Unit 3 Defect Crystal Chemistry
It has already been remarked that point defect populations affect both the physical and chemical properties of materials profoundly. In order to describe these consequences we need a notation for defects that is simple and self-consistent. The most widely employed system is the Kroger-Vink notation which was designed to account for point defect populations in crystals.
When we add or subtract elements from the crystal, we do so by adding or subtracting electrically neutral atoms and thus avoid making judgements and decisions about chemical bond types. When ionic crystals are involved this requires that we separately add or subtract electrons. To illustrate the implications of this idea we will use the notation to describe some defects in a compound of formula MX, where M is a metal and X an anion. It is the simplest to do this by discussing the various types of defect that can occur in such a material, and to commence with uncharged atomic defects.
Atomic Defects
Vacancies. When empty lattice sites occur, they are indicated by the symbols Vm and Vx for the metal (m) and non-metal (x) sites respectively. In the notation the subscript m indicates a missing metal atom and x a non-metal. If we suppose that the oxide NiO is ionic, VNi would imply the removal of a Ni[2+] ion together with two electrons, that is, a neutral Ni atom. Similarly, VO would indicate a vacancy in the oxygen sub-lattice and implies removal of an O[2-] ion from the crystal and the subsequent addition of two electrons to the crystal.
Interstitial Atoms. When atoms occupy interstitial positions, they are denoted by Mi and Xi for metals and anions respectively. Hence Ki represents an interstitial potassium atom in a crystal.
Impurity Atoms. Many materials contain impurity atoms, introduced either on purpose, or as a result of inadequate purification procedures, and it is important to be able to specify the nature of the impurities and where in the crystal they are to be found. This is particularly true for impurities that are deliberately added to control electronic or other properties. In this case the impurity is given its normal chemical symbol and the site occupied is written as a subscript. Thus an Mg atom on a Ni site in NiO would be written as Mg_Ni. The same nomenclature is used if an atom in a crystal occupies the wrong site. Thus it is possible for M atoms to be on X sites, written as Mx, or X atoms to be on M sites, written as Xm. A potassium atom on a bromine site in KBr would be written as K_Br, for example.
Associated Defects. As we will see in following sections, it is also possible for one or more lattice defects to associate with one another, that is, to cluster together. These are indicated by enclosing the components of such a cluster in parenthesis. As an example, (VmVx) would represent a Schottky defect in which the two vacancies were associated as a vacancy pair.
It is seen that the normal symbol for a chemical element represents the species involved, and the subscript represents the position of the atom in the structure.
Charges on Defects
Electrons and Holes. The charged defects that most readily come to mind are electrons. Some fractions of the electrons will be free to move through the crystal. These are denoted by the symbol e'. The superscript ' represents the negative charge on the electron. Although electrons are the only charged subatomic particles to exist in the structure it often simplifies matters to think about the sites where electons are missing. This is analogous to thinking about vacancies instead of atoms. In the case of these 'electron vacancies' we use the symbol h- to denote the defect, which is called an electron hole, or, more commonly, simply a 'hole'. Each hole will bear a positive charge of +1, which is represented by the superscript.
Charges on Defects. Besides the electrons and holes just mentioned, the atomic defects that we have described above can also carry a charge. In ionic crystal, in fact, this may be considered to be the normal state of affairs. The Kroger-Vink notation bypasses the problem of deciding on the real charges on defects by considering only effective charges on defects. The effective charge is the charge that the defect has with respect to the normal crystal lattice. To illustrate this concept, let us consider the situation in an atomic material such as NaCl, which we will suppose to be made up of the charged ions Na[+] and Cl[-].
If we then have a vacancy in the NaCl structure at a sodium position V_Na, what will the effective charge on this defect be? To understand this, you must imagine yourself as 'diffusing' through the NaCl structure. Each time a Na[+] ion is encountered, a region of positve charge will be experienced. If, then, we meet a vacancy instead of a normal ion, this will seem not to be positive at all. Relative to the situation normally met with at the site we will encounter a region which has an effective negative charge, that is, a charge relative to that normally encountered at that position equivalent to -1. In order to distinguish effective charges from real charges, the superscript ' is used for each unit of negative charge and the superscript ' is used for each unit of positive charge. Hence a 'normal' vacancy at a sodium site in NaCl would be written as V'_Na, which corresponds to a missing Na[+] ion. Similarly, a 'normal' vacancy at a chlorine site would seem to be positively charged relative to the normal situation in the crystal. Hence the vacancy has an effective charge of +1, which would be written V-_Cl .
With each of the other defect symbols Vm, Vx, Mi, Mx and associated defects such as (VmVx) an effective charge relative to the host lattice is also possible. Thus Zni-- would indicate a Zn[2+] at an interstitial site which is normally unoccupied and hence without any preexisting charge. In such a case, all the charge on the Zn[2+] ion is experienced as we move through the lattice, and hence the presence of two units of effective charge is recorded im the symbol, viz. 2. Similarly, subsititution of a divalent ion such as Ca[2+] for monovalent Na on a sodium site gives a local electronic charge augmented by one extra positive charge which is then represented as Ca-_Na .
Suppose now a sodium ion in NaCl, represented by Na_Na, is substituted by a potasium ion, represented by K_Na. Clearly the defect will have no effective charge, as to anyone moving through the crystal, the charge felt on encountering the K ion is the same as that experienced on encountering a normal Na ion. This defect is therefore neutral in terms of effective charge. This is written as K[x]_Na when the effective charge situation needs to be specified, the superscript x representing an effectively neutral charge.
It is therefore seen that the idea of the charge ono the defect is separated from the chemical entity which makes up the defect. Real charges are represented by n[+] and n[-], while effective charges are represented by n' and n- or x. It is for this reason that the charges on electrons and electron holes mentioned above were written as ' and -, as these charges are also of importance only relative to the surrounding crystal lattice.
Selected from "Defect Crystal Chemistry and Its Application" K.J.D.Tilley, Blakie&son ltd., 1987
Words and Expressions
defect crystal chemistry 缺陷晶体化学
notation 表示
self-consistent 一致的
vacancy 空位
subscript 下标
sublattice 亚晶格
deliberately 故意地
nomenclature 命名法
cluster 团聚
Schottky defect 肖特基缺陷
subatomic 亚原子的
electron hole 电子空穴
bypass 绕过
divalent 二价的
entity 一体
