Introduction

McMaille (pronounce : MacMy) is a program for indexing powder patterns by Monte Carlo and grid search (maille in french = cell in english). The 2-theta peak positions extracted from a peak hunting program are used together with the intensities in order to build a pseudo powder pattern to which are compared patterns calculated from the cell parameters proposed by a Monte Carlo or by a grid systematic search process. In McMaille versions 0.9-2.0, the calculated intensities were adjusted by a Le Bail fit (applying 3 iterations of the Rietveld decomposition formula) using Gaussian peak shapes. In version 3.0, time is gained by a factor 20 by using columnar peak shapes and a "fit" by percentage of inclusion of the calculated columns inside the "observed" one. The best cells are refined, more or less. This is similar to the (unnamed and still unavailable ?) software by B.M. Kariuki et al., J. Synchrotron Rad. 6. (1999) 87-92, though the latter uses a genetic algorithm and the raw data. Moreover, McMaille proposes an option of simultaneous two phases indexing and an automated expert system (black box mode) with a simplified manual.

Armel Le Bail    -  September/October 2002

McMaille version 3.0 is distributed under the GNU Public Licence conditions.

The zipped package contains the executable for Windows 95/98/NT/XP, as well as the FORTRAN source code (quite short and documented) and some examples described below.

The compiler used for building the executable was Compaq Visual Fortran.

About the .hkl files :
Let the cub.hkl, hex.hkl, rho.hkl, tet.hkl, ort.hkl, mon.hkl, tri.hkl files in the same 
directory as McMaille.exe as well as your parameters .dat files. These .hkl files contain a list of predetermined Miller indices ordered according to a cell having a, b, c, parameters close to each other. 

As soon as a Monte Carlo cell proposal produces Rp < Rmaxref ~0.5 (similar definition as Rp in the Rietveld method), that cell is more closely examined. Because a least square refinement would not be efficient, the cell parameters are changed (NCYCLES times, see below) a bit (in the range 0. to 0.02 Angstroms and 0. to 0.2 degrees), randomly by using the Monte Carlo process, around their values, checking if Rp decreases. Most of the times Rp decreases enormously, sometimes below the selected Rmax (for keeping the cell) and Rmin (for stopping the run cause the cell could be the right one). This cell adjustment is analogous to simulated annealing. Moreover, a second criterium is used being that if the number of expected peaks is explained (NDAT-NIND) with Rp > Rmaxref, that proposal cell is examined too. This is a brute force indexing approach, very simple to develop. Least square parameters refinements (using the old CELREF routine by Laugier & Filhol) are performed at the end on the selected cell(s). 

Some important values defined in the program are below :

               Nhkl Min   Nhkl Max   NCYCLES    NTRIED/NSOL
cubic            6xNDAT     400       200          100
rhombohedral    12xNDAT     600       500         1000
hexagonal       12xNDAT     800       500         1000
tetragonal      12xNDAT     800       500         1000
orthorhombic    20xNDAT    1000      1000        10000
monoclinic      20xNDAT    1000      2000       100000
triclinic       20xNDAT    1000      5000       100000

NDAT    = Number of powder pattern peaks examined
Nhkl    = Number of calculated hkl compared to the data
           (read in the .hkl files)
NCYCLES = Number of random parameter small changes for a given
          selected cell proposal (having Rp < Rmaxref)
NTRIED  = Number of Monte Carlo events
NSOL    = Number of solutions retained having Rp < Rmax
       
The NTRIED/NSOL ratio helps to reduce the number of retained
cells. If the value is < to the numbers listed above, then
Rmax is decreased by 5%. However, the process is not active
if NSOL < 50 and Rmax should be given negative. Avoiding being
overloaded by cell proposal is better resolved by decreasing
the control parameters W (peak width) and/or Nind (number of
non-indexed peak positions tolerated) and/or Rmaxref (the Rp
level below which a cell will be refined).

Running McMaille (by either clicking on McMaille.exe and giving the entry file name - no extension - or in a DOS box by typing "McMaille name" ) requires a parameters data file. A typical data file (should be named name.dat, name being your choice) follows :

SR2CR2O7                       Title
1.54056 0.0 2                  Wavelength, Zeropoint, Ngrid
1 1 1 0 0 0                    Symmetry codes
0.16 6                         W , Nind
3. 15. 200. 1500. 0.1  0.2 0.4 Pmin, Pmax, Vmin, Vmax, Rmin, Rmax, Rmaxref
0.2 0.2                        Spar, Sang  (grid search only)
20000  1                       Ntests, Nruns (Monte Carlo only)
!!!                        A line starting by ! is ignored
11.180   345.                  2-theta, Intensity
12.217  1120.                  Etc
15.835   124.                  20 couples of positions and
18.709   455.                     intensities should cover usual
Etc                               cases, but more may be 
                                  necessary (max = 100)
Or, if W above is negative :
11.180   345.   0.16          2-theta, Intensity, W
12.217  1120.   0.10          Etc
15.835   124.   0.24          triplets of positions,
18.709   455.   0.16              intensities and widths
Etc              

In Black box mode, the file is much shorter :

SR2CR2O7                       Title
1.54056 0.0 3                  Wavelength, Zeropoint, Ngrid
!!!                        A line starting by ! is ignored
11.180   345.                  2-theta, Intensity
12.217  1120.                  Etc
15.835   124.                  20 couples of positions and
18.709   455.                     intensities. You may put more
Etc                               but only 20 will be used.          

Wavelength : your experiment wavelength. If you used CuKalpha, you should have stripped alpha2 before peak positions hunting.

Zeropoint : your powder pattern zeropoint (global value including the zero due to the diffractometer and the zero due to sample misplacement - will be added to the data). It is recommended to have a standard compound mixed with your sample or to apply the harmonics method for zeropoint estimation.

Ngrid : code for the process to be applied
            Ngrid = 0 : Monte Carlo
            Ngrid = 1 : grid search
            Ngrid = 2 : both process
            Ngrid = 3 : black box mode - Monte Carlo on all symmetries
            Ngrid = 4 : black box mode - Monte Carlo on all symmetries + grid search

In black box mode, the next lines should be the 2-theta and intensities couples of values, directly - see the nameb.dat files. 

NOTE : grid search in triclinic is not implemented (would be too long...)

Symmetry codes : 6 codes allowing to select the crystal system to be explored.
                 1st  code : if 0, no search, if 1, search in cubic 
                 2nd code : if 0, no search, if 1, search in hexagonal/trigonal
                                                         if 2, search in rhombohedral (hex. setting)
                 3rd code : if 0, no search, if 1, search in tetragonal
                 4th code : if 0, no search, if 1, search in orthorhombic
                 5th code : if 0, no search, if 1, search in monoclinic
                 6th code : if 0, no search, if 1, search in triclinic

W : the width of the columnar peak shape in degrees. It is recommended to choose W = 2 * FWHM, as a minimum. Using 0.1 < W < 0.3 should produce some correct cells for in-lab data at ~1.5 A wavelength. Using 0.05 < W < 0.15 could be applicable to data coming from a synchrotron Facility at ~0.7 A wavelength (extremely good peak positions are certainly required, anyway). This parameter should reflect your data accuracy, it is close to a tolerated error. Large values (0.30 for a copper target) give more chance to the Monte Carlo process to find easily a minima, but the risk is to be overloaded by false propositions. Play with it... The fact is that most of the test cases will produce the correct solution faster with W=0.5. However, being overloaded by cell proposal is  resolved by decreasing W (peak width) or Nind or Rmaxref. 

 NOTE : if W is negative, then, triplets of 2-theta, I and Width values should be read instead of doublets of 2-theta and I values. Moreover, these widths will be multiplied by -W (then, use W=-1 if you wish not to change the widths, or W=-2 if you want to enlarge the widths by a factor 2, etc).

Nind : Number of non-indexed reflections you tolerate. Why not 2-6 for a set of 20 hkl ? Avoiding being overloaded by cell proposal is resolved by decreasing Nind (or W or Rmaxref).

Pmin, Pmax : minimum and maximum cell parameters for the search. Try first 2-15 or 2-20, then, if no solution appears, increase Pmax. 

NOTE : If Pmin is negative, then it becomes possible to play more on the individual parameter limits, and a supplementary line should be given with 12 values :
a-min, a-max, b-min, bmax, c-min, c-max, alpha-min, alpha-max, beta-min, beta-max, gamma-min, gamma-max.
This may allow to explore in shorter time some special cases (for instance in monoclimic, when a and c are large and b small, the 20 first lines can be h0l lines, so that one can fix a, c and beta and explore b on more than 20 lines).

Vmin, Vmax : minimum and maximum cell volumes for the search. Try first small volumes 20-400, then increase Vmax if no solution occurs.

Rmin, Rmax, Rmaxref : Rp profile reliability factor limits. 
                      There should be Rmin < Rmax < Rmaxref
              Rmin allows to stop the search as soon as a a cell corresponding to
                               Rp <  Rmin is obtained - use 0.01-0.15 or up to 0.20 for
                                bad quality data. Choosing Rmin negative allows to avoid
                                any program stop before the end of the total number of
                                Monte Carlo events or before the total grid search end.
              Rmax is the max Rp value below which a MC-refined cell is kept
                               in memory - use ~0.20 (or up to 0.50 if you wish). Decrease
                               that value if the program produces too much results (no more
                               than 1000 cell will be sorted, anyway). If Rmax is given
                               negative, Rmax will be decreased dynamically (though never
                               below 0.20) by the program if the NTRIED/NSOL ratio is
                               less than values listed above in the method paragraph. Rmax
                               should not be confused with the limit Rp < 0.5 allowing to 
                               select a cell proposal for MC-refinement. That Rp < 0.5
                               limit is fixed in the program, it is not applied however if a
                               cell proposal fits with the expected number of peak positions. 
                               Avoiding being overloaded by cell proposal is better resolved 
                               by decreasing the control parameters W (peak width) and 
                               Nind (number of non-indexed peak positions tolerated), than
                               by decreasing Rmax manually or dynamically.
                               Using Rmax > 0.5 enables the Two Phase mode. Rmaxref
                               will have to be close to Rmax+0.1.
            Rmaxref is the max Rp value below which a cell proposal is Mc-refined.
                              Use 0.4-0.5 is recommended. This is the first criterium for a cell
                              MC-refinement (icode = 1 in the .imp output file), the second 
                              criterium being that if the expected number of peaks is indexed,
                              then the cell is MC-refined whatever Rp (icode = 2). The icode
                              output allows you to know how the cell was obtained.

NOTE : the line including the 2 following parameters is optional (should not occur if NGRID = 0)

Spar : grid search step applied to the cell parameters.
                Recommended values (small values increase calculation time, but too
                large values will not allow the cell to be determined) : 
                    cubic : 0.01 or 0.005
                    hexagonal/rhombohedral/tetragonal : 0.01-0.05
                    orthorhombic : 0.03-0.20 (0.01 is best, but see the time)
                    monoclinic : 0.05-0.30 (0.01 is best, but see the time)
                    triclinic : not implemented 

Sang : grid search step applied to the cell angles.
                 Recommended values (small values influence calculation time) : 
                    monoclinic : 0.05-0.20 (0.01 would be best, but see the time)
                    triclinic : not implemented

NOTE : the line including the 2 following parameters is optional (should not occur if NGRID = 1)

Ntests : number of Monte Carlo tests. Use 500-10000000000 or more.
                       cubic : 500-1000 should be enough
                       hexagonal/tetragonal : 10000-100000 should be enough
                       orthorhombic : 1000000 to 10000000 could be enough
                       monoclinic : 10000000 to 100000000 could be enough
                       triclinic : 1000000000 could be not enough...
    NOTE : If Ntests is given negative, then the following values will be applied,
                 allowing to test simultaneously several crystalline systems with
                 relatively coherent numbers of Monte Carlo tests :
                       cubic : -Ntests
                       hexagonal/tetragonal : -Ntests*50.
                       orthorhombic: -Ntests*50*50
                       monoclinic: -Ntests*50*50*50.
                       triclinic : -Ntests*50*50*50*50
                This is to be used for a long overall night run. In that case, use Ntests 
                 in  the range 1000-2000, this corresponding in tetragonal/hexagonal
                 to 50000-100000, in orthorhombic to 2.5x10⁶-5x10⁶, in monoclinic
                 to 125x10⁶-250x10⁶, in triclinic to 6.25x10⁹-12.5x10⁹.

Nruns : number of Monte Carlo runs. One run will execute Ntests tests.
                   Due to Monte Carlo random number generation, performing 10 runs
                   of 1000 tests may not lead to the same result as 1 run of 10000 tests.
                   Anyway, Nruns = 1 could lead to the expected result.

2-theta, Intensity : values obtained at the peak hunting step. 
                     Recommended : 20 couples of values. Not less than 12.
                                     Max : 100 couples of values.
                     You may play on the intensities and decrease those that seem
                      too high and which will represent a too large part of the total
                      intensity.
NOTE : If W was given negative above, then, triplets of 2-theta, Intensity and W should be read there.

            McMaille expects very accurate peak positions,
                 the same as the other indexing programs.

McMaille produces 4 or 5 types of output files :

name.imp   containing the details of the calculations and a final sorted summary. 
                   There are 2 verbosity levels, low and large. The large verbosity is
                    obtained by entering a negative wavelength (of which of course the
                    sign is then immediately changed).
name.ckm  containing an ordered total list of the "best cells" for the CHEKCELL 
                   program. Note that the FoMs are not real FoMs, but are calculated
                   as the inverse of Rp multiplied by 5... A pseudo-FoM larger than 20
                   is a priori interesting, corresponding to Rp < 25%. A pseudo-FoM
                   close to 50 or larger may indicate the correct cell (Rp < 10%).
                   Depending on the cell proposals, partial lists are also built ;
                      name_cub.ckm  :  cubic
                      name_rho.ckm  :  rhombohedral
                      name_hex.ckm  :  hexagonal/trigonal
                      name_tet.ckm    : tetragonal
                      name_ort.ckm    : orthorhombic
                      name_mon.ckm  : monoclinic
                      name_tri.ckm      : triclinic
                      name_two.ckm   : two phases mode output
name.mcm containing an ordered list of the "best cells" for CRYSFIRE.
name.prf    containing the "best profile" result (with lowest Rp), to be seen by the 
                   WINPLOTR program. For this calculation, Gaussian peak shape is 
                   used, having FWHM = W / 2, where W is the mean columnar width 
                   above (given that it is recommended to use W = 2 * FWHM as a 
                   minimum). The calculated pattern is obtained after 4 Le Bail fit 
                   iterations (see an example).
name-new.dat produced only for NGRID=3 or 4 (black box mode), containing 
                  control parameters for new searches with NGRID = 2 in cubic 
                   symmetry.

The screen output delivers for each symmetry examined the first cell proposal,
and then all the proposals which will correspond to a Rp decrease. This means
that the true cell may not appear here if a false one having a smaller Rp value
is encountered before it. Anyway, the screen output will give you an idea of the
smaller Rp attainable. Then look at the name.imp file and to its sorted summaries.

McMaille is a "brute force" program that can be "almost exhaustive" in grid search mode, provided the grid steps are very short. The only problem is : TIME. Calculations for the triclinic case with 1000 steps for each of the six cell parameters would lead to 1000000000000000000 tests, which corresponds to many centuries at the current speed of 20000 steps per second in McMaille-v3.0 (was "only" 1000 steps per second in McMaille-v2.0)... However, an exhaustive search is quite manageable in grid search mode with a step of 0.01 Angstrom for cubic/hexagonal/tetragonal crystal systems. 

The recommendation is : First use TREOR, DICVOL, ITO, CRYSFIRE. If no result, then apply McMaille with your fastest PC.

If McMaille is so long, and if it is suggested to apply the classical software, what is the McMaille interest ? McMaille is rather insensitive to IMPURITIES. Note that "impurity" means supplementary phase(s) that do not contribute for more than 10% of the total intensity diffracted. You should not expect from McMaille solutions for mixtures of 2 or more unknown major phases (though...). It is obvious that known impurity peaks (identified by a search/match process) should be removed from the list of peaks submitted to McMaille.

Making several successive applications of McMaille is recommended. First cubic, then hexagonal and tetragonal, or those 3 crystal systems in one try. Then orthorhombic, if no clear solution appears at the previous runs. Then monoclinic, if no clear solution appears at the previous runs. Finally triclinic. The black box mode detailed below can do that for you :

BLACK BOX MODE :
That option selected by NGRID=3 (or 4) uses a shortened input for examining your problem in all symmetries (thus it may take one night or more...) by using the following control parameters (in fact, these parameters are modulated according to the estimated problem size, as guessed from the dmax values):

  Symmetry      max MC events     Pmax        Vmax
  cubic                V*0.5    3*dmax      (3*dmax)**3 - no limit
  hex/rhomb/tetra     400000      30         4000
  orthorhombic     4x1000000      20          500-1000-1500-2000
  monoclinic      4x10000000      20          500-1000-1500-2000
  triclinic     4x1000000000      20          250-500-750-1000

Four runs in orthorhombic, monoclinic and triclinic will be made by using
different maximum volumes, successively.
Other global fixed parameters : NDAT cutted at 20 (if not less), NIND = 2,
Pmin = 2., Vmin = 8., W = 0.30*wavelenght/1.54056, 
SPAR = 0.02, SANG = 0.05, Rmin = 0.02, Rmax = 0.15, Rmaxref = 0.40
Dmax is the d value for the first peak position at low diffraction angle.

For recognizing the very best solution in a black box mode output, you have to find, in principle, the cell proposal corresponding to the smallest Rp with highest symmetry and smallest volume, indexing the largest number of peaks. Not always an easy task... so, open your eyes ! Then check your choice(s) by the Chekcell program and by whole pattern fitting by the Pawley or Le Bail methods (Fullprof, Gsas, Rietica, Maud, etc, etc).

FASTER PRELIMINARY TEST :
You may well make the first tries by using a small data set of only NDAT = 12 peak positions, and a large W value (0.5 at 1.54A, or 0.25 at 0.7A), together with Rmax =0.5 and Rmin = 0.01, and a number of non-indexed peaks of 2 or 1. You may well obtain the correct indexing in that way, very fast (speed will be increased by a factor 2 or 3 due to the Nhkl decrease - see above the Nhkl definition) . If no result, go to at least NDAT = 20, and use conditions as recommended in the parameters paragraph above.

Repeat several Monte Carlo runs if nothing is produced (several Monte Carlo runs will not use the same random number sequences, and will not examine the same combinations of cell parameters). This is essentially a question of chance...

Because calculations can be extremely long if you use the grid search procedure with small steps, a WARNING occurs at the beginning of McMaille runs giving an estimation of the calculation time (on the basis of 20000 tests per second obtained with an Intel Pentium IV 2.4GHz processor). Note that these 20000 tests per second were estimated for a cubic case with Nhkl = 400 in the cub.hkl file. In the more complex triclinic case, the test number with Nhkl = 1000 in tri.hkl decresases to 7000 per second. You may obtain more tests per second by decreasing Nhkl (~40000 per second in cubic with Nhkl = 100). The speed will also strongly depend on the number of peak positions selected (20 recommended). In order to have a real idea of the needed time, make a small run (100000 Monte Carlo events, for instance) and extrapolate to the large run. 

TWO PHASES MODE (use cautiously !):
In desperate cases, this mode will propose to interpret the data with two phases. This mode is enabled if Rmax > 0.5. This is quite logical since you will expect that each single phase will represent less than 50% of the total intensity of the powder pattern. Recommended values for Rmax and Rmaxref are 0.6 and 0.7, respectively. You will have to supply at least 30 peak positions, and the number of tolerated non-indexed peaks will have to be high (say 18 non-indexed for 30 peaks). In this mode, a quite large number of cells will be tested so that the speed is considerably decreased. Waiting for faster computers, it is suggested to limit that mode to cubic/hexagonal/rhombohedral/tetragonal/orthorhombic. More than 1000 cells will easily appear and force the run to stop. A list of couples of cells that may explain together a maximum of peak positions is provided at the end of the .imp file. Two examples are distributed with the test files (mixture1 and mixture2). That mode may work or not, of course...

NOTE : pressing the K keystroke (capital letter - for Kill) will stop the program a few seconds later, saving the current results.

The test samples attached with the McMaille package (testn.dat) come mainly from the TREOR and DICVOL distribution package tests (using arbitrarily intensities set to 100.), plus some other example like Y₂O₃, NAC, and the samples 1-3 from the SDPDRR-2 Round Robin. Running them on your own PC should produce the solutions. Examples of time (Pentium IV 2.4GHz) needed by McMaille for its test files are below (all tests by Monte Carlo, not grid search) :

Cimetidine (cim.dat) : monoclinic - 9 seconds
Rp        Vol           Ind        a              b             c       alpha      beta      gamma
0.026   1279.113  21    10.3893  18.8215   6.8215  90.000 106.477  90.000
    M(20) =    503.4126 
    F(20) =    1333.414     (  4.9996987E-04,           30)

NAC (nac.dat) : cubic - < 1 second
Rp        Vol           Ind        a              b             c       alpha      beta      gamma
0.046   1078.129  20   10.2539  10.2539  10.2539  90.000  90.000  90.000
    M(20) =    93.76609 
    F(20) =    66.04718     (  5.9375260E-03,           51)

SDPDRR2 Sample 1 (sample1.dat) : monoclinic - 23 seconds
 Rp        Vol           Ind        a              b             c       alpha      beta      gamma
0.045    651.662    20      8.5301   7.4004  10.3260  90.000  91.336  90.000
    M(20) =    46.97108 
    F(20) =    75.49640     (  5.4063937E-03,           49)

SDPDRR2 Sample 2 (sample2.dat) : monoclinic - > 6 minutes
Start : 17-Oct-2002     18 hour 35 min 36 Sec 
Rp        Vol           Ind        a              b             c       alpha      beta      gamma
0.033   1760.121  22    19.9496   8.1937  11.2441  90.000 106.736  90.000
    M(20) =    101.8119 
    F(20) =    588.4827     (  9.1853255E-04,           37)

SDPDRR2 Sample 3 (sample3.dat) : cubic - 1 second
Rp        Vol           Ind        a              b             c       alpha      beta      gamma
0.056   6735.840  24    18.8856  18.8856  18.8856  90.000  90.000  90.000
    M(20) =    149.7873 
    F(20) =    512.6646     (  7.2244194E-04,           54)

Test 1 - Cd3(OH)5(NO3) (test1.dat) - orthorhombic - 3 seconds
Rp        Vol           Ind        a              b             c       alpha      beta      gamma
0.037    378.227   20    11.0279   3.4202  10.0277  90.000  90.000  90.000
    M(20) =    126.0809 
    F(20) =    183.3493     (  3.7614279E-03,           29)

Test2 (test2.dat) - tetragonal -  < 1 second
Rp        Vol           Ind        a              b             c       alpha      beta      gamma
0.083   1186.855  25    11.1886  11.1886   9.4809  90.000  90.000  90.000
    M(20) =    32.65442 
    F(20) =    58.72479     (  9.4603244E-03,           36)

Test3 (test3.dat) - orthorhombic - 5 seconds
Rp        Vol           Ind        a              b             c       alpha      beta      gamma
0.101   1154.716  25   11.3318   9.2362  11.0328  90.000  90.000  90.000
    M(20) =    17.36584 
    F(20) =    29.50007     (  1.0593196E-02,           64)

Test 4 : monoclinic  - less than 1 minute
Rp        Vol           Ind        a              b             c       alpha      beta      gamma
0.077    684.950   25    6.2461  12.4695   9.1917  90.000 106.911  90.000
    M(20) =    52.42331 
    F(20) =    110.0724     (  6.4892345E-03,           28)

Test 5: (NH4)2S2O3 - monoclinic - 16 seconds
Rp        Vol           Ind        a              b             c       alpha      beta      gamma
0.094    582.592   25    8.8043   6.4951  10.2231  90.000  94.757  90.000
    M(20) =    33.04150 
    F(20) =    59.24461     (  7.1826265E-03,           47)

Test 6 : triclinic - small cell - < 2 minutes
Rp        Vol           Ind        a              b             c       alpha      beta      gamma
0.079    182.342   25     7.6256   5.5093   5.1169  89.828  74.979  62.441
    M(20) =    37.16255 
    F(20) =    53.50393     (  1.2460144E-02,           30)

Test7 - cubic ??? - < 1 second
Rp        Vol           Ind        a              b             c       alpha      beta      gamma
0.110  13743.956 23    23.9536  23.9536  23.9536  90.000  90.000  90.000
    M(20) =    6.623881 
    F(20) =    14.28700     (  1.7071631E-02,           82)

Test 8 - monoclinic - < 2 minutes
Rp        Vol           Ind        a              b             c       alpha      beta      gamma
0.098    149.517   20     5.0750   5.8569   5.0319  90.000  91.444  90.000
    M(20) =    50.94925 
    F(20) =    54.74235     (  1.0148551E-02,           36)

Test 9 - triclinic -  < 1 minute
Rp        Vol           Ind        a              b             c       alpha      beta      gamma
0.069    984.080   20    7.0828  18.8631   8.7848 117.123  94.043  71.092
    M(20) =    52.09227 
    F(20) =    135.3708     (  5.2765133E-03,           28)

Y2O3 - cubic - < 1 second
Rp        Vol           Ind        a              b             c       alpha      beta      gamma
0.073   1190.426  19   10.5983  10.5983  10.5983  90.000  90.000  90.000
    M(20) =    136.5140 
    F(20) =    96.67932     (  3.9031976E-03,           53)

See also the nameb.* files which are corresponding to the Black Box mode.
See also the mixture1 and mixture2 files corresponding to the Two Phases mode.

In mixture1.imp (2 cubic phases), the correct couple of solutions appears in 15th position :

Rp2    Vol    Ind Nsol    a        b         c      alpha  beta  gamma
0.113 1078.288  29  7  10.2544  10.2544  10.2544  90.000  90.000  90.000
0.165 1190.411  14  7  10.5982  10.5982  10.5982  90.000  90.000  90.000

 Rp2    Vol    Ind Nsol    a        b         c      alpha  beta  gamma
0.259 1188.120  30 13  11.1880  11.1880   9.4919  90.000  90.000  90.000
0.106  378.244  15  4  10.0276   3.4206  11.0274  90.000  90.000  90.000

In 15-20 years, computers will be 2¹⁰ to 2¹³ faster (x1000 to x8000 faster), at least, probably. Even grid search in triclinic will be manageable.

I have done a lot already, wasting randomly considerable time ;-)...
But improving the cell proposal lists by more detection of redundant cells (supercells, etc) has to be done, providing a more clean list of possible cells, including the Bravais lattice recognition.