c_12c_3c-001	$C2$ #5	2.15	8	3.79
(Al,P)O$_{4}$-54	AB2_hP108_193_kl_fg2ijl-001	$P6_{3}/mcm$ #193	1.46	18	15.01

AlPO$_{4}$ Framework + Interstitial Molecules

The AlPO$_{4}$ framework structures are interesting because the can served as molecular sieves or as reservoirs of atoms and molecules. While calcination can often remove these atoms, in some cases this causes a structural transformation, as when AlPO$_{4}$-21 becomes AlPO$_{4}$-25 (Richardson, 1999)).

Table 9 lists structures of this type found in the Encyclopedia. The given density, ring, and pore sizes are for the framework structure, exclusive of any added molecules.

Open framework AlPO$_{4}$ structures with included molecular species. In some cases, such as AlPO$_{4}$-53 (A), calcination may remove these molecules, in which case we report the pure framework in Table 8. In other cases, such as AlPO$_{4}$-21, heating causes a structural transformation. The given densities, ring sizes, and pore sizes are for the framework structure, exclusive of any captured species.

Framework	Full Formula	AFLOW Label	Space Group	Density (gm/cm3)	Ring Size	Pore Size (Å)
AlPO$_{4}$-5	(AlPO$_{4}$)$_{6}$·NC$_{9}$	A6B18CD24E6_hP110_184_d_3d_a_4d_d-001	$P6cc$ #184	1.76	12	9.91
AlPO$_{4}$-15	(AlPO$_{4}$)$_{2}$(OH)(H$_{2}$O)$_{2}$·NH$_{4}$	A2B9CD11E2_mP100_14_2e_9e_e_11e_2e-001	$P2_{1}$/c #14	1.84	8	5.37
AlPO$_{4}$-17	(AlPO$_{4}$)$_{9}$(O$_{2}$)$_{9}$O	A9B55C9_hP146_176_hi_a2h8i_hi-001	$P6_{3}$/m #176	1.60	8	6.00
AlPO$_{4}$-21	(AlPO$_{4}$)$_{3}$(OH)·1.33(N$_{2}$C$_{7}$H$_{21}$	A3B4CDE13F3_mP100_14_3e_4e_e_e_13e_3e-001	$P2_{1}/c$ #14	1.85	8	6.16
AlPO$_{4}$-53 (A)	(AlPO$_{4}$)$_{24}$·8.5(CH$_{3}$NH$_{2}$)·14(H$_{2}$O)	A3BCD14E3_oP176_19_6a_2a_2a_28a_6a-001	$P2_{1}2_{1}2_{1}$ #19	1.98	8	6.66

Structures related to AlPO$_{4}$

This is a list of structures in the Encylopedia that are based on AlPO$_{4}$ but do not fit in any of the preceding categories. In practice, this means compounds built on AlPO$_{4}$ with other molecules. This does not include AlPO$_{4}$-n type structures, which are detailed in Table 9.

Compounds in the Encyclopedia consisting of AlPO$_{4}$ with substitutions or additional molecules added to the framework, excluding those that can be fit into Table 9.

Structure	AFLOW Label	Space Group
Variscite 10 AlPO$_{4}$·(H$_{2}$O)$_{2}$	AB4C6D_oP96_61_c_4c_6c_c-001	$Pbca$ #61

References

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Resources

This is a list of resources mentioned in the text:

• The Database of Zeolite Structures provides zeolite framework structural information. This collects many of the AlPO$_{4}$-n structures referred to above.
• Y. Li, J. Yu and C. Zheng have released a Database of Open-Framework Aluminophosphate Structures (2020) including 313 AlPO$_{4}$ and related structures. Most are not frameworks, but include molecules or metallic impurities. They do include CIFs for each structure.