2061. Such decisions would require lengthy discussions, with a t least some of those participating in the discussion acting as devil's advocates. Unlike Mitchell, I would include industrial as well as academic chemists and would not assume that all college chemistry teachers are chemistry experts and all hieh school chemistrv teachers are not. 3econd, I agree with Mitchell that college and high school chemistry teachers should work together to improve instruction. However, I suggest that the average experienced high school chemistry teacher has more to offer the averace experienced college chemistry teacher than vice versa. [F& some reason, college teachers seem to have one year of experience 10 times rather than 10 years of experience more often than do high school teachers, perhaps because teaching is our nrimarv iob.1 The two .. erouns . toeether .. could heln. beeinnine .. high school and college chemistry teachers learn their craft. I notice that Mitchell's DaDer is "Part 1": I h o ~ that e Part 2 provides some suggestions for how to find'the ;me to do all this.
A repeating pattern of atoms or molecules in a crystal is ascribed to eauilibrium nositions in which the constituents of the cry& vibrate about these equilibrium positions. Usuallv. in lecture. once this has been established. solids are treated'as if the nuclei were a t rest a t their equilibrium positions. Nevertheless, our program pertains to simple inorganicmaterials such as alkali halides for which the ions are aenerallv accepted to be on defined ~ositions. As mentioned inour paper, line intensitiesaregiven mainly by thesquare of the modulus of the structure factor. Most physical chemistry textbooks mention the additional variation of intensity due to the angle dependence of scattering factors. atomicvihrations. etc.-Our oattern simulator or& gram simulates only line positions, not intensities. As correctlv nointed out bv Goldbere. an unfortunate tvpographical error in our paper shows t h l t for a face-centered cubic lattice, the atoms are located a t (O,O, O), (a, 0, O), . . . , ( ~ 1 2a, , O), . . . , (a, a, a), while the correct location is (O,O, O), (a, 0, O), , . . ,(a12, al2, O), . . . ,(a, a, a).
William G. Lamb
Silvlo Rodriguez University of the Paclflc
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heg~n Eplscopl School 6300 S.W. Nicol Rd. Portland. OR 97223
On an X-Ray Diffradlon Pattern Simulator To the Editor: The recent article by Rodriguez and Rodriquez (J. Chem. Educ. 1989,66,648) describes a useful tool for those instructors who do not have facilities for the generation of X-ray powder patterns. However, the description given contains one serious. and one less serious error. The serious error reinforces the misconception often given to beginning students that in a crystal structure in the atoms (or ions) are situated a t lattice points such as 0,0,0 and translationally related ~ositions.This misconce~tiondevelons because. in the simple inorganic materials, such as the hkali halides, often discussed when introducing the concept of a crystal lattice, it is indeed true that the ions lie on special positions. However, this is the exception rather than the rule. When atoms, or ions, are locatedar general positions, the computation of the structure factors requires knowledge of those positions. It is for this reason that a previously published ( I ) powder pattern simulation program simulated only line positions but not intensities. The less serious error is that, while it is indeed the case that the structure factors may be calculated from the scattering factors, the scattering factors themselves are functions of the scattering angle, 0, and the thermal motion of the atoms. A third error, ~ossihlvof t w o graphical origin, is that for a face-centered lattice the centering condition involves half-cell translations along two cell axes, not one. While i t is undoubtedly true that instructors with some experience in crystallography will recognize these points immediately, i t is also likely that they would not have been noticed by those with little experience in the field. Literature Cited 1. Miller, J.
S.;Goldberg,S.2. J . Chsm.Educ. 197754.54 Stephen Z. Goldberg Adelphl University BOX701 W e n Clty. NY11530
To the Editor: Given that our article "An X-ray Diffraction Pattern Simulator" was mainly concerned with the generation of a simulated X-ray diffraction pattern, we did not explicitly elaborate on basic points usually covered in most physical chemistry textbooks.
Stocktan. CA 95211
Student Understandlng To the Editor: While students' ability to solve problems may not be equivalent to their understanding molecular concepts, we must be careful in drawing conclusions from our attempts to test students' masterv of contents. Althoueh Pickerine and Sawrey were disheartened by ;he results ;hey o b t a i k d in such an attempt (J. Chem. Educ. 1990,67,253-2551, I take a rosier view of the situation. In the gaslaw problem described in the article, nearly onethird of the students indicated the correct choice, showing essentially random positioning of dots (representingHp molecules) a t both 20 O C and -20 O C . An additional 50% chose an answer that indicated that the particles were randomlv arranged in a circle of smaller circu&ference a t -20 O C . his answer would be correct if the tank were a balloon (and the circle enclosing the dots were, therefore, contracted slightly). This choice, i t seems t o me, does not reflect gross misunderstandine of molecular concents but rather the fact that balloons 6 d movable pistons are more often discussed in lectures on the eas laws than rieid containers are. T h e stoichi&etry problem discussed in the article showed three squares and eieht circles. initiallv s e ~ a r a t e d from one another, "reacting"to form three sets, each containing a square and two circles, with two circles left unattached. When asked to pick the equation which best de2Y scribes the situation, 11% chose the equation "X XY2", while 89% chose the equation "3X 8Y 3XY2
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Sawrey indicates that the first of these equations is the correct answer. I agree that "X 2Y XY2" is the correct balanced eauation for the situation described. However. the students were not asked to choose the "correct balanced eauation": thev were asked to choose the eauation that thev feit "best described the situation". students may well have chosen the longer equation because i t conforms more closely than the balanced equation to the specifics shown in the picture-that three "molecules" were formed from three X's and six Y's and that two Y's were left over. I t is very possible to interpret the students' choice as an indication that they understand the meaning of the chemical equation, the significance of a chemical formula, and the limiting reagent concent. After all. the two eauations are aleebraicallv euuiva l e n t . ' ~ eoften ask studen& to treat chemical equaiiois as algebraic entities (in balancing redox equations, in shifting between net ionic and molecular equations, in setting up equilibrium problems); the fundamental question to be an-
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Volume 68 Number 11 November 1991
969
