To the Editor:

The only purpose of my letter (J. CHEM. EDUC., 34, 310 (1957)) was to call attention to the schismatic terminology for crystal classes tabulated by Professor Fisher (J. CHEM. EDUC., 34, 259 (1957)). I t also ap- pears that Fisher (J. CHEM. EDUC., 34, 458 (1957)) has forgotten or overlooked the footnote he added to his tabulation, in which he stated, referring to those classes of crystals with "one 3 (or Z) and only one," that "the term rhombohedral is not entirely suitable since rhombo- hedron~ are found in only three of the five classes in- volved"' and the "the term trigonal as used in Inter- national Tables for X-ray Crystallography (Vol. 1, 1952) is unsatisfactory since classes 6 and Em2 (which contain trigonal forms, hut which lack rhombohedral space groups) are thereby excluded." The above statements led me to remark that "Fisher rightly con- cludes that on morphological grounds alone there is no suitable or satisfactory terminology for crystal classes," and it is this statement with which Fisher unaccount- ably takes issue. The points to be emphasized are that the terminology adopted by the International Union of Crystallography after careful deliberation is based on symmetry, is unambiguous, is not hard for the stu- dent to grasp, and has the tremendous advantage of being available in the International Tables for X-ray Crystallography. There may be other terminologies with other bases and notations, but their use can lead only to chaos and confusion. Morphology is only a small part of the science of crystallography, and it is accordingly easy to understand how a morphologist can see little value in dividing the hexagonal system (un- restricted sense) into two subsystems. The reason for grouping together as the trigonal system the classes 3, 5, 32, 3m, and Zm, and as the hexagonal system the classes 6, 6, 6/m, 622, 6mm, 6m2, and 6/mmm must be obvious. Classes 6 and 6m2 may, as Fisher says, "bristle with trigonal and ditrigonal forms," but this fact is completely irrelevant to a terminology based on symmetry. There are many properties of crystals other than face development which also cut across the system boundaries.

I t comes as a great surprise to read that Fisher con- siders that "Bunn's table contains what Mysels (J. CHEM. EDUC., 34, 40 (1957)) calls an 'Erroneous Classification of Crystal Systems' " since nowhere does Bunn state or even imply that the shape of the unit cell is a sufficient condition for classification, but, on the other hand, does list essential symmetry for each system.

Also in the footnote is the statement, "However, one or two rhombohedra1 anace erouns are mesent in each of these five .~ .. ,~ rlassw, rhou~$l from one 10 six primitive -par+ gnmpr orcur in t of I . ' The rxprrs*im "rlwrnh,lndriII >p.tw ~nrup" is ambiguous, and the expression "primitive space group" is mean- ingless.

Finally, I must point out that Fisher is wrong in say- ing that "only the simple cubic (of the three isometric cells) is primitive."

(The Editor has kindly sent me a copy of the note which follows. Careful study of its contents suggests that further discussion is bootless.)

UNIVERSITY OF SOUTHERN CALIFORNIA Los ANQELES, CALIFORNIA

To the Editor:

The Editor kindly sent me a copy of the above com- munication from Professor Donohue for my comments prior to its publication. It is an error (cf. the earlier communication: J. CHEM. EDUC., 34, 310 (1957)) to speak of my "terminology for crystal classes," schis- matic or otherwise. There are 32 classes (or point groups) and I made no attempt to present a terminology for these. I feel positive that on morphological grounds alone there is an entirely satisfactory terminology for the crystal classes. I infer that Donohue considers me to be a morphologist; I appreciate this compliment but would prefer to be known as a crystallographer (and mineralogist). Also Donohue has a footnote in which he objects to part of my footnote. The I.T.C. (Inter- national Tables for X-ray Crystallography, Vol. 1, 1952) divides the 25 trigonal space groups into P (primitive) and R (rhombohedral). I t is true that the former is an especially infelicitous term, but my mean- ing should have been clear to those familiar with the 77"" 1.I.b.

Regarding Bunn's table, I believe that Bunn has fallen into the very error that Mysels (J. CHEM. EDUC., 34, 40 (1957)) is inveigling against so creditably. Bunn gives as the truth exactly what Mysels' table presents as an "Erroneous Classification of Crystal Systems." My conclusion is that even a topnotch crystallographer makes an occasional oversimplification or slip when he is talking down to the beginning student (if a t no other time); for calling this to our attention I feel Mysels performed a worth-while service. To spell this out with one (of several possible) example(s), Bunn's table states that the monoclinic unit cell has or = 7 = 90"; p not 90"; a, b, and c unequal. Now every crystallographer knows that there are monoclinic unit cells with & = 90'; similarly a can equal b or/and c in certain individual cases within the limits of our ability to measure at a given temperature.

The I.T.C. has three kinds of isometric cells (or lattices; a cell is just one parallelopipedal unit of the lattice); namely: P (primitive), I (body-centered), and F (face-centered). Only the first is primitive ("simple"); I is doubly primitive, and F is quadruply primitive.

JOURNAL OF CHEMICAL EDUCATION