Problems and procedures in collection of three-dimensional neutron diffraction data for crystal structure determination

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Problems and procedures in collection of

three-dimensional neutron diffraction data for crystal structure determination

George M. Brown, Henri A. Levy

To cite this version:

George M. Brown, Henri A. Levy. Problems and procedures in collection of three-dimensional neutron diffraction data for crystal structure determination. Journal de Physique, 1964, 25 (5), pp.497-502.

�10.1051/jphys:01964002505049700�. �jpa-00205816�

497.

PROBLEMS AND PROCEDURES IN COLLECTION OF THREE-DIMENSIONAL NEUTRON DIFFRACTION DATA FOR CRYSTAL STRUCTURE DETERMINATION

By GEORGE M. BROWN and HENRI A. LEVY,

Chemistry Division Oak Ridge ^National Laboratory (1), ^Oak Ridge, Tennessee, ^{U. S. A.}

Résumé.

²⁰¹⁴

Les données de diffraction neutronique tridimensionnelles ont été relevées _{pour des} cristaux de 13 composés différents sur le diffractomètre automatique à neutrons d’Oak Ridge.

Problèmes et méthodes dans le relevé des données sont discutés depuis ^la sélection des cristaux

jusqu’a l’obtention et l’utilisation des données. La précision ^{des mesures}

^sur

l’appareil ^{est aussi}

discutée.

Abstract.

²⁰¹⁴

Three-dimensional neutron- diffraction data have been collected for crystals ^of

thirteen different compounds

^on

^{the Oak} Ridge automatic three-circle neutron diffractometer.

Problems and procedures ^{in data} collection

are

discussed, from selection of crystals through ^data processing. Precision of measurements

on

the instruments is also discussed.

LE JOURNAL DE

PHYSIQUE

^TOME

25,

^MAI

1964,

Introduction.

^-

During ^two years of operation

of the Oak Ridge ^{automatic neutron diffracto-} meter, three-dimensional data sets have been re-

corded for crystals ^{of thirteen different substances} (see ^Table 1). ^A review of the information derived from certain of these data sets is presented ^{in an} accompanying paper by G. M. Brown and H. A. Levy [I], ^{and a} general description ^{of the}

diffractometer and its operation ^is presented ⁱⁿ

another paper by ^{W. R.} Busing, ^Smith (H. G.),

Peterson (S. W.) ^{and H. A.} Levy [2]. ^The present

purpose is ^to discuss from the aggregate ^{of our} group’s experience in automatic collection of neu- tron diffraction data some procedures that have been found useful and some problems that have arisen.

Selection and preparation ^of crystal specimens.

-

The requirement ^of obtaining ^{data with} good counting statistics in a reasonable period ^{of time}

demands that one use rather large crystals speci-

mens. On the other hand, specimens ^{cannot be}

too large, ^{if extreme} absorption ^{effects are to be}

avoided and, especially, if extinction errors are to be minimized. We prefer ^{to use two or more} crystals ^of widely ^{different sizes whenever this is} possible. ^{For all} reflections likely ^to be affected

by extinction, only data from the smaller crystals

are chosen for structure refinement. For the other

reflections, ^{data are} taken from a large crystal.

First one usually prepares the largest ^available crystal, up ^to the limit imposed by consideration of the area of homogeneous intensity ^{of the beam}

cross section or by ^the absorption property ^{of the}

substance. From this crystal ^all independent ^re-

flections are recorded out to the limiting ^{value of}

sin 6/X of the instrument (~ 0.76~, ^{or at least as}

far out as is useful to measure. A somewhat (1) Operated for the U. S. Atomic Energy ^Commission by ^{Union Carbide} Corporation.

smaller crystal ^{is then chosen for} recording again,

with the monitor count (2) ^set correspondingly higher, those reflections having intensities from the first crystal ^so high ^{as to make one} fear extinction

errors. Similarly, ^a still smaller crystal may be chosen for recording the reflections having the very

highest intensities. Analysis ^{of the sets of data}

for the various crystals (see discussion of averaging

below under heading ^Data Processing) ^{allows one}

to evaluate the effects of extinction independently

of the structural model and to decide, ^for example,

the cutoff levels of intensity above which data for the larger crystals ^{should not} be used in structure refinement.

This procedure allows collection of a set of data

having reasonably low fractional standard errors

overall, ^without including ^data seriously ^affected by extinction. It seems preferable ^{to the alter-}

nate procedure ^of attempting in the final stages ^of

structure refinement to apply corrections for

extinction, especially since proper calculation of corrections is difficult because extinction is gene-

rally anisotropic. It is still advisable, however, ^to

look for residual extinction errors by comparison

of observed and calculated structure factors ^near the end of refinement. A finding ^{of errors at this} stage suggests the need for re-examination of the chosen cutoff levels for data of the different crys-

tals, ^{or even the} advisability ^of omitting ^{a few data} altogether.

The[chloral hydrate ^{data were} obtained from three crystals, weighing - 29, 10, ^{and 2} mg. Of the - 2 150 independent ^{data from the} largest crystal,

^~

^{300 were} rejected ^{because of extinction}

effects. Near the end of refinement, - ^{50 reflec-}

tions of highest intensity ^were omitted from the (2) ^{At each} point ⁱⁿ

^a

scan, reflected counts

are

recorded during ^{the time} required ^for

^a

monitor counter in the inci- dent beam to register

^a

preset ^count [2].

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01964002505049700

498

data of the two smaller crystals, ^{for which} approxi- mately ^{500 and 150} independent measurements had been made, respectively.

The sucrose data are from three crystals ^also.

About 500 of the - 2 800 independent ^observa-

tions from the largest crystal (~ ⁸⁰ mg) ^were rejected. ^{Data from a} crystal weighing ^about

10 mg and from another weighing ^about 5 mg show little, if any, evidence of extinction. Both of these smaller crystals ^{had been immersed} repea-

tedly ⁱⁿ liquid nitrogen ^before they ^were put ^on

the diffractometer.

A crystal specimen ^{is selected} only ^after thorough x-ray examination by precession photo- graphy ^{to determine if it is} truly ^a single crystal.

Often a much larger crystal ^is examined, ^{and the}

actual portion ^{used is} separated from any miso- riented sections. Sometimes the crystal ^is shaped

to a simple geometric form, ^{in order to} simplify

calculation of the absorption corrections that

usually ^are applied.

When a small crystal ^{is to} be used for the pur- pose of reducing extinction _errors, it is preferable

to cut it from a larger ^{one. Otherwise the small} crystal may show ^as much extinction as a larger

one, ^{or even more.} Similarly, the familiar proce- dure of repeated immersion of a specimen ⁱⁿ liquid nitrogen ^is usually ^more effective in reducing

extinction effects for large crystals than for small

ones.

Recording ^{of data.}

^-

So far all of our data have been recorded by ^{the 0}

^-

26, stepscan ^method.

The scan for each reflection is made over a range centered around the computed value of 26 for the

peak. Usually the range of 26 is 5°, ^counts being

recorded on the output paper tape ^{for 51} points

at 0.1 ° intervals, ^{each for the same} preset ^{value of}

the monitor count.

Sometimes the 50 range ^can safely ^{be reduced,}

with some saving ^{of time.} Usually, however, ^even though ^most of the reflections of a series being

recorded are sufficiently ^{narrow in breadth} for,

say, ^a 40 _scan, some require ^{50. The} wider range is safer also whenever peaks ^are likely ^{to f all off}

center in the computed range because of the use of

slightly inaccurate cell parameters in the compu- tation of the orienter settings ; and it is necessary at high angles 20, ^{where the} peaks ^{broaden because}

of the spread ^{of wave} lengths ^{in the neutron beam.}

Data are usually ^collected in order of increasing

value of 0. Inspection of the recorder chart reveals when a different range of ^scan should be chosen.

A problem of resolution appears ^at high ^values

of 0 for crystals having one or more cell translations of about 20 A. A portion ^of neighbor peak may be recorded near the beginning ^or end of the scan

of a given reflection. The processing ^{of the} output

data tape ^{for the} reflection being ^{measured cannot}

then be done properly by ^the computer program

routinely ^{used (see below under the} heading ^Data Processing). It appears that 20 A is the approxi-

mate limit on cell translations of crystals ^{to be}

studied on the instrument, unless the divergence

of the neutron beam and the wave length spread

are reduced, ^{with an} accompanying increase in

recording ^time per reflection.

In the course of collecting ^{a set} of three-dimen- sional data, ^{we often collect} replicate ^{data for a} large ^number of reflections. It was especially ^desi-

rable to do so when the instrument was first put into operation, for the purpose of checking ^{its relia-} bility. ^{As a matter of routine, one or two stan-}

dard reflections of the crystal ^under study ^are

scanned at regular intervals, say every ^{30 to 50} reflections. Also, ^the performance of the instru- ment is checked frequently, every week ^or so, by scanning ^a standard reflection (400) ^{of a standard} crystal ^{of sodium} chloride, kept permanently ^{on a} goniometer head for this purpose.

Data from these two kinds of standard obser- vations are used to choose the proper scale factor to apply ^{to a} given group of intensity ^{data to} bring ^{them to} absolute scale. When the internal standard reflection remains at constant intensity,

the data are scaled by comparison ^{with the inten-} sity ^{of the} (400) reflection of sodium chloride. In the w ork on XeF 2 ^and XeF4 (see ^{review in refe-}

rence [1] and other references there) the obser- vations of the internal standard were very impor- tant, ^because they provided ^a basis for correction of the data for growth ^{of the} crystal specimens during ^the period ^{of data} collection.

Internal standard reflections have in two ins- tances proved, ^{in a rather} interesting way,

7

to be rather _poor standards. In the work on chloral

hydrate, ^the intensity ^{of the} (200) reflection from the largest crystal ^used (29 mg) gradually ^increased

from its original ^{value to}

^a

^{value about 10} % higher ^{over a} period ^{of two} months, during ^which

the intensity ^{of the} (400) reflection from the NaCI standard remained stationary. ^The (200) ^reflec-

tion is a strong ^one, and its measured intensity ^for

the 29 _mg crystal is little more than half of its correct value because of extinction. The increase of intensity ^is tentatively attributed to an increase of mosaic spread ^{in the} crystal resulting ^from

neutron irradiation. Such increases only appeared

in the data from this crystal ^for reflections of high intensity, ^{which were} subject ^{to severe extinction}

errors and which subsequently ^{were deleted from}

the data set.

A similar effect, but in the opposite direction,

was observed in the strongest reflections from a

sucrose crystal weighing about 80 mg. Again, ^no

changes ^{were observed} except ^{for those} reflections

later shown ^to be severely ^affected by extinction.

An explanation ^{in terms of mosaic} spread hardly

seems reasonable in this case.

Data processing.

^-

^{Raw data recorded} by ^the

diffractometer are processed ^{either on the Control}

Data Corporation ^{1 604A} computer ^{or on the}

IBM 7090, ^{after a} preliminary step in which data

are transferred from paper tape ^to magnetic tape.

Details of the processor program will ^not be given here ; only ^the basic process which ^has been adop-

ted and programmed ^for deriving ^the integrated

count for a given reflection will be discussed [4].

The computer first examines the data for a given

reflection to determine if the reflection is " weak "

or " strong ". ^The peak ^{is taken to be} strong only ^{if the} difference Cmax.

^-

Cmin.avg. ^is greater

than or equal ^to 4adif., ^{where Cmax is the} highest

count in the _scan, is the minimum value of the average of all groups of three adjacent ^counts

and adif. is the standard error of the difference.

If the peak ^{is found to be} strong, ^its center, pc, above half-height ^{is next} determined by the pro- gram. For ^a weak peak, ^{pc is taken to be the} midpoint ^{of the scan.}

The n points ^{of an} assigned range centered ^as

closely ^as possible about the value _pc are consi- dered to belong ^{to the} peak. ^An equal ^{number m}

of points ^on each side of the n points ^{are used to}

determine background, ^m being ^{taken as} large ^as possible. ^{The net count under the} peak, Cnet, ^is

obtained by subtracting ^{from the total count under}

the peak, Ctotal, ^a background correction, Cback, computed ^{as the sum of the 2m counts of back-} ground multiplied by the factor n /2m, the ratio of the number of points ^{under the} peak ^{to those of} background. ^The variance, 6cnet, ^{of Cl,et is} given by

The number n used above is an input ^datum

which is set after examination of the peaks ^{on the}

recorder chart. It is fixed at the same value for all reflections processed ^{in a} single processing job,

the value appropriate ^for the widest peaks being processed, unless these peaks ^{are to receive} special

treatment later.

Counts. for fewer and fewer points ^are employed

in determining ^the background ^{as a} peak ^{is more}

and more displaced ^from its proper position ^{at the}

center of the scan. In case of extreme displa- cement, ^the processing ^{for the} particular ^reflection fails, ^{and the} program proceeds ^{to the next reflec-}

tion.

It will be clear that a fundamental assumption

at the basis of this rather simple processing ^scheme

is that the background intensity ^{over the} range of the scan is a linear function of 26. A more sophis-

ticated processing ^{scheme would be} desirable, ^since

the assumption ^of linearity ^{is not} always ^a good

approximation ; ^{but no better one has} yet ^been

devised. It is advisable for the user of the instru- ment to inspect daily the recorder chart for evi- dence of malfunctions of the instrument which will not be recognized ^{as such} by the processor program and which may otherwise go undetected.

For each reflection processed, ^{an IBM card is} automatically punched ^{with values of the} following quantities : ^{the indices} h, 1~, and 1, ^{the orienter} setting angles 20, x, ^{and p ;} Cnet, Cbflk, 6net, and _pc. The deck so produced ^{is used as} input

data for calculation of absorption corrections by

the program ^of Wehe, Busing, ^and Levy [5]. ^The absorption ^{factors are stored on} magnetic tape,

to be applied ^{in the next} stage ^of processing, ^which

also employs ^{the same} deck of data cards. In this next stage ^a so-called data library ^{is set} up ^on

magnetic tape [6]. ^{The data are scaled absolu-} tely by application of the proper factors, ^derived

from the measurements on standard reflections,

and the absorption and Lorentz corrections are

applied. ^For each reflection the values of F2 and and a number of other functions, ^are

recorded ^on the tape, from which they ^{can be read}

and punched ^{on cards at} any time later. Data cards appropriate ^for input ^to the Fortran least- squares program of Busing, Martin, ^and Levy [7]

may be produced automatically.

If desired, ^{a different set of data} cards may be

punched ^for input ^{to a} program that has been written for averaging equivalent ^{data from one or}

several crystals [8]. This program accepts ^{a deck}

of cards each of which bears the indices of a parti-

cular reflection, ^an integer identifying ^the crystal specimen, ^the intensity (scaled and corrected for

absorption), the statistical standard error of the

intensity, and the Lorentz correction factor. The deck must be sorted so that equivalent reflections

are grouped. Averaging, with proper weighting

and with simple rejection criteria, ^{is carried out}

for each independent ^{set of} indices, ^{first over the}

data for each crystal specimen separately ^and then,

if desired, ^{over the data for all the} specimens. ^The

function averaged may be either the intensity ^or

the square of the structure factor. At the user’s

option, input data cards for the least-squares pro- gram may be punched, ^{or a set of} average inten-

sity cards may be punched. ^{The latter} cards,

when sorted ^on intensity, ^{are useful in} appraising

the magnitude ^of extinction effects, by comparison

of the data from different crystal specimens.

Some remarks are required concerning compu- tation of the variance the reciprocal ^{of which}

is the weight of the observation Fob.. in ^least-

squares refinement. The variance ought

ideally ^to be related to G2",t, ^the calculation of

which has been mentioned earlier, ^{in the same} way

that F o 2b,. is related to Cnet. Experience ⁱⁿ many

refinements (see, ^for example, ^reference [9]) sug-

500

TABLE 1

NEUTRON

DIFFRACTION DATA COLLECTED

ON THE

OAK RIDGL

AUTOMATIC THREE-CIRCLE NEUTRON

DIFFRACTOMETER,

^{AS OF}

AUGUST, ¹⁹⁶³

(*) Work of S. W. Peterson, Washington ^State University (see ^reference [3]).

gests, however, that estimates of variance that are more realistic and more appropriate ^for computing weights ^{are obtained} by adding ^a correction term

(kF2)2 ^{to the} variance derived from where k is a constant, usually ^{set at} 0 .03. The extra term makes allowance for instability ^{in the instrument} (see ^below under Precision of Measurements), ^errors

in corrections for absorption, deficiences of the structure model, ^{and so} forth. When replicate ^or equivalent observations are made for a reflection from a given crystal specimen, ^{it is} customary ^to

make the variance correction after averaging ^the

observations. Later, if data for the same reflec- tion from different crystals ^are averaged, they ^are regarded ^as independent and the variance of the average is computed accordingly.

Precision of measurements.

^--

A study ^{of the} precision ^of intensity measurements on the diffrac- tometer was made through statistical analysis ^of

data recorded from a small crystal ^of potassium

chloride [10]. ^Three types ^{of test} have been made

on the data : for consistency ^of replicate ^measu-

rements on a single reflection, ^for consistency ^{of the} equivalent reflections measured for a given form,

and for the external consistency ^of all accessible

independent reflections with the crystal structure,

as given by ^a least-squares ^{fit of} scattering ^factors

and temperature ^factors.

The KCI crystal ^was approximately ^{cubical in} shape ^and weighed ^2.53 milligrams. ^{Data were}

collected at a monitor count settings ^of 60,000 ^to

~00,000. An absorption correction factor was

computed ^and applied for each reflection. The average factor ^was about 1. 05.

Some statistics (3) ^{of a} portion of the KCI data,

relevant to the first and second types ^of test, ^are given in Table 2. The different series of measu-

rements, a, b, etc..., ^{for a} particular reflection or

form were made at different times with different monitor count settings. For each series of measu-

rements an internal estimate, S, ^{and an external} estimate, 6, of the standard error of a single ^obser-

vation are given. The internal estimate is the unbiased estimate of standard error from the

sample, given by ^the equation

where F2 is the mean of the n observations Fi2 ^of

the sample. The external estimate is the mean

of the n standard errors derived from counting ^sta-

tistics (without application ^of the variance correc-

tion discussed in the previous section). ^{When F2 is}

derived from a large count, its distribution about the true value ^{of F2} approximates the normal dis- tribution with variance a2 ; ^{and the} quantity x2 = (n

⁼

is then distributed in the chi- square distribution, ^{on n - I} degrees ^{of free-}

dom [11]. ^The probability that X2 ^{for the} sample ^{be found} greater than the value actually

found may be taken as a measure of consistency ^of

the data in the sample, or as a measure of consis- tency of the internal and external estimates of

error. The ideal value of P,. ^{to be} expected ^on

the average is 0 . 5. For ^a reasonably large sample,

a probability deviating greatly ^from 0.5, approa- (3) See . general discussion

on

satistics in [11] ^{and other}

references there.

TABLE 2

’

PRECISION

OF SOME INTENSITY MEASUREMENTS FROM A

KCI

CRYSTAL

TABLE 3

PRECISION

OF INTENSITY MEASUREMENTS ON TWO STANDARD REFLECTIONS ^OF

K2’bF

ching ^{either zero or} unity, ^indicates inconsistency

in the estimates of error and the presence of syste-

matic errors of some sort.

The data of Table 2, which may be taken ^to

represent fairly ^{the whole set of KCl} data, ^show

that the consistency ^is reasonably satisfactory

within a given ^{series of} measurements, ^{both for} replicate measurements and for measurements of

equivalent reflections. There are no deviations of

probability ^{from the value 0.5 to an extent that}

may be regarded ^as significant by ^the usual criteria.

It is clear, however, ^{that the} consistency ^{of the}

values F2 for the various series of observations of

a given reflection or of a given ^{form is not} quite ^so satisfactory. ^For example, the difference of 0.36 between the values F2 of series a and b of reflec- tion (004) is 3.5 times the standard deviation com-

puted ^{from the values of}

^6.

^{Since the} probability

of obtaining ^{a ratio} greater ^{than this} according ^to

the properties ^of the normal distribution is only

N

5 X 10-4, ^{there is} clearly ^a significant ^difference

between the two averages. The ^same conclusion is reached if one uses the estimates of error S from the two samples and Student’s statistic t. The

probability ^{estimated from} this statistic is about

10-3, ^and the conclusion is essentially ^{the same.}

Discrepancies ^{of this} sort, ^which reflect instru-

mental instability, ^are allowed for by the variance corrections discussed in the previous ^section.

In the least-squares refinement on the KCI data,

the scale factor for the values of F2, ^{the ratio of}

the sodium nuclear scattering amplitude ^{to that}

of chlorine (fixed ^{at 0.98 X 10-12} cm), ^{and the}

thermal parameters of both ions were adjusted.

The variances of the observations ^were corrected in the manner described before weights ^{were calcu-}

lated. Similar least-squares analyses ^{were carried}

out on data from measurements on Nacl and RbCI

crystals. ^The agreement reached in each case

between observed and calculated values of ~li’2 is

strikingly ^close. Thus, ^for NaCI, KCI, ^and RbCI,

the discrepancy ^factors (4) ^{for F2 were} 0.026, 0.019, ^and 0.023 ; and the values of the standard deviation of an observation of unit weight (5) ^were 0.99, 0.86, 0.88, respectively.

The many replicate ^{data of the} reflections used

as internal standards in the course of collecting ^a

data set may also be used to test for consistency.

For example, ^the 50 observations of reflection (060)

and the 48 observations of (400) recorded in the

(5) ^For definition

see

reference [1].

502

work on K2NbF 7 ^are remarkably consistent (see

Table 3). Clearly, ^the instrumental stability ^was quite satisfactory during ^the period of five weeks

required ^{to record the data for} K2NbF7.

Taken altogether, ^{these tests} (6) ^indicate high consistency ^and precision ^{in the} measurements made with the automatic instrument. The indi- cation is borne out by ^the quality ^of the refine- (6) ^The least-squares analyses ^also provide ^{nuclear scat-} tering amplitudes ^for Na, K, ^and Rb, ^{relative to the value}

0.98 X 10-12

cm

for Cl, ^whch

^are

slightly ^{different from} previous values and

more

precisely determined [10].

ments that have been made on neutron data for six substances [1]. ^The discrepancy ^{factors on} F2, ranging from 0.107 to 0.046, ^{and the} generally

small standard ^errors in the structural parameters

attest to the quality ^{of the data.} Some confidence that errors in the observations are being ^estimated nearly correctly ^is engendered by ^{the fact that the}

standard deviation of an observation of unit weight

reached values of 1.02 - ~ .15 in four of these refinements (XeF4, KNbF, ^chloral hydrate, ^and sucrose) and values 1.65 and 1.67 for the other two ~XeF2 ^and BaCl2. 2H 20).

REFERENCES [1] ^BROWN (G. M.) ^{and LEVY} (H. A.), ^J. Physique, 1964,

25, 469,

^"

Recent Crystal ^Structure Determinations

by Neutron Diffraction at Oak Ridge ".

[2] ^BUSING (W. R.), ^SMITH (H. G.), ^PETERSON (S. W.)

and LEVY (H. A.), ^J. Physique, 1964, 25, 495,

"

Experience with the Oak Ridge ^{Automatic Three-}

Circle Neutron Diffractometer ".

[3] ^PETERSON (S. W.), ^Abstracts of ^the Communications Sixth International Congress ^and Symposia, ^Inter-

national Union of Crystallography, ^Rome, Italy, September 1963, p. 30.

[4] ^BUSING (W. R.), ^WEHE (D. J.), ^MARTIN (K). ^and

LEVY (H. A.), Unpublished ^work.

[5] ^WEHE (D. J.), ^BUSING (W. R.) ^{and LEVY} (H. A.),

"

OR ABS, ^{A Fortran} Program ^for Calculating Single Crystal Absorption Corrections ", Report

No. TM-229, ^Oak Ridge ^National Laboratory, ^1962.

[6] ^BUSING (W. R.), Unpublished ^work.

[7] ^BUSING (W. R.), ^MARTIN (K.) ^{and LEVY} (H. A.),

"

OR FLS, ^{A Fortran} Crystallographic ^Least- Squares Program ", Report ^No. TM-305, Oak Ridge

National Laboratory, 1962.

[8] ^BROWN (G. M.), Unpublished ^work.

[9] ^PETERSON (S. W.) ^{and LEVY} (H. A.), ^Acta Cryst., 1957, 10, 70.

[10] ^LEVY (H. A.), ^AGRON (P. A.) and BUSING (W. R.),

Annual Progress Report, Chemistry Division, ^Oak Ridge ^National Laboratory, ORNL-3320, 1962, p. 108.

[11] CRUICKSHANK (D. ^W. J.), Statistics, section 2.6, p .84,

I nternational Tables for X-Ray Crystallography,

vol. 2, ^J. Kasper ^{and K.} Lonsdale, Editors,

Kynoch Press, Birmingham, ^1959.