Understanding phase diagrams

UNDERSTANDING

PHASE

DIAGRAMS

AN EXAMPLE OF THE INTEGRATION OF INTERACTIVE GRAPHICS INTO A CAL AUTHORING SYSTEM A. DEMAID. P. G. The Open

University.

BUTCHERand

M’alton Hall. Xlilion

Ke!nes

J. VERRIEK MKl

6Ak

Eneland

Abstract-This paper describes the philosophy and execution of the first in u-hat is unended to be a series of related computer assisted learning programs designed to teach partxular technologtcsi skills. The skills wth which ue are concerned are those used to interpret diagrams \vhich xpreseni physical phenomena: e.g. phase diagrams. and Pourbali diagrams. This form of reprrsentation traditionall> poses mal.or difficulties to students. requiring the physical mtsrpretdtion of complex diagrams. in addition to an understanding of the concepts and a confident numerical ability \xithtn the theor). Interactive raster scan graphics provides a dynamic medium for manipuIat& diagams that 1s unavailable in an! other me&urn. This new approach linhs such a facihr! into a general purpose C.4L system to provide a po\r,erful and dttracti\e tool for tsachmg the interpretatton of such complex visual representations. The first program which has been written deals with the teaching of phase equtlibrium dlagrams to students of the Open Unr\ersitj course TS251. An Introduction to Materials. The students are taught the fundamentals of the subject through the correspondence text and are pwen a lecture at the start of their week’s summer school. Thu.\ the function of the program 15 not to teach the subject from first principles, but to allou the student to develop coniidence and skill through practice. The mreractibe program does this through the normal methods of questtonmg. assesstng and prompting the student on the vartous aspects of the diagram. wtth the student usm_f both textual (through the keyboard) and positional (through the cursor1 input ivhen answrinp. tn destgninp the program the analogy with a map has been adopted to enable us to recognise subsets of teachmg trchmques and to develop a cnnslstent method of programming. Thus the identification of major topological features and. sa). routes which Intohe calculation are seen to mvolve different structures The material has been developed using the STAF authoring system to present and control the dialogue. and graphics on a SIGMA 5670 series. raster graphxs terminal. Techmcal dctatls of the lmplementatlon are described.

PHASE

DIAGRAMS

\Yith regard to the wide variety and range of experience represented amongst the readership of an article on CAL. we make no apologies for starting this paper \vith a brief statement of what a phase diagram is. and what its importance is to technologists in general. and metallurgists in particular. Figure I shows a niceI> complicated. copper-tin phase equilibrium diagram. the copper-m allo! being more commonI> known as bronze. Fortunate!) the comphcated form of such a diagram can be split into four basic subsets and it is one’of these subsets which we hale chosen as the basis for the first in a series of CAL programs. The lead tin or solder alloy shown in Fig. 2 wholly illustrates the eutectic reaction whtch is the subset of interest. The field of this diagram represents the phase changes Lvhlch occur as a result of varying the composition and temperature of the allo!. Plm! refers to solder for joming copper and iron as containing two parts of tin to one of lead. the reverse proportions hemp favoured h! plumbers for joinmg lead pipes. These two compositlons are shonn on Fig. 2 by the lines A and B. The firs1 alloy freezes ver) rapidly at a lower temperature. lvhereas the second allo), ha> a p:i~t> beha\mur O\‘t”r a conslderable range of temperatures. Therefore uith this kind of diagram the constitutional behatiour of alloys can be seen at a glance and the inelegant recipes of the Romans are replaced. The understanding and interpretation of these diagrams is further complicated b> the requirenl~n~ that equiiibrium coolmg take place. This. b! definition. takes an interminably long time and never occurs in practxe. therefore the diagram 1s used as a guide with the cooling rate ol the melt causmp variations m the predIcted properties. Traditlo~lall~ the teachmp of phase equilibrium diagrams poses problems in con\.enttonai l_:niversiries and in this respect the) ma!’ be part of a iarse group of dlagramatx representations ahlch test the abilities of teachers. Technology is particularl! adept at usmg these diagrams to represent lists. recipes. or conditions. For example. Pourbais diagrams sho\v the \,ariatron of electrochemxal potential \\ith pH in corrosion problems: and bendmg moment diagrams represenl txam loadme m srructares.

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400

300

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Fig. I. Bronze

WEIGHT

phase

PER

qullibnum

CEN’

dugram

CONTEXT

The Open University has not been Immune from problems in teachmg the understandmg of phase diagrams to its students in the course TS31. 411 Introduction to Materials. This course has been running for 8 years. teaching some 500 students per year and consists of a front end contaming the basic science and technology required by a materials engineer followed by a series of case studies showing applications to engineering problems. Case studies include: transformer cores. a milk bottle recycling study. porcelain. and car bodies. As part of their studies phase diagrams are taught m

C:nderstanding

phase didprams

135

conjunctton with the use of a home experiment kit whtch in\,olves preparing brass samples and examming their structure under a microscope. All students are required to attend 1 weeks summer school at Sussex University. the content of the summer school being designed around practical work u hish assumes an understanding of. and ability to interpret, phase diagrams. .\t an early stage in the Me of the course It became apparent that the first requnement was a lecture tutorial on phase diagrams and microstructure vvhrch. however good. was not entirely satisfactory as students did not have sufficient time to develop real profictency before embarkinp on their practical vvork. This was the background to the decision to develop a CAL program to teach phase diagrams. Thus the program has been designed on the assumption that the student has already studied the subject by reading the basic concepts and definitions. and by going through worked examples. So the program will pro\ ide a skilled tutor approachmg the “individuahsed instruction” claim by Hooper [ 11. basic teaching occurs in the program only, as a direct result of student error.

APPROACH The analogy which we have taken in developing the program is that of the map. with boundaries. topography. and routes. The properties of an alloy can vary markedly depending on which area of the diagram is pertinent and the route to a particular temperature and composttion also defines the final properties of an alloy. Boundaries between different areas represent the positions beyond which it is thermodynamtcall! fa\,ourable for a reaction to occur: whether that reaction occurs or not may however be governed by the kinetics. In essence then the equilibrium phase diagram is not mathematicall\ “clean” and thus it cannot be dealt with in the way described by McKenzie[1] where the parameters in a formula can be varied and the result of the variation displayed graphicall!,. One consequence of this is that a necessarily sophisticated representation and display of the information Lvhich the student is being asked to interpret is required. In order to illustrate one of many possible routes through the diagram consider the progressive cooling of an alloy of composition 30”, tin ‘?O”, lead shown in Fig. 3. .4t point .4 the first solids nucleate from the liquid. these solids have a composition indicated by B on the diagram. The precipitation of Y phase depletes the remaining liquid of lead, and on further cooling the composition of liquid will be gilen by the line .4D. similarly the lme BC describes the composition of the r phase on decreasing temperature. At point E the proportion of liquid is given by the ratio CE’CD and this liquid solidifies as an intimate mixture of r. and b in proportions DF CF and DC CF. This then sets the. rather comphcated. scene for the CAL system which was designed SYSTEM

DESIGS

The selection of appropriate hardware and softaare proposed application involved combinations of: Textual and numerical output: GraphIcal output with the ability to selectively Textual and numerical input: Positional input via the cursor:

to run the project

highlIght

was interdependent.

and erase lines and areas:

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Fig. 1. Screen arrangement In the STAF authoring system the University already had a software environment capable of handling the envisaged textual diaiogues on scrolling terminals and wished to capitalise on its experience with this system and also extend it to graphical applications. The need for selective erasure of the graphics screen points to a raster scan graphics terminal and the nature of the application demanded relatively high resolution from such a device. Consequently a SIGMA 5670 series raster scan graphics terminal was purchased which provides not only high resolution graphics 1768 by 512) but also a separately addressable “alpha” screen which can be made to scroll over only part of the screen. Figure 1 shows the screen as it is used, with the top 75”,, (approx.1 used for displaying the graphical information and the dialogue between the program and the student scrolling over the bottom X0,,. The STAF system has been designed to allow the interaction between the student and the computer to be as natural as possible. Thus the language used by the student and the computer is as close to natural English as possible with allowances being made for spelling mistakes and trivial errors of nomenclature. Descriptions of dialogues enabled through STAF are well documented elsewhere[%6]. This project extends this natural interaction between student and computer by adding a pictorial display which may be addressed by both the computer and the student. The aim of this project is to incorporate all of these features into a powerful dynamic teaching program. The package allows interaction with the diagram in the sense that the student may point to lines. areas. and points and in that coordinate readings may be taken using the cursor: all of this IS under control of the teaching program which can follow the student’s attempts to perform set tasks. nhich include calculations. If the student is having difficulty the program will be able to recognise this and take the student through the principles of the calculation on the diagram. This is usually done by an ammated calculation on an alternative diagram. which uses a simpler system (such as that shown in Fig. 51 to illustrate the major teaching points. To identify a position on the screen. and relate it to the phase diagram shovving. the teaching software has to describe the diagram using numerical methods as a sequence of lines (rather than a sequence of data points to be joined). This in turn enables areas to be similarly defined and the structure is established for both animating the diagrams and identifying areas. lines. or positions to which the student is pointing. The routines for handling the diagram have been ivritten in FORTRAN and may be called from the STAF teaching program (“CALC” routines). When ST.AF programs “converse” with these routines parameters may be passed both ways. For example the ST.4F teachmg program may call a rout:ne to display the cursor and return co-ordinates when the student presses the “hit” button. These co-ordinates when returned may be evaluated and discussed with the student before progressing or regressing.

solId tolubility. Thr flashing ares CRETURN3 Cooslder described Use the

1% a

SINGLE

PHRSE

SOLID

SOLUTION

an alloy of ccmpositlon X (see diagram). This as a solId fclutlon of ntckcl ,n capper. cursor and point to a solid ralutron of COPPER

FIN. 5. Complere

The composition

of the software

would IN

be

NICKEL.

sohd solubihty.

suite is as follows:

The STAF teaching program is used to present dialogue accept and match textual and numerical responses control the teaching dialogue keep informatton on student responses and program performance keep student records e.g. how far the student has progressed and the current performance label the diagram (axes excepted) FORTRAN routmes are used to describe the diagram (application specific) pi-n\ tde general purpose graphtcs routmes. This relationship II; shown diagramatically in Fig. 6. It is envisaged that in time general functions \viil be added to the STAF system so that the graphtcs device may be controlled from withm a STAF teaching programme.

rating

purpose dtrectl>

DISCUSSION

The interactive nature of this program offers learning opportunities which are unique to this medium. thib b! vtrtue of the intimate associatton berween the textual and graphtcal Interaction. The programe has not. as Jet. been used with out students on TS251. thus man) of the lessons that will be learnt are about ho\\ students interact with the program and a-ill reflect how students cope. or fail to cope. wth the complextties of the dtagram. The route tracing ability of STAF will be mvaiuable tn determinmg what the real. as opposed to tutor Imagined. problems of understanding and interpretmg thts t!.pe of dtagram are. The program has been written. with student enjoyment ver? much in mmd. in a “game” format. The name of the game IS WORKS METALLURGIST (FIN. 7) and students are accorded a ratmg. dependent on their performance. varying from OFFICE CLEANER (reserved for those who are testing the programr to IS’ORKS XIETALLURGIST (for those
Teac5iP.g

programme ( STAC)

Graphics Fbutines

Fig. 6. Software

or_eamsatlon

Errors in particular sections of the program cause more questions to be asked until proficiency at that ievel is established. Errors are dealt with by teaching in alternative subsets of the equilibrium diagram and then returning to the question which was failed. In the main it has been adopted as policy that two levels of promptmg are employed before teaching on the main diagram takes place. It was not assumed that students were familiar with the use of a terminal and the combination of text and graphics available on the screen was ideal for teaching the use of the terminal (Fig. SI. The STAF teaching programs are inherently portable[7] from computer to computer and it is not envisaged that the FORTRAN routines provided to drive the SIGMA display will in an> way Inhibit this portability. but with the combination of graphics and scrolling text on one screen the application is currently very terminal dependent. Other raster scan devices that provide positional input. either through cross-hairs or a light pen. may however provide alternative solutions in the future.

FI_~ 7. Proqamme

title

L’ndersranding phase dqrrms

cl Cl cl cl cl cl cl

cl cl 0 cl q cl

n

Cl

REFERENCES Hooper R.. Inf J !ic~ti~..E:du.Sc,i. Trchnoi. 5, 359 (19741. McKenzie J., Camput. E&c,. 2. ‘5 (1978). Tawnq D. .A. Lrwn~nq rhro~yh Comptmrs. pp. 1. 29-4’. 212-313. Macmtllan. London ll9’9i. Peterson J. W Xl.. Writing programmes in STAF CALCHEM. Department of Phkslcs dnd Chemlstr;.. Leeds Lnl\ersity. \_ Akscough P. B.. STAF Author Guide. CALCHEM. Department of Physics and Chemistry. Leeds Unl\erSlt1 6. Aykough P. B.. Morris H. and Wilson J A.. Cornput. Educ. 3. 81 (19791. 7 Peterson J. W. M. and Sessions A. E.. Cwnput. Educ. 2. 331 (1978). 1. 2. 3 4.