THE STRUCTURE OF MATTER: A BRIEF REVIEW OF PRESENTDAY CONCEPTIONS. IV. TBE STRUCTURES OF CRYSTALS MAURICE L. HUGGINS, STANRORU UNIVERSITY, CALIFORNIA
Solids may be divided into two classes-crystals, in which the component atoms or molecules are marshalled in an extremely regular manner, and amorphous solids, in which there is no such regularity. The present article deals primarily with the structures of solids of the former class.
The Interaction of X-rays and Crystals If a crystal is placed in the path of a beam of X-rays,' each atom in the crystal-in fact, each electron-will scatter the X-rays in all directions. In general, the scattered X-rays will destructively interfere with each other, but, because of the regularity of the arrangement and the fact that the X-ray wave-lengths are of the same order of magnitude as the distances between atoms in crystals, there will be reinforcement of the scattered rays in certain particular directions (depending on the nature of the structure and the wave-length or wave-lengths present in the X-ray beam). Crystal structure analysis consists in determining these directions, usually photographically, and deducing therefrom-knowing the wavelengths of the X-rays-the arrangement of atoms in the crystal. The three general methods of obtaining the necessary data are: (1) The Laue method, employing a single crystal, set in a fixed position, through which a beam of X-rays containing a whole range of wavelengths is passed: (2) The Bragg method, in which the crystal is rotated and the X-rays used consist mainly of a few definite wave-lengths. (3) The powder method, developed by Hull in this country and Debye and Scherrer in Europe, employing powders, and X-rays containing chiefly one or two wave-lengths. I t has not been found possible to locate directly by means of X-rays the positions of electrons or electron orbits in crystals, but indirectly the distribution of valence electrons can often be, in part a t least, determined.= In each of the crystals described hereafter, the general nature of the valence electron distribution the author believes to be practically as definitely known as the arrangement of atomic centers.
Single-Molecule Crystals; Polar and Non-polar Crystals Each carbon atom in the diamond (Fig. 3) is surrounded by four others at corners of a regular tetrahedron. It is bonded to each by an electron 1 X-rays, it will be remembered, are of the same nature as visible light, but the wave-lengths are only about one-ten-thousandth as geeat, that is, about 10-a cm. lHuggins, Phyr. Rev, 27, 286 (1926); 3. A m Chem. Soc. 44, 1841 (1922).
pair situated midway between the two atomic centers, i. e., by a non-polar single bond. The whole a y s t a l is thus a single molecule. Silicon, germanium, and gray tin have structures of the same type. The bonds are in each case strictly non-polar, but weaker than in the diamond. Cubic zinc sulfide crystals are similar (Fig. 3). RG.3.-Representing the unit cube of the Each atom is bonded by a diamond or cubic ZnS. The large dots represent semi-polar bond to four of the centers of C or Zn atoms; the large circles C or the other kind. The same S centers, and the small circles pairs of valence elec- structure is possessed by trons. In the diamond the electron pairs are midway between adjacent atoms, as shown; in ZnS they AISb, ZnSe, BeS, HgS, CuC1, CuBr, CuI, and AgI. are nearer the S centers than the Zn centers. The structure of the hexIn the face-centered cubic or "cubic close-packed" structure, atomic centers are distributed as shown agonal form of zinc sulfide, by the large dots in this figure. possessed also by ZnO, AlN, BeO, CdS. CdSe, and AgI, closely resembles that of Figure 3 in the arrangement around each atom. Sodium chloride possesses the structure of Figure 4. The valence electron pairs are not on the center lines between atoms, hut are disposed tetrahedrally around the chlorine kernels. The crystal can then be considered as being built up of Na+ and CI- ions. We have no reason, however, FIG.4.-The unit cubeof NaCI. Large dots rep- to believe that the forces resent Na centers, large circles C1 centers, and small holding the atoms together circles pairs of valence electrons. The arrangement are different in nature from of large dots or of large circles, considered separately, is that of atomic centers in a substance having the those holding the Zn and S atoms together in ZnS, but face-centered cubic structure.
in the former crystal they are less localized than in the latter. The other halides of sodium, all those of lithium, potassium, and r u b i d i ~ m ,CsF, ~ MgO, MgS, CaO, CaS, Case, SrO, SrS, SrSe, BaO, Bas, Base, MnO, MnS, CdO, NiO, COO,PbS, AgCI, and AgBr all have the sodium chloride type of arrangement. Figure 5 illustrates the cesium chloride type of structure, possessed also by CsBr, CsI, TICI, TlBr, and TII. . That of CaFz, BaF2, Sr%, CeOz,Thon, and UOz is shown in Figure 6. Layer Molecules
FIG. 5.-The unit cube of CsCl. Large dots denote Cs centers, the large circle a C1 center, and the small circles valence electron pain. In the metals having the "body-centered cubic" structure, the atoms are all of the same kind, their centers being distributed as shown here by the large dots and the lame circle.
In all of the foregoing the whole crystal must be a single molecule (or, perhaps, in crystals of the CsCl type, two molecules), if we are to speak of a molecule at all in connection with ctystals. Some crystals, however, c o n t a i n w h a t might be called "layer molecules"-all the atoms within each layer being held together by definite chemical bonds, while between layers the forces are relatively weak "residual affinities." In crystals of phosphorus (metallic), arsenic, antimony, or bismuth FIG.6.-Theunit cube of the Capzcrystal. Large (Fig. 7), for instance, each atom is bonded by single dots denote Ca centers, large circles F centers, and small circles pairs of valence electrons. non-polar bonds to three others, all in the same layer. In mercuric iodide (Fig. 8) each mer8
Except possibly RbF, for which no unambiguous data are available.
cury atom is bonded to four iodine atoms, all in the same layer, and each iodine to two mercury atoms in the same layer. The structures of CdIz and of Mg(OH)z, Ca(0H)z and Mn(OH)* (Fig. 9) are similar in that only atoms in the same layer are bonded together. In all these cases the crystals cleave readily between the layers. String Molecules A crystal of selenium or tellurium (Fig. 10) contains spirals of atoms extending completely through the crystal from one end to the other, each
FIG.7A.-IIlustTating the arrangement within a FIG.7B.-A two-dimensionalrepre"layer" of a crystal of P. As, Sb, or Bi. Large sentation of the arrangementof layers circles denote atomic centers, small circles valence over each other in a crystal of P, As, electron pairs. Each atomic center is tetrahedrally Sb, or Bi. surrounded by four valence pairs.
atom being bonded to two others within the same spiral. There are no bonds connecting different spirals. Such a structure may be described as being composed of "string molecules." It is quite possible that cellulose and a number of other organic substances are built up of such "string molecules." Island Molecules Most crystals of organic compounds, as well as those of quite a few inorganic substances, are built up of molecular units containing only a few atoms. For instance, in stannic iodide crystals there are definite Sn14 groups, each tin atom being tetrahedrally surrounded by, and bonded to,
VOL.4,No. 1
'I'm
S m u c r u n ~ow
MATTER. IV
FIG.8.-Illustrating the arrangement within a layer of HgL. The large dots denote Hg centers, all in one plane, and the large circles and circled dots represent I centers in planes above and below the Hg plane. The small circles represent pairs of valence electrons.
FIG.9.-Illustrating the arrangement within a small section of each layer in a crystal of CdIn or Mg(OH)*. Large dots represent Cd (or Mg) centers, in plane 0 ; large circles and circled dots represent I (or 0 ) centers, in planes +1 and - 1, respectively; m a l l circles represent valence electron pain. Each I (or 0 ) center is tetrahedrally surrounded by four pairs, one being directly over or under the atomic center. In Mg(OH)% there is alsu a hydrogen center directly over or under each 0 center.
77
FIG.10.-A two-dimensional representation of the Se structure. Large circles represent Se centers and small circles valence pairs.
FIG.11.-The molecular unit (not the unit cube) of heuamethylene-tetramine, GHlrN4. The large circles represent N centers, the circled dots C, the larger dots H, and the small circles electron pairs. This figure will also serve to depict the structure of the AsrOs molecule if the large dots are neglected and the large circles and circled dots are taken to represent As and 0 atoms, respectively.
VOL.4, No. 1
T E ZSTRUCTURE ~ OW MATTER. IV
79
..
four iodine atoms, in agreement with the formula
..:!: ..
:~:S!I:;: :I: ..
The "trioxiden of arsenic contains As406 units (Fig. 11) corresponding to the formula,
Hexamethvlene tetramine.
is similar, arsenic atoms being replaced by those of nitrogen, and oxygen by CHn groups. I n carbon dioxide the three atoms in the molecule are in a straight line, as would be expected from the formula ::o::C::O:: I n crystals of penta-erythritol, C(CH%OH)4,the central carbon atom is not tetrahedrally surrounded. The other carbon atoms are a t corners of a square, with the central carbon somewhere on the four-fold symmetry axis passing through the center of the square. Whether or not this square arrangement exists also in solution or in the liquid or gaseous states is another question, to which we do not know the answer.
Complex Ions The structure of pyrite, FeS2, is like that of sodium chloride (Fig. 4), with the sodium "ions" replaced by divalent iron "ions" and the chloride "ions" replaced by Sz-- groups. (Although convenient to speak of such a structure as being composed of "ions," this use of the word is questionable; each iron atom is bonded by semi-polar bonds to six sulfur atoms and each sulfur is bonded by semi-polar bonds to three iron atoms, as well as by a non-polar bond to another sulfur.) FeAsS and FeAsl are similar, with .. .. and [:Ls:is:]---.. .. groups instead of [ : s : s : ] - - and with the iron kernels having charges of +3 and +4, respectively, instead of $2.
[:&:;:I---
In crystals containing sulfate groups each sulfur is tetrahedrally surrounded by four oxygens. The .. available data favor the structure repre-
[ ] ..:o:..
:I--
sented by the formula, :O:fj:c:
[:
: :O::S::O:
:o: ..
:?:
,rather than that represented by
, although the evidence is perhaps not conclusive.
'"1
Calcite, CaC03, contains CO3 groups in which all three oxygens are .. -:0.. ;o:
equivalent. The x-ray data are best
thestructure,[
"
:o:
,
which may or may not persist in solution. X-ray data from KzSnCla show that there are six chlorine atoms octahedrally distributed around each tin atom, as would be expected from the
..
--
[ ]
I n Ni(NH3)&Y2there are similarly six nitrogens octahedrally placed HJ
around each nickel atom:
H~.N.~Ha ::
.
H? ' N ' ~ H ~
Hydrogen in Crystals One form of ammonium chloride has a structure like that of cesium chloride (Fig. 5), with the cesium "ions" replaced by tetrahedral NH4+ "ions." The hydrogens are on the N C 1 centerlines serving to "bond" the nitrogen and chlorine atoms together, in all probability in the manner indicated in Figure 12. Each hydrogen atom is bonded to two atoms a t once, although one of the bonds must have been formed by a "secondary valence reaction."' A similar state of affairs exists in ice, if we assume to he correct the only structure which has been shown to be in agreement with the available Xray data. Each oxygen is tetrahedrally bonded to four hydrogens; each hydrogen is bonded equally to two oxygens (Fig. 13). The X-ray data on NaHFz and KHFz similarly indicate that in these substances hydrogen is bonded to two other atoms at the same time:
[:E:H:~;]-.
* Cf.Article I11 of this series.
THISJOURNAL, 3, 1426-9 (Dec., 1926).
VOL. 4, No. 1
TEE Srnncrune os MATTER. IV
81
Hydrogen is of course not bonded to two atoms in this way in all crystals. The high temperature form of NH4C1, for instance, has the NaCl type of structure (Fig. 4), with the hydrogens on the cube diagonals. Metals
0
=
--
0
Most of the metals crystallize with either fie. la.-1llustrating the the hexagonal or the cubic "close-packed" structures (Firs. 3 and 4). annmximate relative nositions ,. in which each atom . is surrounded by twelve others, the maximum of adjacent atoms and valence in a crysta1 Of the low number possible. The valence electrons seem ptemperature form of NHdCI. to have little d e c t on the type of structure; (Theposition of the nucleus they are probably not held very tightly in on the ~4centerline is at any definite ~ositions,or a t least are auite mesent not known. even aofree to move from one "equilibrium posi- pmximatel~.) tion" to another. A few of the metals crystallize with the body-centered cubic arrangement (Fig. 5). ~
&
0
0
0
0
0
0
0
0
Fro. 13.-A two-dimensional representation of the structureof ice. Large circles denote oxygen kernels, crosses H nuclei, and small circles valence pairs.
Other Crystals Many more crystals have been studied by means of X-rays, but the above results may be considered as typical. I n nearly every case the data are
in agreement with a tetrahedral arrangement of four electron pairs in the valence shell of each electronegativeatom. The kernels of electropositive atoms in crystals containing electronegative atoms as well are also often surrounded by four electron pairs, but in many other cases there are six or eight pairs. Crystal Formation and Secondary Valence The tendency to form such valence shells, containing four, six, or eight pairs, around the kernels of the more electropositive atoms seems to be 0
-L
+
I
t 0 0
0 0
0
+
0
.A two-dimensional representation of liquiid H*O. Large circles denote oxygen kernels, crosses H nuclei, and small circles valence pairs.
the major cause of crystal formation in most inorganic crystals containing both electropositive and electronegative atoms. I n such cases the crystallization process consists of a succession of "secondary valence reactions," in which a "lone pair" becomes a "bonding pair." Amorphous Solids; Liquids; Solutions I n amorphous solids the arrangement of atoms or molecules is irregular,but does not vary with time; in liquidsthe arrangement is constantly changing. A liquid like carbon tetrachloride undoubtedly consists of CClp molecules in continually changing relationship to each other; but two somewhat
VOL. 4. NO.
1
TRE Smncrum
0s MATTER.
IV
83
different pictures have been proposed for a polar liquid such as water. The traditional view is that it consists of molecules of HzO, (HzO)~, (HzO)~, and perhaps others, in tautomeric equilibrium with each other. The probable structure for ice, mentioned above, suggests, however, that the whole liquid, like the whole crystal, is a single molecule, but of constantly changing structure. A two-dimensional representation of the instantaneous structure of such a liquid is shown in Figure 14. Much can be said in favor of this latter view, which is the one the author believes to be correct. We used to picture a dilute solution of a strong electrolyte as containing ions and un-ionized molecules in equilibrium with each other; hut according to the "interionic attraction theory" of Debye and Hiickel, which seems to be in much better accord with the experimental facts, such dilute solutions contain few or no un-ionized molecules. Instead, it is assumed that on the average each positive ion has immediately around it a slight excess of negative ions and each negative ion is similarly surrounded by a slight excess of positive ions.
