document: the transition from a liquid to an amorphous solid that sometimes occurs upon cooling remains one of the largely unresolved problems of statistical physics  @xcite . at the experimental level , 
   the so - called glass transition is generally associated with a sharp increase in the characteristic relaxation times of the system , and a concomitant departure of laboratory measurements from equilibrium . at the theoretical level 
   , it has been proposed that the transition from a liquid to a glassy state is triggered by an underlying thermodynamic ( equilibrium ) transition  @xcite ; in that view , an `` ideal '' glass transition is believed to occur at the so - called kauzmann temperature , @xmath5 . at @xmath5 , 
   it is proposed that only one minimum - energy basin of attraction is accessible to the system . 
   one of the first arguments of this type is due to gibbs and dimarzio  @xcite , but more recent studies using replica methods have yielded evidence in support of such a transition in lennard - jones glass formers  @xcite . 
   these observations have been called into question by experimental data and recent results of simulations of polydisperse hard - core disks , which have failed to detect any evidence of a thermodynamic transition up to extremely high packing fractions  @xcite . 
   one of the questions that arises is therefore whether the discrepancies between the reported simulated behavior of hard - disk and soft - sphere systems is due to fundamental differences in the models , or whether they are a consequence of inappropriate sampling at low temperatures and high densities . 
   different , alternative theoretical considerations have attempted to establish a connection between glass transition phenomena and the rapid increase in relaxation times that arises in the vicinity of a theoretical critical temperature ( the so - called `` mode - coupling '' temperature , @xmath6 ) , thereby giving rise to a `` kinetic '' or `` dynamic '' transition  @xcite . in recent years , both viewpoints have received some support from molecular simulations . 
   many of these simulations have been conducted in the context of models introduced by stillinger and weber and by kob and andersen  @xcite ; such models have been employed in a number of studies that have helped shape our current views about the glass transition  @xcite .    in its simplest ( `` idealized '' ) version , firstly analyzed in the `` schematic '' approach by bengtzelius et al . 
   @xcite and independently by leutheusser @xcite , the mct predicts a transition from a high temperature liquid ( `` ergodic '' ) state to a low temperature arrested ( `` nonergodic '' ) state at a critical temperature @xmath0 . 
   including transversale currents as additional hydrodynamic variables , the full mct shows no longer a sharp transition at @xmath0 but all structural correlations decay in a final @xmath7-process @xcite . 
   similar effects are expected from inclusion of thermally activated matter transport , that means diffusion in the arrested state @xcite .    in the full mct 
   , the remainders of the transition and the value of @xmath0 have to be evaluated , e.g. , from the approach of the undercooled melt towards the idealized arrested state , either by analyzing the time and temperature dependence in the @xmath8-regime of the structural fluctuation dynamics @xcite or by evaluating the temperature dependence of the so - called @xmath3-parameter @xcite . 
   there are further posibilities to estimates @xmath0 , e.g. , from the temperature dependence of the diffusion coefficients or the relaxation time of the final @xmath7-decay in the melt , as these quantities for @xmath9 display a critical behaviour @xmath10 . 
   however , only crude estimates of @xmath0 can be obtained from these quantities , since near @xmath0 the critical behaviour is masked by the effects of transversale currents and thermally activated matter transport , as mentioned above .    on the other hand , 
   as emphasized and applied in @xcite , the value of @xmath0 predicted by the idealized mct can be calculated once the partial structure factors of the system and their temperature dependence are sufficiently well known . besides temperature and particle concentration , the partial structure factors are the only significant quantities which enter the equations of the so - called nonergodicity parameters of the system . 
   the latter vanish identically for temperatures above @xmath0 and their calculation thus allows a rather precise determination of the critical temperature predicted by the idealized theory .    at this stage 
   it is tempting to consider how well the estimates of @xmath0 from different approaches fit together and whether the @xmath0 estimate from the nonergodicity parameters of the idealized mct compares to the values from the full mct . regarding this 
   , we here investigate a molecular dynamics ( md ) simulation model adapted to the glass - forming ni@xmath1zr@xmath2 transition metal system . 
   the ni@xmath11zr@xmath12-system is well studied by experiments @xcite and by md - simulations @xcite , as it is a rather interesting system whose components are important constituents of a number of multi - component massive metallic glasses . in the present contribution 
   we consider , in particular , the @xmath13 composition and concentrate on the determination of @xmath0 from evaluating and analyzing the nonergodicity parameter , the @xmath14-parameter in the ergodic regime , and the diffusion coefficients . 
   our paper is organized as follows : in section ii , we present the model and give some details of the computations . 
   section iii . 
   gives a brief discussion of some aspects of the mode coupling theory as used here . 
   results of our md - simulations and their analysis are then presented and discussed in section iv . 
   the present simulations are carried out as state - of - the - art isothermal - isobaric ( @xmath15 ) calculations . the newtonian equations of @xmath16 648 atoms ( 518 ni and 130 zr ) are numerically integrated by a fifth order predictor - corrector algorithm with time step @xmath17 = 2.5 10@xmath18s in a cubic volume with periodic boundary conditions and variable box length l. with regard to the electron theoretical description of the interatomic potentials in transition metal alloys by hausleitner and hafner @xcite 
   , we model the interatomic couplings as in @xcite by a volume dependent electron - gas term @xmath19 and pair potentials @xmath20 adapted to the equilibrium distance , depth , width , and zero of the hausleitner - hafner potentials @xcite for ni@xmath1zr@xmath2 @xcite . for this model 
   , simulations were started through heating a starting configuration up to 2000  k which leads to a homogeneous liquid state . 
   the system then is cooled continuously to various annealing temperatures with cooling rate @xmath21 = 1.5 10@xmath22  k / s . afterwards 
   the obtained configurations at various annealing temperatures ( here 1500 - 600 k ) are relaxed by carrying out additional isothermal annealing runs . 
   finally the time evolution of these relaxed configurations is modelled and analyzed . 
   more details of the simulations are given in @xcite . 
   in this section we provide some basic formulae that permit calculation of @xmath0 and the nonergodicity parameters @xmath23 for our system . a more detailed presentation may be found in refs . 
   . the central object of the mct are the partial intermediate scattering functions which are defined for a binary system by @xcite @xmath24)\right\rangle \quad , \label{t.1}\end{aligned}\ ] ] where @xmath25 is a fourier component of the microscopic density of species @xmath26 . 
   the diagonal terms @xmath27 are denoted as the incoherent intermediate scattering function @xmath28)\right\rangle \quad . 
   \label{t.2}\ ] ]    the normalized partial- and incoherent intermediate scattering functions are given by @xmath29 where the @xmath30 are the partial static structure factors . 
   the basic equations of the mct are the set of nonlinear matrix integrodifferential equations @xmath31 where @xmath32 is the @xmath33 matrix consisting of the partial intermediate scattering functions @xmath34 , and the frequency matrix @xmath35 is given by @xmath36_{ij}=q^2k_b t ( x_i / m_i)\sum_{k}\delta_{ik } \left[{\bf s}^{-1}(q)\right]_{kj}\quad . 
   \label{t.6}\ ] ] @xmath37 denotes the @xmath33 matrix of the partial structure factors @xmath38 , @xmath39 and @xmath40 means the atomic mass of the species @xmath26 . 
   the mct for the idealized glass transition predicts @xcite that the memory kern @xmath41 can be expressed at long times by @xmath42 where @xmath43 is the particle density and the vertex @xmath44 is given by @xmath45 and the matrix of the direct correlation function is defined by @xmath46_{ij } \quad . 
   \label{t.9}\ ] ]    the equation of motion for @xmath47 has a similar form as eq.([t.5 ] ) , but the memory function for the incoherent intermediate scattering function is given by @xmath48 @xmath49    in order to characterize the long time behaviour of the intermediate scattering function , the nonergodicity parameters @xmath50 are introduced as @xmath51 these parameters are the solution of eqs . 
   ( [ t.5])-([t.9 ] ) at long times . 
   the meaning of these parameters is the following : if @xmath52 , then the system is in a liquid state with density fluctuation correlations decaying at long times . if @xmath53 , the system is in an arrested , nonergodic state , where density fluctuation correlations are stable for all times . in order to compute @xmath54 , 
   one can use the following iterative procedure  @xcite : @xmath55(q ) \cdot { \bf s } ( q)}{{\bf z } } \nonumber \\ & & + \frac{q^{-2}|{\bf s}(q)| |{\bf n}[{\bf f}^{(l)},{\bf f}^{(l)}](q)| { \bf s}(q)}{\bf z } \quad , \label{t.13}\end{aligned}\ ] ] @xmath56(q ) ) \nonumber \\ & & + q^{-2}| { \bf s}(q)| | { \bf n}[{\bf f}^{(l)},{\bf f}^{(l)}](q)| \nonumber \quad,\end{aligned}\ ] ] where the matrix @xmath57 is given by @xmath58    this iterative procedure , indeed , has two type of solutions , nontrivial ones with @xmath59 and trivial solutions @xmath60 . 
   the incoherent nonergodicity parameter @xmath61 can be evaluated by the following iterative procedure :    @xmath62(q ) \quad . \label{t.15}\ ] ]    as indicated by eq.([t.15 ] ) , computation of the incoherent nonergodicity parameter @xmath63 demands that the coherent nonergodicity parameters are determined in advance .      beyond the details of the mct , equations of motion like ( [ t.5 ] ) can be derived for the correlation functions under rather general assumptions within the lanczos recursion scheme @xcite resp . the mori - zwanzig formalism @xcite . 
   the approach demands that the time dependence of fluctuations a , b , ... is governed by a time evolution operator like the liouvillian and that for two fluctuating quantitites a scalar products ( b , a ) with the meaning of a correlation function can be defined . in case of a tagged particle , this leads for @xmath65 to the exact equation @xmath66 with memory kernel @xmath67 in terms of a continued fraction .    within @xmath67 
   are hidden all the details of the time evolution of @xmath65 . 
   as proposed and applied in @xcite , instead of calculating @xmath67 from the time evolution operator as a continued fraction , it can be evaluated in closed forms once @xmath65 is known , e.g. , from experiments or md - simulations . 
   this can be demonstrated by introduction of @xmath68 with @xmath69 the laplace transform of @xmath70 , and @xmath71 eq.([g.1 ] ) then leads to @xmath72 ^{2}+\left [ \omega \phi _ { c}(\omega ) \right ] ^{2 } } \quad . 
   \label{g.5}\ ] ] on the time axis , @xmath73 is given by @xmath74    adopting some arguments from the schematic mct , eq.([g.1 ] ) allows asymptotically finite correlations @xmath75 , that means an arrested state , if @xmath76 remains finite where the relationship holds @xmath77 in order to characterize the undercooled melt and its transition into the glassy state , we introduced in @xcite the function @xmath78    according to ( [ g.7 ] ) , @xmath79 has the property that @xmath80 in the arrested , nonergodic state . on the other hand , 
   if @xmath81 there is no arrested solution and the correlations @xmath65 decay to zero for @xmath82 , that means , the system is in the liquid state . from that we proposed @xcite to use the value of @xmath3 as a relative measure how much the system has approached the arrested state and to use the temperature dependence of @xmath14 in the liquid state as an indication how the system approaches this state . 
   first we show the results of our simulations concerning the static properties of the system in terms of the partial structure factors @xmath38 and partial correlation functions @xmath83 .    to compute the partial structure factors @xmath38 for a binary system we use the following definition @xcite @xmath84 where @xmath85 are the partial pair correlation functions . 
   the md simulations yield a periodic repetition of the atomic distributions with periodicity length @xmath86 . 
   truncation of the fourier integral in eq.([e.5 ] ) leads to an oscillatory behavior of the partial structure factors at small @xmath87 . in order to reduce the effects of this truncation 
   , we compute from eq.([e.5a ] ) the partial pair correlation functions for distance @xmath88 up to @xmath89 . for numerical evaluation of eq.([e.5 ] ) , a gaussian type damping term is included @xmath90 with @xmath91 . 
   fig.[fig1]- fig.[fig2a ] shows the partial structure factors @xmath38 versus @xmath87 for all temperatures investigated . 
   the figure indicates that the shape of @xmath38 depends weakly on temperature only and that , in particular , the positions of the first maximum and the first minimum in @xmath38 are more or less temperature independent .    to investigate the dynamical properties of the system , 
   we have calculated the incoherent scattering function @xmath92 and the coherent scattering function @xmath34 as defined in equations ( [ t.1 ] ) and ( [ t.2 ] ) . 
   fig.[fig2b ] and fig.[fig3a ] presents the normalized incoherent intermediate scattering functions @xmath65 of both species evaluated from our md data for wave vector @xmath93=@xmath94 with n = 9 , that means @xmath95 nm  @xmath96 . from the figure we see that @xmath65 of both species shows at intermediate temperatures a structural relaxation in three succesive steps as predicted by the idealized schematic mct @xcite . 
   the first step is a fast initial decay on the time scale of the vibrations of atoms ( @xmath97  ps ) . 
   this step is characterized by the mct only globaly . 
   the second step is the @xmath98-relaxation regime . in the early @xmath8-regime 
   the correlator should decrease according to @xmath99 and in the late @xmath8-relaxation regime , which appears only in the melt , according the von schweidler law @xmath100 between them a wide plateau is found near the critical temperature @xmath101 . in the melt , 
   the @xmath7-relaxation takes place as the last decay step after the von schweidler - law . 
   it can be described by the kohlrausch - williams - watts ( kww ) law @xmath102 where the relaxation time @xmath103 near the glass transition shifts drastically to longer times . 
   the inverse power - law decay for the early @xmath8-regime @xmath104 is not seen in our data . 
   this seems to be due to the fact that in our system the power - law decay is dressed by the atomic vibrations ( @xcite and references therein ) .    according to our md - results 
   , @xmath65 decays to zero for longer times at all temperatures investigated . 
   this is in agreement with the full mct . including transversal currents as additional hydrodynamic variables , the full mct @xcite comes to the conclusion that all structural correlations decay in the final @xmath7-process , independent of temperature . 
   similar effects are expected from inclusion of thermally activated matter transport , that means diffusion in the arrested state .    at @xmath105  900  k - 700  k , 
   the @xmath65 drop rather sharply at large @xmath106 . 
   this reflects aging effects which take place , if a system is in a transient , non - steady state @xcite . 
   such a behaviour indicates relaxations of the system on the time scale of the measuring time of the correlations . 
   the nonergodicity parameters are defined by eq.([t.12 ] ) as a non - vanishing asymptotic solution of the mct eq.([t.5 ] ) . fig . 
   [ fig3b ] presents the estimated @xmath87-dependent nonergodicity parameters from the coherent and incoherent scattering functions of ni and zr at t=1005  k.    in order to compute the nonergodicity parameters @xmath23 analytically , we followed for our binary system the self - consistent method as formulated by nauroth and kob @xcite and as sketched in section iii.a . 
   input data for our iterative determination of @xmath107 are the temperature dependent partial structure factors @xmath38 from the previous subsection . 
   the iteration is started by arbitrarily setting @xmath108 , @xmath109 , @xmath110 .    for @xmath111 
   k we always obtain the trivial solution @xmath112 while at t = 1000 k and below we get stable non - vanishing @xmath113 . the stability of the non - vanishing solutions was tested for more than 3000 iteration steps . from this results 
   we expect that @xmath0 for our system lies between 1000 and 1100 k. to estimate @xmath0 more precisely , we interpolated @xmath38 from our md data for temperatures between 1000 and 1100 k by use of the algorithm of press et.al . 
   we observe that at @xmath114  k a non - trivial solution of @xmath23 can be found , but not at @xmath115  k and above . 
   it means that the critical temperature @xmath0 for our system is around 1005 k. the non - trivial solutions @xmath23 for this temperature shall be denoted the critical nonergodicty parameters @xmath116 . 
   they are included in fig . 
   [ fig3b ] .    by use of the critical nonergodicity parameters @xmath116 , the computational procedure was run to determine the critical nonergodicity parameters @xmath117 for the incoherent scattering functions at t = 1005 k . 
   [ fig3b ] also presents our results for the so calculated @xmath117 .      here 
   we present our results about the @xmath118-function @xcite described in section iii.b . 
   the memory functions @xmath119 are evaluated from the md data for @xmath120 by fourier transformation along the positive time axis . for completeness , also @xmath121 and 800 k data are included where the corresponding @xmath120 are extrapolated to longer times by use of an kww approximation . 
   [ fig4a ] and fig . 
   [ fig4b ] show the thus deduced @xmath119 for @xmath122  nm@xmath96 . regarding their qualitative features , the obtained @xmath119 are in full agreement with the results in @xcite for the ni@xmath123zr@xmath123 system . 
   a particular interesting detail is the fact that there exists a minimum in @xmath119 for both species , ni and zr , at all investigated temperatures around a time of 0.1 ps . 
   below this time , @xmath120 reflects the vibrational dynamics of the atoms . above this value , 
   the escape from the local cages takes place in the melt and the @xmath8-regime dynamics are developed . 
   apparently , the minimum is related to this crossover .    in fig . 
   [ fig5 ] and fig . 
   [ fig5a ] we display @xmath124 , that means @xmath119 versus @xmath120 . in this figure 
   we again find the features already described for ni@xmath123zr@xmath123 in @xcite . according to the plot , there exist ( @xmath87-dependent ) limiting values @xmath125 so that @xmath119 for @xmath126 is close to an universal behavior , while for @xmath127 marked deviations are seen . 
   @xmath125 significantly decreases with increasing temperature . 
   it is tempting to identify @xmath119 below @xmath125 with the polynomial form for @xmath119 assumed in the schematic version of the mct @xcite . in fig . 
   [ fig5 ] and fig . 
   [ fig5a ] , the polynomial obtained by fitting the 1000 k data below @xmath125 is included by a dashed line , extrapolating it over the whole @xmath128-range .    by use of the calculated memory functions 
   , we can evaluate the @xmath118 , eq.([g.8 ] ) . in fig.[fig6 ] and fig . 
   [ fig7 ] this quantity is presented versus the corresponding value of @xmath120 and denoted as @xmath129 . 
   for all the investigated temperatures , @xmath129 has a maximum @xmath130 at an intermediate value of @xmath128 . in the high temperature regime , the values of @xmath130 move with decreasing temperature towards the limiting value 1 . 
   this is , in particular , visible in fig . 
   [ fig8 ] where we present @xmath130 as function of temperature for both species , ni and zr , and wave - vectors @xmath95  nm@xmath96 . at temperatures above 1000 k , the @xmath3-values increase approximately linear towards 1 with decreasing temperatures . below 1000 
   k , they remain close below the limiting value of 1 , a behavior denoted in @xcite as a balancing on the borderline between the arrested and the non - arrested state due to thermally induced matter transport by diffusion in the arrested state at the present high temperatures . 
   linear fit of the @xmath3-values for ni above 950  k and for zr above 1000  k predicts a crossover temperature @xmath131 from liquid ( @xmath132 ) to the quasi - arrested ( @xmath133 ) behavior around 970 k from the ni data and around 1020 k from the zr data . 
   we here identify this crossover temperature with the value of @xmath0 as visible in the ergodic , liquid regime and estimate it by the mean value from the ni- and zr - subsystems , that means by @xmath134  k.    while in @xcite for the ni@xmath123zr@xmath123 melt a @xmath0-value of 1120  k was estimated from @xmath14 , the value for the present composition is lower by about 120  k. a significant composition dependence of @xmath0 is expected according to the results of md simulation for the closely related co@xmath11zr@xmath12 system @xcite . over the whole @xmath135-range , @xmath0 was found to vary between 1170 and 650  k in co@xmath11zr@xmath12 , with @xmath0(@xmath136 ) @xmath137 800  k. regarding this , the present data for the ni@xmath11zr@xmath12 system reflect a rather weak @xmath0 variation . 
   from the simulated atomic motions in the computer experiments , the diffusion coefficients of the ni and zr species can be determined as the slope of the atomic mean square displacements in the asymptotic long - time limit @xmath138    fig . 
   [ fig9 ] shows the thus calculated diffusion coefficients of our ni@xmath1zr@xmath2 model for the temperature range between 600 and 2000 k. at temperatures above approximately 1000 k , the diffusion coefficients for both species run parallel to each other in the arrhenius plot , indicating a fixed ratio @xmath139 in this temperature regime . at lower temperatures , 
   the ni atoms have a lower mobility than the zr atoms , yielding around 800 k a value of about 10 for @xmath140 . 
   that means , here the zr atoms carry out a rather rapid motion within a relative immobile ni matrix . 
   according to the mct , above @xmath0 the diffusion coefficients follow a critical power law @xmath141 with non - universal exponent @xmath142 @xcite .    in order to estimate @xmath0 from this relationship 
   , we have adapted the critical power law by a least mean squares fit to the simulated diffusion data for 1000 k and above . according to this fit 
   , the system has a critical temperature of about 850 - 900 k.    similar results for the temperature dependence of the diffusion coefficients have been found in md simulations for other metallic glass forming systems , e.g. , for ni@xmath123zr@xmath123 @xcite , for ni@xmath143zr@xmath12 @xcite , cu@xmath144zr@xmath145 @xcite , or ni@xmath146b@xmath147 @xcite . in all cases , like here , a break is observed in the arrhenius slope . in the mentioned zr - systems , 
   this break is related to a change of the atomic dynamics around @xmath0 whereas for ni@xmath146b@xmath147 system it is ascribed to @xmath148 . as in @xcite @xmath0 and 
   @xmath148 apparently fall together , there is no serious conflict between the obervations . 
   the present contribution reports results from md simulations of a ni@xmath1zr@xmath2 computer model . 
   the model is based on the electron theoretical description of the interatomic potentials for transition metal alloys by hausleitner and hafner @xcite . 
   there are no parameters in the model adapted to the experiments . 
   there is close agreement between the @xmath0 values estimated from the dynamics in the undercooled melt when approaching @xmath0 from the high temperature side . 
   the values are @xmath149  k from the @xmath3-parameters , and @xmath150  k from the diffusion coefficients . 
   as discussed in @xcite , the @xmath0-estimates from the diffusion coefficients seem to depend on the upper limit of the temperature region taken into account in the fit procedure , where an increase in the upper limit increases the estimated @xmath0 . 
   accordingly , there is evidence that the present value of 950 k may underestimate the true @xmath0 by about 10 to 50 k , as it based on an upper limit of 2000 k only . taking this into account , the present estimates from the melt seem to lead to a @xmath0 value around 1000 k. 
   the @xmath0 from the nonergodicity parameters describe the approach of the system towards @xmath0 from the low temperature side . 
   they predict a @xmath0 value of 1005 k. this value is clearly outside the range of our @xmath0 estimates from the high temperature , ergodic melt . 
   we consider this as a significant deviation which , however , is much smaller than the factor of two found in the modelling of a lennard - jones system @xcite . 
   the here observed deviation between the @xmath0 estimates from the ergodic and the so - called nonergodic side reconfirm the finding from the soft spheres model@xcite of an agreement within some 10 @xmath4 between the different @xmath0-estimates .
summary: we use molecular dynamics computer simulations to investigate a critical temperature @xmath0 for a dynamical glass transition as proposed by the mode - coupling theory ( mct ) of dense liquids in a glass forming ni@xmath1zr@xmath2-system . 
   the critical temperature @xmath0 are analyzed from different quantities and checked the consistency of the estimated values , i.e. from ( i ) the non - vanishing nonergodicity parameters as asymptotic solutions of the mct equations in the arrested state , ( ii ) the @xmath3-parameters describing the approach of the melt towards the arrested state on the ergodic side , ( iii ) the diffusion coefficients in the melt . 
   the resulting @xmath0 values are found to agree within about 10  @xmath4 .